Minimum-error quantum distinguishability bounds from matrix monotone functions: A comment on 'Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds' [J. Math. Phys. 50, 032106 (2009)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tyson, Jon

2009-06-15

Matrix monotonicity is used to obtain upper bounds on minimum-error distinguishability of arbitrary ensembles of mixed quantum states. This generalizes one direction of a two-sided bound recently obtained by the author [J. Tyson, J. Math. Phys. 50, 032106 (2009)]. It is shown that the previously obtained special case has unique properties.

Reduction of quantum systems and the local Gauss law

NASA Astrophysics Data System (ADS)

Stienstra, Ruben; van Suijlekom, Walter D.

2018-05-01

We give an operator-algebraic interpretation of the notion of an ideal generated by the unbounded operators associated with the elements of the Lie algebra of a Lie group that implements the symmetries of a quantum system. We use this interpretation to establish a link between Rieffel induction and the implementation of a local Gauss law in lattice gauge theories similar to the method discussed by Kijowski and Rudolph (J Math Phys 43:1796-1808, 2002; J Math Phys 46:032303, 2004).

Unified Theory of Plasma Correlations.

DTIC Science & Technology

1983-06-13

or more generally, the Balescu -Lenard Equation. 2 6 -3 3 An essential element of these studies is that the correlation functions are assumed to be... Balescu , Phys. Fluids 3, 52 (1960). 27. A. Lenard, Ann. Phys. (N.Y.) 3, 390 (1960). 28. R. L. Liboff and A. H. Merchant, J. Math. Phys. 14, 119 (1973

Comment on 'General nonlocality in quantum fields'[J. Math. Phys. 49, 033513 (2008)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang Haijun

2010-05-15

In a recent paper [H.-J. Wang, J. Math. Phys. 49, 033513 (2008)] a complex-geometry model was proposed to interpret the interaction of electromagnetism and the interaction between quarks while the nonlocal effects are involved. In that theoretical frame, from the metric matrix one can obtain a determinant-form condition to describe qualitatively the typical characteristics for the aforementioned interactions. In this comment we attempt to extend this kind of qualitative description to weak interaction by finding out an appropriate metric tensor for it.

Euler polynomials and identities for non-commutative operators

NASA Astrophysics Data System (ADS)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

Comment on: Diffusion through a slab

NASA Astrophysics Data System (ADS)

Gieseler, U. D. J.; Kirk, J. G.

1997-05-01

Mahan [J. Math. Phys. 36, 6758 (1995)] has calculated the transmission coefficient and angular distribution of particles which enter a thick slab at normal incidence and which diffuse in the slab with linear anisotropic, non-absorbing, scattering. Using orthogonality relations derived by McCormick and Kuščer [J. Math. Phys. 6, 1939 (1965); 7, 2036 (1966)] for the eigenfunctions of the problem, this calculation is generalized to a boundary condition with particle input at arbitrary angles. It is also shown how to use the orthogonality relations to relax in a simple way the restriction to a thick slab.

An integrable semi-discrete Degasperis-Procesi equation

NASA Astrophysics Data System (ADS)

Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro

2017-06-01

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota’s bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

Finsler-Geometric Continuum Dynamics and Shock Compression

DTIC Science & Technology

2018-01-01

An important mathe - matical device used in the current derivations centers on the divergence theorem of Finsler geometry first presented by Rund...carbide ceramic. Philos Mag 92:2860–2893 Clayton JD (2012b)On anholonomic deformation, geometry, and differentiation. Math Mech Solids 17:702–735 Clayton... Math Phys 2015:828475 Clayton JD (2015b) Penetration resistance of armor ceramics: dimensional analysis and property correlations. Int J Impact Eng

Closed-form summations of Dowker's and related trigonometric sums

NASA Astrophysics Data System (ADS)

Cvijović, Djurdje; Srivastava, H. M.

2012-09-01

Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101 1989 J. Math. Phys. 30 770-3 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

T-Duality in an H-Flux: Exchange of Momentum and Winding

NASA Astrophysics Data System (ADS)

Han, Fei; Mathai, Varghese

2018-02-01

Using our earlier proposal for Ramond-Ramond fields in an H-flux on loop space (Han et al. in Commun Math Phys 337(1):127-150, 2015. arXiv:1405.1320), we extend the Hori isomorphism in Bouwknegt et al. (Commun Math Phys 249:383-415, 2004. arXiv:hep-th/0306062; Phys Rev Lett 92:181601, 2004. arXiv:hep-th/0312052) from invariant differential forms, to invariant exotic differential forms such that the momentum and winding numbers are exchanged, filling in a gap in the literature. We also extend the compatibility of the action of invariant exact Courant algebroids on the T-duality isomorphism in Cavalcanti and Gualtieri (in: CRM proceedings of lecture notes, vol 50, pp 341-365, American Mathematical Society, Providence, 2010 ), to the T-duality isomorphism on exotic invariant differential forms.

Classification of the line-soliton solutions of KPII

NASA Astrophysics Data System (ADS)

Chakravarty, Sarbarish; Kodama, Yuji

2008-07-01

In the previous papers (notably, Kodama Y 2004 J. Phys. A: Math. Gen. 37 11169-90, Biondini G and Chakravarty S 2006 J. Math. Phys. 47 033514), a large variety of line-soliton solutions of the Kadomtsev-Petviashvili II (KPII) equation was found. The line-soliton solutions are solitary waves which decay exponentially in the (x, y)-plane except along certain rays. In this paper, it is shown that those solutions are classified by asymptotic information of the solution as |y| → ∞. The present work then unravels some interesting relations between the line-soliton classification scheme and classical results in the theory of permutations.

Reflectionless CMV Matrices and Scattering Theory

NASA Astrophysics Data System (ADS)

Chu, Sherry; Landon, Benjamin; Panangaden, Jane

2015-04-01

Reflectionless CMV matrices are studied using scattering theory. By changing a single Verblunsky coefficient, a full-line CMV matrix can be decoupled and written as the sum of two half-line operators. Explicit formulas for the scattering matrix associated to the coupled and decoupled operators are derived. In particular, it is shown that a CMV matrix is reflectionless iff the scattering matrix is off-diagonal which in turn provides a short proof of an important result of Breuer et al. (Commun Math Phys 295:531-550, 2010). These developments parallel those recently obtained for Jacobi matrices Jakšić et al. (Commun Math Phys 827-838, 2014).

Modified n-level, n - 1-mode Tavis-Cummings model and algebraic Bethe ansatz

NASA Astrophysics Data System (ADS)

Skrypnyk, T.

2018-01-01

Using the quantum group technique we construct a one-parametric family of integrable modifications of the n-level, n-1 mode Tavis-Cummings Hamiltonian possessing an additional Stark-type term. We show that in the ‘quasiclassical’ limit the constructed Hamiltonian transforms into the integrable Hamiltonian of the quantum n-level, n-1 mode Tavis-Cummings model with the equal interaction strengths considered in Skrypnyk (2008 J. Phys. A: Math. Theor. 41 475202, 2009 J. Math. Phys. 50 103523). We diagonalize the constructed ‘modified’ Tavis-Cummings Hamiltonian and its second order integrals of motion using the nested Bethe ansatz.

Separation of variables for the Dirac equation in an extended class of Lorentzian metrics with local rotational symmetry

NASA Astrophysics Data System (ADS)

Iyer, B. R.; Kamran, N.

1991-09-01

The question of the separability of the Dirac equation in metrics with local rotational symmetry is reexamined by adapting the analysis of Kamran and McLenaghan [J. Math. Phys. 25, 1019 (1984)] for the metrics admitting a two-dimensional Abelian local isometry group acting orthogonally transitively. This generalized treatment, which involves the choice of a suitable system of local coordinates and spinor frame, allows one to establish the separability of the Dirac equation within the class of metrics for which the previous analysis of Iyer and Vishveshwara [J. Math. Phys. 26, 1034 (1985)] had left the question of separability open.

Comment on “The two dimensional motion of a particle in an inverse square potential: Classical and quantum aspects” [J. Math. Phys. 54, 053509 (2013)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bietenholz, Wolfgang, E-mail: wolbi@nucleares.unam.mx; Chryssomalakos, Chryssomalis, E-mail: chryss@nucleares.unam.mx; Salgado, Marcelo, E-mail: marcelo@nucleares.unam.mx

We comment on a fatal flaw in the analysis contained in the work of Martínez-y-Romero et al., [J. Math. Phys. 54, 053509 (2013)], which concerns the motion of a point particle in an inverse square potential, and show that most conclusions reached there are wrong. In particular, the manifestly senseless claim that, in the attractive potential case, no bounded orbits exist for negative energies, is traced to a sign error. Several more mistakes, both in the classical and the quantum cases, are pointed out.

Radical Computing II

DTIC Science & Technology

1984-06-01

A.Arays, G.V.Sibiriskov. The AVTO -ANALTZE J. Comput. Math. and Mth. Phys., v. 11, N.4, Progrn eg System. J. Comput. Math. and Cinpur. 1971, pp. 1071...1075. Mach., No.3, Kharkov, 1972. 2. S.A.Abhrmov. On Sam Algorithms for Algebraic 13. Z.A.Arays, C.V.Sibiriakov. AVTO -AALM.K. Novo- Transformstions of

Mixing, ergodicity and slow relaxation phenomena

NASA Astrophysics Data System (ADS)

Costa, I. V. L.; Vainstein, M. H.; Lapas, L. C.; Batista, A. A.; Oliveira, F. A.

2006-11-01

Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation-dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed.

(Quasi)-convexification of Barta's (multi-extrema) bounding theorem: Inf_x\\big(\\ssty\\frac{H\\Phi(x)}{\\Phi(x)} \\big) \\le E_gr \\le Sup_x \\big(\\ssty\\frac{H\\Phi(x)}{\\Phi(x)} \\big)

NASA Astrophysics Data System (ADS)

Handy, C. R.

2006-03-01

There has been renewed interest in the exploitation of Barta's configuration space theorem (BCST) (Barta 1937 C. R. Acad. Sci. Paris 204 472) which bounds the ground-state energy, Inf_x\\big({{H\\Phi(x)}\\over {\\Phi(x)}} \\big ) \\leq E_gr \\leq Sup_x \\big({{H\\Phi(x)}\\over {\\Phi(x)}}\\big) , by using any Φ lying within the space of positive, bounded, and sufficiently smooth functions, {\\cal C} . Mouchet's (Mouchet 2005 J. Phys. A: Math. Gen. 38 1039) BCST analysis is based on gradient optimization (GO). However, it overlooks significant difficulties: (i) appearance of multi-extrema; (ii) inefficiency of GO for stiff (singular perturbation/strong coupling) problems; (iii) the nonexistence of a systematic procedure for arbitrarily improving the bounds within {\\cal C} . These deficiencies can be corrected by transforming BCST into a moments' representation equivalent, and exploiting a generalization of the eigenvalue moment method (EMM), within the context of the well-known generalized eigenvalue problem (GEP), as developed here. EMM is an alternative eigenenergy bounding, variational procedure, overlooked by Mouchet, which also exploits the positivity of the desired physical solution. Furthermore, it is applicable to Hermitian and non-Hermitian systems with complex-number quantization parameters (Handy and Bessis 1985 Phys. Rev. Lett. 55 931, Handy et al 1988 Phys. Rev. Lett. 60 253, Handy 2001 J. Phys. A: Math. Gen. 34 5065, Handy et al 2002 J. Phys. A: Math. Gen. 35 6359). Our analysis exploits various quasi-convexity/concavity theorems common to the GEP representation. We outline the general theory, and present some illustrative examples.

The Antiaircraft Journal. Volume 92, Number 5, September-October 1949

DTIC Science & Technology

1949-10-01

philosophical reflections on the subject of po’werand those to whom it should be entrusted. Recall the words of much-studied Machiavelli , than whom...Leavenworth. Kan. Rauch. A. R, Comm. of Basic Phys. Sc.• Res. & Dev. Board, Pentagon. \\Vash. 25. D. C. Rawls . J. W., Jr.. AFF Liaison Off.. Boeing Aircraft

DPEMC: A Monte Carlo for double diffraction

NASA Astrophysics Data System (ADS)

Boonekamp, M.; Kúcs, T.

2005-05-01

We extend the POMWIG Monte Carlo generator developed by B. Cox and J. Forshaw, to include new models of central production through inclusive and exclusive double Pomeron exchange in proton-proton collisions. Double photon exchange processes are described as well, both in proton-proton and heavy-ion collisions. In all contexts, various models have been implemented, allowing for comparisons and uncertainty evaluation and enabling detailed experimental simulations. Program summaryTitle of the program:DPEMC, version 2.4 Catalogue identifier: ADVF Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVF Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer: any computer with the FORTRAN 77 compiler under the UNIX or Linux operating systems Operating system: UNIX; Linux Programming language used: FORTRAN 77 High speed storage required:<25 MB No. of lines in distributed program, including test data, etc.: 71 399 No. of bytes in distributed program, including test data, etc.: 639 950 Distribution format: tar.gz Nature of the physical problem: Proton diffraction at hadron colliders can manifest itself in many forms, and a variety of models exist that attempt to describe it [A. Bialas, P.V. Landshoff, Phys. Lett. B 256 (1991) 540; A. Bialas, W. Szeremeta, Phys. Lett. B 296 (1992) 191; A. Bialas, R.A. Janik, Z. Phys. C 62 (1994) 487; M. Boonekamp, R. Peschanski, C. Royon, Phys. Rev. Lett. 87 (2001) 251806; Nucl. Phys. B 669 (2003) 277; R. Enberg, G. Ingelman, A. Kissavos, N. Timneanu, Phys. Rev. Lett. 89 (2002) 081801; R. Enberg, G. Ingelman, L. Motyka, Phys. Lett. B 524 (2002) 273; R. Enberg, G. Ingelman, N. Timneanu, Phys. Rev. D 67 (2003) 011301; B. Cox, J. Forshaw, Comput. Phys. Comm. 144 (2002) 104; B. Cox, J. Forshaw, B. Heinemann, Phys. Lett. B 540 (2002) 26; V. Khoze, A. Martin, M. Ryskin, Phys. Lett. B 401 (1997) 330; Eur. Phys. J. C 14 (2000) 525; Eur. Phys. J. C 19 (2001) 477; Erratum, Eur. Phys. J. C 20 (2001) 599; Eur. Phys. J. C 23 (2002) 311]. This program implements some of the more significant ones, enabling the simulation of central particle production through color singlet exchange between interacting protons or antiprotons. Method of solution: The Monte Carlo method is used to simulate all elementary 2→2 and 2→1 processes available in HERWIG. The color singlet exchanges implemented in DPEMC are implemented as functions reweighting the photon flux already present in HERWIG. Restriction on the complexity of the problem: The program relying extensively on HERWIG, the limitations are the same as in [G. Marchesini, B.R. Webber, G. Abbiendi, I.G. Knowles, M.H. Seymour, L. Stanco, Comput. Phys. Comm. 67 (1992) 465; G. Corcella, I.G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. Seymour, B. Webber, JHEP 0101 (2001) 010]. Typical running time: Approximate times on a 800 MHz Pentium III: 5-20 min per 10 000 unweighted events, depending on the process under consideration.

Work cost of thermal operations in quantum thermodynamics

NASA Astrophysics Data System (ADS)

Renes, Joseph M.

2014-07-01

Adopting a resource theory framework of thermodynamics for quantum and nano systems pioneered by Janzing et al. (Int. J. Th. Phys. 39, 2717 (2000)), we formulate the cost in the useful work of transforming one resource state into another as a linear program of convex optimization. This approach is based on the characterization of thermal quasiorder given by Janzing et al. and later by Horodecki and Oppenheim (Nat. Comm. 4, 2059 (2013)). Both characterizations are related to an extended version of majorization studied by Ruch, Schranner and Seligman under the name mixing distance (J. Chem. Phys. 69, 386 (1978)).

On the Ambjorn-Olesen electroweak condensates

NASA Astrophysics Data System (ADS)

Bartolucci, Daniele; De Marchis, Francesca

2012-07-01

We obtain sufficient conditions for the existence of the Ambjorn-Olesen ["On electroweak magnetism," Nucl. Phys. B315, 606-614 (1989), 10.1016/0550-3213(89)90004-7] electroweak N-vortices in case N ⩾ 1 and therefore generalize earlier results [D. Bartolucci and G. Tarantello, "Liouville type equations with singular data and their applications to periodic multivortices for the electroweak theory," Commun. Math. Phys. 229, 3-47 (2002), 10.1007/s002200200664; J. Spruck and Y. Yang, "On multivortices in the electroweak theory I: Existence of periodic solutions," Commun. Math. Phys. 144, 1-16 (1992), 10.1007/BF02099188] which handled the cases N ∈ {1, 2, 3, 4}. The variational argument provided here has its own independent interest as it generalizes the one adopted by Ding et al. ["Existence results for mean field equations," Ann. Inst. Henri Poincare, Anal. Non Lineaire 16, 653-666 (1999), 10.1016/S0294-1449(99)80031-6] to obtain solutions for Liouville-type equations on closed 2-manifolds. In fact, we obtain at once a second proof of the existence of supercritical conformal metrics on surfaces with conical singularities and prescribed Gaussian curvature recently established by Bartolucci, De Marchis and Malchiodi [Int. Math. Res. Not. 24, 5625-5643 (2011), 10.1093/imrn/rnq285].

On Darboux's approach to R-separability of variables. Classification of conformally flat 4-dimensional binary metrics

NASA Astrophysics Data System (ADS)

Szereszewski, A.; Sym, A.

2015-09-01

The standard method of separation of variables in PDEs called the Stäckel-Robertson-Eisenhart (SRE) approach originated in the papers by Robertson (1928 Math. Ann. 98 749-52) and Eisenhart (1934 Ann. Math. 35 284-305) on separability of variables in the Schrödinger equation defined on a pseudo-Riemannian space equipped with orthogonal coordinates, which in turn were based on the purely classical mechanics results by Paul Stäckel (1891, Habilitation Thesis, Halle). These still fundamental results have been further extended in diverse directions by e.g. Havas (1975 J. Math. Phys. 16 1461-8 J. Math. Phys. 16 2476-89) or Koornwinder (1980 Lecture Notes in Mathematics 810 (Berlin: Springer) pp 240-63). The involved separability is always ordinary (factor R = 1) and regular (maximum number of independent parameters in separation equations). A different approach to separation of variables was initiated by Gaston Darboux (1878 Ann. Sci. E.N.S. 7 275-348) which has been almost completely forgotten in today’s research on the subject. Darboux’s paper was devoted to the so-called R-separability of variables in the standard Laplace equation. At the outset he did not make any specific assumption about the separation equations (this is in sharp contrast to the SRE approach). After impressive calculations Darboux obtained a complete solution of the problem. He found not only eleven cases of ordinary separability Eisenhart (1934 Ann. Math. 35 284-305) but also Darboux-Moutard-cyclidic metrics (Bôcher 1894 Ueber die Reihenentwickelungen der Potentialtheorie (Leipzig: Teubner)) and non-regularly separable Dupin-cyclidic metrics as well. In our previous paper Darboux’s approach was extended to the case of the stationary Schrödinger equation on Riemannian spaces admitting orthogonal coordinates. In particular the class of isothermic metrics was defined (isothermicity of the metric is a necessary condition for its R-separability). An important sub-class of isothermic metrics are binary metrics. In this paper we solve the following problem: to classify all conformally flat (of arbitrary signature) 4-dimensional binary metrics. Among them there are 1) those that are separable in the sense of SRE metrics Kalnins-Miller (1978 Trans. Am. Math. Soc. 244 241-61 1982 J. Phys. A: Math. Gen. 15 2699-709 1984 Adv. Math. 51 91-106 1983 SIAM J. Math. Anal. 14 126-37) and 2) new examples of non-Stäckel R-separability in 4 dimensions.

The square lattice Ising model on the rectangle II: finite-size scaling limit

NASA Astrophysics Data System (ADS)

Hucht, Alfred

2017-06-01

Based on the results published recently (Hucht 2017 J. Phys. A: Math. Theor. 50 065201), the universal finite-size contributions to the free energy of the square lattice Ising model on the L× M rectangle, with open boundary conditions in both directions, are calculated exactly in the finite-size scaling limit L, M\\to∞ , T\\to Tc , with fixed temperature scaling variable x\\propto(T/Tc-1)M and fixed aspect ratio ρ\\propto L/M . We derive exponentially fast converging series for the related Casimir potential and Casimir force scaling functions. At the critical point T=Tc we confirm predictions from conformal field theory (Cardy and Peschel 1988 Nucl. Phys. B 300 377, Kleban and Vassileva 1991 J. Phys. A: Math. Gen. 24 3407). The presence of corners and the related corner free energy has dramatic impact on the Casimir scaling functions and leads to a logarithmic divergence of the Casimir potential scaling function at criticality.

Virial Expansion Bounds

NASA Astrophysics Data System (ADS)

Tate, Stephen James

2013-10-01

In the 1960s, the technique of using cluster expansion bounds in order to achieve bounds on the virial expansion was developed by Lebowitz and Penrose (J. Math. Phys. 5:841, 1964) and Ruelle (Statistical Mechanics: Rigorous Results. Benjamin, Elmsford, 1969). This technique is generalised to more recent cluster expansion bounds by Poghosyan and Ueltschi (J. Math. Phys. 50:053509, 2009), which are related to the work of Procacci (J. Stat. Phys. 129:171, 2007) and the tree-graph identity, detailed by Brydges (Phénomènes Critiques, Systèmes Aléatoires, Théories de Jauge. Les Houches 1984, pp. 129-183, 1986). The bounds achieved by Lebowitz and Penrose can also be sharpened by doing the actual optimisation and achieving expressions in terms of the Lambert W-function. The different bound from the cluster expansion shows some improvements for bounds on the convergence of the virial expansion in the case of positive potentials, which are allowed to have a hard core.

Improved Critical Eigenfunction Restriction Estimates on Riemannian Surfaces with Nonpositive Curvature

NASA Astrophysics Data System (ADS)

Xi, Yakun; Zhang, Cheng

2017-03-01

We show that one can obtain improved L 4 geodesic restriction estimates for eigenfunctions on compact Riemannian surfaces with nonpositive curvature. We achieve this by adapting Sogge's strategy in (Improved critical eigenfunction estimates on manifolds of nonpositive curvature, Preprint). We first combine the improved L 2 restriction estimate of Blair and Sogge (Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions, Preprint) and the classical improved {L^∞} estimate of Bérard to obtain an improved weak-type L 4 restriction estimate. We then upgrade this weak estimate to a strong one by using the improved Lorentz space estimate of Bak and Seeger (Math Res Lett 18(4):767-781, 2011). This estimate improves the L 4 restriction estimate of Burq et al. (Duke Math J 138:445-486, 2007) and Hu (Forum Math 6:1021-1052, 2009) by a power of {(log logλ)^{-1}}. Moreover, in the case of compact hyperbolic surfaces, we obtain further improvements in terms of {(logλ)^{-1}} by applying the ideas from (Chen and Sogge, Commun Math Phys 329(3):435-459, 2014) and (Blair and Sogge, Concerning Toponogov's Theorem and logarithmic improvement of estimates of eigenfunctions, Preprint). We are able to compute various constants that appeared in (Chen and Sogge, Commun Math Phys 329(3):435-459, 2014) explicitly, by proving detailed oscillatory integral estimates and lifting calculations to the universal cover H^2.

On exponential stability of linear Levin-Nohel integro-differential equations

NASA Astrophysics Data System (ADS)

Tien Dung, Nguyen

2015-02-01

The aim of this paper is to investigate the exponential stability for linear Levin-Nohel integro-differential equations with time-varying delays. To the best of our knowledge, the exponential stability for such equations has not yet been discussed. In addition, since we do not require that the kernel and delay are continuous, our results improve those obtained in Becker and Burton [Proc. R. Soc. Edinburgh, Sect. A: Math. 136, 245-275 (2006)]; Dung [J. Math. Phys. 54, 082705 (2013)]; and Jin and Luo [Comput. Math. Appl. 57(7), 1080-1088 (2009)].

Persistence Probabilities of Two-Sided (Integrated) Sums of Correlated Stationary Gaussian Sequences

NASA Astrophysics Data System (ADS)

Aurzada, Frank; Buck, Micha

2018-02-01

We study the persistence probability for some two-sided, discrete-time Gaussian sequences that are discrete-time analogues of fractional Brownian motion and integrated fractional Brownian motion, respectively. Our results extend the corresponding ones in continuous time in Molchan (Commun Math Phys 205(1):97-111, 1999) and Molchan (J Stat Phys 167(6):1546-1554, 2017) to a wide class of discrete-time processes.

A Charged Particle in a Magnetic Field: A Review of Two Formalisms of Coherent States and the Husimi Function

ERIC Educational Resources Information Center

Herrera, D.; Valencia, A. M.; Pennini, F.; Curilef, S.

2008-01-01

In this work, we review two formalisms of coherent states for the case of a particle in a magnetic field. We focus our revision on both pioneering (Feldman and Kahn 1970 "Phys. Rev." B 1 4584) and recent (Kowalski and Rembielinski 2005 "J. Phys. A: Math. Gen." 38 8247) formulations of coherent states for this problem. We introduce a general…

Mean field limit for bosons with compact kernels interactions by Wigner measures transportation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liard, Quentin, E-mail: quentin.liard@univ-rennes1.fr; Pawilowski, Boris, E-mail: boris.pawilowski@univ-rennes1.fr

2014-09-15

We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner measures approach. We prove in particular the propagation of these measures along the flow of a nonlinear (Hartree) field equation. This enhances and complements some previous results of the same type shown in Z. Ammari and F. Nier and Fröhlich et al. [“Mean field limit for bosons and propagation of Wigner measures,” J. Math. Phys. 50(4), 042107 (2009); Z. Ammari andmore » F. Nier and Fröhlich et al., “Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states,” J. Math. Pures Appl. 95(6), 585–626 (2011); Z. Ammari and F. Nier and Fröhlich et al., “Mean-field- and classical limit of many-body Schrödinger dynamics for bosons,” Commun. Math. Phys. 271(3), 681–697 (2007)].« less

A Solution Space for a System of Null-State Partial Differential Equations: Part 4

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the last of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities that govern CFT correlation functions of 2 N one-leg boundary operators. In the first two articles (Flores and Kleban in Commun Math Phys, 2012; Flores and Kleban, in Commun Math Phys, 2014), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. Using these results in the third article (Flores and Kleban, in Commun Math Phys, 2013), we prove that dim and is spanned by (real-valued) solutions constructed with the Coulomb gas (contour integral) formalism of CFT. In this article, we use these results to prove some facts concerning the solution space . First, we show that each of its elements equals a sum of at most two distinct Frobenius series in powers of the difference between two adjacent points (unless is odd, in which case a logarithmic term may appear). This establishes an important element in the operator product expansion for one-leg boundary operators, assumed in CFT. We also identify particular elements of , which we call connectivity weights, and exploit their special properties to conjecture a formula for the probability that the curves of a multiple-SLE process join in a particular connectivity. This leads to new formulas for crossing probabilities of critical lattice models inside polygons with a free/fixed side-alternating boundary condition, which we derive in Flores et al. (Partition functions and crossing probabilities for critical systems inside polygons, in preparation). Finally, we propose a reason for why the exceptional speeds [certain values that appeared in the analysis of the Coulomb gas solutions in Flores and Kleban (Commun Math Phys, 2013)] and the minimal models of CFT are connected.

Local perturbations perturb—exponentially-locally

NASA Astrophysics Data System (ADS)

De Roeck, W.; Schütz, M.

2015-06-01

We elaborate on the principle that for gapped quantum spin systems with local interaction, "local perturbations [in the Hamiltonian] perturb locally [the groundstate]." This principle was established by Bachmann et al. [Commun. Math. Phys. 309, 835-871 (2012)], relying on the "spectral flow technique" or "quasi-adiabatic continuation" [M. B. Hastings, Phys. Rev. B 69, 104431 (2004)] to obtain locality estimates with sub-exponential decay in the distance to the spatial support of the perturbation. We use ideas of Hamza et al. [J. Math. Phys. 50, 095213 (2009)] to obtain similarly a transformation between gapped eigenvectors and their perturbations that is local with exponential decay. This allows to improve locality bounds on the effect of perturbations on the low lying states in certain gapped models with a unique "bulk ground state" or "topological quantum order." We also give some estimate on the exponential decay of correlations in models with impurities where some relevant correlations decay faster than one would naively infer from the global gap of the system, as one also expects in disordered systems with a localized groundstate.

Classification of constraints and degrees of freedom for quadratic discrete actions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Höhn, Philipp A., E-mail: phoehn@perimeterinstitute.ca

2014-11-15

We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form and employs the canonical formalism developed in Dittrich and Höhn [“Constraint analysis for variational discrete systems,” J. Math. Phys. 54, 093505 (2013); e-print http://arxiv.org/abs/arXiv:1303.4294 [math-ph

Quasi-Hamiltonian structure and Hojman construction

NASA Astrophysics Data System (ADS)

Carinena, Jose F.; Guha, Partha; Ranada, Manuel F.

2007-08-01

Given a smooth vector field [Gamma] and assuming the knowledge of an infinitesimal symmetry X, Hojman [S. Hojman, The construction of a Poisson structure out of a symmetry and a conservation law of a dynamical system, J. Phys. A Math. Gen. 29 (1996) 667-674] proposed a method for finding both a Poisson tensor and a function H such that [Gamma] is the corresponding Hamiltonian system. In this paper, we approach the problem from geometrical point of view. The geometrization leads to the clarification of several concepts and methods used in Hojman's paper. In particular, the relationship between the nonstandard Hamiltonian structure proposed by Hojman and the degenerate quasi-Hamiltonian structures introduced by Crampin and Sarlet [M. Crampin, W. Sarlet, Bi-quasi-Hamiltonian systems, J. Math. Phys. 43 (2002) 2505-2517] is unveiled in this paper. We also provide some applications of our construction.

Double Ramification Cycles and Quantum Integrable Systems

NASA Astrophysics Data System (ADS)

Buryak, Alexandr; Rossi, Paolo

2016-03-01

In this paper, we define a quantization of the Double Ramification Hierarchies of Buryak (Commun Math Phys 336:1085-1107, 2015) and Buryak and Rossi (Commun Math Phys, 2014), using intersection numbers of the double ramification cycle, the full Chern class of the Hodge bundle and psi-classes with a given cohomological field theory. We provide effective recursion formulae which determine the full quantum hierarchy starting from just one Hamiltonian, the one associated with the first descendant of the unit of the cohomological field theory only. We study various examples which provide, in very explicit form, new (1+1)-dimensional integrable quantum field theories whose classical limits are well-known integrable hierarchies such as KdV, Intermediate Long Wave, extended Toda, etc. Finally, we prove polynomiality in the ramification multiplicities of the integral of any tautological class over the double ramification cycle.

Basic Studies in Plasma Physics

DTIC Science & Technology

1998-01-31

Process in One Dimension, (with B. Derrida and E. Speer), Jour. Stat. Phys., 1997, to appear. [16] Comment on "Phase Separation in Two-Dimensional Fluids...Short version to appear in January 1997 in Physics Today ; the long version is to appear in Jour. Stat. Phys., 87, 463-468, 1997. [25] Microscopic...SIAM J. Math. Anal. 27, 110-134, 1996. [31] Microscopic-Shock Profiles: Exact Solution of a Non-Equilibrium System, (with B. Derrida , S. Janowsky and

Automatic computation of the travelling wave solutions to nonlinear PDEs

NASA Astrophysics Data System (ADS)

Liang, Songxin; Jeffrey, David J.

2008-05-01

Various extensions of the tanh-function method and their implementations for finding explicit travelling wave solutions to nonlinear partial differential equations (PDEs) have been reported in the literature. However, some solutions are often missed by these packages. In this paper, a new algorithm and its implementation called TWS for solving single nonlinear PDEs are presented. TWS is implemented in MAPLE 10. It turns out that, for PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases. Program summaryProgram title:TWS Catalogue identifier:AEAM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAM_v1_0.html Program obtainable from:CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions:Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.:1250 No. of bytes in distributed program, including test data, etc.:78 101 Distribution format:tar.gz Programming language:Maple 10 Computer:A laptop with 1.6 GHz Pentium CPU Operating system:Windows XP Professional RAM:760 Mbytes Classification:5 Nature of problem:Finding the travelling wave solutions to single nonlinear PDEs. Solution method:Based on tanh-function method. Restrictions:The current version of this package can only deal with single autonomous PDEs or ODEs, not systems of PDEs or ODEs. However, the PDEs can have any finite number of independent space variables in addition to time t. Unusual features:For PDEs whose balancing numbers are not positive integers, TWS works much better than existing packages. Furthermore, TWS obtains more solutions than existing packages for most cases. Additional comments:It is easy to use. Running time:Less than 20 seconds for most cases, between 20 to 100 seconds for some cases, over 100 seconds for few cases. References: [1] E.S. Cheb-Terrab, K. von Bulow, Comput. Phys. Comm. 90 (1995) 102. [2] S.A. Elwakil, S.K. El-Labany, M.A. Zahran, R. Sabry, Phys. Lett. A 299 (2002) 179. [3] E. Fan, Phys. Lett. 277 (2000) 212. [4] W. Malfliet, Amer. J. Phys. 60 (1992) 650. [5] W. Malfliet, W. Hereman, Phys. Scripta 54 (1996) 563. [6] E.J. Parkes, B.R. Duffy, Comput. Phys. Comm. 98 (1996) 288.

Schur polynomials and biorthogonal random matrix ensembles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tierz, Miguel

The study of the average of Schur polynomials over a Stieltjes-Wigert ensemble has been carried out by Dolivet and Tierz [J. Math. Phys. 48, 023507 (2007); e-print arXiv:hep-th/0609167], where it was shown that it is equal to quantum dimensions. Using the same approach, we extend the result to the biorthogonal case. We also study, using the Littlewood-Richardson rule, some particular cases of the quantum dimension result. Finally, we show that the notion of Giambelli compatibility of Schur averages, introduced by Borodin et al. [Adv. Appl. Math. 37, 209 (2006); e-print arXiv:math-ph/0505021], also holds in the biorthogonal setting.

Asymptotics of quantum weighted Hurwitz numbers

NASA Astrophysics Data System (ADS)

Harnad, J.; Ortmann, Janosch

2018-06-01

This work concerns both the semiclassical and zero temperature asymptotics of quantum weighted double Hurwitz numbers. The partition function for quantum weighted double Hurwitz numbers can be interpreted in terms of the energy distribution of a quantum Bose gas with vanishing fugacity. We compute the leading semiclassical term of the partition function for three versions of the quantum weighted Hurwitz numbers, as well as lower order semiclassical corrections. The classical limit is shown to reproduce the simple single and double Hurwitz numbers studied by Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74). The KP-Toda τ-function that serves as generating function for the quantum Hurwitz numbers is shown to have the τ-function of Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74) as its leading term in the classical limit, and, with suitable scaling, the same holds for the partition function, the weights and expectations of Hurwitz numbers. We also compute the zero temperature limit of the partition function and quantum weighted Hurwitz numbers. The KP or Toda τ-function serving as generating function for the quantum Hurwitz numbers are shown to give the one for Belyi curves in the zero temperature limit and, with suitable scaling, the same holds true for the partition function, the weights and the expectations of Hurwitz numbers.

1 D analysis of Radiative Shock damping by lateral radiative losses

NASA Astrophysics Data System (ADS)

Busquet, Michel; Audit, Edouard

2008-11-01

We have demonstrated the effect of the lateral radiative losses in radiative shocks propagative in layered quasi-planar atmospheres.[1,2] The damping of the precursor is sensitive to the fraction of self-emitted radiation reflected by the walls (called albedo) We have given recently an experimental determination of the wall albedo.[2] For parametric analysis of this effect, we implement lateral losses in the 1D hydro-rad code MULTI [3] and compared results with 2D simulations. [1] S.Leygnac, et al., Phys. Plasmas 13, 113301 (2006) [2] M.Busquet, et al, High Energy Density Plasmas 3, 8-11 (2007); M.Gonzalez, et al, Laser Part. Beams 24, 1-6 (2006) [3] Ramis et al, Comp. Phys. Comm., 49, 475 (1988)

Shock-wave ion acceleration by an ultra-relativistic short laser pulse

NASA Astrophysics Data System (ADS)

Zhidkov, A.; Batishchev, O.; Uesaka, M.

2002-11-01

Research on ion acceleration by intense short laser pulses grows in the last few years [1-9] because of various applications. However, the study is mainly focused on the forward ion acceleration. We study ion inward acceleration, which in contrast to other mechanisms has density of ions per unit energy not decreased with the laser intensity [8]. Magnetic field generated due to a finite size of laser spot can affect electron distribution. In the present work we study the effect of magnetic field on the shock wave formation and ion acceleration in a solid target via 2D PIC and Vlasov simulation. Though the PIC simulation can provide detailed information, in relativistic plasmas it may not calculate B correctly: (i) too many particles are needed to make B disappeared in thermal plasmas, (ii) local scheme [10] does not satisfy curl(Epl)=0. Therefore, two approaches are used in the present study. [1] S. P. Hatchett et al., Phys. Plas. 7, 2076 (2000); [2] A. Maksimchuk et al., Phys. Rev. Lett. 84, 4108 (2000); [3] E.L. Clark et al., Phys. Rev. Lett. 85, 1654 (2000); [4] A. Zhidkov et al., Phys. Rev. E60, 3273 (1999); E61, R2224 (2000); [5] Y. Murakami et al, Phys. Plasmas 8,4138 (2001); [6] T.Zh. Esirkepov et al, JETP Lett. 70, 82 (1999); [7] A. Pukhov, Phys. Rev. Lett. 86, 3562(2001); [8] A.A. Andreev et al., Plasma Phys. Contr. Fusion (2002); [9] O.V. Batishchev et al., Plasma Phys. Rep. 20, 587 (1994); [10] J. Villasenor et al., Comp. Phys. Comm. 69, 306 (1992).

Tikekar superdense stars in electric fields

NASA Astrophysics Data System (ADS)

Komathiraj, K.; Maharaj, S. D.

2007-04-01

We present exact solutions to the Einstein-Maxwell system of equations with a specified form of the electric field intensity by assuming that the hypersurface {t=constant} are spheroidal. The solution of the Einstein-Maxwell system is reduced to a recurrence relation with variable rational coefficients which can be solved in general using mathematical induction. New classes of solutions of linearly independent functions are obtained by restricting the spheroidal parameter K and the electric field intensity parameter α. Consequently, it is possible to find exact solutions in terms of elementary functions, namely, polynomials and algebraic functions. Our result contains models found previously including the superdense Tikekar neutron star model [J. Math. Phys. 31, 2454 (1990)] when K=-7 and α=0. Our class of charged spheroidal models generalize the uncharged isotropic Maharaj and Leach solutions [J. Math. Phys. 37, 430 (1996)]. In particular, we find an explicit relationship directly relating the spheroidal parameter K to the electromagnetic field.

Addendum to "Charm and bottom quark masses: An update"

NASA Astrophysics Data System (ADS)

Chetyrkin, Konstantin G.; Kühn, Johann H.; Maier, Andreas; Maierhöfer, Philipp; Marquard, Peter; Steinhauser, Matthias; Sturm, Christian

2017-12-01

We update the experimental moments for the charm quark as computed in [J. H. Kühn, M. Steinhauser, and C. Sturm, Nucl. Phys. B778, 192 (2007), 10.1016/j.nuclphysb.2007.04.036] and used in [K. G. Chetyrkin, J. H. Kühn, A. Maier, P. Maierhöfer, P. Marquard, M. Steinhauser, and C. Sturm, Phys. Rev. D 80, 074010 (2009),, 10.1103/PhysRevD.80.074010 K. Chetyrkin, J. H. Kühn, A. Maier, P. Maierhöfer, P. Marquard, M. Steinhauser, and C. Sturm, Theor. Math. Phys. 170, 217 (2012), 10.1007/s11232-012-0024-7] for the determination of the charm-quark mass. The new value for the MS ¯ charm-quark mass reads mc(3 GeV )=0.993 ±0.008 GeV .

On the universality of knot probability ratios

NASA Astrophysics Data System (ADS)

Janse van Rensburg, E. J.; Rechnitzer, A.

2011-04-01

Let pn denote the number of self-avoiding polygons of length n on a regular three-dimensional lattice, and let pn(K) be the number which have knot type K. The probability that a random polygon of length n has knot type K is pn(K)/pn and is known to decay exponentially with length (Sumners and Whittington 1988 J. Phys. A: Math. Gen. 21 1689-94, Pippenger 1989 Discrete Appl. Math. 25 273-8). Little is known rigorously about the asymptotics of pn(K), but there is substantial numerical evidence (Orlandini et al 1988 J. Phys. A: Math. Gen. 31 5953-67, Marcone et al 2007 Phys. Rev. E 75 41105, Rawdon et al 2008 Macromolecules 41 4444-51, Janse van Rensburg and Rechnitzer 2008 J. Phys. A: Math. Theor. 41 105002) that pn(K) grows as p_n(K) \\simeq C_K \\mu _\\emptyset ^n n^{\\alpha -3+N_K}, \\qquad as\\quad n \\rightarrow \\infty, where NK is the number of prime components of the knot type K. It is believed that the entropic exponent, α, is universal, while the exponential growth rate, μ∅, is independent of the knot type but varies with the lattice. The amplitude, CK, depends on both the lattice and the knot type. The above asymptotic form implies that the relative probability of a random polygon of length n having prime knot type K over prime knot type L is \\frac{p_n(K)/p_n}{p_n(L)/p_n} = \\frac{p_n(K)}{p_n(L)} \\simeq \\left[ \\frac{C_K}{C_L} \\right].\\\\[-8pt] In the thermodynamic limit this probability ratio becomes an amplitude ratio; it should be universal and depend only on the knot types K and L. In this communication we examine the universality of these probability ratios for polygons in the simple cubic, face-centred cubic and body-centred cubic lattices. Our results support the hypothesis that these are universal quantities. For example, we estimate that a long random polygon is approximately 28 times more likely to be a trefoil than be a figure-eight, independent of the underlying lattice, giving an estimate of the intrinsic entropy associated with knot types in closed curves.

Theory of Soliton Waves.

DTIC Science & Technology

1984-11-01

equation of Kadomtsev and Petviashvili (1970): (ut + 6uu x + U )x = 3 a Uyy, 0 - ± 1. (12) This equation turns out to be integrable for a = ± 1. For...1982b: "Comments on Inverse Scattering for the Kadomtsev - Petviashvili equation ", in Math methods in Hydro. & Integrability in Dyn. Systems, A. I. P. Conf...358. . Joseph, R. I., 1977: J. Phys. A., vol 10, p L225-L227. Kadomtsev , B. B. and Petviashvili , V. I., 1970: Soy. Phys. Doklady, vol 15, pp 539-541

CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae

NASA Astrophysics Data System (ADS)

van de Leur, Johan W.; Orlov, Alexander Yu.; Shiota, Takahiro

2012-06-01

We develop the theory of CKP hierarchy introduced in the papers of Kyoto school [Date E., Jimbo M., Kashiwara M., Miwa T., J. Phys. Soc. Japan 50 (1981), 3806-3812] (see also [Kac V.G., van de Leur J.W., Adv. Ser. Math. Phys., Vol. 7, World Sci. Publ., Teaneck, NJ, 1989, 369-406]). We present appropriate bosonization formulae. We show that in the context of the CKP theory certain orthogonal polynomials appear. These polynomials are polynomial both in even and odd (in Grassmannian sense) variables.

Approximation of Viscoelastic Stresses from Newtonian Turbulent Kinematics

DTIC Science & Technology

1988-09-01

birefringence of polyethylene oxide solutions in a four roll mill. J.Poly.Sci.:Poly.Phys.Ed. 14, 1111-1119. Dandridge, A., Meeten , G.H., Layec-Raphalen, M.N...flows. Poly. Comm. 25, 144-146. Metzner, A.B., & Astarita, G . 1967 External flow of viscoelastic materials: fluid property restrictions on the use of...dumbbell model for dilute solutions. Rheol.Acta 23, 151-162. Philippoff, W. 1956 Flow-birefringence and stress. Nature 178 , 811-812. Ryskin, G . 1987a

Higher-spin theory and holography

NASA Astrophysics Data System (ADS)

Gaberdiel, Matthias; Vasiliev, Mikhail

2013-05-01

This special issue of Journal of Physics A: Mathematical and Theoretical reviews recent developments in higher-spin gauge theories and their applications to holographic dualities. The analysis of higher-spin theories has a very long history, but it took until the mid 1980s for the first consistent higher-spin interactions to be constructed by Bengtsson, Bengtsson and Brink [1] and Berends, Burgers and van Dam [2]. Somewhat later it was shown by Fradkin and Vasiliev [3] that consistent higher-spin gauge theories that involve gravity should necessarily be defined on a curved background. The first consistent interacting higher-spin theories were then formulated at the classical level by Vasiliev in the early 1990s [4]. These higher-spin theories involve an infinite number of massless higher-spin fields that support higher-spin gauge symmetries, and indeed, are largely characterized by this underlying gauge symmetry. The simplest examples are provided by higher-spin theories on (anti)-de Sitter spaces, and in a sense, this anticipated the AdS/CFT correspondence. Indeed, in the tensionless limit of string theory, the massive excitations of string theory become massless, and hence define higher-spin gauge fields. On the other hand, from the dual gauge theory perspective, this is the limit in which the field theory becomes free, and therefore has many conserved higher-spin currents. By the usual AdS/CFT dictionary, these are dual to the higher-spin gauge symmetries of the bulk description. Following this line of argument, Sundborg [5] and Witten [6] suggested in 2001 that a duality relating a higher-spin theory on AdSd to a weakly coupled (d - 1)-dimensional conformal field theory should exist. A concrete proposal was then made by Klebanov and Polyakov [7] who conjectured that the simplest version of a higher-spin gauge theory on AdS4 should be dual to the 3d O(N ) vector model. Recently, much support for this conjecture was obtained by Giombi and Yin [8], and in turn, this has triggered a significant amount of activity in this general area. Among other things, the constraints that are implied by the higher-spin symmetries were analysed (see the paper by Maldacena and Zhiboedov in this issue [9]), and a fairly concrete proposal for how higher-spin theories are related to string theory was made (see the paper by Chang, Minwalla, Sharma and Yin in this issue [10]). Furthermore, a lower dimensional version of the conjecture was put forward by Gaberdiel and Gopakumar [11] that was subsequently also checked in some detail. These dualities hold the promise of offering insights into the inner workings of the AdS/CFT correspondence since they are complex enough to capture the essence of the duality, while at the same time being sufficiently simple in order to allow for a detailed analysis. Moreover, the methods specifically developed in higher-spin theory may be useful for understanding a general mechanism underlying holography, both in higher-spin models and beyond (see the paper by Vasiliev in this issue [12]). Another fascinating aspect of these higher-spin theories lies in the fact that the higher-spin symmetries mix generically fields of different spin, and in particular, the spin-2 metric and higher-spin excitations are related to one another by gauge transformations. As a result, higher-spin theories require a modification of the standard framework of Riemannian geometry since the usual diffeomorphism-invariant tensors are not gauge invariant any longer. In particular, higher-spin theories may therefore open the way towards understanding fundamental concepts of space-time geometry; for example, they may well have key lessons in store for how string theory resolves space-time singularities. In this issue we have collected together a number of review papers, summarizing the aforementioned recent developments, as well as research papers indicating current directions of interest in the study of higher-spin gauge theories. We hope that it will be useful, both for beginners interested in an introduction to the subject, and for experts already working in the field. Three of the reviews deal with the holographic dualities mentioned above: the paper by Giombi and Yin [13] reviews the situation for AdS4/CFT3, while the review by Gaberdiel and Gopakumar [14] deals with the lower-dimensional AdS3/CFT2 version. In addition, the review by Jevicki, Jin and Ye [15] explains a possible way of proving the duality using collective fields. There are two reviews on the construction of black holes in higher-spin gauge theories: the review by Iazeolla and Sundell [16] reviews the situation for 4d higher-spin theories, while the review by Ammon, Gutperle, Kraus and Perlmutter [17] deals with the three-dimensional case for which much progress has been made recently. Finally, the review of Sagnotti [18] explains various general aspects of higher-spin gauge theories. The research papers deal with different aspects of current developments; some are concerned with the holographic duality, while others develop the general theory of higher-spin fields. References [1] Bengtsson A K H, Bengtsson I and Brink L 1983 Cubic interaction terms for arbitrarily extended supermultiplets Nucl. Phys. B 227 41 [2] Berends F A, Burgers G J H Van Dam H 1984 On spin three self interactions Z. Phys. C 24 247 [3] Fradkin E S Vasiliev M A 1987 On the gravitational interaction of massless higher-spin fields Phys. Lett. B 189 89 [4] Vasiliev M A 1992 More on equations of motion for interacting massless fields of all spins in 3+1 dimensions Phys. Lett. B 285 225 [5] Sundborg B 2001 Stringy gravity, interacting tensionless strings and massless higher spins Nucl. Phys. Proc. Suppl. 102 113 (arXiv:hep-th/0103247) [6] Witten E 2001 Spacetime reconstruction Talk at the John Schwarz 60th Birthday Symp. (http://theory.caltech.edu/jhs60/witten/1.html) [7] Klebanov I R Polyakov A M 2002 AdS dual of the critical O (N ) vector model Phys. Lett. B 550 213 (arXiv:hep-th/0210114) [8] Giombi S Yin X 2010 Higher spin gauge theory and holography: the three-point functions J. High Energy Phys. JHEP09(2010)115 (arXiv:0912.3462 [hep-th]) [9] Maldacena J Zhiboedov A 2013 Constraining conformal field theories with a higher spin symmetry J. Phys. A: Math. Theor. 46 214011 (arXiv:1204.3882 [hep-th]) [10] Chang C-M, Minwalla A, Sharma T Yin X 2013 ABJ triality: from higher spin fields to strings J. Phys. A: Math. Theor. 46 214009 (arXiv:1207.4485 [hep-th]) [11] Gaberdiel M R Gopakumar R 2011 An AdS3 dual for minimal model CFTs Phys. Rev. D 83 066007 (arXiv:1011.2986 [hep-th]) [12] Vasiliev M A 2013 Holography, unfolding and higher-spin theory J. Phys. A: Math. Theor. 46 214013 (arXiv:1203.5554 [hep-th]) [13] Giombi S Yin X 2013 The higher spin/vector model duality J. Phys. A: Math. Theor. 46 214003 (arXiv:1208.4036 [hep-th]) [14] Gaberdiel M R Gopakumar R 2013 Minimal model holography J. Phys. A: Math. Theor. 46 214002 (arXiv:1207.6697 [hep-th]) [15] Jevicki A, Jin K Ye Q 2013 Perturbative and non-perturbative aspects in vector model/higher spin duality J. Phys. A: Math. Theor. 46 214005 (arXiv:1212.5215 [hep-th]) [16] Iazeolla C Sundell P 2013 Biaxially symmetric solutions to 4D higher-spin gravity J. Phys. A: Math. Theor. 46 214004 (arXiv:1208.4077 [hep-th]) [17] Ammon M, Gutperle M, Kraus P Perlmutter E 2013 Black holes in three dimensional higher spin gravity: a review J. Phys. A: Math. Theor. 46 214001 (arXiv:1208.5182 [hep-th]) [18] Sagnotti A 2013 Notes on strings and higher spins J. Phys. A: Math. Theor. 46 214006 (arXiv:1112.4285 [hep-th])

Totally Asymmetric Limit for Models of Heat Conduction

NASA Astrophysics Data System (ADS)

De Carlo, Leonardo; Gabrielli, Davide

2017-08-01

We consider one dimensional weakly asymmetric boundary driven models of heat conduction. In the cases of a constant diffusion coefficient and of a quadratic mobility we compute the quasi-potential that is a non local functional obtained by the solution of a variational problem. This is done using the dynamic variational approach of the macroscopic fluctuation theory (Bertini et al. in Rev Mod Phys 87:593, 2015). The case of a concave mobility corresponds essentially to the exclusion model that has been discussed in Bertini et al. (J Stat Mech L11001, 2010; Pure Appl Math 64(5):649-696, 2011; Commun Math Phys 289(1):311-334, 2009) and Enaud and Derrida (J Stat Phys 114:537-562, 2004). We consider here the convex case that includes for example the Kipnis-Marchioro-Presutti (KMP) model and its dual (KMPd) (Kipnis et al. in J Stat Phys 27:6574, 1982). This extends to the weakly asymmetric regime the computations in Bertini et al. (J Stat Phys 121(5/6):843-885, 2005). We consider then, both microscopically and macroscopically, the limit of large externalfields. Microscopically we discuss some possible totally asymmetric limits of the KMP model. In one case the totally asymmetric dynamics has a product invariant measure. Another possible limit dynamics has instead a non trivial invariant measure for which we give a duality representation. Macroscopically we show that the quasi-potentials of KMP and KMPd, which are non local for any value of the external field, become local in the limit. Moreover the dependence on one of the external reservoirs disappears. For models having strictly positive quadratic mobilities we obtain instead in the limit a non local functional having a structure similar to the one of the boundary driven asymmetric exclusion process.

Modular invariant representations of infinite-dimensional Lie algebras and superalgebras

PubMed Central

Kac, Victor G.; Wakimoto, Minoru

1988-01-01

In this paper, we launch a program to describe and classify modular invariant representations of infinite-dimensional Lie algebras and superalgebras. We prove a character formula for a large class of highest weight representations L(λ) of a Kac-Moody algebra [unk] with a symmetrizable Cartan matrix, generalizing the Weyl-Kac character formula [Kac, V. G. (1974) Funct. Anal. Appl. 8, 68-70]. In the case of an affine [unk], this class includes modular invariant representations of arbitrary rational level m = t/u, where t [unk] Z and u [unk] N are relatively prime and m + g ≥ g/u (g is the dual Coxeter number). We write the characters of these representations in terms of theta functions and calculate their asymptotics, generalizing the results of Kac and Peterson [Kac, V. G. & Peterson, D. H. (1984) Adv. Math. 53, 125-264] and of Kac and Wakimoto [Kac, V. G. & Wakimoto, M. (1988) Adv. Math. 70, 156-234] for the u = 1 (integrable) case. We work out in detail the case [unk] = A1(1), in particular classifying all its modular invariant representations. Furthermore, we show that the modular invariant representations of the Virasoro algebra Vir are precisely the “minimal series” of Belavin et al. [Belavin, A. A., Polyakov, A. M. & Zamolodchikov, A. B. (1984) Nucl. Phys. B 241, 333-380] using the character formulas of Feigin and Fuchs [Feigin, B. L. & Fuchs, D. B. (1984) Lect. Notes Math. 1060, 230-245]. We show that tensoring the basic representation and modular invariant representations of A1(1) produces all modular invariant representations of Vir generalizing the results of Goddard et al. [Goddard P., Kent, A. & Olive, D. (1986) Commun. Math. Phys. 103, 105-119] and of Kac and Wakimoto [Kac, V. G. & Wakimoto, M. (1986) Lect. Notes Phys. 261, 345-371] in the unitary case. We study the general branching functions as well. All these results are generalized to the Kac-Moody superalgebras introduced by Kac [Kac, V. G. (1978) Adv. Math. 30, 85-136] and to N = 1 super Virasoro algebras. We work out in detail the case of the superalgebra B(0, 1)(1), showing, in particular, that restricting to its even part produces again all modular invariant representations of Vir. These results lead to general conjectures about asymptotic behavior of positive energy representations and classification of modular invariant representations. PMID:16593954

Lozenge Tiling Dynamics and Convergence to the Hydrodynamic Equation

NASA Astrophysics Data System (ADS)

Laslier, Benoît; Toninelli, Fabio Lucio

2018-03-01

We study a reversible continuous-time Markov dynamics of a discrete (2 + 1)-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the {L× L} torus, or as a conservative dynamics for a two-dimensional system of interlaced particles. The particle interlacement constraints imply that the equilibrium measures are far from being product Bernoulli: particle correlations decay like the inverse distance squared and interface height fluctuations behave on large scales like a massless Gaussian field. We consider a particular choice of the transition rates, originally proposed in Luby et al. (SIAM J Comput 31:167-192, 2001): in terms of interlaced particles, a particle jump of length n that preserves the interlacement constraints has rate 1/(2 n). This dynamics presents special features: the average mutual volume between two interface configurations decreases with time (Luby et al. 2001) and a certain one-dimensional projection of the dynamics is described by the heat equation (Wilson in Ann Appl Probab 14:274-325, 2004). In this work we prove a hydrodynamic limit: after a diffusive rescaling of time and space, the height function evolution tends as L\\to∞ to the solution of a non-linear parabolic PDE. The initial profile is assumed to be C 2 differentiable and to contain no "frozen region". The explicit form of the PDE was recently conjectured (Laslier and Toninelli in Ann Henri Poincaré Theor Math Phys 18:2007-2043, 2017) on the basis of local equilibrium considerations. In contrast with the hydrodynamic equation for the Langevin dynamics of the Ginzburg-Landau model (Funaki and Spohn in Commun Math Phys 85:1-36, 1997; Nishikawa in Commun Math Phys 127:205-227, 2003), here the mobility coefficient turns out to be a non-trivial function of the interface slope.

The nodal count {0,1,2,3,…} implies the graph is a tree

PubMed Central

Band, Ram

2014-01-01

Sturm's oscillation theorem states that the nth eigenfunction of a Sturm–Liouville operator on the interval has n−1 zeros (nodes) (Sturm 1836 J. Math. Pures Appl. 1, 106–186; 373–444). This result was generalized for all metric tree graphs (Pokornyĭ et al. 1996 Mat. Zametki 60, 468–470 (doi:10.1007/BF02320380); Schapotschnikow 2006 Waves Random Complex Media 16, 167–178 (doi:10.1080/1745530600702535)) and an analogous theorem was proved for discrete tree graphs (Berkolaiko 2007 Commun. Math. Phys. 278, 803–819 (doi:10.1007/S00220-007-0391-3); Dhar & Ramaswamy 1985 Phys. Rev. Lett. 54, 1346–1349 (doi:10.1103/PhysRevLett.54.1346); Fiedler 1975 Czechoslovak Math. J. 25, 607–618). We prove the converse theorems for both discrete and metric graphs. Namely if for all n, the nth eigenfunction of the graph has n−1 zeros, then the graph is a tree. Our proofs use a recently obtained connection between the graph's nodal count and the magnetic stability of its eigenvalues (Berkolaiko 2013 Anal. PDE 6, 1213–1233 (doi:10.2140/apde.2013.6.1213); Berkolaiko & Weyand 2014 Phil. Trans. R. Soc. A 372, 20120522 (doi:10.1098/rsta.2012.0522); Colin de Verdière 2013 Anal. PDE 6, 1235–1242 (doi:10.2140/apde.2013.6.1235)). In the course of the proof, we show that it is not possible for all (or even almost all, in the metric case) the eigenvalues to exhibit a diamagnetic behaviour. In addition, we develop a notion of ‘discretized’ versions of a metric graph and prove that their nodal counts are related to those of the metric graph. PMID:24344337

Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay

NASA Astrophysics Data System (ADS)

Dai, Qiuyi; Yang, Zhifeng

2014-10-01

In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561-1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011).

Three-Level Systems as Amplifiers and Attenuators: A Thermodynamic Analysis

NASA Astrophysics Data System (ADS)

Boukobza, E.; Tannor, D. J.

2007-06-01

Thermodynamics of a three-level maser was studied in the pioneering work of Scovil Schulz-DuBois [Phys. Rev. Lett. 2, 262 (1959)PRLTAO0031-900710.1103/PhysRevLett.2.262]. In this Letter we consider the same three-level model, but we give a full thermodynamic analysis based on Hamiltonian and dissipative Lindblad superoperators. The first law of thermodynamics is obtained using a recently developed alternative [Phys. Rev. A 74, 063823 (2006)PLRAAN1050-294710.1103/PhysRevA.74.063823] to Alicki’s definitions for heat flux and power [J. Phys. AJPHAC50305-4470 12, L103 (1979)10.1088/0305-4470/12/5/007]. Using a novel variation on Spohn’s entropy production function [J. Math. Phys. (N.Y.)JMAPAQ0022-2488 19, 1227 (1978)10.1063/1.523789], we obtain Carnot’s efficiency inequality and the Scovil Schulz-DuBois maser efficiency formula when the three-level system is operated as a heat engine (amplifier). Finally, we show that the three-level system has two other modes of operation—a refrigerator mode and a squanderer mode —both of which attenuate the electric field.

Revised and extended UTILITIES for the RATIP package

NASA Astrophysics Data System (ADS)

Nikkinen, J.; Fritzsche, S.; Heinäsmäki, S.

2006-09-01

During the last years, the RATIP package has been found useful for calculating the excitation and decay properties of free atoms. Based on the (relativistic) multiconfiguration Dirac-Fock method, this program is used to obtain accurate predictions of atomic properties and to analyze many recent experiments. The daily work with this package made an extension of its UTILITIES [S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163] desirable in order to facilitate the data handling and interpretation of complex spectra. For this purpose, we make available an enlarged version of the UTILITIES which mainly supports the comparison with experiment as well as large Auger computations. Altogether 13 additional tasks have been appended to the program together with a new menu structure to improve the interactive control of the program. Program summaryTitle of program: RATIP Catalogue identifier: ADPD_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADPD_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Reference in CPC to previous version: S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163 Catalogue identifier of previous version: ADPD Authors of previous version: S. Fritzsche, Department of Physics, University of Kassel, Heinrich-Plett-Strasse 40, D-34132 Kassel, Germany Does the new version supersede the original program?: yes Computer for which the new version is designed and others on which it has been tested: IBM RS 6000, PC Pentium II-IV Installations: University of Kassel (Germany), University of Oulu (Finland) Operating systems: IBM AIX, Linux, Unix Program language used in the new version: ANSI standard Fortran 90/95 Memory required to execute with typical data: 300 kB No. of bits in a word: All real variables are parameterized by a selected kind parameter and, thus, can be adapted to any required precision if supported by the compiler. Currently, the kind parameter is set to double precision (two 32-bit words) as used also for other components of the RATIP package [S. Fritzsche, C.F. Fischer, C.Z. Dong, Comput. Phys. Comm. 124 (2000) 341; G. Gaigalas, S. Fritzsche, Comput. Phys. Comm. 134 (2001) 86; S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163; S. Fritzsche, J. Elec. Spec. Rel. Phen. 114-116 (2001) 1155] No. of lines in distributed program, including test data, etc.:231 813 No. of bytes in distributed program, including test data, etc.: 3 977 387 Distribution format: tar.gzip file Nature of the physical problem: In order to describe atomic excitation and decay properties also quantitatively, large-scale computations are often needed. In the framework of the RATIP package, the UTILITIES support a variety of (small) tasks. For example, these tasks facilitate the file and data handling in large-scale applications or in the interpretation of complex spectra. Method of solution: The revised UTILITIES now support a total of 29 subtasks which are mainly concerned with the manipulation of output data as obtained from other components of the RATIP package. Each of these tasks are realized by one or several subprocedures which have access to the corresponding modules of the main components. While the main menu defines seven groups of subtasks for data manipulations and computations, a particular task is selected from one of these group menus. This allows to enlarge the program later if technical support for further tasks will become necessary. For each selected task, an interactive dialog about the required input and output data as well as a few additional information are printed during the execution of the program. Reasons for the new version: The requirement for enlarging the previous version of the UTILITIES [S. Fritzsche, Comput. Phys. Comm. 141 (2001) 163] arose from the recent application of the RATIP package for large-scale radiative and Auger computations. A number of new subtasks now refer to the handling of Auger amplitudes and their proper combination in order to facilitate the interpretation of complex spectra. A few further tasks, such as the direct access to the one-electron matrix elements for some given set of orbital functions, have been found useful also in the analysis of data. Summary of revisions: extraction and handling of atomic data within the framework of RATIP. With the revised version, we now 'add' another 13 tasks which refer to the manipulation of data files, the generation and interpretation of Auger spectra, the computation of various one- and two-electron matrix elements as well as the evaluation of momentum densities and grid parameters. Owing to the rather large number of subtasks, the main menu has been divided into seven groups from which the individual tasks can be selected very similarly as before. Typical running time: The program responds promptly for most of the tasks. The responding time for some tasks, such as the generation of a relativistic momentum density, strongly depends on the size of the corresponding data files and the number of grid points. Unusual features of the program: A total of 29 different tasks are supported by the program. Starting from the main menu, the user is guided interactively through the program by a dialog and a few additional explanations. For each task, a short summary about its function is displayed before the program prompts for all the required input data.

A novel semi-quantum secret sharing scheme based on Bell states

NASA Astrophysics Data System (ADS)

Yin, Aihan; Wang, Zefan; Fu, Fangbo

2017-05-01

A semi-quantum secret sharing (SQSS) scheme based on Bell states is proposed in this paper. The sender who can perform any relevant quantum operations uses Bell states to share the secret keys with her participants that are limited to perform classical operations on the transmitted qubits. It is found that our scheme is easy to generalize from three parties to multiparty and more efficient than the previous schemes [Q. Li, W. H. Chan and D. Y. Long, Phys. Rev. A 82 (2010) 022303; L. Z. Li, D. W. Qiu and P. Mateus, J. Phys. A: Math. Theor. 26 (2013) 045304; C. Xie, L. Z. Li and D. W. Qiu, Int. J. Theor. Phys. 54 (2015) 3819].

BFACF-style algorithms for polygons in the body-centered and face-centered cubic lattices

NASA Astrophysics Data System (ADS)

Janse van Rensburg, E. J.; Rechnitzer, A.

2011-04-01

In this paper, the elementary moves of the BFACF-algorithm (Aragão de Carvalho and Caracciolo 1983 Phys. Rev. B 27 1635-45, Aragão de Carvalho and Caracciolo 1983 Nucl. Phys. B 215 209-48, Berg and Foester 1981 Phys. Lett. B 106 323-6) for lattice polygons are generalized to elementary moves of BFACF-style algorithms for lattice polygons in the body-centered (BCC) and face-centered (FCC) cubic lattices. We prove that the ergodicity classes of these new elementary moves coincide with the knot types of unrooted polygons in the BCC and FCC lattices and so expand a similar result for the cubic lattice (see Janse van Rensburg and Whittington (1991 J. Phys. A: Math. Gen. 24 5553-67)). Implementations of these algorithms for knotted polygons using the GAS algorithm produce estimates of the minimal length of knotted polygons in the BCC and FCC lattices.

Local energy decay for linear wave equations with variable coefficients

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

2005-06-01

A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

Multi-Scale Behavioral Modeling and Analysis Promoting a Fundamental Understanding of Agent-Based System Design and Operation

DTIC Science & Technology

2007-03-01

Chains," Mathematics of Control, Signals, and Systems, vol. 3(1), pp. 1-29, 1990. [4] A . Arnold, J . A . Carrillo, and I. Gamba, "Low and High Field...Aronson, C. L. A ., and J . L. Vázquez, "Interfaces with a corner point in one- dimensional porous medium flow," Comm. Pure Appl. Math, vol. 38(4), pp. 375...K. Levin, "Damage analysis of fiber composites," Computer Methods in Applied Mechanics and Engineering. [10] K. S. Barber, A . Goel, T. J . Graser, T

Comment on ``The problem of deficiency indices for discrete Schrödinger operators on locally finite graphs'' [J. Math. Phys. 52, 063512 (2011)

NASA Astrophysics Data System (ADS)

Golénia, Sylvain; Schumacher, Christoph

2013-06-01

In this comment we answer negatively to our conjecture concerning the deficiency indices. More precisely, given any non-negative integer n, there is locally finite graph on which the adjacency matrix has deficiency indices (n, n).

Weyl's type estimates on the eigenvalues of critical Schrödinger operators using improved Hardy-Sobolev inequalities

NASA Astrophysics Data System (ADS)

Zographopoulos, N. B.

2009-11-01

Motivated by the work (Karachalios N I 2008 Lett. Math. Phys. 83 189-99), we present explicit asymptotic estimates on the eigenvalues of the critical Schrödinger operator, involving inverse-square potential, based on improved Hardy-Sobolev-type inequalities.

Path integration of the time-dependent forced oscillator with a two-time quadratic action

NASA Astrophysics Data System (ADS)

Zhang, Tian Rong; Cheng, Bin Kang

1986-03-01

Using the prodistribution theory proposed by DeWitt-Morette [C. DeWitt-Morette, Commun. Math. Phys. 28, 47 (1972); C. DeWitt-Morette, A. Maheshwari, and B. Nelson, Phys. Rep. 50, 257 (1979)], the path integration of a time-dependent forced harmonic oscillator with a two-time quadratic action has been given in terms of the solutions of some integrodifferential equations. We then evaluate explicitly both the classical path and the propagator for the specific kernel introduced by Feynman in the polaron problem. Our results include the previous known results as special cases.

Variational processes and stochastic versions of mechanics

NASA Astrophysics Data System (ADS)

Zambrini, J. C.

1986-09-01

The dynamical structure of any reasonable stochastic version of classical mechanics is investigated, including the version created by Nelson [E. Nelson, Quantum Fluctuations (Princeton U.P., Princeton, NJ, 1985); Phys. Rev. 150, 1079 (1966)] for the description of quantum phenomena. Two different theories result from this common structure. One of them is the imaginary time version of Nelson's theory, whose existence was unknown, and yields a radically new probabilistic interpretation of the heat equation. The existence and uniqueness of all the involved stochastic processes is shown under conditions suggested by the variational approach of Yasue [K. Yasue, J. Math. Phys. 22, 1010 (1981)].

Lagrangian dynamics for classical, Brownian, and quantum mechanical particles

NASA Astrophysics Data System (ADS)

Pavon, Michele

1996-07-01

In the framework of Nelson's stochastic mechanics [E. Nelson, Dynamical Theories of Brownian Motion (Princeton University, Princeton, 1967); F. Guerra, Phys. Rep. 77, 263 (1981); E. Nelson, Quantum Fluctuations (Princeton University, Princeton, 1985)] we seek to develop the particle counterpart of the hydrodynamic results of M. Pavon [J. Math. Phys. 36, 6774 (1995); Phys. Lett. A 209, 143 (1995)]. In particular, a first form of Hamilton's principle is established. We show that this variational principle leads to the correct equations of motion for the classical particle, the Brownian particle in thermodynamical equilibrium, and the quantum particle. In the latter case, the critical process q satisfies a stochastic Newton law. We then introduce the momentum process p, and show that the pair (q,p) satisfies canonical-like equations.

Second quantization of a covariant relativistic spacetime string in Steuckelberg-Horwitz-Piron theory

NASA Astrophysics Data System (ADS)

Suleymanov, Michael; Horwitz, Lawrence; Yahalom, Asher

2017-06-01

A relativistic 4D string is described in the framework of the covariant quantum theory first introduced by Stueckelberg [ Helv. Phys. Acta 14, 588 (1941)], and further developed by Horwitz and Piron [ Helv. Phys. Acta 46, 316 (1973)], and discussed at length in the book of Horwitz [Relativistic Quantum Mechanics, Springer (2015)]. We describe the space-time string using the solutions of relativistic harmonic oscillator [ J. Math. Phys. 30, 66 (1989)]. We first study the problem of the discrete string, both classically and quantum mechanically, and then turn to a study of the continuum limit, which contains a basically new formalism for the quantization of an extended system. The mass and energy spectrum are derived. Some comparison is made with known string models.

Evaluating Small Sphere Limit of the Wang-Yau Quasi-Local Energy

NASA Astrophysics Data System (ADS)

Chen, Po-Ning; Wang, Mu-Tao; Yau, Shing-Tung

2018-01-01

In this article, we study the small sphere limit of the Wang-Yau quasi-local energy defined in Wang and Yau (Phys Rev Lett 102(2):021101, 2009, Commun Math Phys 288(3):919-942, 2009). Given a point p in a spacetime N, we consider a canonical family of surfaces approaching p along its future null cone and evaluate the limit of the Wang-Yau quasi-local energy. The evaluation relies on solving an "optimal embedding equation" whose solutions represent critical points of the quasi-local energy. For a spacetime with matter fields, the scenario is similar to that of the large sphere limit found in Chen et al. (Commun Math Phys 308(3):845-863, 2011). Namely, there is a natural solution which is a local minimum, and the limit of its quasi-local energy recovers the stress-energy tensor at p. For a vacuum spacetime, the quasi-local energy vanishes to higher order and the solution of the optimal embedding equation is more complicated. Nevertheless, we are able to show that there exists a solution that is a local minimum and that the limit of its quasi-local energy is related to the Bel-Robinson tensor. Together with earlier work (Chen et al. 2011), this completes the consistency verification of the Wang-Yau quasi-local energy with all classical limits.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-04-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Quantitative Pointwise Estimate of the Solution of the Linearized Boltzmann Equation

NASA Astrophysics Data System (ADS)

Lin, Yu-Chu; Wang, Haitao; Wu, Kung-Chien

2018-06-01

We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad's angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543-1608, 2004), (Bull Inst Math Acad Sin 1:1-78, 2006), (Bull Inst Math Acad Sin 6:151-243, 2011) and Lee et al. (Commun Math Phys 269:17-37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.

Preliminary Reports, Memoranda and Technical Notes of the Materials Research Council Summer Conference, La Jolla, CA

DTIC Science & Technology

1975-07-01

1298 (1974); T. Wei, S. Etemad, A. F. Garito and A. J. Heeger, Phys. Lett. 4_5a 269 (1973). G. A. Vhomas, et. al .. Solid State Comm. 0£, 000...C. Beer, Eds. (Academic Press, New York 1975) Vol. 11 (to be published). H. Fetterman et al ., IEEE Trans. MTT-22, 1013 (1974) 8. A. H. Silver...increasing temperature over extensive ranges. Such measure- ments were reported by Johnston et al .?1 for the fast ionic conductor RbAgJ,. Thermal

Automated evaluation of matrix elements between contracted wavefunctions: A Mathematica version of the FRODO program

NASA Astrophysics Data System (ADS)

Angeli, C.; Cimiraglia, R.

2013-02-01

A symbolic program performing the Formal Reduction of Density Operators (FRODO), formerly developed in the MuPAD computer algebra system with the purpose of evaluating the matrix elements of the electronic Hamiltonian between internally contracted functions in a complete active space (CAS) scheme, has been rewritten in Mathematica. New version : A program summaryProgram title: FRODO Catalogue identifier: ADV Y _v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVY_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3878 No. of bytes in distributed program, including test data, etc.: 170729 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer on which the Mathematica computer algebra system can be installed Operating system: Linux Classification: 5 Catalogue identifier of previous version: ADV Y _v1_0 Journal reference of previous version: Comput. Phys. Comm. 171(2005)63 Does the new version supersede the previous version?: No Nature of problem. In order to improve on the CAS-SCF wavefunction one can resort to multireference perturbation theory or configuration interaction based on internally contracted functions (ICFs) which are obtained by application of the excitation operators to the reference CAS-SCF wavefunction. The previous formulation of such matrix elements in the MuPAD computer algebra system, has been rewritten using Mathematica. Solution method: The method adopted consists in successively eliminating all occurrences of inactive orbital indices (core and virtual) from the products of excitation operators which appear in the definition of the ICFs and in the electronic Hamiltonian expressed in the second quantization formalism. Reasons for new version: Some years ago we published in this journal a couple of papers [1, 2] hereafter to be referred to as papers I and II, respectively dedicated to the automated evaluation of the matrix elements of the molecular electronic Hamiltonian between internally contracted functions [3] (ICFs). In paper II the program FRODO (after Formal Reduction Of Density Operators) was presented with the purpose of providing working formulas for each occurrence of the ICFs. The original FRODO program was written in the MuPAD computer algebra system [4] and was actively used in our group for the generation of the matrix elements to be employed in the third-order n-electron valence state perturbation theory (NEVPT) [5-8] as well as in the internally contracted configuration interaction (IC-CI) [9]. We present a new version of the program FRODO written in the Mathematica system [10]. The reason for the rewriting of the program lies in the fact that, on the one hand, MuPAD does not seem to be any longer available as a stand-alone system and, on the other hand, Mathematica, due to its ubiquitousness, appears to be increasingly the computer algebra system most widely used nowadays. Restrictions: The program is limited to no more than doubly excited ICFs. Running time: The examples described in the Readme file take a few seconds to run. References: [1] C. Angeli, R. Cimiraglia, Comp. Phys. Comm. 166 (2005) 53. [2] C. Angeli, R. Cimiraglia, Comp. Phys. Comm. 171 (2005) 63. [3] H.-J. Werner, P. J. Knowles, Adv. Chem. Phys. 89 (1988) 5803. [4] B. Fuchssteiner, W. Oevel: http://www.mupad.de Mupad research group, university of Paderborn. Mupad version 2.5.3 for Linux. [5] C. Angeli, R. Cimiraglia, S. Evangelisti, T. Leininger, J.-P. Malrieu, J. Chem. Phys. 114 (2001) 10252. [6] C. Angeli, R. Cimiraglia, J.-P. Malrieu, J. Chem. Phys. 117 (2002) 9138. [7] C. Angeli, B. Bories, A. Cavallini, R. Cimiraglia, J. Chem. Phys. 124 (2006) 054108. [8] C. Angeli, M. Pastore, R. Cimiraglia, Theor. Chem. Acc. 117 (2007) 743. [9] C. Angeli, R. Cimiraglia, Mol. Phys. in press, DOI:10.1080/00268976.2012.689872 [10] http://www.wolfram.com/Mathematica. Mathematica version 8 for Linux.

Electrical Resistance of the Low Dimensional Critical Branching Random Walk

NASA Astrophysics Data System (ADS)

Járai, Antal A.; Nachmias, Asaf

2014-10-01

We show that the electrical resistance between the origin and generation n of the incipient infinite oriented branching random walk in dimensions d < 6 is O( n 1- α ) for some universal constant α > 0. This answers a question of Barlow et al. (Commun Math Phys 278:385-431, 2008).

Numerical simulation of a lattice polymer model at its integrable point

NASA Astrophysics Data System (ADS)

Bedini, A.; Owczarek, A. L.; Prellberg, T.

2013-07-01

We revisit an integrable lattice model of polymer collapse using numerical simulations. This model was first studied by Blöte and Nienhuis (1989 J. Phys. A: Math. Gen. 22 1415) and it describes polymers with some attraction, providing thus a model for the polymer collapse transition. At a particular set of Boltzmann weights the model is integrable and the exponents ν = 12/23 ≈ 0.522 and γ = 53/46 ≈ 1.152 have been computed via identification of the scaling dimensions xt = 1/12 and xh = -5/48. We directly investigate the polymer scaling exponents via Monte Carlo simulations using the pruned-enriched Rosenbluth method algorithm. By simulating this polymer model for walks up to length 4096 we find ν = 0.576(6) and γ = 1.045(5), which are clearly different from the predicted values. Our estimate for the exponent ν is compatible with the known θ-point value of 4/7 and in agreement with very recent numerical evaluation by Foster and Pinettes (2012 J. Phys. A: Math. Theor. 45 505003).

Singular perturbations with boundary conditions and the Casimir effect in the half space

NASA Astrophysics Data System (ADS)

Albeverio, S.; Cognola, G.; Spreafico, M.; Zerbini, S.

2010-06-01

We study the self-adjoint extensions of a class of nonmaximal multiplication operators with boundary conditions. We show that these extensions correspond to singular rank 1 perturbations (in the sense of Albeverio and Kurasov [Singular Perturbations of Differential Operaters (Cambridge University Press, Cambridge, 2000)]) of the Laplace operator, namely, the formal Laplacian with a singular delta potential, on the half space. This construction is the appropriate setting to describe the Casimir effect related to a massless scalar field in the flat space-time with an infinite conducting plate and in the presence of a pointlike "impurity." We use the relative zeta determinant (as defined in the works of Müller ["Relative zeta functions, relative determinants and scattering theory," Commun. Math. Phys. 192, 309 (1998)] and Spreafico and Zerbini ["Finite temperature quantum field theory on noncompact domains and application to delta interactions," Rep. Math. Phys. 63, 163 (2009)]) in order to regularize the partition function of this model. We study the analytic extension of the associated relative zeta function, and we present explicit results for the partition function and for the Casimir force.

Examining the Gender Gap in Introductory Physics

NASA Astrophysics Data System (ADS)

Kost, Lauren; Pollock, Steven; Finkelstein, Noah

2009-05-01

Our previous research[1] showed that despite the use of interactive engagement techniques in the introductory physics course, the gap in performance between males and females on a mechanics conceptual learning survey persisted from pre- to post-test, at our institution. Such findings were counter to previously published work[2]. Follow-up studies[3] identified correlations between student performance on the conceptual learning survey and students' prior physics and math knowledge and their incoming attitudes and beliefs about physics and learning physics. The results indicate that the gender gap at our institution is predominantly associated with differences in males' and females' previous physics and math knowledge, and attitudes and beliefs. Our current work extends these results in two ways: 1) we look at the gender gap in the second semester of the introductory sequence and find results similar to those in the first semester course and 2) we identify ways in which males and females differentially experience several aspects of the introductory course. [1] Pollock, et al, Phys Rev: ST: PER 3, 010107. [2] Lorenzo, et al, Am J Phys 74, 118. [3] Kost, et al, PERC Proceedings 2008.

Finite-size effects for anisotropic 2D Ising model with various boundary conditions

NASA Astrophysics Data System (ADS)

Izmailian, N. Sh

2012-12-01

We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.

Non-CMC Solutions of the Einstein Constraint Equations on Compact Manifolds with Apparent Horizon Boundaries

NASA Astrophysics Data System (ADS)

Holst, Michael; Meier, Caleb; Tsogtgerel, G.

2018-01-01

In this article we continue our effort to do a systematic development of the solution theory for conformal formulations of the Einstein constraint equations on compact manifolds with boundary. By building in a natural way on our recent work in Holst and Tsogtgerel (Class Quantum Gravity 30:205011, 2013), and Holst et al. (Phys Rev Lett 100(16):161101, 2008, Commun Math Phys 288(2):547-613, 2009), and also on the work of Maxwell (J Hyperbolic Differ Eqs 2(2):521-546, 2005a, Commun Math Phys 253(3):561-583, 2005b, Math Res Lett 16(4):627-645, 2009) and Dain (Class Quantum Gravity 21(2):555-573, 2004), under reasonable assumptions on the data we prove existence of both near- and far-from-constant mean curvature (CMC) solutions for a class of Robin boundary conditions commonly used in the literature for modeling black holes, with a third existence result for CMC appearing as a special case. Dain and Maxwell addressed initial data engineering for space-times that evolve to contain black holes, determining solutions to the conformal formulation on an asymptotically Euclidean manifold in the CMC setting, with interior boundary conditions representing excised interior black hole regions. Holst and Tsogtgerel compiled the interior boundary results covered by Dain and Maxwell, and then developed general interior conditions to model the apparent horizon boundary conditions of Dainand Maxwell for compact manifolds with boundary, and subsequently proved existence of solutions to the Lichnerowicz equation on compact manifolds with such boundary conditions. This paper picks up where Holst and Tsogtgerel left off, addressing the general non-CMC case for compact manifolds with boundary. As in our previous articles, our focus here is again on low regularity data and on the interaction between different types of boundary conditions. While our work here serves primarily to extend the solution theory for the compact with boundary case, we also develop several technical tools that have potential for use for other cases.

An Algebraic Construction of Duality Functions for the Stochastic {U_q( A_n^{(1)})} Vertex Model and Its Degenerations

NASA Astrophysics Data System (ADS)

Kuan, Jeffrey

2018-03-01

A recent paper (Kuniba in Nucl Phys B 913:248-277, 2016) introduced the stochastic U}_q(A_n^{(1)})} vertex model. The stochastic S-matrix is related to the R-matrix of the quantum group {U_q(A_n^{(1)})} by a gauge transformation. We will show that a certain function {D^+_{m intertwines with the transfer matrix and its space reversal. When interpreting the transfer matrix as the transition matrix of a discrete-time totally asymmetric particle system on the one-dimensional lattice Z , the function {D^+m} becomes a Markov duality function {Dm} which only depends on q and the vertical spin parameters μ_x. By considering degenerations in the spectral parameter, the duality results also hold on a finite lattice with closed boundary conditions, and for a continuous-time degeneration. This duality function had previously appeared in a multi-species ASEP(q, j) process (Kuan in A multi-species ASEP(q, j) and q-TAZRP with stochastic duality, 2017). The proof here uses that the R-matrix intertwines with the co-product, but does not explicitly use the Yang-Baxter equation. It will also be shown that the stochastic U}_q(A_n^{(1)})} is a multi-species version of a stochastic vertex model studied in Borodin and Petrov (Higher spin six vertex model and symmetric rational functions, 2016) and Corwin and Petrov (Commun Math Phys 343:651-700, 2016). This will be done by generalizing the fusion process of Corwin and Petrov (2016) and showing that it matches the fusion of Kulish and yu (Lett Math Phys 5:393-403, 1981) up to the gauge transformation. We also show, by direct computation, that the multi-species q-Hahn Boson process (which arises at a special value of the spectral parameter) also satisfies duality with respect to D_∞, generalizing the single-species result of Corwin (Int Math Res Not 2015:5577-5603, 2015).

Quasi-Classical Asymptotics for the Pauli Operator

NASA Astrophysics Data System (ADS)

Sobolev, Alexander V.

We study the behaviour of the sums of the eigenvalues of the Pauli operator in , in a magnetic field and electric field V(x) as the Planck constant ħ tends to zero and the magnetic field strength μ tends to infinity. We show that for the sum obeys the natural Weyl type formula where σ = (d- 2)/2 + γ, with an explicit constant Cγ, d. If the field B has a constant direction, then this formula is uniform in μ>= 0. The method is based on Colin de Verdiere's approach proposed in his work on ``magnetic bottles'' (Commun. Math Phys, 105 , 327-335 (1986)).

On the Distribution of Free Path Lengths for the Periodic Lorentz Gas III

NASA Astrophysics Data System (ADS)

Caglioti, Emanuele; Golse, François

For r(0,1), let Zr={xR2|dist(x,Z2)>r/2} and define τr(x,v)=inf{t>0|x+tv∂Zr}. Let Φr(t) be the probability that τr(x,v)>=t for x and v uniformly distributed in Zr and §1 respectively. We prove in this paper that as t-->+∞. This result improves upon the bounds on Φr in Bourgain-Golse-Wennberg [Commun. Math. Phys. 190, 491-508 (1998)]. We also discuss the applications of this result in the context of kinetic theory.

Scattering in the Energy Space for Boussinesq Equations

NASA Astrophysics Data System (ADS)

Muñoz, Claudio; Poblete, Felipe; Pozo, Juan C.

2018-01-01

In this note we show that all small solutions in the energy space of the generalized 1D Boussinesq equation must decay to zero as time tends to infinity, strongly on slightly proper subsets of the space-time light cone. Our result does not require any assumption on the power of the nonlinearity, working even for the supercritical range of scattering. For the proof, we use two new Virial identities in the spirit of works (Kowalczyk et al. in J Am Math Soc 30:769-798, 2017; Kowalczyk et al. in Lett Math Phys 107(5):921-931, 2017). No parity assumption on the initial data is needed.

The electric Aharonov-Bohm effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weder, Ricardo

The seminal paper of Aharonov and Bohm [Phys. Rev. 115, 485 (1959)] is at the origin of a very extensive literature in some of the more fundamental issues in physics. They claimed that electromagnetic fields can act at a distance on charged particles even if they are identically zero in the region of space where the particles propagate, that the fundamental electromagnetic quantities in quantum physics are not only the electromagnetic fields but also the circulations of the electromagnetic potentials; what gives them a real physical significance. They proposed two experiments to verify their theoretical conclusions. The magnetic Aharonov-Bohm effect,more » where an electron is influenced by a magnetic field that is zero in the region of space accessible to the electron, and the electric Aharonov-Bohm effect where an electron is affected by a time-dependent electric potential that is constant in the region where the electron is propagating, i.e., such that the electric field vanishes along its trajectory. The Aharonov-Bohm effects imply such a strong departure from the physical intuition coming from classical physics that it is no wonder that they remain a highly controversial issue after more than fifty years, in spite of the fact that they are discussed in most of the text books in quantum mechanics. The magnetic case has been studied extensively. The experimental issues were settled by the remarkable experiments of Tonomura et al. [Phys. Rev. Lett. 48, 1443 (1982); Phys. Rev. Lett. 56, 792 (1986)] with toroidal magnets, that gave a strong evidence of the existence of the effect, and by the recent experiment of Caprez et al. [Phys. Rev. Lett. 99, 210401 (2007)] that shows that the results of the Tonomura et al. experiments cannot be explained by the action of a force. The theoretical issues were settled by Ballesteros and Weder [Commun. Math. Phys. 285, 345 (2009); J. Math. Phys. 50, 122108 (2009); Commun. Math. Phys. 303, 175 (2011)] who rigorously proved that quantum mechanics predicts the experimental results of Tonomura et al. and of Caprez et al. The electric Aharonov-Bohm effect has been much less studied. Actually, its existence, that has not been confirmed experimentally, is a very controversial issue. In their 1959 paper Aharonov and Bohm proposed an ansatz for the solution to the Schroedinger equation in regions where there is a time-dependent electric potential that is constant in space. It consists in multiplying the free evolution by a phase given by the integral in time of the potential. The validity of this ansatz predicts interference fringes between parts of a coherent electron beam that are subjected to different potentials. In this paper we prove that the exact solution to the Schroedinger equation is given by the Aharonov-Bohm ansatz up to an error bound in norm that is uniform in time and that decays as a constant divided by the velocity. Our results give, for the first time, a rigorous proof that quantum mechanics predicts the existence of the electric Aharonov-Bohm effect, under conditions that we provide. We hope that our results will stimulate the experimental research on the electric Aharonov-Bohm effect.« less

Some Lagrangians for systems without a Lagrangian

NASA Astrophysics Data System (ADS)

Nucci, M. C.; Leach, P. G. L.

2011-03-01

We demonstrate how to construct many different Lagrangians for two famous examples that were deemed by Douglas (1941 Trans. Am. Math. Soc. 50 71-128) not to have a Lagrangian. Following Bateman's dictum (1931 Phys. Rev. 38 815-9), we determine different sets of equations that are compatible with those of Douglas and derivable from a variational principle.

Thermo-Mechanical and Thermal Behavior of High-Temperature Structural Materials.

DTIC Science & Technology

1980-12-31

glass insulating tape to prevent fracture due to unknown stresses at Lhe rod ends. Because of the very high density of cracks in the alumina, this...143. [31] 0. L. Bowie, J. Math. Phys. 35 (1956) 60. [32] F. Erdogan : in Fracture Mechanics of Ceramics, Vol. 1, ed. by R. C. f Bradt, D. P. H

Monopole-antimonopole interaction potential

NASA Astrophysics Data System (ADS)

Saurabh, Ayush; Vachaspati, Tanmay

2017-11-01

We numerically study the interactions of twisted monopole-antimonopole pairs in the 't Hooft-Polyakov model for a range of values of the scalar to vector mass ratio. We also recover the sphaleron solution at maximum twist discovered by Taubes [Commun. Math. Phys. 86, 257 (1982), 10.1007/BF01206014] and map out its energy and size as functions of parameters.

Multilevel Iterative Methods in Nonlinear Computational Plasma Physics

NASA Astrophysics Data System (ADS)

Knoll, D. A.; Finn, J. M.

1997-11-01

Many applications in computational plasma physics involve the implicit numerical solution of coupled systems of nonlinear partial differential equations or integro-differential equations. Such problems arise in MHD, systems of Vlasov-Fokker-Planck equations, edge plasma fluid equations. We have been developing matrix-free Newton-Krylov algorithms for such problems and have applied these algorithms to the edge plasma fluid equations [1,2] and to the Vlasov-Fokker-Planck equation [3]. Recently we have found that with increasing grid refinement, the number of Krylov iterations required per Newton iteration has grown unmanageable [4]. This has led us to the study of multigrid methods as a means of preconditioning matrix-free Newton-Krylov methods. In this poster we will give details of the general multigrid preconditioned Newton-Krylov algorithm, as well as algorithm performance details on problems of interest in the areas of magnetohydrodynamics and edge plasma physics. Work supported by US DoE 1. Knoll and McHugh, J. Comput. Phys., 116, pg. 281 (1995) 2. Knoll and McHugh, Comput. Phys. Comm., 88, pg. 141 (1995) 3. Mousseau and Knoll, J. Comput. Phys. (1997) (to appear) 4. Knoll and McHugh, SIAM J. Sci. Comput. 19, (1998) (to appear)

Organic Metals and Semiconductors: The Chemistry of Polyacetylene, (CH)x, and Its Derivatives.

DTIC Science & Technology

1979-10-21

Park, Y.W., and Shirakawa, H.: 1978, J. Amer. .4.. Chem. Soc. 100, pp. 1013-1015. 10. Gau, S.C., Milliken, J., Pron , A., MacDiarmid, A.G., and Hee- ger...Clarke, T.C., Geiss, R.R., Kwak, J.F., and Street, G.B.: 1978, Chem. Comm., pp. 489-490. 1 17. Pron , A., MacDiarmid, A.G., and Heeger, A.J.: 1979, unpub...J., Heeger, A.J., Pron , A. and Mac- Diarmid, A.G.: 1979, Phys. Rev. B 20, pp. 223-230. 21. Clarke, T.C., Geiss, R.H., Gill, W.D., Grant, P.M

Meixner Class of Non-commutative Generalized Stochastic Processes with Freely Independent Values II. The Generating Function

NASA Astrophysics Data System (ADS)

Bożejko, Marek; Lytvynov, Eugene

2011-03-01

Let T be an underlying space with a non-atomic measure σ on it. In [ Comm. Math. Phys. 292, 99-129 (2009)] the Meixner class of non-commutative generalized stochastic processes with freely independent values, {ω=(ω(t))_{tin T}} , was characterized through the continuity of the corresponding orthogonal polynomials. In this paper, we derive a generating function for these orthogonal polynomials. The first question we have to answer is: What should serve as a generating function for a system of polynomials of infinitely many non-commuting variables? We construct a class of operator-valued functions {Z=(Z(t))_{tin T}} such that Z( t) commutes with ω( s) for any {s,tin T}. Then a generating function can be understood as {G(Z,ω)=sum_{n=0}^infty int_{T^n}P^{(n)}(ω(t_1),dots,ω(t_n))Z(t_1)dots Z(t_n)} {σ(dt_1) dots σ(dt_n)} , where {P^{(n)}(ω(t_1),dots,ω(t_n))} is (the kernel of the) n th orthogonal polynomial. We derive an explicit form of G( Z, ω), which has a resolvent form and resembles the generating function in the classical case, albeit it involves integrals of non-commuting operators. We finally discuss a related problem of the action of the annihilation operators {partial_t,t in T} . In contrast to the classical case, we prove that the operators ∂ t related to the free Gaussian and Poisson processes have a property of globality. This result is genuinely infinite-dimensional, since in one dimension one loses the notion of globality.

COMMENT: Comment on 'A summation formula for Clausen's series 3F2(1) with an application to Goursat's function 2F2(x)'

NASA Astrophysics Data System (ADS)

Kim, Yong Sup; Rathie, Arjun K.

2008-02-01

In a recent paper, Miller (2005 J. Phys. A: Math. Gen. 38 3541-5) obtained a new summation formula for the Clausen's series 3F2(1). The aim of this comment is to point out that the summation formula obtained by Miller is not a new one.

New horizons in Biophysics

PubMed Central

2011-01-01

This editorial celebrates the re-launch of PMC Biophysics previously published by PhysMath Central, in its new format as BMC Biophysics published by BioMed Central with an expanded scope and Editorial Board. BMC Biophysics will fill its own niche in the BMC series alongside complementary companion journals including BMC Bioinformatics, BMC Medical Physics, BMC Structural Biology and BMC Systems Biology. PMID:21595996

Closed, analytic, boson realizations for Sp(4)

NASA Astrophysics Data System (ADS)

Klein, Abraham; Zhang, Qing-Ying

1986-08-01

The problem of determing a boson realization for an arbitrary irrep of the unitary simplectic algebra Sp(2d) [or of the corresponding discrete unitary irreps of the unbounded algebra Sp(2d,R)] has been solved completely in recent papers by Deenen and Quesne [J. Deenen and C. Quesne, J. Math. Phys. 23, 878, 2004 (1982); 25, 1638 (1984); 26, 2705 (1985)] and by Moshinsky and co-workers [O. Castaños, E. Chacón, M. Moshinsky, and C. Quesne, J. Math. Phys. 26, 2107 (1985); M. Moshinsky, ``Boson realization of symplectic algebras,'' to be published]. This solution is not known in closed analytic form except for d=1 and for special classes of irreps for d>1. A different method of obtaining a boson realization that solves the full problem for Sp(4) is described. The method utilizes the chain Sp(2d)⊇SU(2)×SU(2) ×ṡṡṡ×SU(2) (d times), which, for d≥4, does not provide a complete set of quantum numbers. Though a simple solution of the missing label problem can be given, this solution does not help in the construction of a mapping algorithm for general d.

Generalizations of the classical Yang-Baxter equation and O-operators

NASA Astrophysics Data System (ADS)

Bai, Chengming; Guo, Li; Ni, Xiang

2011-06-01

Tensor solutions (r-matrices) of the classical Yang-Baxter equation (CYBE) in a Lie algebra, obtained as the classical limit of the R-matrix solution of the quantum Yang-Baxter equation, is an important structure appearing in different areas such as integrable systems, symplectic geometry, quantum groups, and quantum field theory. Further study of CYBE led to its interpretation as certain operators, giving rise to the concept of {O}-operators. The O-operators were in turn interpreted as tensor solutions of CYBE by enlarging the Lie algebra [Bai, C., "A unified algebraic approach to the classical Yang-Baxter equation," J. Phys. A: Math. Theor. 40, 11073 (2007)], 10.1088/1751-8113/40/36/007. The purpose of this paper is to extend this study to a more general class of operators that were recently introduced [Bai, C., Guo, L., and Ni, X., "Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras," Commun. Math. Phys. 297, 553 (2010)], 10.1007/s00220-010-0998-7 in the study of Lax pairs in integrable systems. Relations between O-operators, relative differential operators, and Rota-Baxter operators are also discussed.

Pulled Motzkin paths

NASA Astrophysics Data System (ADS)

Janse van Rensburg, E. J.

2010-08-01

In this paper the models of pulled Dyck paths in Janse van Rensburg (2010 J. Phys. A: Math. Theor. 43 215001) are generalized to pulled Motzkin path models. The generating functions of pulled Motzkin paths are determined in terms of series over trinomial coefficients and the elastic response of a Motzkin path pulled at its endpoint (see Orlandini and Whittington (2004 J. Phys. A: Math. Gen. 37 5305-14)) is shown to be R(f) = 0 for forces pushing the endpoint toward the adsorbing line and R(f) = f(1 + 2cosh f))/(2sinh f) → f as f → ∞, for forces pulling the path away from the X-axis. In addition, the elastic response of a Motzkin path pulled at its midpoint is shown to be R(f) = 0 for forces pushing the midpoint toward the adsorbing line and R(f) = f(1 + 2cosh (f/2))/sinh (f/2) → 2f as f → ∞, for forces pulling the path away from the X-axis. Formal combinatorial identities arising from pulled Motzkin path models are also presented. These identities are the generalization of combinatorial identities obtained in directed paths models to their natural trinomial counterparts.

High Tc: The Discovery of RBCO

NASA Astrophysics Data System (ADS)

Chu, C. W.

2007-03-01

It was said by Emerson that ``there is no history; there is only biography.'' This is especially true when the events are recounted by a person who, himself, has been heavily involved and the line between history and autobiography can become blurred. However, it is reasonable to say that discovery itself is not a series of accidents but an inevitable product of each development stage of scientific knowledge as was also pointed out by Holden et al. (1) The discovery of RBCO (2,3) with R = Y, La, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu is no exception. In this presentation, I will briefly recount several events that were crucial to the discovery of RBCO: those before 1986 (4) that sowed the seeds in our group important to our later high temperature superconductivity effort; those in 1986 (5) that were critical to our discovery of the 93 K RBCO soon after the discovery of the 35 K high temperature superconductor by M"uller and Bednorz (6); and those in 1987 when the barrier of the liquid nitrogen boiling temperature of 77 K was finally conquered. 1. G. J. Holton et al., American Scientist 84, 364 (1996). 2. M. K. Wu et al., Phys. Rev. Lett. 58, 908 (1987). 3. P. H. Hor et al., Phys. Rev. Lett. 58, 1891 (1987). 4. C. W. Chu et al., S. S. Comm. 18, 977 (1976); C. W. Chu and V. Diatchenko, Phys. Rev. Lett. 41, 572 (1978); T. H. Lin et al., Phys. Rev. B(RC) 29, 1493 (1984); J. H. Lin et al., J. Low Temp. Phys. 58, 363 (1985). 5. C. W. Chu et al., Phys. Rev. Lett. 58, 405 (1987); C. W. Chu et al., Science 235, 567 (1987). 6. J. G. Bednorz and K. A. M"uller, Z. Phys. B64, 189 (1986).

A Global Theory of Internal Solitary Waves in Two-Fluid Systems.

DTIC Science & Technology

1985-09-01

Large Amplitude Since the branch of solutions S from Theorem 2.1 is unbounded in R x (H (T) fl C O , 1 (T)) and the range of I is bounded, the norms...all k i’. L (T) and (b) ’k + A and IwkI , + as k. H (T) 0 Then wk converges to w(XlX 2 ) in C(S) fl C (B r) T*) for each bounded set B. The function w...Beale, J. T., The existence of solitary water waves, Comm. Pure Appi. Math. 30 (1977), 373-389. 7. Beir-ao da Veiga , H., Serapioni, R., and Valli, A

Le continu contre l'espace

NASA Astrophysics Data System (ADS)

Salanskis, Jean-Michel

Disons pour conclure que, en tout état de cause, la façon de concevoir philosophiquement le conflit du continu et de l'espace que nous avons trouvée chez Hegel n'est pas homogène avec le style et les modalités de la pensée mathématique: 1) d'une part, le lien classique, le lien de référence entre continu et espace en mathématiques n'est pas que l'espace serait premier et privé de pensée, et le continu second, venant dissoudre l'espace en apportant la qualité, l'infini et la pensée, mais tout au contraire, il consiste en ce que l'espace est fondé sur l'abîme infinitaire du continu ; 2) d'autre part, l'éventuel divorce entre l'espace et le continu dans l'aire mathématique n'est pas celui d'une réflexivité purement conceptuelle du continu avec un positivisme géométrique, n'équivaut pas à une rupture disciplinaire ; il est plutôt le symptôme de la dérive d'une herméneutique à l'égard d'une autre, au sein d'un continent juridique commun définissant la discipline (la mathématique ensembliste), cette dérive pouvant, à la limite, induire une refonte de ce sol juridique, sans que jamais il soit question pour autant de nier l'unité des mathématiques, à comprendre ici comme l'unité ultime de responsabilité de la communauté mathématique à l'égard des trois questions Qu'est-ce que l'espace?”, “Qu'est-ce que le continu?” et “Qu'est-ce que l'infini?”.

One loop back reaction on power law inflation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abramo, L.R.; Woodard, R.P.

1999-08-01

We consider quantum-mechanical corrections to a homogeneous, isotropic, and spatially flat geometry whose scale factor expands classically as a general power of the comoving time. The effects of both gravitons and the scalar inflaton are computed at one loop using the manifestly causal formalism of Schwinger [J. Math. Phys. {bold 2}, 407 (1961); {ital Particles, Sources and Fields} (Addison, Wesley, Reading, MA, 1970)] with the Feynman rules recently developed by Iliopoulos {ital et al.} [Nucl. Phys. B {bold 534}, 419 (1998)]. We find no significant effect, in marked contrast to the result obtained by Mukhanov and co-workers [Phys. Rev. Lett.more » {bold 78}, 1624 (1998); Phys. Rev. D {bold 56}, 3248 (1997)] for chaotic inflation based on a quadratic potential. By applying the canonical technique of Mukhanov and co-workers to the exponential potentials of power law inflation, we show that the two methods produce the same results, within the approximations employed, for these backgrounds. We therefore conclude that the shape of the inflaton potential can have an enormous impact on the one loop back reaction. {copyright} {ital 1999} {ital The American Physical Society}« less

Strong Turbulence in Alkali Halide Negative Ion Plasmas

NASA Astrophysics Data System (ADS)

Sheehan, Daniel

1999-11-01

Negative ion plasmas (NIPs) are charge-neutral plasmas in which the negative charge is dominated by negative ions rather than electrons. They are found in laser discharges, combustion products, semiconductor manufacturing processes, stellar atmospheres, pulsar magnetospheres, and the Earth's ionosphere, both naturally and man-made. They often display signatures of strong turbulence^1. Development of a novel, compact, unmagnetized alkali halide (MX) NIP source will be discussed, it incorporating a ohmically-heated incandescent (2500K) tantulum solenoid (3cm dia, 15 cm long) with heat shields. The solenoid ionizes the MX vapor and confines contaminant electrons, allowing a very dry (electron-free) source. Plasma densities of 10^10 cm-3 and positive to negative ion mass ratios of 1 <= fracm_+m- <= 20 are achievable. The source will allow tests of strong turbulence theory^2. 1 Sheehan, D.P., et al., Phys. Fluids B5, 1593 (1993). 2 Tsytovich, V. and Wharton, C.W., Comm. Plasma Phys. Cont. Fusion 4, 91 (1978).

On the Runge-Lenz-Pauli vector operator as an aid to the calculation of atomic processes in laboratory and astrophysical plasmas

NASA Astrophysics Data System (ADS)

Hey, J. D.

2015-09-01

On the basis of the original definition and analysis of the vector operator by Pauli (1926 Z. Phys. 36 336-63), and further developments by Flamand (1966 J. Math. Phys. 7 1924-31), and by Becker and Bleuler (1976 Z. Naturforsch. 31a 517-23), we consider the action of the operator on both spherical polar and parabolic basis state wave functions, both with and without direct use of Pauli’s identity (Valent 2003 Am. J. Phys. 71 171-75). Comparison of the results, with the aid of two earlier papers (Hey 2006 J. Phys. B: At. Mol. Opt. Phys. 39 2641-64, Hey 2007 J. Phys. B: At. Mol. Opt. Phys. 40 4077-96), yields a convenient ladder technique in the form of a recurrence relation for calculating the transformation coefficients between the two sets of basis states, without explicit use of generalized hypergeometric functions. This result is therefore very useful for application to Stark effect and impact broadening calculations applied to high-n radio recombination lines from tenuous space plasmas. We also demonstrate the versatility of the Runge-Lenz-Pauli vector operator as a means of obtaining recurrence relations between expectation values of successive powers of quantum mechanical operators, by using it to provide, as an example, a derivation of the Kramers-Pasternack relation. It is suggested that this operator, whose potential use in Stark- and Zeeman-effect calculations for magnetically confined fusion edge plasmas (Rosato, Marandet and Stamm 2014 J. Phys. B: At. Mol. Opt. Phys. 47 105702) and tenuous space plasmas ( H II regions) has not been fully explored and exploited, may yet be found to yield a number of valuable results for applications to plasma diagnostic techniques based upon rate calculations of atomic processes.

Time-resolved particle image velocimetry measurements of the 3D single-mode Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Xu, Qian

The Richtmyer-Meshkov Instability (RMI) (Commun. Pure Appl. Math 23, 297-319, 1960; Izv. Akad. Nauk. SSSR Maekh. Zhidk. Gaza. 4, 151-157, 1969) occurs due to an impulsive acceleration acting on a perturbed interface between two fluids of different densities. In the experiments presented in this thesis, single mode 3D RMI experiments are performed. An oscillating speaker generates a single mode sinusoidal initial perturbation at an interface of two gases, air and SF6. A Mach 1.19 shock wave accelerates the interface and generates the Richtmyer-Meshkov Instability. Both gases are seeded with propylene glycol particles which are illuminated by an Nd: YLF pulsed laser. Three high-speed video cameras record image sequences of the experiment. Particle Image Velocimetry (PIV) is applied to measure the velocity field. Measurements of the amplitude for both spike and bubble are obtained, from which the growth rate is measured. For both spike and bubble experiments, amplitude and growth rate match the linear stability theory at early time, but fall into a non-linear region with amplitude measurements lying between the modified 3D Sadot et al. model ( Phys. Rev. Lett. 80, 1654-1657, 1998) and the Zhang & Sohn model (Phys. Fluids 9. 1106-1124, 1997; Z. Angew. Math Phys 50. 1-46, 1990) at late time. Amplitude and growth rate curves are found to lie above the modified 3D Sadot et al. model and below Zhang & Sohn model for the spike experiments. Conversely, for the bubble experiments, both amplitude and growth rate curves lie above the Zhang & Sohn model, and below the modified 3D Sadot et al. model. Circulation is also calculated using the vorticity and velocity fields from the PIV measurements. The calculated circulation are approximately equal and found to grow with time, a result that differs from the modified Jacobs and Sheeley's circulation model (Phys. Fluids 8, 405-415, 1996).

The Analytic Structures of Dynamical Systems.

DTIC Science & Technology

1986-01-01

equations , rational solutions, and the Painlev6 property for the Kadomtsev - Petviashvili and Hirota-Satsuma equations ", J. Math. Phys. 26 2174 (1985) 5...of rational solutions. This also obtains the Lax pairs for the modified equations . In this paper we apply this method to the Kadomtsev - Petviashvili ...3 . . . . .. .. ," ,",,....". . ".’..’.-.: -.... ., Modified equations , rational solutions, and the Painlev6 property for the Kadomtsev

Nonlinear Waves

DTIC Science & Technology

1989-06-15

Hamiltonian Formulation of the Kadomtsev - Petviashvili and Benjamin-Ono Equations , A.S. Fokas and P.M. Santini, J. Math. Phys. 29 (3) 604-617 (1988...Prototypes are the so-called Kadomtsev -Petviashvilli and Davey-Stewartson equations . These equations arise in a variety of physical instances such as water...plasma physics. Moreover the study of solutions to some of the underlying nonlinear evolution equations has led naturally to the investigation and new

Hypergeometric type operators and their supersymmetric partners

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cotfas, Nicolae; Cotfas, Liviu Adrian

2011-05-15

The generalization of the factorization method performed by Mielnik [J. Math. Phys. 25, 3387 (1984)] opened new ways to generate exactly solvable potentials in quantum mechanics. We present an application of Mielnik's method to hypergeometric type operators. It is based on some solvable Riccati equations and leads to a unitary description of the quantum systems exactly solvable in terms of orthogonal polynomials or associated special functions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Inoue, H., E-mail: h-inoue@math.kyushu-u.ac.jp; Takakura, M., E-mail: mayumi@fukuoka-u.ac.jp

Bagarello, Inoue, and Trapani [J. Math. Phys. 55, 033501 (2014)] investigated some operators defined by the Riesz bases. These operators connect with quasi-Hermitian quantum mechanics, and its relatives. In this paper, we introduce a notion of generalized Riesz bases which is a generalization of Riesz bases and investigate some operators defined by the generalized Riesz bases by changing the frameworks of the operators defined in the work of Bagarello, Inoue, and Trapani.

A Solution Space for a System of Null-State Partial Differential Equations: Part 1

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the first of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations (PDEs) in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). In CFT, these are null-state equations and conformal Ward identities. They govern partition functions for the continuum limit of a statistical cluster or loop-gas model, such as percolation, or more generally the Potts models and O( n) models, at the statistical mechanical critical point. (SLE partition functions also satisfy these equations.) For such a lattice model in a polygon with its 2 N sides exhibiting a free/fixed side-alternating boundary condition , this partition function is proportional to the CFT correlation function where the w i are the vertices of and where is a one-leg corner operator. (Partition functions for "crossing events" in which clusters join the fixed sides of in some specified connectivity are linear combinations of such correlation functions.) When conformally mapped onto the upper half-plane, methods of CFT show that this correlation function satisfies the system of PDEs that we consider. In this first article, we use methods of analysis to prove that the dimension of this solution space is no more than C N , the Nth Catalan number. While our motivations are based in CFT, our proofs are completely rigorous. This proof is contained entirely within this article, except for the proof of Lemma 14, which constitutes the second article (Flores and Kleban, in Commun Math Phys, arXiv:1404.0035, 2014). In the third article (Flores and Kleban, in Commun Math Phys, arXiv:1303.7182, 2013), we use the results of this article to prove that the solution space of this system of PDEs has dimension C N and is spanned by solutions constructed with the CFT Coulomb gas (contour integral) formalism. In the fourth article (Flores and Kleban, in Commun Math Phys, arXiv:1405.2747, 2014), we prove further CFT-related properties about these solutions, some useful for calculating cluster-crossing probabilities of critical lattice models in polygons.

Maple procedures for the coupling of angular momenta. IX. Wigner D-functions and rotation matrices

NASA Astrophysics Data System (ADS)

Pagaran, J.; Fritzsche, S.; Gaigalas, G.

2006-04-01

The Wigner D-functions, Dpqj(α,β,γ), are known for their frequent use in quantum mechanics. Defined as the matrix elements of the rotation operator Rˆ(α,β,γ) in R and parametrized in terms of the three Euler angles α, β, and γ, these functions arise not only in the transformation of tensor components under the rotation of the coordinates, but also as the eigenfunctions of the spherical top. In practice, however, the use of the Wigner D-functions is not always that simple, in particular, if expressions in terms of these and other functions from the theory of angular momentum need to be simplified before some computations can be carried out in detail. To facilitate the manipulation of such Racah expressions, here we present an extension to the RACAH program [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51] in which the properties and the algebraic rules of the Wigner D-functions and reduced rotation matrices are implemented. Care has been taken to combine the standard knowledge about the rotation matrices with the previously implemented rules for the Clebsch-Gordan coefficients, Wigner n-j symbols, and the spherical harmonics. Moreover, the application of the program has been illustrated below by means of three examples. Program summaryTitle of program:RACAH Catalogue identifier:ADFv_9_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFv_9_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Catalogue identifier of previous version: ADFW, ADHW, title RACAH Journal reference of previous version(s): S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51; S. Fritzsche, S. Varga, D. Geschke, B. Fricke, Comput. Phys. Comm. 111 (1998) 167; S. Fritzsche, T. Inghoff, M. Tomaselli, Comput. Phys. Comm. 153 (2003) 424. Does the new version supersede the previous one: Yes, in addition to the spherical harmonics and recoupling coefficients, the program now supports also the occurrence of the Wigner rotation matrices in the algebraic expressions to be evaluated. Licensing provisions:None Computer for which the program is designed and others on which it is operable: All computers with a license for the computer algebra package Maple [Maple is a registered trademark of Waterloo Maple Inc.] Installations:University of Kassel (Germany) Operating systems under which the program has been tested: Linux 8.2+ Program language used:MAPLE, Release 8 and 9 Memory required to execute with typical data:10-50 MB No. of lines in distributed program, including test data, etc.:52 653 No. of bytes in distributed program, including test data, etc.:1 195 346 Distribution format:tar.gzip Nature of the physical problem: The Wigner D-functions and (reduced) rotation matrices occur very frequently in physical applications. They are known not only as the (infinite) representation of the rotation group but also to obey a number of integral and summation rules, including those for their orthogonality and completeness. Instead of the direct computation of these matrices, therefore, one first often wishes to find algebraic simplifications before the computations can be carried out in practice. Reasons for new version: The RACAH program has been found an efficient tool during recent years, in order to evaluate and simplify expressions from Racah's algebra. Apart from the Wigner n-j symbols ( j=3,6,9) and spherical harmonics, we now extended the code to allow for Wigner rotation matrices. This extension will support the study of those quantum processes especially where different axis of quantization occurs in course of the theoretical deviations. Summary of revisions: In a revised version of the RACAH program [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51; S. Fritzsche, T. Inghoff, M. Tomaselli, Comput. Phys. Comm. 153 (2003) 424], we now also support the occurrence of the Wigner D-functions and reduced rotation matrices. By following our previous design, the (algebraic) properties of these rotation matrices as well as a number of summation and integration rules are implemented to facilitate the algebraic simplification of expressions from the theories of angular momentum and the spherical tensor operators. Restrictions onto the complexity of the problem: The definition as well as the properties of the rotation matrices, as used in our implementation, are based mainly on the book of Varshalovich et al. [D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific, Singapore, 1988], Chapter 4. From this monograph, most of the relations involving the Wigner D-functions and rotation matrices are taken into account although, in practice, only a rather selected set was needed to be implemented explicitly owing to the symmetries of these functions. In the integration over the rotation matrices, products of up to three Wigner D-functions or reduced matrices (with the same angular arguments) are recognized and simplified properly; for the integration over a solid angle, however, the domain of integration must be specified for the Euler angles α and γ. This restriction arose because MAPLE does not generate a constant of integration when the limits in the integral are omitted. For any integration over the angle β the range of the integration, if omitted, is always taken from 0 to π. Unusual features of the program: The RACAH program is designed for interactive use that allows a quick and algebraic evaluation of (complex) expression from Racah's algebra. It is based on a number of well-defined data structures that are now extended to incorporate the Wigner rotation matrices. For these matrices, the transformation properties, sum rules, recursion relations, as well as a variety of special function expansions have been added to the previous functionality of the RACAH program. Moreover, the knowledge about the orthogonality as well as the completeness of the Wigner D-functions is also implemented. Typical running time:All the examples presented in Section 4 take only a few seconds on a 1.5 GHz Pentium Pro computer.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code.

NASA Astrophysics Data System (ADS)

Chacon, L.; Knoll, D. A.

2004-11-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended primitive-variable MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field, non-dissipative, and stable in the absence of physical dissipation.(L. Chacón , phComput. Phys. Comm.) submitted (2004) PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, first and second-order implicit schemes are available, although higher-order temporal implicit schemes can be effortlessly implemented within the Newton-Krylov framework. A successful, scalable, MG physics-based preconditioning strategy, similar in concept to previous 2D MHD efforts,(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002); phJ. Comput. Phys., 188 (2), 573-592 (2003) has been developed. We are currently in the process of parallelizing the code using the PETSc library, and a Newton-Krylov-Schwarz approach for the parallel treatment of the preconditioner. In this poster, we will report on both the serial and parallel performance of PIXIE3D, focusing primarily on scalability and CPU speedup vs. an explicit approach.

Squeezed states and Hermite polynomials in a complex variable

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ali, S. Twareque, E-mail: twareque.ali@concordia.ca; Górska, K., E-mail: katarzyna.gorska@ifj.edu.pl; Horzela, A., E-mail: andrzej.horzela@ifj.edu.pl

2014-01-15

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavormore » of the classical approach of V. Bargmann [Commun. Pure Appl. Math. 14, 187 (1961)].« less

Revised Geometric Measure of Entanglement in Infinite Dimensional Multipartite Quantum Systems

NASA Astrophysics Data System (ADS)

Wang, Yinzhu; Wang, Danxia; Huang, Li

2018-05-01

In Cao and Wang (J. Phys.: Math. Theor. 40, 3507-3542, 2007), the revised geometric measure of entanglement (RGME) for states in finite dimensional bipartite quantum systems was proposed. Furthermore, in Cao and Wang (Commun. Theor. Phys. 51(4), 613-620, 2009), the authors obtained the revised geometry measure of entanglement for multipartite states including three-qubit GHZ state, W state, and the generalized Smolin state in the presence of noise and the two-mode squeezed thermal state, and defined the Gaussian geometric entanglement measure. In this paper, we generalize the RGME to infinite dimensional multipartite quantum systems, and prove that this measure satisfies some necessary properties as a well-defined entanglement measure, including monotonicity under local operations and classical communications.

The gap equation for spin-polarized fermions

NASA Astrophysics Data System (ADS)

Freiji, Abraham; Hainzl, Christian; Seiringer, Robert

2012-01-01

We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For cosh (δμ/T) ⩽ 2, with T the temperature and δμ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in [Frank, R. L., Hainzl, C., Naboko, S., and Seiringer, R., J., Geom. Anal. 17, 559-567 (2007), 10.1007/BF02937429; Hainzl, C., Hamza, E., Seiringer, R., and Solovej, J. P., Commun., Math. Phys. 281, 349-367 (2008), 10.1007/s00220-008-0489-2; and Hainzl, C. and Seiringer, R., Phys. Rev. B 77, 184517-110 435 (2008)], 10.1103/PhysRevB.77.184517. For cosh (δμ/T) > 2 the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.

Travelling-wave amplitudes as solutions of the phase-field crystal equation

NASA Astrophysics Data System (ADS)

Nizovtseva, I. G.; Galenko, P. K.

2018-01-01

The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E 70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B 75, 064107 (doi:10.1103/PhysRevB.75.064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen-Cahn type (Galenko & Jou 2005 Phys. Rev. E 71, 046125 (doi:10.1103/PhysRevE.71.046125)) for which the complete set of analytical travelling-wave solutions is obtained by the method (Malfliet & Hereman 1996 Phys. Scr. 15, 563-568 (doi:10.1088/0031-8949/54/6/003); Wazwaz 2004 Appl. Math. Comput. 154, 713-723 (doi:10.1016/S0096-3003(03)00745-8)). The general solution of travelling waves is based on the function of hyperbolic tangent. Together with its set of particular solutions, the general solution is analysed within an example of specific task about the crystal front invading metastable liquid (Galenko et al. 2015 Phys. D 308, 1-10 (doi:10.1016/j.physd.2015.06.002)). The influence of the driving force on the phase-field profile, amplitude velocity and correlation length is investigated for various relaxation times of the gradient flow. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

Stochastic mechanics of reciprocal diffusions

NASA Astrophysics Data System (ADS)

Levy, Bernard C.; Krener, Arthur J.

1996-02-01

The dynamics and kinematics of reciprocal diffusions were examined in a previous paper [J. Math. Phys. 34, 1846 (1993)], where it was shown that reciprocal diffusions admit a chain of conservation laws, which close after the first two laws for two disjoint subclasses of reciprocal diffusions, the Markov and quantum diffusions. For the case of quantum diffusions, the conservation laws are equivalent to Schrödinger's equation. The Markov diffusions were employed by Schrödinger [Sitzungsber. Preuss. Akad. Wiss. Phys. Math Kl. 144 (1931); Ann. Inst. H. Poincaré 2, 269 (1932)], Nelson [Dynamical Theories of Brownian Motion (Princeton University, Princeton, NJ, 1967); Quantum Fluctuations (Princeton University, Princeton, NJ, 1985)], and other researchers to develop stochastic formulations of quantum mechanics, called stochastic mechanics. We propose here an alternative version of stochastic mechanics based on quantum diffusions. A procedure is presented for constructing the quantum diffusion associated to a given wave function. It is shown that quantum diffusions satisfy the uncertainty principle, and have a locality property, whereby given two dynamically uncoupled but statistically correlated particles, the marginal statistics of each particle depend only on the local fields to which the particle is subjected. However, like Wigner's joint probability distribution for the position and momentum of a particle, the finite joint probability densities of quantum diffusions may take negative values.

Context-invariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Loubenets, Elena R.

We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and context-invariant, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and all the quantum product expectations—via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence ofmore » this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every N-partite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasi-classical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)].« less

Vanishing Corrections for the Position in a Linear Model of FKPP Fronts

NASA Astrophysics Data System (ADS)

Berestycki, Julien; Brunet, Éric; Harris, Simon C.; Roberts, Matt

2017-02-01

Take the linearised FKPP equation {partialth = partial2xh + h} with boundary condition h( m( t), t) = 0. Depending on the behaviour of the initial condition h 0( x) = h( x, 0) we obtain the asymptotics—up to a o(1) term r( t)—of the absorbing boundary m( t) such that {ω(x) := lim_{tto∞} h(x + m(t) ,t)} exists and is non-trivial. In particular, as in Bramson's results for the non-linear FKPP equation, we recover the celebrated {-3/2 log t} correction for initial conditions decaying faster than {x^{ν}e^{-x}} for some {ν < -2}. Furthermore, when we are in this regime, the main result of the present work is the identification (to first order) of the r( t) term, which ensures the fastest convergence to {ω(x)}. When h 0( x) decays faster than {x^{ν}e^{-x}} for some {ν < -3}, we show that r( t) must be chosen to be {-3√{π/t}}, which is precisely the term predicted heuristically by Ebert-van Saarloos (Phys. D Nonlin. Phenom. 146(1): 1-99, 2000) in the non-linear case (see also Mueller and Munier Phys Rev E 90(4):042143, 2014, Henderson, Commun Math Sci 14(4):973-985, 2016, Brunet and Derrida Stat Phys 1-20, 2015). When the initial condition decays as {x^{ν}e^{-x}} for some {ν in [-3, -2)}, we show that even though we are still in the regime where Bramson's correction is {-3/2 log t}, the Ebert-van Saarloos correction has to be modified. Similar results were recently obtained by Henderson CommunMath Sci 14(4):973-985, 2016 using an analytical approach and only for compactly supported initial conditions.

Deriving amplitude equations for weakly-nonlinear oscillators and their generalizations

NASA Astrophysics Data System (ADS)

O'Malley, Robert E., Jr.; Williams, David B.

2006-06-01

Results by physicists on renormalization group techniques have recently sparked interest in the singular perturbations community of applied mathematicians. The survey paper, [Phys. Rev. E 54(1) (1996) 376-394], by Chen et al. demonstrated that many problems which applied mathematicians solve using disparate methods can be solved using a single approach. Analysis of that renormalization group method by Mudavanhu and O'Malley [Stud. Appl. Math. 107(1) (2001) 63-79; SIAM J. Appl. Math. 63(2) (2002) 373-397], among others, indicates that the technique can be streamlined. This paper carries that analysis several steps further to present an amplitude equation technique which is both well adapted for use with a computer algebra system and easy to relate to the classical methods of averaging and multiple scales.

Quantum Communication Using Coherent Rejection Sampling

NASA Astrophysics Data System (ADS)

Anshu, Anurag; Devabathini, Vamsi Krishna; Jain, Rahul

2017-09-01

Compression of a message up to the information it carries is key to many tasks involved in classical and quantum information theory. Schumacher [B. Schumacher, Phys. Rev. A 51, 2738 (1995), 10.1103/PhysRevA.51.2738] provided one of the first quantum compression schemes and several more general schemes have been developed ever since [M. Horodecki, J. Oppenheim, and A. Winter, Commun. Math. Phys. 269, 107 (2007); , 10.1007/s00220-006-0118-xI. Devetak and J. Yard, Phys. Rev. Lett. 100, 230501 (2008); , 10.1103/PhysRevLett.100.230501A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, Proc. R. Soc. A 465, 2537 (2009), 10.1098/rspa.2009.0202]. However, the one-shot characterization of these quantum tasks is still under development, and often lacks a direct connection with analogous classical tasks. Here we show a new technique for the compression of quantum messages with the aid of entanglement. We devise a new tool that we call the convex split lemma, which is a coherent quantum analogue of the widely used rejection sampling procedure in classical communication protocols. As a consequence, we exhibit new explicit protocols with tight communication cost for quantum state merging, quantum state splitting, and quantum state redistribution (up to a certain optimization in the latter case). We also present a port-based teleportation scheme which uses a fewer number of ports in the presence of information about input.

The Hölder continuity of spectral measures of an extended CMV matrix

NASA Astrophysics Data System (ADS)

Munger, Paul E.; Ong, Darren C.

2014-09-01

We prove results about the Hölder continuity of the spectral measures of the extended CMV matrix, given power law bounds of the solution of the eigenvalue equation. We thus arrive at a unitary analogue of the results of Damanik, Killip, and Lenz ["Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity," Commun. Math. Phys. 212, 191-204 (2000)] about the spectral measure of the discrete Schrödinger operator.

The Hölder continuity of spectral measures of an extended CMV matrix.

PubMed

Munger, Paul E; Ong, Darren C

2014-09-01

We prove results about the Hölder continuity of the spectral measures of the extended CMV matrix, given power law bounds of the solution of the eigenvalue equation. We thus arrive at a unitary analogue of the results of Damanik, Killip, and Lenz ["Uniform spectral properties of one-dimensional quasicrystals, III. α-continuity," Commun. Math. Phys.55, 191-204 (2000)] about the spectral measure of the discrete Schrödinger operator.

Exact evaluations of some Meijer G-functions and probability of all eigenvalues real for the product of two Gaussian matrices

NASA Astrophysics Data System (ADS)

Kumar, Santosh

2015-11-01

We provide a proof to a recent conjecture by Forrester (2014 J. Phys. A: Math. Theor. 47 065202) regarding the algebraic and arithmetic structure of Meijer G-functions which appear in the expression for probability of all eigenvalues real for the product of two real Gaussian matrices. In the process we come across several interesting identities involving Meijer G-functions.

Free boundary skin current magnetohydrodynamic equilibria

NASA Astrophysics Data System (ADS)

Reusch, Michael F.

1988-10-01

Function theoretic methods in the complex plane are used to develop simple parametric hodograph formulas that generate sharp boundary equilibria of arbitrary shape. The related method of Gorenflo [Z. Angew. Math. Phys. 16, 279 (1965)] and Merkel (Ph.D. thesis, University of Munich, 1965) is discussed. A numerical technique for the construction of solutions, based on one of the methods, is presented. A study is made of the bifurcations of an equilibrium of general form.

Development of Vector Parabolic Equation Technique for Propagation in Urban and Tunnel Environments

DTIC Science & Technology

2010-09-01

relativistic quantum mechanics J. Phys. A: Math. Gen. 16 1869–84 [8] Nottale L 1995 Scale relativity, fractal space- time and quantum mechanics Quantum...proportional to the “ time ” elapsed. By performing various approximations to the transfer function, several approximate absorbing boundary condi- tions...The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing

Eigenfunctions and heat kernels of super Maass Laplacians on the super Poincaré upper half-plane

NASA Astrophysics Data System (ADS)

Oshima, Kazuto

1992-03-01

Heat kernels of ``super Maass Laplacians'' are explicitly constructed on super Poincaré upper half-plane by a serious treatment of a complete set of eigenfunctions. By component decomposition an explicit treatment can be done for arbitrary weight and a knowledge of classical Maass Laplacians becomes helpful. The result coincides with that of Aoki [Commun. Math. Phys. 117, 405 (1988)] which was obtained by solving differential equations.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code

NASA Astrophysics Data System (ADS)

Chacon, Luis

2006-10-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field to machine precision, non-dissipative, and linearly and nonlinearly stable in the absence of physical dissipation. PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, second-order implicit schemes such as Crank-Nicolson and BDF2 (2^nd order backward differentiation formula) are available. PIXIE3D is fully parallel (employs PETSc for parallelism), and exhibits excellent parallel scalability. A parallel, scalable, MG preconditioning strategy, based on physics-based preconditioning ideas, has been developed for resistive MHD, and is currently being extended to Hall MHD. In this poster, we will report on progress in the algorithmic formulation for extended MHD, as well as the the serial and parallel performance of PIXIE3D in a variety of problems and geometries. L. Chac'on, Comput. Phys. Comm., 163 (3), 143-171 (2004) L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002); J. Comput. Phys., 188 (2), 573-592 (2003) L. Chac'on, 32nd EPS Conf. Plasma Physics, Tarragona, Spain, 2005 L. Chac'on et al., 33rd EPS Conf. Plasma Physics, Rome, Italy, 2006

Solutions to the 1d Klein Gordon equation with cut-off Coulomb potentials

NASA Astrophysics Data System (ADS)

Hall, Richard L.

2007-12-01

In a recent paper by Barton [G. Barton, J. Phys. A: Math. Gen. 40 (2007) 1011], the 1-dimensional Klein Gordon equation was solved analytically for the non-singular Coulomb-like potential V(|x|)=-α/(|x|+a). In the present Letter, these results are completely confirmed by a numerical formulation that also allows a solution for an alternative cut-off Coulomb potential V(|x|)=-α/|x|, |x|>a, and otherwise V(|x|)=-α/a.

Classification of quantum groups and Belavin–Drinfeld cohomologies for orthogonal and symplectic Lie algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kadets, Boris; Karolinsky, Eugene; Pop, Iulia

2016-05-15

In this paper we continue to study Belavin–Drinfeld cohomology introduced in Kadets et al., Commun. Math. Phys. 344(1), 1-24 (2016) and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra #Mathematical Fraktur Small G#. Here we compute Belavin–Drinfeld cohomology for all non-skewsymmetric r-matrices on the Belavin–Drinfeld list for simple Lie algebras of type B, C, and D.

Nonlocal symmetries and Bäcklund transformations for the self-dual Yang-Mills system

NASA Astrophysics Data System (ADS)

Papachristou, C. J.; Harrison, B. Kent

1988-01-01

The observation is made that generalized evolutionary isovectors of the self-dual Yang-Mills equation, obtained by ``verticalization'' of the geometrical isovectors derived in a previous paper [J. Math. Phys. 28, 1261 (1987)], generate Bäcklund transformations for the self-dual system. In particular, new Bäcklund transformations are obtained by ``verticalizing'' the generators of point transformations on the solution manifold. A geometric ansatz for the derivation of such (generally nonlocal) symmetries is proposed.

Polynomial decay rate of a thermoelastic Mindlin-Timoshenko plate model with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-02-01

In this article, we are concerned with the polynomial stabilization of a two-dimensional thermoelastic Mindlin-Timoshenko plate model with no mechanical damping. The model is subject to Dirichlet boundary conditions on the elastic as well as the thermal variables. The work complements our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 64:1305-1325, 2013) on the polynomial stabilization of a Mindlin-Timoshenko model in a radially symmetric domain under Dirichlet boundary conditions on the displacement and thermal variables and free boundary conditions on the shear angle variables. In particular, our aim is to investigate the effect of the Dirichlet boundary conditions on all the variables on the polynomial decay rate of the model. By once more applying a frequency domain method in which we make critical use of an inequality for the trace of Sobolev functions on the boundary of a bounded, open connected set we show that the decay is slower than in the model considered in the cited work. A comparison of our result with our polynomial decay result for a magnetoelastic Mindlin-Timoshenko model subject to Dirichlet boundary conditions on the elastic variables in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) also indicates a correlation between the robustness of the coupling between parabolic and hyperbolic dynamics and the polynomial decay rate in the two models.

Quantum Markov chains, sufficiency of quantum channels, and Rényi information measures

NASA Astrophysics Data System (ADS)

Datta, Nilanjana; Wilde, Mark M.

2015-12-01

A short quantum Markov chain is a tripartite state {ρ }{ABC} such that system A can be recovered perfectly by acting on system C of the reduced state {ρ }{BC}. Such states have conditional mutual information I(A;B| C) equal to zero and are the only states with this property. A quantum channel {N} is sufficient for two states ρ and σ if there exists a recovery channel using which one can perfectly recover ρ from {N}(ρ ) and σ from {N}(σ ). The relative entropy difference D(ρ \\parallel σ )-D({N}(ρ )\\parallel {N}(σ )) is equal to zero if and only if {N} is sufficient for ρ and σ. In this paper, we show that these properties extend to Rényi generalizations of these information measures which were proposed in (Berta et al 2015 J. Math. Phys. 56 022205; Seshadreesan et al 2015 J. Phys. A: Math. Theor. 48 395303), thus providing an alternate characterization of short quantum Markov chains and sufficient quantum channels. These results give further support to these quantities as being legitimate Rényi generalizations of the conditional mutual information and the relative entropy difference. Along the way, we solve some open questions of Ruskai and Zhang, regarding the trace of particular matrices that arise in the study of monotonicity of relative entropy under quantum operations and strong subadditivity of the von Neumann entropy.

Mutually orthogonal Latin squares from the inner products of vectors in mutually unbiased bases

NASA Astrophysics Data System (ADS)

Hall, Joanne L.; Rao, Asha

2010-04-01

Mutually unbiased bases (MUBs) are important in quantum information theory. While constructions of complete sets of d + 1 MUBs in {\\bb C}^d are known when d is a prime power, it is unknown if such complete sets exist in non-prime power dimensions. It has been conjectured that complete sets of MUBs only exist in {\\bb C}^d if a maximal set of mutually orthogonal Latin squares (MOLS) of side length d also exists. There are several constructions (Roy and Scott 2007 J. Math. Phys. 48 072110; Paterek, Dakić and Brukner 2009 Phys. Rev. A 79 012109) of complete sets of MUBs from specific types of MOLS, which use Galois fields to construct the vectors of the MUBs. In this paper, two known constructions of MUBs (Alltop 1980 IEEE Trans. Inf. Theory 26 350-354 Wootters and Fields 1989 Ann. Phys. 191 363-381), both of which use polynomials over a Galois field, are used to construct complete sets of MOLS in the odd prime case. The MOLS come from the inner products of pairs of vectors in the MUBs.

ODPEVP: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Vinitsky, S. I.; Abrashkevich, A. G.

2009-08-01

A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions on the finite interval. The program calculates also potential matrix elements - integrals of the eigenfunctions multiplied by their first derivatives with respect to the parameter. Eigenvalues and matrix elements computed by the ODPEVP program can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs [O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Commun. 177 (2007) 649-675; O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich, Comput. Phys. Commun. 179 (2008) 685-693]. As a test desk, the program is applied to the calculation of the potential matrix elements for an integrable 2D-model of three identical particles on a line with pair zero-range potentials, a 3D-model of a hydrogen atom in a homogeneous magnetic field and a hydrogen atom on a three-dimensional sphere. Program summaryProgram title: ODPEVP Catalogue identifier: AEDV_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3001 No. of bytes in distributed program, including test data, etc.: 24 195 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: depends on the number and order of finite elements; the number of points; and the number of eigenfunctions required. Test run requires 4 MB Classification: 2.1, 2.4 External routines: GAULEG [3] Nature of problem: The three-dimensional boundary problem for the elliptic partial differential equation with an axial symmetry similar to the Schrödinger equation with the Coulomb and transverse oscillator potentials is reduced to the two-dimensional one. The latter finds wide applications in modeling of photoionization and recombination of oppositively charged particles (positrons, antiprotons) in the magnet-optical trap [4], optical absorption in quantum wells [5], and channeling of likely charged particles in thin doped films [6,7] or neutral atoms and molecules in artificial waveguides or surfaces [8,9]. In the adiabatic approach [10] known in mathematics as Kantorovich method [11] the solution of the two-dimensional elliptic partial differential equation is expanded over basis functions with respect to the fast variable (for example, angular variable) and depended on the slow variable (for example, radial coordinate ) as a parameter. An averaging of the problem by such a basis leads to a system of the second-order ordinary differential equations which contain potential matrix elements and the first-derivative coupling terms (see, e.g., [12,13,14]). The purpose of this paper is to present the finite element method procedure based on the use of high-order accuracy approximations for calculating eigenvalues, eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions on the finite interval. The program developed calculates potential matrix elements - integrals of the eigenfunctions multiplied by their derivatives with respect to the parameter. These matrix elements can be used for solving the bound state and multi-channel scattering problems for a system of the coupled second-order ordinary differential equations with the help of the KANTBP programs [1,2]. Solution method: The parametric self-adjoined Sturm-Liouville problem with the parametric third type boundary conditions is solved by the finite element method using high-order accuracy approximations [15]. The generalized algebraic eigenvalue problem AF=EBF with respect to a pair of unknown ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [16]. First derivatives of the eigenfunctions with respect to the parameter which contained in potential matrix elements of the coupled system equations are obtained by solving the inhomogeneous algebraic equations. As a test desk, the program is applied to the calculation of the potential matrix elements for an integrable 2D-model of three identical particles on a line with pair zero-range potentials described in [1,17,18], a 3D-model of a hydrogen atom in a homogeneous magnetic field described in [14,19] and a hydrogen atom on a three-dimensional sphere [20]. Restrictions: The computer memory requirements depend on: the number and order of finite elements; the number of points; and the number of eigenfunctions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see sections below and listing for details). The user must also supply DOUBLE PRECISION functions POTCCL and POTCC1 for evaluating potential function U(ρ,z) of Eq. (1) and its first derivative with respect to parameter ρ. The user should supply DOUBLE PRECISION functions F1FUNC and F2FUNC that evaluate functions f(z) and f(z) of Eq. (1). The user must also supply subroutine BOUNCF for evaluating the parametric third type boundary conditions. Running time: The running time depends critically upon: the number and order of finite elements; the number of points on interval [z,z]; and the number of eigenfunctions required. The test run which accompanies this paper took 2 s with calculation of matrix potentials on the Intel Pentium IV 2.4 GHz. References:O. Chuluunbaatar, A.A. Gusev, A.G. Abrashkevich, A. Amaya-Tapia, M.S. Kaschiev, S.Y. Larsen, S.I. Vinitsky, Comput. Phys. Comm. 177 (2007) 649-675 O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, A.G. Abrashkevich, Comput. Phys. Comm. 179 (2008) 685-693. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. O. Chuluunbaatar, A.A. Gusev, S.I. Vinitsky, V.L. Derbov, L.A. Melnikov, V.V. Serov, Phys. Rev. A 77 (2008) 034702-1-4. E.M. Kazaryan, A.A. Kostanyan, H.A. Sarkisyan, Physica E 28 (2005) 423-430. Yu.N. Demkov, J.D. Meyer, Eur. Phys. J. B 42 (2004) 361-365. P.M. Krassovitskiy, N.Zh. Takibaev, Bull. Russian Acad. Sci. Phys. 70 (2006) 815-818. V.S. Melezhik, J.I. Kim, P. Schmelcher, Phys. Rev. A 76 (2007) 053611-1-15. F.M. Pen'kov, Phys. Rev. A 62 (2000) 044701-1-4. M. Born, X. Huang, Dynamical Theory of Crystal Lattices, The Clarendon Press, Oxford, England, 1954. L.V. Kantorovich, V.I. Krylov, Approximate Methods of Higher Analysis, Wiley, New York, 1964. U. Fano, Colloq. Int. C.N.R.S. 273 (1977) 127;A.F. Starace, G.L. Webster, Phys. Rev. A 19 (1979) 1629-1640. C.V. Clark, K.T. Lu, A.F. Starace, in: H.G. Beyer, H. Kleinpoppen (eds.), Progress in Atomic Spectroscopy, Part C, Plenum, New York, 1984, pp. 247-320. O. Chuluunbaatar, A.A. Gusev, V.L. Derbov, M.S. Kaschiev, L.A. Melnikov, V.V. Serov, S.I. Vinitsky, J. Phys. A 40 (2007) 11485-11524. A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64. K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982. O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269. Yu.A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361. O. Chuluunbaatar, A.A. Gusev, V.P. Gerdt, V.A. Rostovtsev, S.I. Vinitsky, A.G. Abrashkevich, M.S. Kaschiev, V.V. Serov, Comput. Phys. Comm. 178 (2008) 301-330. A.G. Abrashkevich, M.S. Kaschiev, S.I. Vinitsky, J. Comp. Phys. 163 (2000) 328-348.

GRASP92: a package for large-scale relativistic atomic structure calculations

NASA Astrophysics Data System (ADS)

Parpia, F. A.; Froese Fischer, C.; Grant, I. P.

2006-12-01

Program summaryTitle of program: GRASP92 Catalogue identifier: ADCU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADCU_v1_1 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: no Programming language used: Fortran Computer: IBM POWERstation 320H Operating system: IBM AIX 3.2.5+ RAM: 64M words No. of lines in distributed program, including test data, etc.: 65 224 No of bytes in distributed program, including test data, etc.: 409 198 Distribution format: tar.gz Catalogue identifier of previous version: ADCU_v1_0 Journal reference of previous version: Comput. Phys. Comm. 94 (1996) 249 Does the new version supersede the previous version?: Yes Nature of problem: Prediction of atomic spectra—atomic energy levels, oscillator strengths, and radiative decay rates—using a 'fully relativistic' approach. Solution method: Atomic orbitals are assumed to be four-component spinor eigenstates of the angular momentum operator, j=l+s, and the parity operator Π=βπ. Configuration state functions (CSFs) are linear combinations of Slater determinants of atomic orbitals, and are simultaneous eigenfunctions of the atomic electronic angular momentum operator, J, and the atomic parity operator, P. Lists of CSFs are either explicitly prescribed by the user or generated from a set of reference CSFs, a set of subshells, and rules for deriving other CSFs from these. Approximate atomic state functions (ASFs) are linear combinations of CSFs. A variational functional may be constructed by combining expressions for the energies of one or more ASFs. Average level (AL) functionals are weighted sums of energies of all possible ASFs that may be constructed from a set of CSFs; the number of ASFs is then the same as the number, n, of CSFs. Optimal level (OL) functionals are weighted sums of energies of some subset of ASFs; the GRASP92 package is optimized for this latter class of functionals. The composition of an ASF in terms of CSFs sharing the same quantum numbers is determined using the configuration-interaction (CI) procedure that results upon varying the expansion coefficients to determine the extremum of a variational functional. Radial functions may be determined by numerically solving the multiconfiguration Dirac-Fock (MCDF) equations that result upon varying the orbital radial functions or some subset thereof so as to obtain an extremum of the variational functional. Radial wavefunctions may also be determined using a screened hydrogenic or Thomas-Fermi model, although these schemes generally provide initial estimates for MCDF self-consistent-field (SCF) calculations. Transition properties for pairs of ASFs are computed from matrix elements of multipole operators of the electromagnetic field. All matrix elements of CSFs are evaluated using the Racah algebra. Reasons for the new version: During recent studies using the general relativistic atomic structure package (GRASP92), several errors were found, some of which might have been present already in the earlier GRASP92 version (program ABJN_v1_0, Comput. Phys. Comm. 55 (1989) 425). These errors were reported and discussed by Froese Fischer, Gaigalas, and Ralchenko in a separate publication [C. Froese Fischer, G. Gaigalas, Y. Ralchenko, Comput. Phys. Comm. 175 (2006) 738-744. [7

First law of black hole mechanics as a condition for stationarity

NASA Astrophysics Data System (ADS)

McCormick, Stephen

2014-11-01

In earlier work, we provided a Hilbert manifold structure for the phase space for the Einstein-Yang-Mills equations, and used this to prove a condition for initial data to be stationary [S. McCormick, Adv. Theor. Math. Phys. 18, 799 (2014)]. Here we use the same phase space to consider the evolution of initial data exterior to some closed 2-surface boundary, and establish a condition for stationarity in this case. It is shown that the differential relationship given in the first law of black hole mechanics is exactly the condition required for the initial data to be stationary; this was first argued nonrigorously by Sudarsky and Wald [Phys. Rev. D 46, 1453 (1992)]. Furthermore, we give evidence to suggest that if this differential relationship holds then the boundary surface is the bifurcation surface of a bifurcate Killing horizon.

On the Construction and the Structure of Off-Shell Supermultiplet Quotients

NASA Astrophysics Data System (ADS)

Hübsch, Tristan; Katona, Gregory A.

2012-11-01

Recent efforts to classify representations of supersymmetry with no central charge [C. F. Doran et al., Adv. Theor. Math. Phys.15, 1909 (2011)] have focused on supermultiplets that are aptly depicted by Adinkras, wherein every supersymmetry generator transforms each component field into precisely one other component field or its derivative. Herein, we study gauge-quotients of direct sums of Adinkras by a supersymmetric image of another Adinkra and thus solve a puzzle in the paper by Doran et al., Int. J. Mod. Phys. A22, 869 (2007): such (gauge-)quotients are not Adinkras but more general types of supermultiplets, each depicted as a connected network of Adinkras. Iterating this gauge-quotient construction then yields an indefinite sequence of ever larger supermultiplets, reminiscent of Weyl's construction that is known to produce all finite-dimensional unitary representations in Lie algebras.

Gleason-Busch theorem for sequential measurements

NASA Astrophysics Data System (ADS)

Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah

2017-12-01

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.

Quantum Communication Using Coherent Rejection Sampling.

PubMed

Anshu, Anurag; Devabathini, Vamsi Krishna; Jain, Rahul

2017-09-22

Compression of a message up to the information it carries is key to many tasks involved in classical and quantum information theory. Schumacher [B. Schumacher, Phys. Rev. A 51, 2738 (1995)PLRAAN1050-294710.1103/PhysRevA.51.2738] provided one of the first quantum compression schemes and several more general schemes have been developed ever since [M. Horodecki, J. Oppenheim, and A. Winter, Commun. Math. Phys. 269, 107 (2007); CMPHAY0010-361610.1007/s00220-006-0118-xI. Devetak and J. Yard, Phys. Rev. Lett. 100, 230501 (2008); PRLTAO0031-900710.1103/PhysRevLett.100.230501A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, Proc. R. Soc. A 465, 2537 (2009)PRLAAZ1364-502110.1098/rspa.2009.0202]. However, the one-shot characterization of these quantum tasks is still under development, and often lacks a direct connection with analogous classical tasks. Here we show a new technique for the compression of quantum messages with the aid of entanglement. We devise a new tool that we call the convex split lemma, which is a coherent quantum analogue of the widely used rejection sampling procedure in classical communication protocols. As a consequence, we exhibit new explicit protocols with tight communication cost for quantum state merging, quantum state splitting, and quantum state redistribution (up to a certain optimization in the latter case). We also present a port-based teleportation scheme which uses a fewer number of ports in the presence of information about input.

Ramsey interferometry of Rydberg ensembles inside microwave cavities

NASA Astrophysics Data System (ADS)

Sommer, Christian; Genes, Claudiu

2018-06-01

We study ensembles of Rydberg atoms in a confined electromagnetic environment such as is provided by a microwave cavity. The competition between standard free space Ising type and cavity-mediated interactions leads to the emergence of different regimes where the particle‑particle couplings range from the typical van der Waals r ‑6 behavior to r ‑3 and to r-independence. We apply a Ramsey spectroscopic technique to map the two-body interactions into a characteristic signal such as intensity and contrast decay curves. As opposed to previous treatments requiring high-densities for considerable contrast and phase decay (Takei et al 2016 Nat. Comms. 7 13449; Sommer et al 2016 Phys. Rev. A 94 053607), the cavity scenario can exhibit similar behavior at much lower densities.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, R.; Harrison, D. E. Jr.

A variable time step integration algorithm for carrying out molecular dynamics simulations of atomic collision cascades is proposed which evaluates the interaction forces only once per time step. The algorithm is tested on some model problems which have exact solutions and is compared against other common methods. These comparisons show that the method has good stability and accuracy. Applications to Ar/sup +/ bombardment of Cu and Si show good accuracy and improved speed to the original method (D. E. Harrison, W. L. Gay, and H. M. Effron, J. Math. Phys. /bold 10/, 1179 (1969)).

An Analytical Model of Periodic Waves in Shallow Water--Summary.

DTIC Science & Technology

1984-01-01

Petviashvili equation , and is based on a Riemann theta function of genus 2. These bi-periodic waves are direct generalizations of the well-known (simply... Petviashvili (KP; 1970) equation , (ut 6uux + U ) 3uyy -0, (1) is a scaled, dimensionless equation that describes the evolution of long water waves of...Fluid Mech., vol. 92, pp 691-715 Dubrovin, B. A., 1981, Russ. Math. Surveys, vol. 36, pp 11-92 Kadomtsev , B. B. & V. I. Petviashvili , 1970,) Soy. Phys

From sequences to polynomials and back, via operator orderings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amdeberhan, Tewodros, E-mail: tamdeber@tulane.edu; Dixit, Atul, E-mail: adixit@tulane.edu; Moll, Victor H., E-mail: vhm@tulane.edu

2013-12-15

Bender and Dunne [“Polynomials and operator orderings,” J. Math. Phys. 29, 1727–1731 (1988)] showed that linear combinations of words q{sup k}p{sup n}q{sup n−k}, where p and q are subject to the relation qp − pq = ı, may be expressed as a polynomial in the symbol z=1/2 (qp+pq). Relations between such polynomials and linear combinations of the transformed coefficients are explored. In particular, examples yielding orthogonal polynomials are provided.

Launch Safety, Toxicity, and Environmental Effects of the High Performance Oxidizer ClF(5)

DTIC Science & Technology

1994-03-31

Pentafluoride," J. Phys. Chem. 74, 1183 (1970). 7. J. A. Blauer, H. G. McMath, F. C. Jaye, and V. S, Engleman, " Decomposition Kinetics of Chlorine Trifluoride ...similar. A greater concern is propellant release in the stratosphere. Fluorine atoms lead to catalytic decomposition of 03 at rates similar to chlorine ...Propulsion Meeting - Publication 550, 3, 447 (1990). 4. R. F. Sawyer, E. T. McMullen, and P. Purgalis, "The Reaction of Hydrazine and Chlorine Pentafluoride

Symmetry and singularity properties of second-order ordinary differential equations of Lie's type III

NASA Astrophysics Data System (ADS)

Andriopoulos, K.; Leach, P. G. L.

2007-04-01

We extend the work of Abraham-Shrauner [B. Abraham-Shrauner, Hidden symmetries and linearization of the modified Painleve-Ince equation, J. Math. Phys. 34 (1993) 4809-4816] on the linearization of the modified Painleve-Ince equation to a wider class of nonlinear second-order ordinary differential equations invariant under the symmetries of time translation and self-similarity. In the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations.

Quantum Dilogarithms and Partition q-Series

NASA Astrophysics Data System (ADS)

Kato, Akishi; Terashima, Yuji

2015-08-01

In our previous work (Kato and Terashima, Commun Math Phys. arXiv:1403.6569, 2014), we introduced the partition q-series for mutation loop γ—a loop in exchange quiver. In this paper, we show that for a certain class of mutation sequences, called reddening sequences, the graded version of partition q-series essentially coincides with the ordered product of quantum dilogarithm associated with each mutation; the partition q-series provides a state-sum description of combinatorial Donaldson-Thomas invariants introduced by Keller.

A note on blowup of smooth solutions for relativistic Euler equations with infinite initial energy

NASA Astrophysics Data System (ADS)

Dong, Jianwei; Zhu, Junhui

2018-04-01

We study the singularity formation of smooth solutions of the relativistic Euler equations in (3+1)-dimensional spacetime for infinite initial energy. We prove that the smooth solution blows up in finite time provided that the radial component of the initial generalized momentum is sufficiently large without the conditions M(0)>0 and s2<1/3c2 , which were two key constraints stated in Pan and Smoller (Commun Math Phys 262:729-755, 2006).

Some practical observations on the predictor jump method for solving the Laplace equation

NASA Astrophysics Data System (ADS)

Duque-Carrillo, J. F.; Vega-Fernández, J. M.; Peña-Bernal, J. J.; Rossell-Bueno, M. A.

1986-01-01

The best conditions for the application of the predictor jump (PJ) method in the solution of the Laplace equation are discussed and some practical considerations for applying this new iterative technique are presented. The PJ method was remarked on in a previous article entitled ``A new way for solving Laplace's problem (the predictor jump method)'' [J. M. Vega-Fernández, J. F. Duque-Carrillo, and J. J. Peña-Bernal, J. Math. Phys. 26, 416 (1985)].

Multiple Scattering Treatment for Use in the LOWTRAN and FASCODE Models

DTIC Science & Technology

1986-04-07

Subroutines MSRAD, FLXADD, and ALEVEL and functions BETABS and PLANCK were added. Ine main program has been altered to allow the path geometry...body radiance for a particular wavenumber and temperature in units of Wcn-2 sterad- 1 /cm- 1 , while subroutine ALEVEL returns the layer number corre...and G. M. Wing (1960) J. Math . Phys., 1, 280. Ben-Shalom, A., B. Barzilia, D. Cabib, A. D. Devir, S. G. Lipson and U. P. o.C Oppenheim (1980) Applied

New realizations of 𝒩 = 2l-conformal Newton-Hooke superalgebra

NASA Astrophysics Data System (ADS)

Masterov, Ivan

2015-04-01

By applying Niederer-like transformation, we construct a representation of the 𝒩 = 2l-conformal Newton-Hooke (NH) superalgebra for the case of a negative cosmological constant in terms of linear differential operators as well as its dynamical realization. Another variant of 𝒩 = 2 supersymmetric Pais-Uhlenbeck oscillator for a particular choice of its frequencies is proposed. The advantages of such realizations as compared to their analogues introduced in [I. Masterov, J. Math. Phys.53, 072904 (2012)], are discussed.

Differential invariants and exact solutions of the Einstein equations

NASA Astrophysics Data System (ADS)

Lychagin, Valentin; Yumaguzhin, Valeriy

2017-06-01

In this paper (cf. Lychagin and Yumaguzhin, in Anal Math Phys, 2016) a class of totally geodesics solutions for the vacuum Einstein equations is introduced. It consists of Einstein metrics of signature (1,3) such that 2-dimensional distributions, defined by the Weyl tensor, are completely integrable and totally geodesic. The complete and explicit description of metrics from these class is given. It is shown that these metrics depend on two functions in one variable and one harmonic function.

Poly-symplectic Groupoids and Poly-Poisson Structures

NASA Astrophysics Data System (ADS)

Martinez, Nicolas

2015-05-01

We introduce poly-symplectic groupoids, which are natural extensions of symplectic groupoids to the context of poly-symplectic geometry, and define poly-Poisson structures as their infinitesimal counterparts. We present equivalent descriptions of poly-Poisson structures, including one related with AV-Dirac structures. We also discuss symmetries and reduction in the setting of poly-symplectic groupoids and poly-Poisson structures, and use our viewpoint to revisit results and develop new aspects of the theory initiated in Iglesias et al. (Lett Math Phys 103:1103-1133, 2013).

Letters

NASA Astrophysics Data System (ADS)

2001-01-01

The Editor welcomes letters, by e-mail to ped@iop.org or by post to Dirac House, Temple Back, Bristol BS1 6BE, UK. Contents: Maths for physics? Help! Fire! Energy and mass Maths for physics? As a maths graduate working as a university research associate I should be well qualified to support my daughter, who has just started AS-level physics, with the maths she needs for the course. There seems to be little integration between the maths and physics departments, so that maths needed for physics has not yet been covered in maths lessons. This is a problem I remember from my own school days, but the shorter timescale and modular nature of the AS and A2 levels means that it is essential that this mismatch of knowledge is resolved now. I would like to know whether physics teachers in the UK have encountered this problem and whether there is a deficiency in the maths syllabus in relation to the requirements of the AS and A2 levels in Physics or whether this is a problem peculiar to my daughter's school. Eleanor Parent of A-level student, Sheffield, UK Help! Fire! Is there a crisis in physics education? Is physics didactics coming to an end? Yes and no. Being a delegate from Norway at the on-going conference Physics on Stage (6-10 November 2000) at CERN in Geneva, I have had the opportunity to discuss this with people from all over Europe. Yes, there is a crisis. (Look at the proceedings for details on this.) I'd like to take a broader look at this situation. Like Hari Seldon in Isaac Asimov's Foundation Trilogy, I believe that there is nothing like a real crisis to get things going... Famous is the quote from the American Patent Office around 1890: 'Everything has been invented that could be invented'. Fortunately, this spurred action. The Michelson and Morley experiment heralded a most exciting period for physics. Just a cosmic blink later we put a person on the Moon. Coming back to the crisis - I am certain that in the near future we will see an interesting development within curriculum, presentation, outlook and attitude towards physics. Vegard Engstrom Physics Education Student Trondheim, Norway Energy and mass I stand accused [1] of 'adding to the confusion which is rife in this topic area'. The topic in question is E = mc2, which is being discussed in connection with its appearance in A-level syllabuses. One may (as I sometimes do) have qualms that such a topic (with numerical questions) be taught to children with a background of classical physics only. However, it is there, and the article under discussion [2] was meant to provide a meaningful and helpful insight into an experiment that (a) cannot be described by Newtonian mechanics, and (b) prepares the ground for relativity. Cockroft and Walton, in the first transmutation of a nucleus by an accelerated proton, observed the following reaction: _1^1H + _3^7Li rightarrow _2^4He + _2^4He + 17 MeV The masses of the nuclei involved were known (measured by Aston [3]), the kinetic energy of the proton beam known, and the kinetic energies of the helium nuclei were measured. Even if relativity had not been invented, a classical physicist would have noticed that something non-Newtonian was going on-and come up with the observation that the kinetic energy 'gained' (ΔE) was related to the mass 'loss' (Δm) by c2. Further experimentation with other nuclei would have revealed the same connection: ΔE = (Δm)c2. This is a very clear, insightful, experimental example of a breakdown of Newtonian mechanics, one that an A-level student could appreciate with understanding and interest. Since the models/theories of physics are designed to describe experimental results and observations, he or she would be wanting to know what was happening to Newtonian physics. Whether or not the student was capable of appreciating relativity at this point, the insight that something is wrong with Newtonian mechanics would be firmly established. The points raised by Keith Atkin belong, in my opinion, at the later stage, when the first relativity course is being presented, and the relationship between mass and energy developed. His reference [4], 'Energy has mass' by Bondi and Spurgin, and a letter [5], 'Mass and energy' by Peierls, presenting a different point of view, provide food for thought. References [1] Atkin K 2000 Clarifying the concept Phys. Educ. 35 319 [2] Tudor Jones G 2000 Concern about post-16 A-level Phys. Educ. 35 250 [3] Aston F W 1927 Bakerian Lecture-A new mass-spectrograph and the whole number rule Proc. Roy. Soc. 115A 487 [4] Bondi H and Spurgin C B 1987 Energy has mass Phys. Bull. 38 62 [5] Peierls R 1987 Mass and energy Phys. Bull. 38 127 Goronwy Tudor Jones Lecturer School of Continuing Studies, The University of Birmingham

A comparative study of the single-mode Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Bai, X.; Deng, X.-L.; Jiang, L.

2018-07-01

In this work, the single-mode Richtmyer-Meshkov instability is studied numerically to find a reasonable nonlinear theoretical model which can be applied to predict the interface evolution from the linear stage to the early nonlinear stage. The cut-cell-based sharp-interface methods MuSiC+ (Chang et al. in J Comput Phys 242:946-990, 2013) and CCGF (Bai and Deng in Adv Appl Math Mech 9(5):1052-1075, 2017) are applied to generate numerical results for comparisons. Classical Air-SF6 and Air-Helium conditions are applied in this study, and initial amplitude and Atwood number are varied for comparison. Comparisons to the simulation results from the literature show the applicability of MuSiC+ and CCGF. Comparisons to the nonlinear theoretical models show that ZS (Zhang and Sohn in Phys Lett A 212:149-155, 1996; Phys Fluids 9:1106-1124, 1997), SEA (Sadot et al. in Phys Rev Lett 80:1654-1657, 1998), and DR (Dimonte and Ramaprabhu in Phys Fluids 22:014104, 2010) models are valid for both spike and bubble growth rates, and MIK (Mikaelian in Phys Rev E 67:026319, 2003) and ZG (Zhang and Guo in J Fluid Mech 786:47-61, 2016) models are valid for bubble growth rate, when the initial perturbation is small and the Atwood number is low, but only the DR model is applicable for both spike and bubble growth rates when the initial perturbation amplitude and the Atwood number are large. A new term of non-dimensional initial perturbation amplitude is presented and multiplied to the DR model to get a unified fitted DR model, which gives consistent results to the simulation ones for small and large initial amplitudes.

A comparative study of the single-mode Richtmyer-Meshkov instability

NASA Astrophysics Data System (ADS)

Bai, X.; Deng, X.-L.; Jiang, L.

2017-11-01

In this work, the single-mode Richtmyer-Meshkov instability is studied numerically to find a reasonable nonlinear theoretical model which can be applied to predict the interface evolution from the linear stage to the early nonlinear stage. The cut-cell-based sharp-interface methods MuSiC+ (Chang et al. in J Comput Phys 242:946-990, 2013) and CCGF (Bai and Deng in Adv Appl Math Mech 9(5):1052-1075, 2017) are applied to generate numerical results for comparisons. Classical Air-SF6 and Air-Helium conditions are applied in this study, and initial amplitude and Atwood number are varied for comparison. Comparisons to the simulation results from the literature show the applicability of MuSiC+ and CCGF. Comparisons to the nonlinear theoretical models show that ZS (Zhang and Sohn in Phys Lett A 212:149-155, 1996; Phys Fluids 9:1106-1124, 1997), SEA (Sadot et al. in Phys Rev Lett 80:1654-1657, 1998), and DR (Dimonte and Ramaprabhu in Phys Fluids 22:014104, 2010) models are valid for both spike and bubble growth rates, and MIK (Mikaelian in Phys Rev E 67:026319, 2003) and ZG (Zhang and Guo in J Fluid Mech 786:47-61, 2016) models are valid for bubble growth rate, when the initial perturbation is small and the Atwood number is low, but only the DR model is applicable for both spike and bubble growth rates when the initial perturbation amplitude and the Atwood number are large. A new term of non-dimensional initial perturbation amplitude is presented and multiplied to the DR model to get a unified fitted DR model, which gives consistent results to the simulation ones for small and large initial amplitudes.

Well-posedness and Scattering for the Boltzmann Equations: Soft Potential with Cut-off

NASA Astrophysics Data System (ADS)

He, Lingbing; Jiang, Jin-Cheng

2017-07-01

We prove the global existence of the unique mild solution for the Cauchy problem of the cut-off Boltzmann equation for soft potential model γ =2-N with initial data small in L^N_{x,v} where N=2,3 is the dimension. The proof relies on the existing inhomogeneous Strichartz estimates for the kinetic equation by Ovcharov (SIAM J Math Anal 43(3):1282-1310, 2011) and convolution-like estimates for the gain term of the Boltzmann collision operator by Alonso et al. (Commun Math Phys 298:293-322, 2010). The global dynamics of the solution is also characterized by showing that the small global solution scatters with respect to the kinetic transport operator in L^N_{x,v}. Also the connection between function spaces and cut-off soft potential model -N<γ <2-N is characterized in the local well-posedness result for the Cauchy problem with large initial data.

Nonlocal operators, parabolic-type equations, and ultrametric random walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacón-Cortes, L. F., E-mail: fchaconc@math.cinvestav.edu.mx; Zúñiga-Galindo, W. A., E-mail: wazuniga@math.cinvestav.edu.mx

2013-11-15

In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the numbermore » of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.« less

Isospectral discrete and quantum graphs with the same flip counts and nodal counts

NASA Astrophysics Data System (ADS)

Juul, Jonas S.; Joyner, Christopher H.

2018-06-01

The existence of non-isomorphic graphs which share the same Laplace spectrum (to be referred to as isospectral graphs) leads naturally to the following question: what additional information is required in order to resolve isospectral graphs? It was suggested by Band, Shapira and Smilansky that this might be achieved by either counting the number of nodal domains or the number of times the eigenfunctions change sign (the so-called flip count) (Band et al 2006 J. Phys. A: Math. Gen. 39 13999–4014 Band and Smilansky 2007 Eur. Phys. J. Spec. Top. 145 171–9). Recent examples of (discrete) isospectral graphs with the same flip count and nodal count have been constructed by Ammann by utilising Godsil–McKay switching (Ammann private communication). Here, we provide a simple alternative mechanism that produces systematic examples of both discrete and quantum isospectral graphs with the same flip and nodal counts.

Universality for 1d Random Band Matrices: Sigma-Model Approximation

NASA Astrophysics Data System (ADS)

Shcherbina, Mariya; Shcherbina, Tatyana

2018-02-01

The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233-1260, 2016; Commun Math Phys 351:1009-1044, 2017). We consider random Hermitian block band matrices consisting of W× W random Gaussian blocks (parametrized by j,k \\in Λ =[1,n]^d\\cap Z^d ) with a fixed entry's variance J_{jk}=δ _{j,k}W^{-1}+β Δ _{j,k}W^{-2} , β >0 in each block. Taking the limit W→ ∞ with fixed n and β , we derive the sigma-model approximation of the second correlation function similar to Efetov's one. Then, considering the limit β , n→ ∞, we prove that in the dimension d=1 the behaviour of the sigma-model approximation in the bulk of the spectrum, as β ≫ n , is determined by the classical Wigner-Dyson statistics.

Quantum correlations in a family of bipartite separable qubit states

NASA Astrophysics Data System (ADS)

Xie, Chuanmei; Liu, Yimin; Chen, Jianlan; Zhang, Zhanjun

2017-03-01

Quantum correlations (QCs) in some separable states have been proposed as a key resource for certain quantum communication tasks and quantum computational models without entanglement. In this paper, a family of nine-parameter separable states, obtained from arbitrary mixture of two sets of bi-qubit product pure states, is considered. QCs in these separable states are studied analytically or numerically using four QC quantifiers, i.e., measurement-induced disturbance (Luo in Phys Rev A77:022301, 2008), ameliorated MID (Girolami et al. in J Phys A Math Theor 44:352002, 2011),quantum dissonance (DN) (Modi et al. in Phys Rev Lett 104:080501, 2010), and new quantum dissonance (Rulli in Phys Rev A 84:042109, 2011), respectively. First, an inherent symmetry in the concerned separable states is revealed, that is, any nine-parameter separable states concerned in this paper can be transformed to a three-parameter kernel state via some certain local unitary operation. Then, four different QC expressions are concretely derived with the four QC quantifiers. Furthermore, some comparative studies of the QCs are presented, discussed and analyzed, and some distinct features about them are exposed. We find that, in the framework of all the four QC quantifiers, the more mixed the original two pure product states, the bigger QCs the separable states own. Our results reveal some intrinsic features of QCs in separable systems in quantum information.

Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids

NASA Astrophysics Data System (ADS)

Banerjee, Supratik; Kritsuk, Alexei G.

2018-02-01

Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by Banerjee and Galtier [Phys. Rev. E 93, 033120 (2016), 10.1103/PhysRevE.93.033120; J. Phys. A: Math. Theor. 50, 015501 (2017), 10.1088/1751-8113/50/1/015501], an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic, and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be nontrivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.

Nonlinear heating of ions by electron cyclotron frequency waves

NASA Astrophysics Data System (ADS)

Zestanakis, P. A.; Hizanidis, K.; Ram, A. K.; Kominis, Y.

2010-11-01

We study the nonlinear interaction of ions with electron cyclotron (EC) wave packets in a magnetized plasma. Previous studies have shown that such interactions with high frequency electrostatic lower hybrid waves can lead to coherent energization of ions. It requires the frequency bandwidth of the wave packet to be broader than the ion cyclotron frequency [1,2]. For the electromagnetic high frequency EC waves we have developed a more general theory, based on the Lie transform canonical perturbation method [3,4]. We apply the theory to the case of two overlapping EC beams. The wave frequency of each beam is assumed to be frequency modulated with a modulation bandwidth comparable to the ion cyclotron frequency. We present results for both X-mode and O-mode and illustrate the conditions for ion energization. [4pt] [1] D. Benisti, A. K. Ram, and A. Bers, Phys. Plasmas 5, 3224 (1998). [0pt] [2] A. K. Ram, A. Bers, and D. Benisti , J. Geophys. Res. 103, 9431 (1998). [0pt] [3] J.R. Cary and A.N. Kaufman, Phys. Fluids 24, 1238 (1981). [0pt] [4] R.L. Dewar, J. Phys A-Math. Gen 9, 2043 (1976).

Work distributions of one-dimensional fermions and bosons with dual contact interactions

NASA Astrophysics Data System (ADS)

Wang, Bin; Zhang, Jingning; Quan, H. T.

2018-05-01

We extend the well-known static duality [M. Girardeau, J. Math. Phys. 1, 516 (1960), 10.1063/1.1703687; T. Cheon and T. Shigehara, Phys. Rev. Lett. 82, 2536 (1999), 10.1103/PhysRevLett.82.2536] between one-dimensional (1D) bosons and 1D fermions to the dynamical version. By utilizing this dynamical duality, we find the duality of nonequilibrium work distributions between interacting 1D bosonic (Lieb-Liniger model) and 1D fermionic (Cheon-Shigehara model) systems with dual contact interactions. As a special case, the work distribution of the Tonks-Girardeau gas is identical to that of 1D noninteracting fermionic system even though their momentum distributions are significantly different. In the classical limit, the work distributions of Lieb-Liniger models (Cheon-Shigehara models) with arbitrary coupling strength converge to that of the 1D noninteracting distinguishable particles, although their elementary excitations (quasiparticles) obey different statistics, e.g., the Bose-Einstein, the Fermi-Dirac, and the fractional statistics. We also present numerical results of the work distributions of Lieb-Liniger model with various coupling strengths, which demonstrate the convergence of work distributions in the classical limit.

Computation Through Neuronal Oscillations

NASA Astrophysics Data System (ADS)

Hepp, K.

Some of us believe that natural sciences are governed by simple and predictive general principles. This hope has not yet been fulfilled in physics for unifying gravitation and quantum mechanics. Epigenetics has shaken the monopoly of the genetic code to determine inheritance (Alberts et al., Molecular Biology of the Cell. Garland, New York, 2008). It is therefore not surprising that quantum mechanics does not explain consciousness or more generally the coherence of the brain in perception, action and cognition. In an other context, others (Tegmark, Phys Rev E 61:4194-4206, 2000) and we (Koch and Hepp, Nature 440:611-612, 2006; Koch and Hepp, Visions of Discovery: New Light on Physics, Cosmology, and Consciousness. Cambridge University Press, Cambridge, 2011) have strongly argued against the absurdity of such a claim, because consciousness is a higher brain function and not a molecular binding mechanism. Decoherence in the warm and wet brain is by many orders of magnitude too strong. Moreover, there are no efficient algorithms for neural quantum computations. However, the controversy over classical and quantum consciousness will probably never be resolved (see e.g. Hepp, J Math Phys 53:095222, 2012; Hameroff and Penrose, Phys Life Rev 11:39-78, 2013).

Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids.

PubMed

Banerjee, Supratik; Kritsuk, Alexei G

2018-02-01

Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by Banerjee and Galtier [Phys. Rev. E 93, 033120 (2016)2470-004510.1103/PhysRevE.93.033120; J. Phys. A: Math. Theor. 50, 015501 (2017)1751-811310.1088/1751-8113/50/1/015501], an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic, and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be nontrivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.

Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds

NASA Astrophysics Data System (ADS)

Tyson, Jon

2009-03-01

We prove a concise factor-of-2 estimate for the failure rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT, 1979]. A modification to the minimal principle of Cocha and Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a suboptimal measurement which has an error rate within a factor of 2 of the optimal by construction. This measurement is quadratically weighted and has appeared as the first iterate of a sequence of measurements proposed by Ježek et al. [Phys. Rev. A 65, 060301 (2002)]. Unlike the so-called pretty good measurement, it coincides with Holevo's asymptotically optimal measurement in the case of nonequiprobable pure states. A quadratically weighted version of the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is proven. Bounds on the distinguishability of syndromes in the sense of Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a corollary. An appendix relates our bounds to the trace-Jensen inequality.

HELAC-PHEGAS: A generator for all parton level processes

NASA Astrophysics Data System (ADS)

Cafarella, Alessandro; Papadopoulos, Costas G.; Worek, Malgorzata

2009-10-01

The updated version of the HELAC-PHEGAS event generator is presented. The matrix elements are calculated through Dyson-Schwinger recursive equations using color connection representation. Phase-space generation is based on a multichannel approach, including optimization. HELAC-PHEGAS generates parton level events with all necessary information, in the most recent Les Houches Accord format, for the study of any process within the Standard Model in hadron and lepton colliders. New version program summaryProgram title: HELAC-PHEGAS Catalogue identifier: ADMS_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADMS_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 35 986 No. of bytes in distributed program, including test data, etc.: 380 214 Distribution format: tar.gz Programming language: Fortran Computer: All Operating system: Linux Classification: 11.1, 11.2 External routines: Optionally Les Houches Accord (LHA) PDF Interface library ( http://projects.hepforge.org/lhapdf/) Catalogue identifier of previous version: ADMS_v1_0 Journal reference of previous version: Comput. Phys. Comm. 132 (2000) 306 Does the new version supersede the previous version?: Yes, partly Nature of problem: One of the most striking features of final states in current and future colliders is the large number of events with several jets. Being able to predict their features is essential. To achieve this, the calculations need to describe as accurately as possible the full matrix elements for the underlying hard processes. Even at leading order, perturbation theory based on Feynman graphs runs into computational problems, since the number of graphs contributing to the amplitude grows as n!. Solution method: Recursive algorithms based on Dyson-Schwinger equations have been developed recently in order to overcome the computational obstacles. The calculation of the amplitude, using Dyson-Schwinger recursive equations, results in a computational cost growing asymptotically as 3 n, where n is the number of particles involved in the process. Off-shell subamplitudes are introduced, for which a recursion relation has been obtained allowing to express an n-particle amplitude in terms of subamplitudes, with 1-, 2-, … up to (n-1) particles. The color connection representation is used in order to treat amplitudes involving colored particles. In the present version HELAC-PHEGAS can be used to efficiently obtain helicity amplitudes, total cross sections, parton-level event samples in LHA format, for arbitrary multiparticle processes in the Standard Model in leptonic, pp¯ and pp collisions. Reasons for new version: Substantial improvements, major functionality upgrade. Summary of revisions: Color connection representation, efficient integration over PDF via the PARNI algorithm, interface to LHAPDF, parton level events generated in the most recent LHA format, k reweighting for Parton Shower matching, numerical predictions for amplitudes for arbitrary processes for phase-space points provided by the user, new user interface and the possibility to run over computer clusters. Running time: Depending on the process studied. Usually from seconds to hours. References:A. Kanaki, C.G. Papadopoulos, Comput. Phys. Comm. 132 (2000) 306. C.G. Papadopoulos, Comput. Phys. Comm. 137 (2001) 247. URL: http://www.cern.ch/helac-phegas.

Multithreaded transactions in scientific computing. The Growth06_v2 program

NASA Astrophysics Data System (ADS)

Daniluk, Andrzej

2009-07-01

Writing a concurrent program can be more difficult than writing a sequential program. Programmer needs to think about synchronization, race conditions and shared variables. Transactions help reduce the inconvenience of using threads. A transaction is an abstraction, which allows programmers to group a sequence of actions on the program into a logical, higher-level computation unit. This paper presents a new version of the GROWTHGr and GROWTH06 programs. New version program summaryProgram title: GROWTH06_v2 Catalogue identifier: ADVL_v2_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVL_v2_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 65 255 No. of bytes in distributed program, including test data, etc.: 865 985 Distribution format: tar.gz Programming language: Object Pascal Computer: Pentium-based PC Operating system: Windows 9x, XP, NT, Vista RAM: more than 1 MB Classification: 4.3, 7.2, 6.2, 8, 14 Catalogue identifier of previous version: ADVL_v2_0 Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 678 Does the new version supersede the previous version?: Yes Nature of problem: The programs compute the RHEED intensities during the growth of thin epitaxial structures prepared using the molecular beam epitaxy (MBE). The computations are based on the use of kinematical diffraction theory. Solution method: Epitaxial growth of thin films is modelled by a set of non-linear differential equations [1]. The Runge-Kutta method with adaptive stepsize control was used for solving initial value problem for non-linear differential equations [2]. Reasons for new version: According to the users' suggestions functionality of the program has been improved. Moreover, new use cases have been added which make the handling of the program easier and more efficient than the previous ones [3]. Summary of revisions:The design pattern (See Fig. 2 of Ref. [3]) has been modified according to the scheme shown on Fig. 1. A graphical user interface (GUI) for the program has been reconstructed. Fig. 2 presents a hybrid diagram of a GUI that shows how onscreen objects connect to use cases. The program has been compiled with English/USA regional and language options. Note: The figures mentioned above are contained in the program distribution file. Unusual features: The program is distributed in the form of source project GROWTH06_v2.dpr with associated files, and should be compiled using Borland Delphi compilers versions 6 or latter (including Borland Developer Studio 2006 and Code Gear compilers for Delphi). Additional comments: Two figures are included in the program distribution file. These are captioned Static classes model for Transaction design pattern. A model of a window that shows how onscreen objects connect to use cases. Running time: The typical running time is machine and user-parameters dependent. References: [1] A. Daniluk, Comput. Phys. Comm. 170 (2005) 265. [2] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in Pascal: The Art of Scientific Computing, first ed., Cambridge University Press, 1989. [3] M. Brzuszek, A. Daniluk, Comput. Phys. Comm. 175 (2006) 678.

The Critical Z-Invariant Ising Model via Dimers: Locality Property

NASA Astrophysics Data System (ADS)

Boutillier, Cédric; de Tilière, Béatrice

2011-01-01

We study a large class of critical two-dimensional Ising models, namely critical Z-invariant Ising models. Fisher (J Math Phys 7:1776-1781, 1966) introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer model corresponding to the critical Z-invariant Ising model, consisting of explicit expressions which only depend on the local geometry of the underlying isoradial graph. Our main result is an explicit local formula for the inverse Kasteleyn matrix, in the spirit of Kenyon (Invent Math 150(2):409-439, 2002), as a contour integral of the discrete exponential function of Mercat (Discrete period matrices and related topics, 2002) and Kenyon (Invent Math 150(2):409-439, 2002) multiplied by a local function. Using results of Boutillier and de Tilière (Prob Theor Rel Fields 147(3-4):379-413, 2010) and techniques of de Tilière (Prob Th Rel Fields 137(3-4):487-518, 2007) and Kenyon (Invent Math 150(2):409-439, 2002), this yields an explicit local formula for a natural Gibbs measure, and a local formula for the free energy. As a corollary, we recover Baxter's formula for the free energy of the critical Z-invariant Ising model (Baxter, in Exactly solved models in statistical mechanics, Academic Press, London, 1982), and thus a new proof of it. The latter is equal, up to a constant, to the logarithm of the normalized determinant of the Laplacian obtained in Kenyon (Invent Math 150(2):409-439, 2002).

ISICS2008: An expanded version of ISICS for calculating K-, L-, and M-shell cross sections from PWBA and ECPSSR theory

NASA Astrophysics Data System (ADS)

Cipolla, Sam J.

2009-09-01

New version program summaryProgram title: ISICS2008 Catalogue identifier: ADDS_v4_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADDS_v4_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5420 No. of bytes in distributed program, including test data, etc.: 107 669 Distribution format: tar.gz Programming language: C Computer: 80 486 or higher level PCs Operating system: Windows XP and all earlier operating systems Classification: 16.7 Catalogue identifier of previous version: ADDS_v3_0 Journal reference of previous version: Comput. Phys. Comm. 179 (2008) 616 Does the new version supersede the previous version?: Yes Nature of problem: Ionization and X-ray production cross section calculations for ion-atom collisions. Solution method: Numerical integration of form factor using a logarithmic transform and Gaussian quadrature, plus exact integration limits. Reasons for new version: Addition of relativistic treatment of both projectile and K-shell electrons. Summary of revisions: A new addition to ISICS is the option (R) to calculate ECPSSR cross sections that account for the relativistic treatment of both projectile and K-shell electron, as proposed recently by Lapicki [1], accordingly as σKRECPSSR=Cṡ(1+0.07(()ṡσ(√{(mKRυ1R)}/Z,ςθ), where υ1R is the relativistic projectile velocity. The option can also be invoked in calculating ECPSShsR, where hsR stands for the Hartree-Slater description of the K-shell electron, which was already incorporated into ISICS2006 [2,3], and is now expressed in this option as, σKRECPSShsR=CṡhsR((2υ1R)/(Zςθ),Z/137)ṡ(1+0.07(()ṡσ(υ1R/Z,ςθ) using the function hsR that is already incorporated into ISICS2006. It should be noted that these expressions are corrected versions [4] from the ones published in Ref. [1]. In this new version, ISICS2008, the option line in the main menu that read "Use Relativistic Proj. velocity" has been replaced by "R option for K-shell … Uses Rel. Proj. vel.". As before, various combinations of options can be utilized and each is denoted in the output. Restrictions: The consumed CPU time increases with the atomic shell (K,L,M), but execution is still very fast. Additional comments: A revised User Manual is included in the distribution file. Running time: This depends on which shell and the number of different energies to be used in the calculation. The running time is not significantly changed from the previous version. As before, to calculate K-shell cross sections for protons striking carbon for 19 different proton energies it took less than 10 s; to calculate M-shell cross sections for protons on gold for 21 proton energies it took 4.2 min. References:G. Lapicki, J. Phys. B: At. Mol. Op. Phys. 41 (2008) 115201. S. Cipolla, Comput. Phys. Comm. 176 (2007) 157. S. Cipolla, Nucl. Instrum. Methods Phys. Res. B 261 (2007) 142. G. Lapicki, private communication.

Riemann-Hypothesis Millennium-Problem(MP) Physics Proof via CATEGORY-SEMANTICS(C-S)/F =C Aristotle SQUARE-of-OPPOSITION(SoO) DEduction-LOGIC DichotomY

NASA Astrophysics Data System (ADS)

Baez, Joao-Joan; Lapidaryus, Michelle; Siegel, Edward Carl-Ludwig

2013-03-01

Riemann-hypothesis physics-proof combines: Siegel-Antono®-Smith[AMS Joint Mtg.(2002)- Abs.973-03-126] digits on-average statistics HIll[Am. J. Math 123, 3, 887(1996)] logarithm-function's (1,0)- xed-point base =units =scale-invariance proven Newcomb [Am. J. Math. 4, 39(1881)]-Weyl[Goett. Nachr.(1914); Math. Ann.7, 313(1916)]-Benford[Proc. Am. Phil. Soc. 78, 4, 51(1938)]-law [Kac,Math. of Stat.-Reasoning(1955); Raimi, Sci. Am. 221, 109(1969)] algebraic-inversion to ONLY Bose-Einstein quantum-statistics(BEQS) with digit d = 0 gapFUL Bose-Einstein Condensation(BEC) insight that digits are quanta are bosons because bosons are and always were quanta are and always were digits, via Siegel-Baez category-semantics tabular list-format matrix truth-table analytics in Plato-Aristotle classic ''square-of-opposition'' : FUZZYICS =CATEGORYICS/Category-Semantics, with Goodkind Bose-Einstein Condensation (BEC) ABOVE ground-state with/and Rayleigh(cut-limit of ''short-cut method''1870)-Polya(1922)-''Anderson''(1958) localization [Doyle and Snell,Random-Walks and Electrical-Networks, MAA(1981)-p.99-100!!!] in Brillouin[Wave-Propagation in Periodic-Structures(1946) Dover(1922)]-Hubbard-Beeby[J.Phys.C(1967)] Siegel[J.Nonxline-Sol.40,453(1980)] generalized-disorder collective-boson negative-dispersion mode-softening universality-principle(G...P) first use of the ``square-of-opposition'' in physics since Plato and Aristote!!!

A novel noncommutative KdV-type equation, its recursion operator, and solitons

NASA Astrophysics Data System (ADS)

Carillo, Sandra; Lo Schiavo, Mauro; Porten, Egmont; Schiebold, Cornelia

2018-04-01

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived.

Orthogonal polynomials, Laguerre Fock space, and quasi-classical asymptotics

NASA Astrophysics Data System (ADS)

Engliš, Miroslav; Ali, S. Twareque

2015-07-01

Continuing our earlier investigation of the Hermite case [S. T. Ali and M. Engliš, J. Math. Phys. 55, 042102 (2014)], we study an unorthodox variant of the Berezin-Toeplitz quantization scheme associated with Laguerre polynomials. In particular, we describe a "Laguerre analogue" of the classical Fock (Segal-Bargmann) space and the relevant semi-classical asymptotics of its Toeplitz operators; the former actually turns out to coincide with the Hilbert space appearing in the construction of the well-known Barut-Girardello coherent states. Further extension to the case of Legendre polynomials is likewise discussed.

An Approach for the Adaptive Solution of Optimization Problems Governed by Partial Differential Equations with Uncertain Coefficients

DTIC Science & Technology

2012-05-01

Acad. Sci. Fennicae. Ser. A. I. Math.-Phys., 1947(37):79, 1947. [65] G. E. Karniadakis, C.-H. Su, D. Xiu, D. Lucor, C. Schwab, and R. A. Todor ...treatment of uncertainties in aerodynamic design. AIAA Journal, 47(3):646–654, 2009. [106] C. Schwab and R. A. Todor . Karhunen-Loève approximation of random...integrals. Prentice-Hall Inc., Englewood Cliffs, N.J., 1971. Prentice-Hall Series in Automatic Computation. [113] R. A. Todor and C. Schwab

Digest - International Conference on Optical and Millimeter Wave Propagation and Scattering in the Atmosphere Held in Florence, Italy on May 27-30, 1986.

DTIC Science & Technology

1986-05-01

Physics Division, Graduate School of Applied Science and Technology, The Hebrew University of Jerusalem , Jerusalem , ISRAEL Introduction The correlation...A.M. Yaqlom, J. Math. Phys., 1, 48, 1960. 8] G. Eichmann , J.O.S.A., 61, 161, 1971. 9) D. Eve, Proc. Roy. Soc. (London), A347, 405, 1976. 10] L.S...the Turbulent Atmosphere on Wave Propagation, Israel Program for Scientific Translations, Jerusalem , 1971. 123 Fried, D.L., J. Opt. Soc. Am. 55, 1427

Rigidity in vacuum under conformal symmetry

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.; Vega, Carlos

2018-04-01

Motivated in part by Eardley et al. (Commun Math Phys 106(1):137-158, 1986), in this note we obtain a rigidity result for globally hyperbolic vacuum spacetimes in arbitrary dimension that admit a timelike conformal Killing vector field. Specifically, we show that if M is a Ricci flat, timelike geodesically complete spacetime with compact Cauchy surfaces that admits a timelike conformal Killing field X, then M must split as a metric product, and X must be Killing. This gives a partial proof of the Bartnik splitting conjecture in the vacuum setting.

Lee-Yang Polynomials and Ground States of Spin Systems

NASA Astrophysics Data System (ADS)

Slawny, Joseph

2014-08-01

We obtain two kinds of results on the region in the space of the interactions of lattice systems where the Lee-Yang property holds (LY domain). First we show that the LY domain is related to interactions with exactly two ground states. Then we give a description of the full LY domain of an extended "plaquette model" analyzed by Lebowitz and Ruelle (Commun Math Phys 304:711-722, 2011). This allows us to prove a permanence property of the system, which we conjecture to hold in general.

Stochastic wave-function unravelling of the generalized Lindblad equation

NASA Astrophysics Data System (ADS)

Semin, V.; Semina, I.; Petruccione, F.

2017-12-01

We investigate generalized non-Markovian stochastic Schrödinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010), 10.1063/1.3514539]. We show that these SSEs can be translated in a nonlinear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath, and the results of the simulations are compared with the exact solution of the generalized master equation.

Magic informationally complete POVMs with permutations

NASA Astrophysics Data System (ADS)

Planat, Michel; Gedik, Zafer

2017-09-01

Eigenstates of permutation gates are either stabilizer states (for gates in the Pauli group) or magic states, thus allowing universal quantum computation (Planat, Rukhsan-Ul-Haq 2017 Adv. Math. Phys. 2017, 5287862 (doi:10.1155/2017/5287862)). We show in this paper that a subset of such magic states, when acting on the generalized Pauli group, define (asymmetric) informationally complete POVMs. Such informationally complete POVMs, investigated in dimensions 2-12, exhibit simple finite geometries in their projector products and, for dimensions 4 and 8 and 9, relate to two-qubit, three-qubit and two-qutrit contextuality.

Wall-crossing between stable and co-stable ADHM data

NASA Astrophysics Data System (ADS)

Ohkawa, Ryo

2018-06-01

We prove formula between Nekrasov partition functions defined from stable and co-stable ADHM data for the plane following method by Nakajima and Yoshioka (Kyoto J Math 51(2):263-335, 2011) based on the theory of wall-crossing formula developed by Mochizuki (Donaldson type invariants for algebraic surfaces: transition of moduli stacks, Lecture notes in mathematics, vol 1972, Springer, Berlin, 2009). This formula is similar to conjectures by Ito et al. [J High Energy Phys 2013(5):045, 2013, (4.1), (4.2)] for A1 singularity.

``Models'' CAVEAT EMPTOR!!!: ``Toy Models Too-Often Yield Toy-Results''!!!: Statistics, Polls, Politics, Economics, Elections!!!: GRAPH/Network-Physics: ``Equal-Distribution for All'' TRUMP-ED BEC ``Winner-Take-All'' ``Doctor Livingston I Presume?''

NASA Astrophysics Data System (ADS)

Preibus-Norquist, R. N. C.-Grover; Bush-Romney, G. W.-Willard-Mitt; Dimon, J. P.; Adelson-Koch, Sheldon-Charles-David-Sheldon; Krugman-Axelrod, Paul-David; Siegel, Edward Carl-Ludwig; D. N. C./O. F. P./''47''%/50% Collaboration; R. N. C./G. O. P./''53''%/49% Collaboration; Nyt/Wp/Cnn/Msnbc/Pbs/Npr/Ft Collaboration; Ftn/Fnc/Fox/Wsj/Fbn Collaboration; Lb/Jpmc/Bs/Boa/Ml/Wamu/S&P/Fitch/Moodys/Nmis Collaboration

2013-03-01

``Models''? CAVEAT EMPTOR!!!: ``Toy Models Too-Often Yield Toy-Results''!!!: Goldenfeld[``The Role of Models in Physics'', in Lects.on Phase-Transitions & R.-G.(92)-p.32-33!!!]: statistics(Silver{[NYTimes; Bensinger, ``Math-Geerks Clearly-Defeated Pundits'', LATimes, (11/9/12)])}, polls, politics, economics, elections!!!: GRAPH/network/net/...-PHYSICS Barabasi-Albert[RMP (02)] (r,t)-space VERSUS(???) [Where's the Inverse/ Dual/Integral-Transform???] (Benjamin)Franklin(1795)-Fourier(1795; 1897;1822)-Laplace(1850)-Mellin (1902) Brillouin(1922)-...(k,)-space, {Hubbard [The World According to Wavelets,Peters (96)-p.14!!!/p.246: refs.-F2!!!]},and then (2) Albert-Barabasi[]Bose-Einstein quantum-statistics(BEQS) Bose-Einstein CONDENSATION (BEC) versus Bianconi[pvt.-comm.; arXiv:cond-mat/0204506; ...] -Barabasi [???] Fermi-Dirac

Einstein Critical-Slowing-Down is Siegel CyberWar Denial-of-Access Queuing/Pinning/ Jamming/Aikido Via Siegel DIGIT-Physics BEC ``Intersection''-BECOME-UNION Barabasi Network/GRAPH-Physics BEC: Strutt/Rayleigh-Siegel Percolation GLOBALITY-to-LOCALITY Phase-Transition Critical-Phenomenon

NASA Astrophysics Data System (ADS)

Buick, Otto; Falcon, Pat; Alexander, G.; Siegel, Edward Carl-Ludwig

2013-03-01

Einstein[Dover(03)] critical-slowing-down(CSD)[Pais, Subtle in The Lord; Life & Sci. of Albert Einstein(81)] is Siegel CyberWar denial-of-access(DOA) operations-research queuing theory/pinning/jamming/.../Read [Aikido, Aikibojitsu & Natural-Law(90)]/Aikido(!!!) phase-transition critical-phenomenon via Siegel DIGIT-Physics (Newcomb[Am.J.Math. 4,39(1881)]-{Planck[(1901)]-Einstein[(1905)])-Poincare[Calcul Probabilités(12)-p.313]-Weyl [Goett.Nachr.(14); Math.Ann.77,313 (16)]-{Bose[(24)-Einstein[(25)]-Fermi[(27)]-Dirac[(1927)]}-``Benford''[Proc.Am.Phil.Soc. 78,4,551 (38)]-Kac[Maths.Stat.-Reasoning(55)]-Raimi[Sci.Am. 221,109 (69)...]-Jech[preprint, PSU(95)]-Hill[Proc.AMS 123,3,887(95)]-Browne[NYT(8/98)]-Antonoff-Smith-Siegel[AMS Joint-Mtg.,S.-D.(02)] algebraic-inversion to yield ONLY BOSE-EINSTEIN QUANTUM-statistics (BEQS) with ZERO-digit Bose-Einstein CONDENSATION(BEC) ``INTERSECTION''-BECOME-UNION to Barabasi[PRL 876,5632(01); Rev.Mod.Phys.74,47(02)...] Network /Net/GRAPH(!!!)-physics BEC: Strutt/Rayleigh(1881)-Polya(21)-``Anderson''(58)-Siegel[J.Non-crystalline-Sol.40,453(80)

Controlled Neutralization of Anions in Cryogenic Matrices by Near-Threshold Photodetachment

NASA Astrophysics Data System (ADS)

Ludwig, Ryan M.; Moore, David T.

2014-06-01

Using matrix isolation FTIR, we have observed the formation of anionic copper carbonyl complexes [Cu(CO)n]- (n=1-3) following co-deposition of Cu- and counter-cations (Ar+ or Kr+) into argon matrices doped with CO. The infrared bands have been previously assigned in argon matrix studies employing laser ablation, however they were quite weak compared to the bands for the corresponding neutral species. In the current study, when the deposition is carried out in fully darkened conditions at 10 K with high CO concentrations (1-2%), only the bands for the anionic complexes are observed initially via FTIR. However, upon mild irradiation with broadband visible light, the anionic bands are rapidly depleted, with concomitant appearance of bands corresponding to neutral copper carbonyl complexes. This photo-triggered neutralization is attributed to photodetachment of electrons from the anions, which then "flow" through the solid argon matrix to recombine in the matrix with non-adjacent trapping sites. This mechanism is supported by the appearance of a new band near 1515 wn, assigned to the (CO)2- species in argon. The wavelength dependence of the photodetachment will be discussed in detail, although preliminary indications are that the thresholds for the copper carbonyls, which are normally in the infrared, are shifted into the visible region of the spectrum in argon matrices. This likely occurs because the conduction band of solid argon is known to lie about 1 eV above the vacuum level, and thus the electron must have at least this much energy in order to escape into the matrix and find a trapping site. Funding support from NSF CAREER Award CHE-0955637 is gratefully acknowledged Ryan M. Ludwig and David T. Moore, J. Chem. Phys. 139, 244202 (2013) Zhou, M.; Andrews, L., J. Chem. Phys. 111, 4548 (1999). Thompson, W.E.; Jacox, M.E.; J. Chem. Phys. 91, 735 (1991). Stanzel, J. et al.; Collect. Czech. Chem. Comm. 72, 1 (2007). Harbich, W. et al.; Phys. Rev. B. 76, 104306 (2007).

Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential

NASA Astrophysics Data System (ADS)

Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.

1995-08-01

The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.

Symmetry investigations on the incompressible stationary axisymmetric Euler equations with swirl

NASA Astrophysics Data System (ADS)

Frewer, M.; Oberlack, M.; Guenther, S.

2007-08-01

We discuss the incompressible stationary axisymmetric Euler equations with swirl, for which we derive via a scalar stream function an equivalent representation, the Bragg-Hawthorne equation [Bragg, S.L., Hawthorne, W.R., 1950. Some exact solutions of the flow through annular cascade actuator discs. J. Aero. Sci. 17, 243]. Despite this obvious equivalence, we will show that under a local Lie point symmetry analysis the Bragg-Hawthorne equation exposes itself as not being fully equivalent to the original Euler equations. This is reflected in the way that it possesses additional symmetries not being admitted by its counterpart. In other words, a symmetry of the Bragg-Hawthorne equation is in general not a symmetry of the Euler equations. Not the differential Euler equations but rather a set of integro-differential equations attains full equivalence to the Bragg-Hawthorne equation. For these intermediate Euler equations, it is interesting to note that local symmetries of the Bragg-Hawthorne equation transform to local as well as to nonlocal symmetries. This behaviour, on the one hand, is in accordance with Zawistowski's result [Zawistowski, Z.J., 2001. Symmetries of integro-differential equations. Rep. Math. Phys. 48, 269; Zawistowski, Z.J., 2004. General criterion of invariance for integro-differential equations. Rep. Math. Phys. 54, 341] that it is possible for integro-differential equations to admit local Lie point symmetries. On the other hand, with this transformation process we collect symmetries which cannot be obtained when carrying out a usual local Lie point symmetry analysis. Finally, the symmetry classification of the Bragg-Hawthorne equation is used to find analytical solutions for the phenomenon of vortex breakdown.

From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction

NASA Astrophysics Data System (ADS)

de Tilière, Béatrice

2013-04-01

Fisher established an explicit correspondence between the 2-dimensional Ising model defined on a graph G and the dimer model defined on a decorated version {{G}} of this graph (Fisher in J Math Phys 7:1776-1781, 1966). In this paper we explicitly relate the dimer model associated to the critical Ising model and critical cycle rooted spanning forests (CRSFs). This relation is established through characteristic polynomials, whose definition only depends on the respective fundamental domains, and which encode the combinatorics of the model. We first show a matrix-tree type theorem establishing that the dimer characteristic polynomial counts CRSFs of the decorated fundamental domain {{G}_1}. Our main result consists in explicitly constructing CRSFs of {{G}_1} counted by the dimer characteristic polynomial, from CRSFs of G 1, where edges are assigned Kenyon's critical weight function (Kenyon in Invent Math 150(2):409-439, 2002); thus proving a relation on the level of configurations between two well known 2-dimensional critical models.

Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions, and transmutations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khmelnytskaya, Kira V., E-mail: khmel@uaq.edu.mx; Kravchenko, Vladislav V., E-mail: vkravchenko@math.cinvestav.edu.mx; Torba, Sergii M., E-mail: storba@math.cinvestav.edu.mx

2016-05-15

The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable, see Kravchenko and Ramirez [Adv. Appl. Cliord Algebr. 21(3), 547–559 (2011)]. Using this relation, we solve the problem of the transmission through an inhomogeneous layer of a normally incident electromagnetic time-dependent plane wave. The solution is written in terms of a pair of Darboux-associated transmutation operators [Kravchenko, V. V. and Torba, S. M., J. Phys. A: Math. Theor. 45, 075201 (2012)], and combined with the recent results on their construction [Kravchenko, V.more » V. and Torba, S. M., Complex Anal. Oper. Theory 9, 379-429 (2015); Kravchenko, V. V. and Torba, S. M., J. Comput. Appl. Math. 275, 1–26 (2015)] can be used for efficient computation of the transmitted modulated signals. We develop the corresponding numerical method and illustrate its performance with examples.« less

Quantum Error Correction for Metrology

NASA Astrophysics Data System (ADS)

Sushkov, Alex; Kessler, Eric; Lovchinsky, Igor; Lukin, Mikhail

2014-05-01

The question of the best achievable sensitivity in a quantum measurement is of great experimental relevance, and has seen a lot of attention in recent years. Recent studies [e.g., Nat. Phys. 7, 406 (2011), Nat. Comms. 3, 1063 (2012)] suggest that in most generic scenarios any potential quantum gain (e.g. through the use of entangled states) vanishes in the presence of environmental noise. To overcome these limitations, we propose and analyze a new approach to improve quantum metrology based on quantum error correction (QEC). We identify the conditions under which QEC allows one to improve the signal-to-noise ratio in quantum-limited measurements, and we demonstrate that it enables, in certain situations, Heisenberg-limited sensitivity. We discuss specific applications to nanoscale sensing using nitrogen-vacancy centers in diamond in which QEC can significantly improve the measurement sensitivity and bandwidth under realistic experimental conditions.

A large class of solvable multistate Landau–Zener models and quantum integrability

NASA Astrophysics Data System (ADS)

Chernyak, Vladimir Y.; Sinitsyn, Nikolai A.; Sun, Chen

2018-06-01

The concept of quantum integrability has been introduced recently for quantum systems with explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett. 120 190402). Within the multistate Landau–Zener (MLZ) theory, however, there has been a successful alternative approach to identify and solve complex time-dependent models (Sinitsyn and Chernyak 2017 J. Phys. A: Math. Theor. 50 255203). Here we compare both methods by applying them to a new class of exactly solvable MLZ models. This class contains systems with an arbitrary number of interacting states and shows quick growth with N number of exact adiabatic energy crossing points, which appear at different moments of time. At each N, transition probabilities in these systems can be found analytically and exactly but complexity and variety of solutions in this class also grow with N quickly. We illustrate how common features of solvable MLZ systems appear from quantum integrability and develop an approach to further classification of solvable MLZ problems.

Progress in Developing a New Field-theoretical Crossover Equation-of-State

NASA Technical Reports Server (NTRS)

Rudnick, Joseph; Barmatz, M.; Zhong, Fang

2003-01-01

A new field-theoretical crossover equation-of-state model is being developed. This model of a liquid-gas critical point provides a bridge between the asymptotic equation-of-state behavior close to the transition, obtained by the Guida and Zinn-Justin parametric model [J. Phys. A: Math. Gen. 31, 8103 (1998)], and the expected mean field behavior farther away. The crossover is based on the beta function for the renormalized fourth-order coupling constant and incorporates the correct crossover exponents and critical amplitude ratios in both regimes. A crossover model is now being developed that is consistent with predictions along the critical isochore and along the coexistence curve of the minimal subtraction renormalization approach developed by Dohm and co-workers and recently applied to the O(1) universality class [Phys. Rev. E, 67, 021106 (2003)]. Experimental measurements of the heat capacity at constant volume, isothermal susceptibility, and coexistence curve near the He-3 critical point are being compared to the predictions of this model. The results of these comparisons will be presented.

Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependence

NASA Astrophysics Data System (ADS)

Shen, Wenxian

2017-09-01

This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or almost periodic dependence as special cases. We first show the existence, uniqueness, and stability of strictly positive entire solutions of such equations. Next, we show the stability of uniformly continuous transition waves connecting the unique strictly positive entire solution and the trivial solution zero and satisfying certain decay property at the end close to the trivial solution zero (if it exists). The existence of transition waves has been studied in Liang and Zhao (2010 J. Funct. Anal. 259 857-903), Nadin (2009 J. Math. Pures Appl. 92 232-62), Nolen et al (2005 Dyn. PDE 2 1-24), Nolen and Xin (2005 Discrete Contin. Dyn. Syst. 13 1217-34) and Weinberger (2002 J. Math. Biol. 45 511-48) for random dispersal Fisher-KPP equations with time and space periodic dependence, in Nadin and Rossi (2012 J. Math. Pures Appl. 98 633-53), Nadin and Rossi (2015 Anal. PDE 8 1351-77), Nadin and Rossi (2017 Arch. Ration. Mech. Anal. 223 1239-67), Shen (2010 Trans. Am. Math. Soc. 362 5125-68), Shen (2011 J. Dynam. Differ. Equ. 23 1-44), Shen (2011 J. Appl. Anal. Comput. 1 69-93), Tao et al (2014 Nonlinearity 27 2409-16) and Zlatoš (2012 J. Math. Pures Appl. 98 89-102) for random dispersal Fisher-KPP equations with quite general time and/or space dependence, and in Coville et al (2013 Ann. Inst. Henri Poincare 30 179-223), Rawal et al (2015 Discrete Contin. Dyn. Syst. 35 1609-40) and Shen and Zhang (2012 Comm. Appl. Nonlinear Anal. 19 73-101) for nonlocal dispersal Fisher-KPP equations with time and/or space periodic dependence. The stability result established in this paper implies that the transition waves obtained in many of the above mentioned papers are asymptotically stable for well-fitted perturbation. Up to the author’s knowledge, it is the first time that the stability of transition waves of Fisher-KPP equations with general time and space dependence is studied.

Gender disparities in second-semester college physics: The incremental effects of a ``smog of bias''

NASA Astrophysics Data System (ADS)

Kost-Smith, Lauren E.; Pollock, Steven J.; Finkelstein, Noah D.

2010-07-01

Our previous research [Kost , Phys. Rev. ST Phys. Educ. Res. 5, 010101 (2009)10.1103/PhysRevSTPER.5.010101] examined gender differences in the first-semester, introductory physics class at the University of Colorado at Boulder. We found that: (1) there were gender differences in several aspects of the course, including conceptual survey performance, (2) these differences persisted despite the use of interactive engagement techniques, and (3) the post-test gender differences could largely be attributed to differences in males’ and females’ prior physics and math performance and their incoming attitudes and beliefs. In the current study, we continue to characterize gender differences in our physics courses by examining the second-semester, electricity and magnetism course. We analyze three factors: student retention from Physics 1 to Physics 2, student performance, and students’ attitudes and beliefs about physics, and find gender differences in all three of these areas. Specifically, females are less likely to stay in the physics major than males. Despite males and females performing about equally on the conceptual pretest, we find that females score about 6 percentage points lower than males on the conceptual post-test. In most semesters, females outperform males on homework and participation, and males outperform females on exams, resulting in course grades of males and females that are not significantly different. In terms of students’ attitudes and beliefs, we find that both males and females shift toward less expertlike beliefs over the course of Physics 2. Shifts are statistically equal for all categories except for the Personal Interest category, where females have more negative shifts than males. A large fraction of the conceptual post-test gender gap (up to 60%) can be accounted for by differences in males’ and females’ prior physics and math performance and their pre-Physics 2 attitudes and beliefs. Taken together, the results of this study suggest that it is an accumulation of small gender differences over time that may be responsible for the large differences that we observe in physics participation of males and females.

The Parisi Formula has a Unique Minimizer

NASA Astrophysics Data System (ADS)

Auffinger, Antonio; Chen, Wei-Kuo

2015-05-01

In 1979, Parisi (Phys Rev Lett 43:1754-1756, 1979) predicted a variational formula for the thermodynamic limit of the free energy in the Sherrington-Kirkpatrick model, and described the role played by its minimizer. This formula was verified in the seminal work of Talagrand (Ann Math 163(1):221-263, 2006) and later generalized to the mixed p-spin models by Panchenko (Ann Probab 42(3):946-958, 2014). In this paper, we prove that the minimizer in Parisi's formula is unique at any temperature and external field by establishing the strict convexity of the Parisi functional.

Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures

NASA Astrophysics Data System (ADS)

Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell

2017-06-01

We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C* algebra framework introduced by Bellissard and collaborators [Coherent and Dissipative Transport in Aperiodic Solids, Lecture Notes in Physics (Springer, 2003), Vol. 597, pp. 413-486 and J. Math. Phys. 35(10), 5373-5451 (1994)] to study aperiodic solids (disordered crystals, quasicrystals, and amorphous materials), notably in the presence of magnetic fields (quantum Hall effect). We also present numerical approximations and test our methods on a one-dimensional incommensurate bilayer system.

Moduli of quantum Riemannian geometries on <=4 points

NASA Astrophysics Data System (ADS)

Majid, S.; Raineri, E.

2004-12-01

We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously [S. Majid, Commun. Math. Phys. 225, 131 (2002)]. The full moduli space is found for ⩽3 points, and a restricted moduli space for 4 points. Generalized Levi-Cività connections and their curvatures are found for a variety of models including models of a discrete torus. The topological part of the moduli space is found for ⩽9 points based on the known atlas of regular graphs. We also remark on aspects of quantum gravity in this approach.

Coherent attack on oblivious transfer based on single-qubit rotations

NASA Astrophysics Data System (ADS)

He, Guang Ping

2018-04-01

Recently a bit-string quantum oblivious transfer (OT) protocol based on single-qubit rotations was proposed (Rodrigues et al 2017 J. Phys. A: Math. Theor. 50 205301) and proven secure against few-qubit measurements. However, it was left as an open question whether the protocol remains secure against general attacks. Here, we close the gap by showing that if the receiver Bob can perform collective measurements on all qubits, then he can learn Alice’s secret message with a probability close to one. Thus the protocol fails to meet the security criterion of OT.

Faithful actions of locally compact quantum groups on classical spaces

NASA Astrophysics Data System (ADS)

Goswami, Debashish; Roy, Sutanu

2017-07-01

We construct examples of locally compact quantum groups coming from bicrossed product construction, including non-Kac ones, which can faithfully and ergodically act on connected classical (noncompact) smooth manifolds. However, none of these actions can be isometric in the sense of Goswami (Commun Math Phys 285(1):141-160, 2009), leading to the conjecture that the result obtained by Goswami and Joardar (Rigidity of action of compact quantum groups on compact, connected manifolds, 2013. arXiv:1309.1294) about nonexistence of genuine quantum isometry of classical compact connected Riemannian manifolds may hold in the noncompact case as well.

The Stratonovich formulation of quantum feedback network rules

NASA Astrophysics Data System (ADS)

Gough, John E.

2016-12-01

We express the rules for forming quantum feedback networks using the Stratonovich form of quantum stochastic calculus rather than the Itō or SLH (J. E. Gough and M. R. James, "Quantum feedback networks: Hamiltonian formulation," Commun. Math. Phys. 287, 1109 (2009), J. E. Gough and M. R. James, "The Series product and its application to quantum feedforward and feedback networks," IEEE Trans. Autom. Control 54, 2530 (2009)) form. Remarkably the feedback reduction rule implies that we obtain the Schur complement of the matrix of Stratonovich coupling operators where we short out the internal input/output coefficients.

Comment on ‘Special-case closed form of the Baker-Campbell-Hausdorff formula’

NASA Astrophysics Data System (ADS)

Lo, C. F.

2016-05-01

Recently Van-Brunt and Visser (2015 J. Phys. A: Math. Theor. 48 225207) succeeded in explicitly evaluating the Baker-Campbell-Hausdorff (BCH) expansion series for the noncommuting operators X and Y, provided that the two operators satisfy the commutation relation: [X,Y]={uX}+{vY}+{cI}, and the operator I commutes with both of them. In this comment we show that the closed-form BCH formula of this special case can be straightforwardly derived by the means of the Wei-Norman theorem and no summation of the infinite series is needed.

f1: a code to compute Appell's F1 hypergeometric function

NASA Astrophysics Data System (ADS)

Colavecchia, F. D.; Gasaneo, G.

2004-02-01

In this work we present the FORTRAN code to compute the hypergeometric function F1( α, β1, β2, γ, x, y) of Appell. The program can compute the F1 function for real values of the variables { x, y}, and complex values of the parameters { α, β1, β2, γ}. The code uses different strategies to calculate the function according to the ideas outlined in [F.D. Colavecchia et al., Comput. Phys. Comm. 138 (1) (2001) 29]. Program summaryTitle of the program: f1 Catalogue identifier: ADSJ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSJ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computers: PC compatibles, SGI Origin2∗ Operating system under which the program has been tested: Linux, IRIX Programming language used: Fortran 90 Memory required to execute with typical data: 4 kbytes No. of bits in a word: 32 No. of bytes in distributed program, including test data, etc.: 52 325 Distribution format: tar gzip file External subprograms used: Numerical Recipes hypgeo [W.H. Press et al., Numerical Recipes in Fortran 77, Cambridge Univ. Press, 1996] or chyp routine of R.C. Forrey [J. Comput. Phys. 137 (1997) 79], rkf45 [L.F. Shampine and H.H. Watts, Rep. SAND76-0585, 1976]. Keywords: Numerical methods, special functions, hypergeometric functions, Appell functions, Gauss function Nature of the physical problem: Computing the Appell F1 function is relevant in atomic collisions and elementary particle physics. It is usually the result of multidimensional integrals involving Coulomb continuum states. Method of solution: The F1 function has a convergent-series definition for | x|<1 and | y|<1, and several analytic continuations for other regions of the variable space. The code tests the values of the variables and selects one of the precedent cases. In the convergence region the program uses the series definition near the origin of coordinates, and a numerical integration of the third-order differential parametric equation for the F1 function. Also detects several special cases according to the values of the parameters. Restrictions on the complexity of the problem: The code is restricted to real values of the variables { x, y}. Also, there are some parameter domains that are not covered. These usually imply differences between integer parameters that lead to negative integer arguments of Gamma functions. Typical running time: Depends basically on the variables. The computation of Table 4 of [F.D. Colavecchia et al., Comput. Phys. Comm. 138 (1) (2001) 29] (64 functions) requires approximately 0.33 s in a Athlon 900 MHz processor.

Scalable algorithms for 3D extended MHD.

NASA Astrophysics Data System (ADS)

Chacon, Luis

2007-11-01

In the modeling of plasmas with extended MHD (XMHD), the challenge is to resolve long time scales while rendering the whole simulation manageable. In XMHD, this is particularly difficult because fast (dispersive) waves are supported, resulting in a very stiff set of PDEs. In explicit schemes, such stiffness results in stringent numerical stability time-step constraints, rendering them inefficient and algorithmically unscalable. In implicit schemes, it yields very ill-conditioned algebraic systems, which are difficult to invert. In this talk, we present recent theoretical and computational progress that demonstrate a scalable 3D XMHD solver (i.e., CPU ˜N, with N the number of degrees of freedom). The approach is based on Newton-Krylov methods, which are preconditioned for efficiency. The preconditioning stage admits suitable approximations without compromising the quality of the overall solution. In this work, we employ optimal (CPU ˜N) multilevel methods on a parabolized XMHD formulation, which renders the whole algorithm scalable. The (crucial) parabolization step is required to render XMHD multilevel-friendly. Algebraically, the parabolization step can be interpreted as a Schur factorization of the Jacobian matrix, thereby providing a solid foundation for the current (and future extensions of the) approach. We will build towards 3D extended MHDootnotetextL. Chac'on, Comput. Phys. Comm., 163 (3), 143-171 (2004)^,ootnotetextL. Chac'on et al., 33rd EPS Conf. Plasma Physics, Rome, Italy, 2006 by discussing earlier algorithmic breakthroughs in 2D reduced MHDootnotetextL. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) and 2D Hall MHD.ootnotetextL. Chac'on et al., J. Comput. Phys., 188 (2), 573-592 (2003)

Time-reversal symmetry in nonstationary Markov processes with application to some fluctuation theorems

NASA Astrophysics Data System (ADS)

Van Vliet, Carolyne M.

2012-11-01

Nonequilibrium processes require that the density operator of an interacting system with Hamiltonian H(t)=H0(t)+λV converges and produces entropy. Employing projection operators in the state space, the density operator is developed to all orders of perturbation and then resummed. In contrast to earlier treatments by Van Hove [Physica0031-891410.1016/S0031-8914(54)92646-4 21, 517 (1955)] and others [U. Fano, Rev. Mod. Phys.0034-686110.1103/RevModPhys.29.74 29, 74 (1959); U. Fano, in Lectures on the Many-Body Problem, Vol 2, edited by E. R. Caniello (Academic Press, New York, 1964); R. Zwanzig, in Lectures in Theoretical Physics, Vol. III, edited by W. E. Britten, B. W. Downs, and J. Downs (Wiley Interscience, New York, 1961), pp. 116-141; K. M. Van Vliet, J. Math. Phys.0022-248810.1063/1.523833 19, 1345 (1978); K. M. Van Vliet, Can. J. Phys. 56, 1206 (1978)], closed expressions are obtained. From these we establish the time-reversal symmetry property P(γ,t|γ',t')=P˜(γ',t'|γ,t), where the tilde refers to the time-reversed protocol; also a nonstationary Markovian master equation is derived. Time-reversal symmetry is then applied to thermostatted systems yielding the Crooks-Tasaki fluctuation theorem (FT) and the quantum Jarzynski work-energy theorem, as well as the general entropy FT. The quantum mechanical concepts of work and entropy are discussed in detail. Finally, we present a nonequilibrium extension of Mazo's lemma of linear response theory, obtaining some applications via this alternate route.

Generalized spheroidal wave equation and limiting cases

NASA Astrophysics Data System (ADS)

Figueiredo, B. D. Bonorino

2007-01-01

We find sets of solutions to the generalized spheroidal wave equation (GSWE) or, equivalently, to the confluent Heun equation. Each set is constituted by three solutions, one given by a series of ascending powers of the independent variable, and the others by series of regular and irregular confluent hypergeometric functions. For a fixed set, the solutions converge over different regions of the complex plane but present series coefficients proportional to each other. These solutions for the GSWE afford solutions to a double-confluent Heun equation by a taking-limit process due to Leaver. [E. W. Leaver, J. Math. Phys. 27, 1238 (1986)]. Another procedure, called Whittaker-Ince limit [B. D. Figueiredo, J. Math. Phys. 46, 113503 (2005)], provides solutions in series of powers and Bessel functions for two other equations with a different type of singularity at infinity. In addition, new solutions are obtained for the Whittaker-Hill and Mathieu equations [F. M. Arscott, Proc. R. Soc. Edinburg A67, 265 (1967)] by considering these as special cases of both the confluent and double-confluent Heun equations. In particular, we find that each of the Lindemann-Stieltjes solutions for the Mathieu equation [E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press (1945)] is associated with two expansions in series of Bessel functions. We also discuss a set of solutions in series of hypergeometric and confluent hypergeometric functions for the GSWE and use their Leaver limits to obtain infinite-series solutions for the Schrödinger equation with an asymmetric double-Morse potential. Finally, the possibility of extending the solutions of the GSWE to the general Heun equation is briefly discussed.

On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains

NASA Astrophysics Data System (ADS)

Li, Siran

2017-10-01

In this paper we consider the one-dimensional Navier-Stokes system for a heat-conducting, compressible reacting mixture which describes the dynamic combustion of fluids of mixed kinds on unbounded domains. This model has been discussed on bounded domains by Chen (SIAM J Math Anal 23:609-634, 1992) and Chen-Hoff-Trivisa (Arch Ration Mech Anal 166:321-358, 2003), among others, in which the reaction rate function is a discontinuous function obeying the Arrhenius' law of thermodynamics. We prove the global existence of weak solutions to this model on one-dimensional unbounded domains with large initial data in H^1. Moreover, the large-time behaviour of the weak solution is identified. In particular, the uniform-in-time bounds for the temperature and specific volume have been established via energy estimates. For this purpose we utilise techniques developed by Kazhikhov-Shelukhin (cf. Kazhikhov in Siber Math J 23:44-49, 1982; Solonnikov and Kazhikhov in Annu Rev Fluid Mech 13:79-95, 1981) and refined by Jiang (Commun Math Phys 200:181-193, 1999, Proc R Soc Edinb Sect A 132:627-638, 2002), as well as a crucial estimate in the recent work by Li-Liang (Arch Ration Mech Anal 220:1195-1208, 2016). Several new estimates are also established, in order to treat the unbounded domain and the reacting terms.

Scanned gate microscopy of inter-edge channel scattering in the quantum Hall regime

NASA Astrophysics Data System (ADS)

Woodside, Michael T.; Vale, Chris; McEuen, Paul L.; Kadow, C.; Maranowski, K. D.; Gossard, A. C.

2000-03-01

Novel scanned probe techniques have recently been used to study in detail the microscopic properties of 2D electron gases in the quantum Hall regime [1]. We report local measurements of the scattering between edge states in a quantum Hall conductor with non-equilibrium edge state populations. Using an atomic force microscope (AFM) tip as a local gate to perturb the edge states, we find that the scattering is dominated by individual, microscopic scattering sites, which we directly image and characterise. The dependence of the scattering on the AFM tip voltage reveals that it involves tunneling both through quasi-bound impurity states and through disorder-induced weak links between the edge states. [1] S. H. Tessmer et al., Nature 392, 51 (1998); K. L. McCormick et al., Phys. Rev. B 59, 4654 (1999); A. Yacoby et al., Solid State Comm. 111, 1 (1999).

1 D analysis of Radiative Shock damping by lateral radiative losses.

NASA Astrophysics Data System (ADS)

Busquet, Michel; Colombier, Jean-Philippe; Stehle, Chantal

2007-11-01

It has been shown theoretically and experimentally [1] that the radiative precursor in front of a strong shock in hi-Z material is slowed down by lateral radiative losses. The 2D simulation showed that the shock front and the precursor front remain planar, with an increase of density and a decrease of temperature close to the walls. The damping of the precursor is obviously sensitive to the fraction of self-emitted radiation reflected by the walls (the albedo). In order to perform parametric studies we include the albedo controlled lateral radiative losses in the 1D hydro-code MULTI (created by Ramis et al [2]) both in terms of energy balance and of spectral diagnostic. [1] Gonzales et al, Laser Part. Beams 24, 1-6 (2006) ; Busquet et al, High Energy Density Physics (2007), doi: 10.1016/j.hedp.2007.01.002 [2] Ramis et al, Comp. Phys. Comm., 49 (1988), 475

Exploring New Phenomena in Salty Water Under Planetary Conditions

NASA Astrophysics Data System (ADS)

Goncharov, A. F.; Bove, L. E.; Klotz, S.; Gaal, R.; Saitta, A. M.; Gillet, P.

2015-12-01

Compressed water is overspread on Earth at depth and in the extra-terrestrial space, both interstellar and on outer planets and moons (ice bodies) [1]. Under the conditions experienced in these celestial bodies water displays an incredibly rich phase diagram, including sixteen known crystalline phases, three amorphous ones, and predicted exotic properties like plasticity [2], ionization [3], and superionicity [4]. In this talk I will review our recent experimental results on salty (LiCl, NaCl, MgCl2) water under extreme conditions including: plasticity [5], pressure-induced polyamorphism [6], salty ice crystallization under high pressure [7], and hydrogen bond symmetrisation at Mbar pressures [8]. [1] De Pater, I., and Lissauer, J.J. Planetary Sciences. Cambridge University Press (2004). [2] Wang, Y., Liu, H., et al. Nat. Comm. 563 1566 (2011).[3] Aragones, L., and Vega, C., J. Chem. Phys. 130, 244504 (2009).[4] Cavazzoni, C., et al., Science 283, 44-46 (1999).[5] Bove, L. E., Dreyfus, C. et al., JCP 139, 044501 (2013) ; Ruiz, G. N., Bove, L. E. et al., PCCP 16 18553-18562 (2014).[6] Bove, L. E., Klotz, S. et al., Phys. Rev. Lett. 106, 125701 (2011); Ludl, A. A., Bove, L. E. et al., PCCP 17, 14054 (2015). [7] Klotz, S., Bove, L. E. t al., Nat. Mat. 8, 405 (2009) ; Ludl A. A., Bove, L. E., submitted (2015).[8] Bove L. E. , Gaal, R. et al., PNAS 112, 27 (2015).

More N =4 superconformal bootstrap

NASA Astrophysics Data System (ADS)

Beem, Christopher; Rastelli, Leonardo; van Rees, Balt C.

2017-08-01

In this long overdue second installment, we continue to develop the conformal bootstrap program for N =4 superconformal field theories (SCFTs) in four dimensions via an analysis of the correlation function of four stress-tensor supermultiplets. We review analytic results for this correlator and make contact with the SCFT/chiral algebra correspondence of Beem et al. [Commun. Math. Phys. 336, 1359 (2015), 10.1007/s00220-014-2272-x]. We demonstrate that the constraints of unitarity and crossing symmetry require the central charge c to be greater than or equal to 3 /4 in any interacting N =4 SCFT. We apply numerical bootstrap methods to derive upper bounds on scaling dimensions and operator product expansion coefficients for several low-lying, unprotected operators as a function of the central charge. We interpret our bounds in the context of N =4 super Yang-Mills theories, formulating a series of conjectures regarding the embedding of the conformal manifold—parametrized by the complexified gauge coupling—into the space of scaling dimensions and operator product expansion coefficients. Our conjectures assign a distinguished role to points on the conformal manifold that are self-dual under a subgroup of the S -duality group. This paper contains a more detailed exposition of a number of results previously reported in Beem et al. [Phys. Rev. Lett. 111, 071601 (2013), 10.1103/PhysRevLett.111.071601] in addition to new results.

Spontaneous collapse: A solution to the measurement problem and a source of the decay in mesonic systems

NASA Astrophysics Data System (ADS)

Simonov, Kyrylo; Hiesmayr, Beatrix C.

2016-11-01

Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor-oscillating neutral mesons for the two most promising collapse models, the QMUPL (quantum mechanics with universal position localization) model and the mass-proportional CSL (continuous spontaneous localization) model. Our results are showing (i) a strong sensitivity to the very assumptions of the noise field underlying those two collapse models and (ii) under particular assumptions the CSL case allows one even to recover the decay dynamics. This in turn allows one to predict the effective collapse rates solely based on the measured values for the oscillation (mass differences) and the measured values of the decay constants. The four types of neutral mesons (K meson, D meson, Bd meson, and Bs meson) lead surprisingly to ranges comparable to those put forward by Adler [J. Phys. A: Math. Theor. 40, 2935 (2007), 10.1088/1751-8113/40/12/S03] and Ghirardi, Rimini, and Weber [Phys. Rev. D 34, 470 (1986), 10.1103/PhysRevD.34.470]. Our results show that these systems at high energies are very sensitive to possible modifications of the standard quantum theory, making them a very powerful laboratory to rule out certain collapse scenarios and study the detailed physical processes solving the measurement problem.

A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields

NASA Astrophysics Data System (ADS)

Benguria, R. D.; Van Den Bosch, H.

2015-05-01

We consider the Pauli operator in ℝ3 for magnetic fields in L3/2 that decay at infinity as |x|-2-β with β > 0. In this case, we are able to prove that the existence of a zero mode for this operator is equivalent to a quantity δ(B), defined below, being equal to zero. Complementing a result from Balinsky et al. [J. Phys. A: Math. Gen. 34, L19-L23 (2001)], this implies that for the class of magnetic fields considered, Sobolev, Hardy, and Cwikel, Lieb, Rosenblum (CLR) inequalities hold whenever the magnetic field has no zero mode.

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

NASA Astrophysics Data System (ADS)

Leonenko, N. N.; Ruiz-Medina, M. D.

2006-07-01

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

Use or Reduction of Propagation and Noise Effects in Distributed Military Systems: Electromagnetic Wave Propagation Panel Symposium Held in Rethymno, Crete, Greece on 15-18 October 1990 (Utilisation ou Reduction des Effets de la Propagation et du Bruit dans les Systemes Militaires Distribues)

DTIC Science & Technology

1991-06-01

resolution are essential. The resulting frequency Paul A K., Anharmonic Frequency Analysis, pattern would be nonuniform and would change Mati. Comp...veloppement laire donnte par Ia relation empiri- de la trainte ainsi que Ie mouvemnent des par que 1231 ticules neutres dans Ia haute atmosph~re. log D...1515, 1973b. Bahar, E., Depolarization in nonuniform multi- layered structures--Full wave solutions, J. Math. Phys,, 15(2), 202-208, 1974, Ba , and M

Long-time asymptotic analysis of the Korteweg-de Vries equation via the dbar steepest descent method: the soliton region

NASA Astrophysics Data System (ADS)

Giavedoni, Pietro

2017-03-01

We address the problem of long-time asymptotics for the solutions of the Korteweg-de Vries equation under low regularity assumptions. We consider decaying initial data admitting only a finite number of moments. For the so-called ‘soliton region’, an improved asymptotic estimate is provided, in comparison with the one in Grunert and Teschl (2009 Math. Phys. Anal. Geom. 12 287-324). Our analysis is based on the dbar steepest descent method proposed by Miller and McLaughlin. Dedicated to Dora, Paolo and Sanja, with deep gratitude for their love and support.

Exotic equilibria of Harary graphs and a new minimum degree lower bound for synchronization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Canale, Eduardo A., E-mail: ecanale@pol.una.py; Monzón, Pablo, E-mail: monzon@fing.edu.uy

2015-02-15

This work is concerned with stability of equilibria in the homogeneous (equal frequencies) Kuramoto model of weakly coupled oscillators. In 2012 [R. Taylor, J. Phys. A: Math. Theor. 45, 1–15 (2012)], a sufficient condition for almost global synchronization was found in terms of the minimum degree–order ratio of the graph. In this work, a new lower bound for this ratio is given. The improvement is achieved by a concrete infinite sequence of regular graphs. Besides, non standard unstable equilibria of the graphs studied in Wiley et al. [Chaos 16, 015103 (2006)] are shown to exist as conjectured in that work.

Exponential stabilization of magnetoelastic waves in a Mindlin-Timoshenko plate by localized internal damping

NASA Astrophysics Data System (ADS)

Grobbelaar-Van Dalsen, Marié

2015-08-01

This article is a continuation of our earlier work in Grobbelaar-Van Dalsen (Z Angew Math Phys 63:1047-1065, 2012) on the polynomial stabilization of a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. We introduce nonlinear damping that is effective only in a small portion of the interior of the plate. It turns out that the model is uniformly exponentially stable when the function , that represents the locally distributed damping, behaves linearly near the origin. However, the use of Mindlin-Timoshenko plate theory in the model enforces a restriction on the region occupied by the plate.

The Multi-Orientable Random Tensor Model, a Review

NASA Astrophysics Data System (ADS)

Tanasa, Adrian

2016-06-01

After its introduction (initially within a group field theory framework) in [Tanasa A., J. Phys. A: Math. Theor. 45 (2012), 165401, 19 pages, arXiv:1109.0694], the multi-orientable (MO) tensor model grew over the last years into a solid alternative of the celebrated colored (and colored-like) random tensor model. In this paper we review the most important results of the study of this MO model: the implementation of the 1/N expansion and of the large N limit (N being the size of the tensor), the combinatorial analysis of the various terms of this expansion and finally, the recent implementation of a double scaling limit.

Global and Local Existence for the Dissipative Critical SQG Equation with Small Oscillations

NASA Astrophysics Data System (ADS)

Lazar, Omar

2015-09-01

This article is devoted to the study of the critical dissipative surface quasi-geostrophic ( SQG) equation in . For any initial data belonging to the space , we show that the critical (SQG) equation has at least one global weak solution in time for all 1/4 ≤ s ≤ 1/2 and at least one local weak solution in time for all 0 < s < 1/4. The proof for the global existence is based on a new energy inequality which improves the one obtain in Lazar (Commun Math Phys 322:73-93, 2013) whereas the local existence uses more refined energy estimates based on Besov space techniques.

Quantum turing machine and brain model represented by Fock space

NASA Astrophysics Data System (ADS)

Iriyama, Satoshi; Ohya, Masanori

2016-05-01

The adaptive dynamics is known as a new mathematics to treat with a complex phenomena, for example, chaos, quantum algorithm and psychological phenomena. In this paper, we briefly review the notion of the adaptive dynamics, and explain the definition of the generalized Turing machine (GTM) and recognition process represented by the Fock space. Moreover, we show that there exists the quantum channel which is described by the GKSL master equation to achieve the Chaos Amplifier used in [M. Ohya and I. V. Volovich, J. Opt. B 5(6) (2003) 639., M. Ohya and I. V. Volovich, Rep. Math. Phys. 52(1) (2003) 25.

NP-hardness of the cluster minimization problem revisited

NASA Astrophysics Data System (ADS)

Adib, Artur B.

2005-10-01

The computational complexity of the 'cluster minimization problem' is revisited (Wille and Vennik 1985 J. Phys. A: Math. Gen. 18 L419). It is argued that the original NP-hardness proof does not apply to pairwise potentials of physical interest, such as those that depend on the geometric distance between the particles. A geometric analogue of the original problem is formulated, and a new proof for such potentials is provided by polynomial time transformation from the independent set problem for unit disk graphs. Limitations of this formulation are pointed out, and new subproblems that bear more direct consequences to the numerical study of clusters are suggested.

Origin of families of fermions and their mass matrices

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bracic, A. Borstnik; Borstnik, N. S. Mankoc; Department of Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana

We are proposing a new way of describing families of quarks and leptons, using the approach unifying all the internal degrees of freedom, proposed by one of us [N. Mankoc Borstnik, Phys. Lett. B 292, 25 (1992).][N. Mankoc-Borstnik, J. Math. Phys. (N.Y.) 34, 3731 (1993).][N. Mankoc Borstnik, J. Math. Phys. (N.Y.) 36, 1593 (1995).][N. S. Mankoc Borstnik, Mod. Phys. Lett. A 10, 587 (1995).][N. S. Mankoc Borstnik and S. Fajfer, Nuovo Cimento Soc. Ital. Fis. B 112, 1637 (1997).][A. Borstnik and N. S. Mankoc Borstnik, in Proceedings to the International Workshop on ''What Comes Beyond the Standard Model, Bled, Slovenia,more » 1998, edited by N. Mankoc Borstnik, H. B. Nielsen, and C. Froggatt (DMFA, Zaloznistvo, 1999), p. 52.][N. S. Mankoc Borstnik and H. B. Nielsen, Phys. Rev. 62, 04010 (2000).][N. S. Mankoc Borstnik, Int. J. Theor. Phys. 40, 315 (2001), and references therein.][A. Borstnik and N. S. Mankoc Borstnik, in Proceedings to the International Workshop on ''What Comes Beyond the Standard Model'', Bled 2000, 2001, 2002 Volume 2, edited by N. Mankoc Borstnik, H. B. Nielsen, C. Froggatt, and D. Lukman (DMFA, Zaloznistvo, 2002), p. 27 and the paper (unpublished).][A. Borstnik and N. S. Mankoc Borstnik, in Proceedings to the Euroconference on Symmetries Beyond the Standard Model, Portoroz, 2003 edited by N. Mankoc Borstnik, H. B. Nielsen, C. Froggatt, and D. Lukman (DMFA, Zaloznistvo, 2003), pp. 27-51.]. Spinors, living in d(=1+13)-dimensional space, carry in this approach only the spin and interact with only the gravity through vielbeins and two kinds of the spin connection fields--the gauge fields of the Poincare group (p{sup a},S{sup ab}) and the second kind of the Clifford algebra objects (S-tilde{sup ab}). All the quarks and the leptons of one family appear in one Weyl representation of a chosen handedness of the Lorentz group, if analyzed with respect to the standard model gauge groups, which are subgroups of the group SO(1,13): the right handed (with respect to SO(1,3)) weak chargeless quarks and leptons and the left handed weak charged quarks and leptons (with the right handed neutrino included). A part of the starting Lagrange density of a Weyl spinor in d=1+13 transforms right handed quarks and leptons into left handed quarks and leptons manifesting as the Yukawa couplings of the standard model. A kind of the Clifford algebra objects generates families of quarks and leptons and contributes to diagonal and off-diagonal Yukawa couplings. The approach predicts an even number of families, treating leptons and quarks equivalently (we do not study a possible appearance of Majorana fermions yet). In this paper we investigate within this approach the appearance of the Yukawa couplings within one family of quarks and leptons as well as among the families (without assuming any Higgs fields like in the standard model). We present the mass matrices for four families and investigate whether our way of generating families might explain the origin of families of quarks and leptons as well as their observed properties--the masses and the mixing matrices. Numerical results are presented in Ref. [M. Breskvar, D. Lukman, and N. S. Mankoc Borstnik, hep-ph/0606159.].« less

On the equilibrium state of a small system with random matrix coupling to its environment

NASA Astrophysics Data System (ADS)

Lebowitz, J. L.; Pastur, L.

2015-07-01

We consider a random matrix model of interaction between a small n-level system, S, and its environment, a N-level heat reservoir, R. The interaction between S and R is modeled by a tensor product of a fixed n× n matrix and a N× N Hermitian random matrix. We show that under certain ‘macroscopicity’ conditions on R, the reduced density matrix of the system {{ρ }S}=T{{r}R}ρ S\\cup R(eq), is given by ρ S(c)˜ exp \\{-β {{H}S}\\}, where HS is the Hamiltonian of the isolated system. This holds for all strengths of the interaction and thus gives some justification for using ρ S(c) to describe some nano-systems, like biopolymers, in equilibrium with their environment (Seifert 2012 Rep. Prog. Phys. 75 126001). Our results extend those obtained previously in (Lebowitz and Pastur 2004 J. Phys. A: Math. Gen. 37 1517-34) (Lebowitz et al 2007 Contemporary Mathematics (Providence RI: American Mathematical Society) pp 199-218) for a special two-level system.

Bounds on Herglotz functions and fundamental limits of broadband passive quasistatic cloaking

NASA Astrophysics Data System (ADS)

Cassier, Maxence; Milton, Graeme W.

2017-07-01

Using a sum rule, we derive new bounds on Herglotz functions that generalize those given in Bernland et al. [J. Phys. A: Math. Theor. 44(14), 145205 (2011)] and Gustafsson and Sjöberg [New J. Phys. 12(4), 043046 (2010)]. These bounds apply to a wide class of linear passive systems such as electromagnetic passive materials. Among these bounds, we describe the optimal ones and also discuss their meaning in various physical situations like in the case of a transparency window, where we exhibit sharp bounds. Then, we apply these bounds in the context of broadband passive cloaking in the quasistatic regime to refute the following challenging question: is it possible to construct a passive cloaking device that cloaks an object over a whole frequency band? Our rigorous approach, although limited to quasistatics, gives quantitative limitations on the cloaking effect over a finite frequency range by providing inequalities on the polarizability tensor associated with the cloaking device. We emphasize that our results hold for a cloak or object of any geometrical shape.

Minimizing irreversible losses in quantum systems by local counterdiabatic driving

PubMed Central

Sels, Dries; Polkovnikov, Anatoli

2017-01-01

Counterdiabatic driving protocols have been proposed [Demirplak M, Rice SA (2003) J Chem Phys A 107:9937–9945; Berry M (2009) J Phys A Math Theor 42:365303] as a means to make fast changes in the Hamiltonian without exciting transitions. Such driving in principle allows one to realize arbitrarily fast annealing protocols or implement fast dissipationless driving, circumventing standard adiabatic limitations requiring infinitesimally slow rates. These ideas were tested and used both experimentally and theoretically in small systems, but in larger chaotic systems, it is known that exact counterdiabatic protocols do not exist. In this work, we develop a simple variational approach allowing one to find the best possible counterdiabatic protocols given physical constraints, like locality. These protocols are easy to derive and implement both experimentally and numerically. We show that, using these approximate protocols, one can drastically suppress heating and increase fidelity of quantum annealing protocols in complex many-particle systems. In the fast limit, these protocols provide an effective dual description of adiabatic dynamics, where the coupling constant plays the role of time and the counterdiabatic term plays the role of the Hamiltonian. PMID:28461472

A non-Hermitian analysis of strongly correlated quantum systems

NASA Astrophysics Data System (ADS)

Nakamura, Yuichi; Hatano, Naomichi

2006-03-01

We study a non-Hermitian generalization of strongly correlated quantum systems in which the transfer energy of electrons is asymmetric. Hatano and Nelson[1] applied this technique to non-interacting random electron systems. They related a non-Hermitian critical point to the inverse localization length of the Hermitian systems. We here conjecture that we can obtain in the same way the correlation length of Hermitian interacting non-random systems[2]. We show for the Hubbard model and the antiferromagnetic XXZ model in one dimension that the non-Hermitian critical point of the ground state, where the energy gap vanishes, is equal to the inverse correlation length. We also show that the conjecture is consistent with numerical results for S=1/2 frustrated quantum spin chains with the nearest- and next-nearest-neighbor interactions including the Majumdar-Ghosh model[3]. [1] N. Hatano and D. R. Nelson, PRL 77 (1996) 570; PRB 56 (1997) 8651. [2] Y. Nakamura and N. Hatano, Physica B, accepted. [3] C. K. Majumdar and D. K. Ghosh, J. Phys. C3 (1970) 911; J. Math. Phys. 10 (1969) 1388, 1399.

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs

NASA Astrophysics Data System (ADS)

Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin

2018-05-01

It is generally argued that the solution to a stochastic PDE with multiplicative noise—such as \\dot{u}= 1/2 u''+uξ, where {ξ} denotes space-time white noise—routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.

Smoothing of Transport Plans with Fixed Marginals and Rigorous Semiclassical Limit of the Hohenberg-Kohn Functional

NASA Astrophysics Data System (ADS)

Cotar, Codina; Friesecke, Gero; Klüppelberg, Claudia

2018-06-01

We prove rigorously that the exact N-electron Hohenberg-Kohn density functional converges in the strongly interacting limit to the strictly correlated electrons (SCE) functional, and that the absolute value squared of the associated constrained search wavefunction tends weakly in the sense of probability measures to a minimizer of the multi-marginal optimal transport problem with Coulomb cost associated to the SCE functional. This extends our previous work for N = 2 ( Cotar etal. in Commun Pure Appl Math 66:548-599, 2013). The correct limit problem has been derived in the physics literature by Seidl (Phys Rev A 60 4387-4395, 1999) and Seidl, Gorigiorgi and Savin (Phys Rev A 75:042511 1-12, 2007); in these papers the lack of a rigorous proofwas pointed out.We also give amathematical counterexample to this type of result, by replacing the constraint of given one-body density—an infinite dimensional quadratic expression in the wavefunction—by an infinite-dimensional quadratic expression in the wavefunction and its gradient. Connections with the Lawrentiev phenomenon in the calculus of variations are indicated.

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs

NASA Astrophysics Data System (ADS)

Khoshnevisan, Davar; Kim, Kunwoo; Xiao, Yimin

2018-04-01

It is generally argued that the solution to a stochastic PDE with multiplicative noise—such as \\dot{u}= 1/2 u''+uξ, where {ξ} denotes space-time white noise—routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.

The Role of Scientific Communication Skills in Trainees' Intention to Pursue Biomedical Research Careers: A Social Cognitive Analysis.

PubMed

Cameron, Carrie; Lee, Hwa Young; Anderson, Cheryl; Byars-Winston, Angela; Baldwin, Constance D; Chang, Shine

2015-01-01

Scientific communication (SciComm) skills are indispensable for success in biomedical research, but many trainees may not have fully considered the necessity of regular writing and speaking for research career progression. Our purpose was to investigate the relationship between SciComm skill acquisition and research trainees' intentions to remain in research careers. We used social cognitive career theory (SCCT) to test a model of the relationship of SciComm skills to SciComm-related cognitive variables in explaining career intentions. A sample of 510 graduate students and postdoctoral fellows at major academic health science centers in the Texas Medical Center, Houston, Texas, were surveyed online. Results suggested that interest in performing SciComm tasks, SciComm outcome expectations (SCOEs), and SciComm productivity predicted intention to remain in a research career, while SciComm self-efficacy did not directly predict career intention. SCOEs also predicted interest in performing SciComm tasks. As in other SCCT studies, SciComm self-efficacy predicted SCOEs. We conclude that social cognitive factors of SciComm skill acquisition and SciComm productivity significantly predict biomedical trainees' intentions to pursue research careers whether within or outside academia. While further studies are needed, these findings may lead to evidence-based interventions to help trainees remain in their chosen career paths. © 2015 C. Cameron et al. CBE—Life Sciences Education © 2015 The American Society for Cell Biology. This article is distributed by The American Society for Cell Biology under license from the author(s). It is available to the public under an Attribution–Noncommercial–Share Alike 3.0 Unported Creative Commons License (http://creativecommons.org/licenses/by-nc-sa/3.0).

Exact mean-energy expansion of Ginibre's gas for coupling constants Γ =2 ×(oddinteger)

NASA Astrophysics Data System (ADS)

Salazar, R.; Téllez, G.

2017-12-01

Using the approach of a Vandermonde determinant to the power Γ =Q2/kBT expansion on monomial functions, a way to find the excess energy Uexc of the two-dimensional one-component plasma (2DOCP) on hard and soft disks (or a Dyson gas) for odd values of Γ /2 is provided. At Γ =2 , the present study not only corroborates the result for the particle-particle energy contribution of the Dyson gas found by Shakirov [Shakirov, Phys. Lett. A 375, 984 (2011), 10.1016/j.physleta.2011.01.004] by using an alternative approach, but also provides the exact N -finite expansion of the excess energy of the 2DOCP on the hard disk. The excess energy is fitted to the ansatz of the form Uexc=K1N +K2√{N }+K3+K4/N +O (1 /N2) to study the finite-size correction, with Ki coefficients and N the number of particles. In particular, the bulk term of the excess energy is in agreement with the well known result of Jancovici for the hard disk in the thermodynamic limit [Jancovici, Phys. Rev. Lett. 46, 386 (1981), 10.1103/PhysRevLett.46.386]. Finally, an expression is found for the pair correlation function which still keeps a link with the random matrix theory via the kernel in the Ginibre ensemble [Ginibre, J. Math. Phys. 6, 440 (1965), 10.1063/1.1704292] for odd values of Γ /2 . A comparison between the analytical two-body density function and histograms obtained with Monte Carlo simulations for small systems and Γ =2 ,6 ,10 ,... shows that the approach described in this paper may be used to study analytically the crossover behavior from systems in the fluid phase to small crystals.

Complex topological structures of frustrated liquid crystals with potential for optics and photonics (Presentation Recording)

NASA Astrophysics Data System (ADS)

Žumer, Slobodan; Čančula, Miha; Čopar, Simon; Ravnik, Miha

2015-10-01

Geometrical constrains and intrinsic chirality in nematic mesophases enable formation of stable and metastable complex defect structures. Recently selected knotted and linked disclinations have been formed using laser manipulation of nematic braids entangling colloidal particles in nematic colloids [Tkalec et al., Science 2011; Copar et al., PNAS 2015]. In unwinded chiral nematic phases stable and metastable toron and hopfion defects have been implemented by laser tweezers [Smalyukh et al., Nature Materials 2010; Chen et al., PRL2013] and in chiral nematic colloids particles dressed by solitonic deformations [Porenta et al., Sci. Rep. 2014]. Modelling studies based on the numerical minimisation of the phenomenological free energy, supported with the adapted topological theory [Copar and Zumer, PRL 2011; Copar, Phys. Rep. 2014] allow describing the observed nematic defect structures and also predicting numerous structures in confined blue phases [Fukuda and Zumer, Nature Comms 2011 and PRL 2011] and stable knotted disclinations in cholesteric droplets with homeotropic boundary [Sec et al., Nature Comms 2014]. Coupling the modeling with finite difference time domain light field computation enables understanding of light propagation and light induced restructuring in these mesophases. The method was recently demonstrated for the description of low intensity light beam changes during the propagation along disclination lines [Brasselet et al., PRL 2009; Cancula et al., PRE 2014]. Allowing also high intensity light an order restructuring is induced [Porenta et al., Soft Matter 2012; Cancula et al., 2015]. These approaches help to uncover the potential of topological structures for beyond-display optical and photonic applications.

Properties of Nonabelian Quantum Hall States

NASA Astrophysics Data System (ADS)

Simon, Steven H.

2004-03-01

The quantum statistics of particles refers to the behavior of a multiparticle wavefunction under adiabatic interchange of two identical particles. While a three dimensional world affords the possibilities of Bosons or Fermions, the two dimensional world has more exotic possibilities such as Fractional and Nonabelian statistics (J. Frölich, in ``Nonperturbative Quantum Field Theory", ed, G. t'Hooft. 1988). The latter is perhaps the most interesting where the wavefunction obeys a ``nonabelian'' representation of the braid group - meaning that braiding A around B then B around C is not the same as braiding B around C then A around B. This property enables one to think about using these exotic systems for robust topological quantum computation (M. Freedman, A. Kitaev, et al, Bull Am Math Soc 40, 31 (2003)). Surprisingly, it is thought that quasiparticles excitations with such nonabelian statistics may actually exist in certain quantum Hall states that have already been observed. The most likely such candidate is the quantum Hall ν=5/2 state(R. L. Willett et al, Phys. Rev. Lett. 59, 1776-1779 (1987)), thought to be a so-called Moore-Read Pfaffian state(G. Moore and N. Read, Nucl Phys. B360 362 (1991)), which can be thought of as a p-wave paired superconducting state of composite fermions(M. Greiter, X. G. Wen, and F. Wilczek, PRL 66, 3205 (1991)). Using this superconducting analogy, we use a Chern-Simons field theory approach to make a number of predictions as to what experimental signatures one should expect for this state if it really is this Moore-Read state(K. Foster, N. Bonesteel, and S. H. Simon, PRL 91 046804 (2003)). We will then discuss how the nonabelian statistics can be explored in detail using a quantum monte-carlo approach (Y. Tserkovnyak and S. H. Simon, PRL 90 106802 (2003)), (I. Finkler, Y. Tserkovnyak, and S. H. Simon, work in progress.) that allows one to explicitly drag one particle around another and observe the change in the wavefunctions. Unfortunately, it turns out that the Moore-Read state is not suited for topological quantum computationfootnote[3]M. Freedman, A. Kitaev, et al, Bull Am Math Soc 40, 31 (2003). so we will turn our attention to more the so-called parafermionic states(E. Rezayi and N. Read, Phys. Rev. B 59, 8084-8092 (1999).) which may also exist in nature.

Use of Data Comm by Flight Crew in High-Density Terminal Areas

NASA Technical Reports Server (NTRS)

Baxley, Brian T.; Norman, Robert M.; Ellis, Kyle K. E.; Latorella, Kara A.; Comstock, James R.; Adams, Cathy A.

2010-01-01

This paper describes a collaborative FAA and NASA experiment using 22 commercial airline pilots to determine the effect of using Datalink Communication (Data Comm) to issue messages in busy, terminal area operations. Four conditions were defined that span current day to future flight deck equipage levels (voice communication only, Data Comm only, Data Comm with Moving Map Display, Data Comm with Moving Map displaying taxi route), and each condition was used to create an arrival and a departure scenario at the Boston Logan Airport. These eight scenarios were repeated twice for a total of 16 scenarios for each of the eleven crews. Quantitative data was collected on subject reaction time and eye tracking information. Questionnaires collected subjective feedback on workload and acceptability to the flight crew for using Data Comm in a busy terminal area. 95% of the Data Comm messages were responded to by the flight crew within one minute; however, post experiment debrief comments revealed almost unanimous consensus that two minutes was a reasonable expectation for crew response. Eye tracking data indicated an insignificant decrease in head-up time for the Pilot Flying when Data Comm was introduced; however, the Pilot Monitoring had significantly less head-up time. Data Comm workload was rated as operationally acceptable by both crew members in all conditions in flight at any altitude above the Final Approach Fix in terms of response time and workload. Results also indicate the use of Data Comm during surface operations was acceptable, the exception being the simultaneous use of voice, Data Comm, and audio chime required for an aircraft to cross an active runway. Many crews reported they believed Data Comm messages would be acceptable after the Final Approach Fix or to cross a runway if the message was not accompanied by a chime and there was not a requirement to immediately respond to the uplink message.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walton, Mark A.

Quantum mechanics in phase space (or deformation quantization) appears to fail as an autonomous quantum method when infinite potential walls are present. The stationary physical Wigner functions do not satisfy the normal eigen equations, the *-eigen equations, unless an ad hoc boundary potential is added [N.C. Dias, J.N. Prata, J. Math. Phys. 43 (2002) 4602 (quant-ph/0012140)]. Alternatively, they satisfy a different, higher-order, '*-eigen-* equation', locally, i.e. away from the walls [S. Kryukov, M.A. Walton, Ann. Phys. 317 (2005) 474 (quant-ph/0412007)]. Here we show that this substitute equation can be written in a very simple form, even in the presence ofmore » an additional, arbitrary, but regular potential. The more general applicability of the *-eigen-* equation is then demonstrated. First, using an idea from [D.B. Fairlie, C.A. Manogue, J. Phys. A 24 (1991) 3807], we extend it to a dynamical equation describing time evolution. We then show that also for general contact interactions, the *-eigen-* equation is satisfied locally. Specifically, we treat the most general possible (Robin) boundary conditions at an infinite wall, general one-dimensional point interactions, and a finite potential jump. Finally, we examine a smooth potential, that has simple but different expressions for x positive and negative. We find that the *-eigen-* equation is again satisfied locally. It seems, therefore, that the *-eigen-* equation is generally relevant to the matching of Wigner functions; it can be solved piece-wise and its solutions then matched.« less

On the realization of quantum Fisher information

NASA Astrophysics Data System (ADS)

Saha, Aparna; Talukdar, B.; Chatterjee, Supriya

2017-03-01

With special attention to the role of information theory in physical sciences we present analytical results for the coordinate- and momentum-space Fisher information of some important one-dimensional quantum systems which differ in spacing of their energy levels. The studies envisaged allow us to relate the coordinate-space information ({I}ρ ) with the familiar energy levels of the quantum system. The corresponding momentum-space information ({I}γ ) does not obey such a simple relationship with the energy spectrum. Our results for the product ({I}ρ {I}γ ) depend quadratically on the principal quantum number n and satisfy an appropriate uncertainty relation derived by Dehesa et al (2007 J. Phys. A: Math. Theor. 40 1845)

Yet another proof of Hawking and Ellis's Lemma 8.5.5

NASA Astrophysics Data System (ADS)

Krasnikov, S.

2014-11-01

The fact that the null generators of a future Cauchy horizon are past-complete was first proved by Hawking and Ellis (1973 The Large Scale Structure of Spacetime (Cambridge: Cambridge University Press)). Then, Budzyński, Kondracki and Królak outlined a proof free from the error found in the original one (2000 New properties of Cauchy and event horizons arXiv:gr-qc/0011033). Now, Minguzzi has published his version of the proof (2014 J. Math. Phys. 55 082503), patching a previously unnoticed hole in the preceding two. I am not aware of any flaws in that last proof, but it is quite difficult. In this note, I present a simpler one.

Comment on ‘Monogamy of multi-qubit entanglement using Rényi entropy’

NASA Astrophysics Data System (ADS)

Yu, Long-Bao; Zhang, Li-Hua; Zhao, Jun-Long; Tang, Yong-Sheng

2018-02-01

In an article in 2010, Kim et al introduced the definition of Rényi-α entanglement for bipartite quantum states and established an analytic formula of Rényi-α entanglement for arbitrary two-qubit states with α≥slant 1 . They also derived a monogamy of entanglement in multi-qubit systems in terms of Rényi-α entanglement for α≥slant 2 Kim et al (2010 J. Phys. A: Math. Theor. 43 445305). We find the proofs of theorems 2 and 3 contain some errors and we also present an improved derivation to overcome this flaw. The alternative derivation shows that the main conclusions remain valid despite the invalidity of the proofs.

Rayleigh-Taylor instability in accelerated elastic-solid slabs

NASA Astrophysics Data System (ADS)

Piriz, S. A.; Piriz, A. R.; Tahir, N. A.

2017-12-01

We develop the linear theory for the asymptotic growth of the incompressible Rayleigh-Taylor instability of an accelerated solid slab of density ρ2, shear modulus G , and thickness h , placed over a semi-infinite ideal fluid of density ρ1<ρ2 . It extends previous results for Atwood number AT=1 [B. J. Plohr and D. H. Sharp, Z. Angew. Math. Phys. 49, 786 (1998), 10.1007/s000330050121] to arbitrary values of AT and unveil the singular feature of an instability threshold below which the slab is stable for any perturbation wavelength. As a consequence, an accelerated elastic-solid slab is stable if ρ2g h /G ≤2 (1 -AT) /AT .

FAST TRACK COMMUNICATION: Criticality-induced universality in ratchets

NASA Astrophysics Data System (ADS)

Chacón, Ricardo

2010-08-01

Conclusive mathematical arguments are presented supporting the ratchet conjecture (Chacón 2007 J. Phys. A: Math. Theor. 40 F413), i.e. the existence of a universal force waveform which optimally enhances directed transport by symmetry breaking. Specifically, such a particular waveform is shown to be unique for both temporal and spatial biharmonic forces, and general (non-perturbative) laws providing the dependence of the strength of directed transport on the force parameters are deduced for these forces. The theory explains previous results for a great diversity of systems subjected to such biharmonic forces and provides a universal quantitative criterion to optimize any application of the ratchet effect induced by symmetry breaking of temporal and spatial biharmonic forces.

Linear frictional forces cause orbits to neither circularize nor precess

NASA Astrophysics Data System (ADS)

Hamilton, B.; Crescimanno, M.

2008-06-01

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure to damped systems suggested recently by Tarasov (2005 J. Phys. A: Math. Gen. 38 2145). In this generalized algebraic structure the orbit-averaged Runge-Lenz vector remains a constant in the linearly damped Kepler problem to leading order in the damping coefficient. Beyond Kepler, we prove that, for any potential proportional to a power of the radius, the orbit shape and precession angle remain constant to leading order in the linear friction coefficient.

On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with a Quadratic Trap

NASA Astrophysics Data System (ADS)

Chen, Xuwen

2013-11-01

We consider the dynamics of the three-dimensional N-body Schrödinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N 3 β-1 V( N β x). We justify the mean-field approximation and offer a rigorous derivation of the three-dimensional cubic nonlinear Schrödinger equation (NLS) with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon (Commun Math Phys 279:169-185, 2008) for by adapting and simplifying an argument in Chen and Pavlović (Annales Henri Poincaré, 2013) which solves the problem for in the absence of a trap.

Rigidity of outermost MOTS: the initial data version

NASA Astrophysics Data System (ADS)

Galloway, Gregory J.

2018-03-01

In the paper Commun Anal Geom 16(1):217-229, 2008, a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen concerning the topology of higher dimensional black holes (Commun Math Phys 266(2):571-576, 2006). The proof of this rigidity result involved bending the initial data manifold in the vicinity of the MOTS within the ambient spacetime. In this note we show how to circumvent this step, and thereby obtain a pure initial data version of this rigidity result and its consequence concerning the topology of black holes.

Convexity of quantum χ2-divergence.

PubMed

Hansen, Frank

2011-06-21

The general quantum χ(2)-divergence has recently been introduced by Temme et al. [Temme K, Kastoryano M, Ruskai M, Wolf M, Verstrate F (2010) J Math Phys 51:122201] and applied to quantum channels (quantum Markov processes). The quantum χ(2)-divergence is not unique, as opposed to the classical χ(2)-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family of quantum χ(2)-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ(2)(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ(2)-divergence is a convex function in its two arguments.

Monodomain dynamics for rigid rod and platelet suspensions in strongly coupled coplanar linear flow and magnetic fields. II. Kinetic theory

NASA Astrophysics Data System (ADS)

Forest, M. Gregory; Sircar, Sarthok; Wang, Qi; Zhou, Ruhai

2006-10-01

We establish reciprocity relations of the Doi-Hess kinetic theory for rigid rod macromolecular suspensions governed by the strong coupling among an excluded volume potential, linear flow, and a magnetic field. The relation provides a reduction of the flow and field driven Smoluchowski equation: from five parameters for coplanar linear flows and magnetic field, to two field parameters. The reduced model distinguishes flows with a rotational component, which map to simple shear (with rate parameter) subject to a transverse magnetic field (with strength parameter), and irrotational flows, for which the reduced model consists of a triaxial extensional flow (with two extensional rate parameters). We solve the Smoluchowski equation of the reduced model to explore: (i) the effect of introducing a coplanar magnetic field on each sheared monodomain attractor of the Doi-Hess kinetic theory and (ii) the coupling of coplanar extensional flow and magnetic fields. For (i), we show each sheared attractor (steady and unsteady, with peak axis in and out of the shearing plane, periodic and chaotic orbits) undergoes its own transition sequence versus magnetic field strength. Nonetheless, robust predictions emerge: out-of-plane degrees of freedom are arrested with increasing field strength, and a unique flow-aligning or tumbling/wagging limit cycle emerges above a threshold magnetic field strength or modified geometry parameter value. For (ii), irrotational flows coupled with a coplanar magnetic field yield only steady states. We characterize all (generically biaxial) equilibria in terms of an explicit Boltzmann distribution, providing a natural generalization of analytical results on pure nematic equilibria [P. Constantin, I. Kevrekidis, and E. S. Titi, Arch. Rat. Mech. Anal. 174, 365 (2004); P. Constantin, I. Kevrekidis, and E. S. Titi, Discrete and Continuous Dynamical Systems 11, 101 (2004); P. Constantin and J. Vukadinovic, Nonlinearity 18, 441 (2005); H. Liu, H. Zhang, and P. Zhang, Comm. Math. Sci. 3, 201 (2005); C. Luo, H. Zhang, and P. Zhang, Nonlinearity 18, 379 (2005); I. Fatkullin and V. Slastikov, Nonlinearity 18, 2565 (2005); H. Zhou, H. Wang, Q. Wang, and M. G. Forest, Nonlinearity 18, 2815 (2005)] and extensional flow-induced equilibria [Q. Wang, S. Sircar, and H. Zhou, Comm. Math. Sci. 4, 605 (2005)]. We predict large parameter regions of bi-stable equilibria; the lowest energy state always has principal axis aligned in the flow plane, while another minimum energy state often exists, with primary alignment transverse to the coplanar field.

Spectral monodromy of non-self-adjoint operators

NASA Astrophysics Data System (ADS)

Phan, Quang Sang

2014-01-01

In the present paper, we build a combinatorial invariant, called the "spectral monodromy" from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc ["Quantum monodromy in integrable systems," Commun. Math. Phys. 203(2), 465-479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat ["On global action-angle coordinates," Commun. Pure Appl. Math. 33(6), 687-706 (1980)].

Flight Crew Workload, Acceptability, and Performance When Using Data Comm in a High-Density Terminal Area Simulation

NASA Technical Reports Server (NTRS)

Norman, R. Michael; Baxley, Brian T.; Adams, Cathy A.; Ellis, Kyle K. E.; Latorella, Kara A.; Comstock, James R., Jr.

2013-01-01

This document describes a collaborative FAA/NASA experiment using 22 commercial airline pilots to determine the effect of using Data Comm to issue messages during busy, terminal area operations. Four conditions were defined that span current day to future flight deck equipage: Voice communication only, Data Comm only, Data Comm with Moving Map Display, and Data Comm with Moving Map displaying taxi route. Each condition was used in an arrival and a departure scenario at Boston Logan Airport. Of particular interest was the flight crew response to D-TAXI, the use of Data Comm by Air Traffic Control (ATC) to send taxi instructions. Quantitative data was collected on subject reaction time, flight technical error, operational errors, and eye tracking information. Questionnaires collected subjective feedback on workload, situation awareness, and acceptability to the flight crew for using Data Comm in a busy terminal area. Results showed that 95% of the Data Comm messages were responded to by the flight crew within one minute and 97% of the messages within two minutes. However, post experiment debrief comments revealed almost unanimous consensus that two minutes was a reasonable expectation for crew response. Flight crews reported that Expected D-TAXI messages were useful, and employment of these messages acceptable at all altitude bands evaluated during arrival scenarios. Results also indicate that the use of Data Comm for all evaluated message types in the terminal area was acceptable during surface operations, and during arrivals at any altitude above the Final Approach Fix, in terms of response time, workload, situation awareness, and flight technical performance. The flight crew reported the use of Data Comm as implemented in this experiment as unacceptable in two instances: in clearances to cross an active runway, and D-TAXI messages between the Final Approach Fix and 80 knots during landing roll. Critical cockpit tasks and the urgency of out-the window scan made the additional head down time to respond to Data Comm messages undesirable during these events. However, most crews also stated that Data Comm messages without an accompanying audio chime and no expectation of an immediate response could be acceptable even during these events.

A Constructive Approach to Regularity of Lagrangian Trajectories for Incompressible Euler Flow in a Bounded Domain

NASA Astrophysics Data System (ADS)

Besse, Nicolas; Frisch, Uriel

2017-04-01

The 3D incompressible Euler equations are an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or absence of boundaries. For a good understanding, it is crucial to carry out, besides mathematical studies, high-accuracy and well-resolved numerical exploration. Such studies can be very demanding in computational resources, but recently it has been shown that very substantial gains can be achieved first, by using Cauchy's Lagrangian formulation of the Euler equations and second, by taking advantage of analyticity results of the Lagrangian trajectories for flows whose initial vorticity is Hölder-continuous. The latter has been known for about 20 years (Serfati in J Math Pures Appl 74:95-104, 1995), but the combination of the two, which makes use of recursion relations among time-Taylor coefficients to obtain constructively the time-Taylor series of the Lagrangian map, has been achieved only recently (Frisch and Zheligovsky in Commun Math Phys 326:499-505, 2014; Podvigina et al. in J Comput Phys 306:320-342, 2016 and references therein). Here we extend this methodology to incompressible Euler flow in an impermeable bounded domain whose boundary may be either analytic or have a regularity between indefinite differentiability and analyticity. Non-constructive regularity results for these cases have already been obtained by Glass et al. (Ann Sci Éc Norm Sup 45:1-51, 2012). Using the invariance of the boundary under the Lagrangian flow, we establish novel recursion relations that include contributions from the boundary. This leads to a constructive proof of time-analyticity of the Lagrangian trajectories with analytic boundaries, which can then be used subsequently for the design of a very high-order Cauchy-Lagrangian method.

Leading Wave Amplitude of a Tsunami

NASA Astrophysics Data System (ADS)

Kanoglu, U.

2015-12-01

Okal and Synolakis (EGU General Assembly 2015, Geophysical Research Abstracts-Vol. 17-7622) recently discussed that why the maximum amplitude of a tsunami might not occur for the first wave. Okal and Synolakis list observations from 2011 Japan tsunami, which reached to Papeete, Tahiti with a fourth wave being largest and 72 min later after the first wave; 1960 Chilean tsunami reached Hilo, Hawaii with a maximum wave arriving 1 hour later with a height of 5m, first wave being only 1.2m. Largest later waves is a problem not only for local authorities both in terms of warning to the public and rescue efforts but also mislead the public thinking that it is safe to return shoreline or evacuated site after arrival of the first wave. Okal and Synolakis considered Hammack's (1972, Ph.D. Dissertation, Calif. Inst. Tech., 261 pp., Pasadena) linear dispersive analytical solution with a tsunami generation through an uplifting of a circular plug on the ocean floor. They performed parametric study for the radius of the plug and the depth of the ocean since these are the independent scaling lengths in the problem. They identified transition distance, as the second wave being larger, regarding the parameters of the problem. Here, we extend their analysis to an initial wave field with a finite crest length and, in addition, to a most common tsunami initial wave form of N-wave as presented by Tadepalli and Synolakis (1994, Proc. R. Soc. A: Math. Phys. Eng. Sci., 445, 99-112). We compare our results with non-dispersive linear shallow water wave results as presented by Kanoglu et al. (2013, Proc. R. Soc. A: Math. Phys. Eng. Sci., 469, 20130015), investigating focusing feature. We discuss the results both in terms of leading wave amplitude and tsunami focusing. Acknowledgment: The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement no 603839 (Project ASTARTE - Assessment, Strategy and Risk Reduction for Tsunamis in Europe)

Inelastic collapse and near-wall localization of randomly accelerated particles.

PubMed

Belan, S; Chernykh, A; Lebedev, V; Falkovich, G

2016-05-01

Inelastic collapse of stochastic trajectories of a randomly accelerated particle moving in half-space z>0 has been discovered by McKean [J. Math. Kyoto Univ. 2, 227 (1963)] and then independently rediscovered by Cornell et al. [Phys. Rev. Lett. 81, 1142 (1998)PRLTAO0031-900710.1103/PhysRevLett.81.1142]. The essence of this phenomenon is that the particle arrives at the wall at z=0 with zero velocity after an infinite number of inelastic collisions if the restitution coefficient β of particle velocity is smaller than the critical value β_{c}=exp(-π/sqrt[3]). We demonstrate that inelastic collapse takes place also in a wide class of models with spatially inhomogeneous random forcing and, what is more, that the critical value β_{c} is universal. That class includes an important case of inertial particles in wall-bounded random flows. To establish how inelastic collapse influences the particle distribution, we derive the exact equilibrium probability density function ρ(z,v) for the particle position and velocity. The equilibrium distribution exists only at β<β_{c} and indicates that inelastic collapse does not necessarily imply near-wall localization.

Kinetic energy of shakeoff atomic electrons from 37K β+ decay

NASA Astrophysics Data System (ADS)

Behr, J. A.; Gorelov, A.; Farfan, C.; Smale, S.; Olchanski, K.; Kurchananov, L.; Anholm, M.; Behling, R. S.; Fenker, B.; Shidling, P. D.; Mehlman, M.; Melconian, D.; Ashery, D.; Gwinner, G.; Trinat Collaboration

2013-10-01

We have measured the kinetic energies from 0 to 30 eV of atomic shakeoff electrons from the β+ decay of 37K. Despite much experimental and theoretical work on the distribution of final ion charge states, shakeoff electrons from β- decay have only been measured with energies above 150 eV [Mitrokhovich, Nucl. Phys. Atom. Energy, 11, 125 (2010)]. We use our magneto-optical trap's time-varying magnetic quadrupole field combined with a uniform electric field as a spectrometer. Our result has more 15 eV electrons than a model using the sudden approximation and hydrogenic wavefunctions [Levinger, Phys. Rev. 90, 11 (1958)]. The total energy carried away by electrons is, as expected, a negligible correction to superallowed Ft values. Understanding the energy of these low-energy electrons is important for their use in precision β decay to select events coming from trapped atoms and start time-of-flight for the recoil ions. Our results could provide a benchmark for shakeoff electron calculations used for biological radiation damage [Lee, Comp. Math. Meth in Medicine doi:10.1155/2012/651475]. Support: NSERC, NRC through TRIUMF, DOE ER41747 ER40773, State of Texas, Israel Science Foundation.

Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case

DOE Office of Scientific and Technical Information (OSTI.GOV)

De Nittis, Giuseppe, E-mail: gidenittis@mat.puc.cl; Gomi, Kiyonori, E-mail: kgomi@math.shinshu-u.ac.jp

2016-05-15

Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related “Real” (resp. “Quaternionic”) Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in De Nittis and Gomi [J. Geom. Phys. 86, 303–338 (2014)] for the “Real” case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1–55 (2015)] for the “Quaternionic” case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article and its companion [G. Demore » Nittis and K. Gomi (unpublished)] we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the “Real” case we generalize the Chern-Weil theory and we show that the assignment of a “Real” connection, along with the related differential Chern class and its holonomy, suffices for the classification of “Real” vector bundles in low dimensions.« less

Phys FilmMakers: teaching science students how to make YouTube-style videos

NASA Astrophysics Data System (ADS)

Coates, Rebecca L.; Kuhai, Alvina; Turlej, Laurence Z. J.; Rivlin, Tom; McKemmish, Laura K.

2018-01-01

Phys FilmMakers (PFM) is a new type of course in which a science expert and science communicator partner teach physics students how to make YouTube-style videos on cutting-edge scientific research within the university department. Here, we describe this new course, outline its key components and provide recommendations for others considering implementing a similar FilmMakers-style course using feedback from course tutors and students. We discuss successful and less successful teaching techniques as well as use our experience to identify areas that science students in particular often have difficulties: finding an interesting ‘hook’ for the video, imagining creative B-roll and making a succinct video by removing extraneous (though usually correct and often interesting) material. The course has two major components: workshop sessions in which students learn the key elements of film-making and independent video production where PFM students partner with senior PhD or post-doc researchers to produce a video on their research. This partnership with the department means that the videos produced serve not only as interesting ‘edutainment’ to encourage teenagers and young adults into Science, Technology, Engineering and Maths subjects, but also provide valuable outreach for the academic department.

Existence of Corotating and Counter-Rotating Vortex Pairs for Active Scalar Equations

NASA Astrophysics Data System (ADS)

Hmidi, Taoufik; Mateu, Joan

2017-03-01

In this paper, we study the existence of corotating and counter-rotating pairs of simply connected patches for Euler equations and the {(SQG)_{α}} equations with {α in (0,1)}. From the numerical experiments implemented for Euler equations in Deem and Zabusky (Phys Rev Lett 40(13):859-862, 1978), Pierrehumbert (J Fluid Mech 99:129-144, 1980), Saffman and Szeto (Phys Fluids 23(12):2339-2342, 1980) it is conjectured the existence of a curve of steady vortex pairs passing through the point vortex pairs. There are some analytical proofs based on variational principle (Keady in J Aust Math Soc Ser B 26:487-502, 1985; Turkington in Nonlinear Anal Theory Methods Appl 9(4):351-369, 1985); however, they do not give enough information about the pairs, such as the uniqueness or the topological structure of each single vortex. We intend in this paper to give direct proofs confirming the numerical experiments and extend these results for the {(SQG)_{α}} equation when {α in (0,1)}. The proofs rely on the contour dynamics equations combined with a desingularization of the point vortex pairs and the application of the implicit function theorem.

NextGen flight deck data comm: auxiliary synthetic speech - phase I

DOT National Transportation Integrated Search

2012-10-22

Data Comma digital, text-based controller-pilot communication systemis critical to many NextGen improvements. With Data Comm, communication becomes a visual task. Although Data Comm brings many advantages, interacting with a visual display may ...

A new version of Visual tool for estimating the fractal dimension of images

NASA Astrophysics Data System (ADS)

Grossu, I. V.; Felea, D.; Besliu, C.; Jipa, Al.; Bordeianu, C. C.; Stan, E.; Esanu, T.

2010-04-01

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images (Grossu et al., 2009 [1]). The earlier version was limited to bi-dimensional sets of points, stored in bitmap files. The application was extended for working also with comma separated values files and three-dimensional images. New version program summaryProgram title: Fractal Analysis v02 Catalogue identifier: AEEG_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9999 No. of bytes in distributed program, including test data, etc.: 4 366 783 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 30 M Classification: 14 Catalogue identifier of previous version: AEEG_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 1999 Does the new version supersede the previous version?: Yes Nature of problem: Estimating the fractal dimension of 2D and 3D images. Solution method: Optimized implementation of the box-counting algorithm. Reasons for new version:The previous version was limited to bitmap image files. The new application was extended in order to work with objects stored in comma separated values (csv) files. The main advantages are: Easier integration with other applications (csv is a widely used, simple text file format); Less resources consumed and improved performance (only the information of interest, the "black points", are stored); Higher resolution (the points coordinates are loaded into Visual Basic double variables [2]); Possibility of storing three-dimensional objects (e.g. the 3D Sierpinski gasket). In this version the optimized box-counting algorithm [1] was extended to the three-dimensional case. Summary of revisions:The application interface was changed from SDI (single document interface) to MDI (multi-document interface). One form was added in order to provide a graphical user interface for the new functionalities (fractal analysis of 2D and 3D images stored in csv files). Additional comments: User friendly graphical interface; Easy deployment mechanism. Running time: In the first approximation, the algorithm is linear. References:[1] I.V. Grossu, C. Besliu, M.V. Rusu, Al. Jipa, C.C. Bordeianu, D. Felea, Comput. Phys. Comm. 180 (2009) 1999-2001.[2] F. Balena, Programming Microsoft Visual Basic 6.0, Microsoft Press, US, 1999.

NextGen flight deck Data Comm : auxiliary synthetic speech phase I

DOT National Transportation Integrated Search

2012-12-31

Data Comma text-based controller-pilot communication systemis critical to many NextGen improvements. With Data Comm, communication becomes a visual task. Interacting with a visual Data Comm display may yield an unsafe increase in head-down time...

Drifting solutions with elliptic symmetry for the compressible Navier-Stokes equations with density-dependent viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

An, Hongli, E-mail: kaixinguoan@163.com; Yuen, Manwai, E-mail: nevetsyuen@hotmail.com

2014-05-15

In this paper, we investigate the analytical solutions of the compressible Navier-Stokes equations with dependent-density viscosity. By using the characteristic method, we successfully obtain a class of drifting solutions with elliptic symmetry for the Navier-Stokes model wherein the velocity components are governed by a generalized Emden dynamical system. In particular, when the viscosity variables are taken the same as Yuen [M. W. Yuen, “Analytical solutions to the Navier-Stokes equations,” J. Math. Phys. 49, 113102 (2008)], our solutions constitute a generalization of that obtained by Yuen. Interestingly, numerical simulations show that the analytical solutions can be used to explain the driftingmore » phenomena of the propagation wave like Tsunamis in oceans.« less

A symmetric integral identity for Bessel functions with applications to integral geometry

NASA Astrophysics Data System (ADS)

Salman, Yehonatan

2017-12-01

In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.

Presymplectic current and the inverse problem of the calculus of variations

NASA Astrophysics Data System (ADS)

Khavkine, Igor

2013-11-01

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159-178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45-64 (1982)] from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.

Conditional quantum entropy power inequality for d-level quantum systems

NASA Astrophysics Data System (ADS)

Jeong, Kabgyun; Lee, Soojoon; Jeong, Hyunseok

2018-04-01

We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic functions also given by Audenaert et al (2016 J. Math. Phys. 57 052202). Here, we make particular use of the fact that a specific local measurement after a partial swap operation (or partial swap quantum channel) acting only on finite dimensional bipartite subsystems does not affect the majorization relation for the conditional output states when a separable ancillary subsystem is involved. We expect our conditional quantum entropy power inequality to be useful, and applicable in bounding and analyzing several capacity problems for quantum channels.

On the Grothendieck rings of equivariant fusion categories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burciu, Sebastian, E-mail: sebastian.burciu@imar.ro

2015-07-15

In this paper, we describe a Mackey type decomposition for group actions on abelian categories. This allows us to define new Mackey functors which associates to any subgroup the K-theory of the corresponding equivariantized abelian category. In the case of an action by tensor autoequivalences, the Mackey functor at the level of Grothendieck rings has a Green functor structure. As an application we give a description of the Grothendieck rings of equivariantized fusion categories under group actions by tensor autoequivalences on graded fusion categories. In this settings, a new formula for the tensor product of any two simple objects ofmore » an equivariantized fusion category is given, simplifying the fusion formula from Burciu and Natale [J. Math. Phys. 54, 013511 (2013)].« less

Comment on “Approximate solutions of the Dirac equation for the Rosen-Morse potential including the spin-orbit centrifugal term” [J. Math. Phys. 51, 023525 (2010)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghoumaid, A.; Benamira, F.; Guechi, L.

2016-02-15

It is shown that the application of the Nikiforov-Uvarov method by Ikhdair for solving the Dirac equation with the radial Rosen-Morse potential plus the spin-orbit centrifugal term is inadequate because the required conditions are not satisfied. The energy spectra given is incorrect and the wave functions are not physically acceptable. We clarify the problem and prove that the spinor wave functions are expressed in terms of the generalized hypergeometric functions {sub 2}F{sub 1}(a, b, c; z). The energy eigenvalues for the bound states are given by the solution of a transcendental equation involving the hypergeometric function.

Plethystic vertex operators and boson-fermion correspondences

NASA Astrophysics Data System (ADS)

Fauser, Bertfried; Jarvis, Peter D.; King, Ronald C.

2016-10-01

We study the algebraic properties of plethystic vertex operators, introduced in (2010 J. Phys. A: Math. Theor. 43 405202), underlying the structure of symmetric functions associated with certain generalized universal character rings of subgroups of the general linear group, defined to stabilize tensors of Young symmetry type characterized by a partition of arbitrary shape π. Here we establish an extension of the well-known boson-fermion correspondence involving Schur functions and their associated (Bernstein) vertex operators: for each π, the modes generated by the plethystic vertex operators and their suitably constructed duals, satisfy the anticommutation relations of a complex Clifford algebra. The combinatorial manipulations underlying the results involve exchange identities exploiting the Hopf-algebraic structure of certain symmetric function series and their plethysms.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chi, Dongpyo, E-mail: dpchi@snu.ac.kr; Ha, Seung-Yeal, E-mail: syha@snu.ac.kr; Choi, Sun-Ho, E-mail: lpgilin@gmail.com

We study sufficient conditions for the asymptotic emergence of synchronous behaviors in a holonomic particle system on a sphere, which was recently introduced by Lohe [“Non-Abelian Kuramoto model and synchronization,” J. Phys. A: Math. Theor. 42, 395101–395126 (2009)]. These conditions depend only on the coupling strength and initial position diameter. For identical particles, we show that the position diameter approaches zero asymptotically under these sufficient conditions, i.e., all particles approach to the same position. For non-identical particles, the particle positions do not shrink to one point, but can be squeezed into some small region whose diameter is inversely proportional tomore » the coupling strength, when the coupling strength is large. We also provide several numerical results to confirm our analytical findings.« less

Viscous Rayleigh-Taylor instability in spherical geometry

NASA Astrophysics Data System (ADS)

Mikaelian, Karnig O.

2016-02-01

We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955), 10.1093/qjmam/8.1.1] analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer a somewhat improved one. A third DR, based on transforming a planar DR into a spherical one, suffers no unphysical predictions and compares reasonably well with the exact work of Chandrasekhar and a more recent numerical analysis of the problem [Terrones and Carrara, Phys. Fluids 27, 054105 (2015), 10.1063/1.4921648].

Statistics of time delay and scattering correlation functions in chaotic systems. II. Semiclassical approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novaes, Marcel

2015-06-15

We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys.more » 56, 062110 (2015)].« less

Einstein-Weyl spaces and third-order differential equations

NASA Astrophysics Data System (ADS)

Tod, K. P.

2000-08-01

The three-dimensional null-surface formalism of Tanimoto [M. Tanimoto, "On the null surface formalism," Report No. gr-qc/9703003 (1997)] and Forni et al. [Forni et al., "Null surfaces formation in 3D," J. Math Phys. (submitted)] are extended to describe Einstein-Weyl spaces, following Cartan [E. Cartan, "Les espaces généralisées et l'integration de certaines classes d'equations différentielles," C. R. Acad. Sci. 206, 1425-1429 (1938); "La geometria de las ecuaciones diferenciales de tercer order," Rev. Mat. Hispano-Am. 4, 1-31 (1941)]. In the resulting formalism, Einstein-Weyl spaces are obtained from a particular class of third-order differential equations. Some examples of the construction which include some new Einstein-Weyl spaces are given.

Scattering on two Aharonov-Bohm vortices

NASA Astrophysics Data System (ADS)

Bogomolny, E.

2016-12-01

The problem of two Aharonov-Bohm (AB) vortices for the Helmholtz equation is examined in detail. It is demonstrated that the method proposed by Myers (1963 J. Math. Phys. 6 1839) for slit diffraction can be generalised to obtain an explicit solution for AB vortices. Due to the singular nature of AB interaction the Green function and scattering amplitude for two AB vortices obey a series of partial differential equations. Coefficients entering these equations, fulfil ordinary non-linear differential equations whose solutions can be obtained by solving the Painlevé III equation. The asymptotics of necessary functions for very large and very small vortex separations are calculated explicitly. Taken together, this means that the problem of two AB vortices is exactly solvable.

Inverse square law isothermal property in relativistic charged static distributions

NASA Astrophysics Data System (ADS)

Hansraj, Sudan; Qwabe, Nkululeko

2017-12-01

We analyze the impact of the inverse square law fall-off of the energy density in a charged isotropic spherically symmetric fluid. Initially, we impose a linear barotropic equation of state p = αρ but this leads to an intractable differential equation. Next, we consider the neutral isothermal metric of Saslaw et al. [Phys. Rev. D 13, 471 (1996)] in an electric field and the usual inverse square law of energy density and pressure results thus preserving the equation of state. Additionally, we discard a linear equation of state and endeavor to find new classes of solutions with the inverse square law fall-off of density. Certain prescribed forms of the spatial and temporal gravitational forms result in new exact solutions. An interesting result that emerges is that while isothermal fluid spheres are unbounded in the neutral case, this is not so when charge is involved. Indeed it was found that barotropic equations of state exist and hypersurfaces of vanishing pressure exist establishing a boundary in practically all models. One model was studied in depth and found to satisfy other elementary requirements for physical admissibility such as a subluminal sound speed as well as gravitational surface redshifts smaller than 2. Buchdahl [Acta Phys. Pol. B 10, 673 (1965)], Böhmer and Harko [Gen. Relat. Gravit. 39, 757 (2007)] and Andréasson [Commum. Math. Phys. 198, 507 (2009)] mass-radius bounds were also found to be satisfied. Graphical plots utilizing constants selected from the boundary conditions established that the model displayed characteristics consistent with physically viable models.

Characterizing the gender gap in introductory physics

NASA Astrophysics Data System (ADS)

Kost, Lauren E.; Pollock, Steven J.; Finkelstein, Noah D.

2009-06-01

Previous research [S. J. Pollock , Phys. Rev. ST Phys. Educ. Res. 3, 1 (2007)] showed that despite the use of interactive engagement techniques, the gap in performance between males and females on a conceptual learning survey persisted from pretest to post-test at the University of Colorado at Boulder. Such findings were counter to previously published work [M. Lorenzo , Am. J. Phys. 74, 118 (2006)]. This study begins by identifying a variety of other gender differences. There is a small but significant difference in the course grades of males and females. Males and females have significantly different prior understandings of physics and mathematics. Females are less likely to take high school physics than males, although they are equally likely to take high school calculus. Males and females also differ in their incoming attitudes and beliefs about physics. This collection of background factors is analyzed to determine the extent to which each factor correlates with performance on a conceptual post-test and with gender. Binned by quintiles, we observe that males and females with similar pretest scores do not have significantly different post-test scores (p>0.2) . The post-test data are then modeled using two regression models (multiple regression and logistic regression) to estimate the gender gap in post-test scores after controlling for these important prior factors. These prior factors account for about 70% of the observed gender gap. The results indicate that the gender gap exists in interactive physics classes at our institution but is largely associated with differences in previous physics and math knowledge and incoming attitudes and beliefs.

Optimal Jet Finder (v1.0 C++)

NASA Astrophysics Data System (ADS)

Chumakov, S.; Jankowski, E.; Tkachov, F. V.

2006-10-01

We describe a C++ implementation of the Optimal Jet Definition for identification of jets in hadronic final states of particle collisions. We explain interface subroutines and provide a usage example. The source code is available from http://www.inr.ac.ru/~ftkachov/projects/jets/. Program summaryTitle of program: Optimal Jet Finder (v1.0 C++) Catalogue identifier: ADSB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSB_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer: any computer with a standard C++ compiler Tested with:GNU gcc 3.4.2, Linux Fedora Core 3, Intel i686; Forte Developer 7 C++ 5.4, SunOS 5.9, UltraSPARC III+; Microsoft Visual C++ Toolkit 2003 (compiler 13.10.3077, linker 7.10.30777, option /EHsc), Windows XP, Intel i686. Programming language used: C++ Memory required:˜1 MB (or more, depending on the settings) No. of lines in distributed program, including test data, etc.: 3047 No. of bytes in distributed program, including test data, etc.: 17 884 Distribution format: tar.gz Nature of physical problem: Analysis of hadronic final states in high energy particle collision experiments often involves identification of hadronic jets. A large number of hadrons detected in the calorimeter is reduced to a few jets by means of a jet finding algorithm. The jets are used in further analysis which would be difficult or impossible when applied directly to the hadrons. Grigoriev et al. [D.Yu. Grigoriev, E. Jankowski, F.V. Tkachov, Phys. Rev. Lett. 91 (2003) 061801] provide brief introduction to the subject of jet finding algorithms and a general review of the physics of jets can be found in [R. Barlow, Rep. Prog. Phys. 36 (1993) 1067]. Method of solution: The software we provide is an implementation of the so-called Optimal Jet Definition (OJD). The theory of OJD was developed in [F.V. Tkachov, Phys. Rev. Lett. 73 (1994) 2405; Erratum, Phys. Rev. Lett. 74 (1995) 2618; F.V. Tkachov, Int. J. Modern Phys. A 12 (1997) 5411; F.V. Tkachov, Int. J. Modern Phys. A 17 (2002) 2783]. The desired jet configuration is obtained as the one that minimizes Ω, a certain function of the input particles and jet configuration. A FORTRAN 77 implementation of OJD is described in [D.Yu. Grigoriev, E. Jankowski, F.V. Tkachov, Comput. Phys. Comm. 155 (2003) 42]. Restrictions on the complexity of the program: Memory required by the program is proportional to the number of particles in the input × the number of jets in the output. For example, for 650 particles and 20 jets ˜300 KB memory is required. Typical running time: The running time (in the running mode with a fixed number of jets) is proportional to the number of particles in the input × the number of jets in the output × times the number of different random initial configurations tried ( ntries). For example, for 65 particles in the input and 4 jets in the output, the running time is ˜4ṡ10 s per try (Pentium 4 2.8 GHz).

Commissural NTS lesions enhance the pressor response to central cholinergic and adrenergic activation.

PubMed

Vieira, Alexandre A; De Luca, Laurival A; Colombari, Eduardo; Colombari, Debora S A; Menani, José V

2012-07-11

Electrolytic lesions of the commissural nucleus of the solitary tract (commNTS) in rats enhance the pressor response to bilateral carotid occlusion or to intravenous infusion of hypertonic NaCl without changing baroreflex responses. In an opposite direction, commNTS lesions abolish the pressor responses to peripheral chemoreflex activation. These opposite effects of commNTS lesions apparently result from an impairment of sympathetic activation in one case and in a facilitation of vasopressin secretion in the others. In the present study, we investigated the effects of the electrolytic lesions of the commNTS in the pressor responses that depend on sympathetic activation and vasopressin secretion produced by central cholinergic or adrenergic activation with intracerebroventricular (i.c.v.) injections of carbachol or noradrenaline, respectively, in unanesthetized rats. Male Holtzman rats (280-320 g, n=8-15/group) with acute (1 day) or chronic (21 days) sham or commNTS lesions (1 mA×10 s) and a stainless steel cannula implanted in the lateral ventricle were used. Acute commNTS lesions increased the pressor response to i.c.v. injection of carbachol (0.5 nmol/1μ1) (52 ± 2, vs. sham: 37 ± 2mm Hg) or noradrenaline (80 nmol/1μl) (45 ± 6, vs. sham: 30 ± 3 mm Hg), whereas chronic commNTS lesions did not affect the pressor responses to the same treatments. Lesions of the commNTS impaired chemoreflex responses produced by intravenous KCN, without changing baroreflex responses. The results suggest that commNTS-dependent inhibitory signals are involved in the modulation of the pressor responses to central cholinergic and adrenergic activation, probably limiting vasopressin secretion. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Origin of families of fermions and their mass matrices

NASA Astrophysics Data System (ADS)

Bračič, A. Borštnik; Borštnik, N. S. Mankoč

2006-10-01

We are proposing a new way of describing families of quarks and leptons, using the approach unifying all the internal degrees of freedom, proposed by one of us [N. Mankoč Borštnik, Phys. Lett. B 292, 25 (1992).PYLBAJ0370-269310.1016/0370-2693(92)90603-2][N. Mankoč-Borštnik, J. Math. Phys. (N.Y.)JMAPAQ0022-2488 34, 3731 (1993).10.1063/1.530055][N. Mankoč Borštnik, J. Math. Phys. (N.Y.)JMAPAQ0022-2488 36, 1593 (1995).10.1063/1.531071][N. S. Mankoč Borštnik, Mod. Phys. Lett. AMPLAEQ0217-7323 10, 587 (1995).10.1142/S0217732395000624][N. S. Mankoč Borštnik and S. Fajfer, Nuovo Cimento Soc. Ital. Fis. BNIFBAP0369-4100 112, 1637 (1997).][A. Borštnik and N. S. Mankoč Borštnik, in Proceedings to the International Workshop on “What Comes Beyond the Standard Model, Bled, Slovenia, 1998, edited by N. Mankoč Borštnik, H. B. Nielsen, and C. Froggatt (DMFA, Založništvo, 1999), p. 52.][N. S. Mankoč Borštnik and H. B. Nielsen, Phys. Rev. 62, 04010 (2000).PHRVAO0031-899X][N. S. Mankoč Borštnik, Int. J. Theor. Phys. 40, 315 (2001), and references therein.IJTPBM0020-774810.1023/A:1003708032726][A. Borštnik and N. S. Mankoč Borštnik, in Proceedings to the International Workshop on “What Comes Beyond the Standard Model”, Bled 2000, 2001, 2002 Volume 2, edited by N. Mankoč Borštnik, H. B. Nielsen, C. Froggatt, and D. Lukman (DMFA, Založništvo, 2002), p. 27 and the paper (unpublished).][A. Borštnik and N. S. Mankoč Borštnik, in Proceedings to the Euroconference on Symmetries Beyond the Standard Model, Portorož, 2003 edited by N. Mankoč Borštnik, H. B. Nielsen, C. Froggatt, and D. Lukman (DMFA, Založništvo, 2003), pp. 27 51.]. Spinors, living in d(=1+13)-dimensional space, carry in this approach only the spin and interact with only the gravity through vielbeins and two kinds of the spin connection fields—the gauge fields of the Poincaré group (pa,Sab) and the second kind of the Clifford algebra objects (S˜ab). All the quarks and the leptons of one family appear in one Weyl representation of a chosen handedness of the Lorentz group, if analyzed with respect to the standard model gauge groups, which are subgroups of the group SO(1,13): the right handed (with respect to SO(1,3)) weak chargeless quarks and leptons and the left handed weak charged quarks and leptons (with the right handed neutrino included). A part of the starting Lagrange density of a Weyl spinor in d=1+13 transforms right handed quarks and leptons into left handed quarks and leptons manifesting as the Yukawa couplings of the standard model. A kind of the Clifford algebra objects generates families of quarks and leptons and contributes to diagonal and off-diagonal Yukawa couplings. The approach predicts an even number of families, treating leptons and quarks equivalently (we do not study a possible appearance of Majorana fermions yet). In this paper we investigate within this approach the appearance of the Yukawa couplings within one family of quarks and leptons as well as among the families (without assuming any Higgs fields like in the standard model). We present the mass matrices for four families and investigate whether our way of generating families might explain the origin of families of quarks and leptons as well as their observed properties—the masses and the mixing matrices. Numerical results are presented in Ref. [M. Breskvar, D. Lukman, and N. S. Mankoč Borštnik, hep-ph/0606159.].

Imaging quantum transport using scanning gate microscopy

NASA Astrophysics Data System (ADS)

Hackens, Benoit

2014-03-01

Quantum transport in nanodevices is usually probed thanks to measurements of the electrical resistance or conductance, which lack the spatial resolution necessary to probe electron behaviour inside the devices. In this talk, we will show that scanning gate microscopy (SGM) yields real-space images of quantum transport phenomena inside archetypal mesoscopic devices such as quantum point contacts and quantum rings. We will first discuss the SGM technique, which is based on mapping the electrical conductance of a device as an electrically-biased sharp metallic tip scans in its vicinity. With SGM, we demonstrated low temperature imaging of the electron probability density and interferences in embedded mesoscopic quantum rings [B. Hackens et al., Nat. Phys. 2, 826 (2006)]. At high magnetic field, thanks to the SGM conductance maps, one can decrypt complex transport phenomena such as tunneling between quantum Hall edge state, either direct or through localized states [B. Hackens et al., Nat. Comm. 1, 39 (2010)]. Moreover, the technique also allows to perform local spectroscopy of electron transport through selected localized states [F. Martins et al., New J. of Phys. 15, 013049 (2013); F. Martins et al., Sci. Rep. 3, 1416 (2013)]. Overall, these examples show that scanning gate microscopy is a powerful tool for imaging charge carrier behavior inside devices fabricated from a variety of materials, and opens the way towards a more intimate manipulation of charge and quasiparticle transport. This work was performed in collaboration with F. Martins, S. Faniel, B. Brun, M. Pala, X. Wallart, L. Desplanque, B. Rosenow, T. Ouisse, H. Sellier, S. Huant and V. Bayot.

Nonlinear Convective Models of RR Lyrae Stars

NASA Astrophysics Data System (ADS)

Feuchtinger, M.; Dorfi, E. A.

The nonlinear behavior of RR Lyrae pulsations is investigated using a state-of-the-art numerical technique solving the full time-dependent system of radiation hydrodynamics. Grey radiative transfer is included by a variable Eddington-factor method and we use the time-dependent turbulent convection model according to Kuhfuss (1986, A&A 160, 116) in the version of Wuchterl (1995, Comp. Phys. Comm. 89, 19). OPAL opacities extended by the Alexander molecule opacities at temperatures below 6000 K and an equation of state according to Wuchterl (1990, A&A 238, 83) close the system. The resulting nonlinear system is discretized on an adaptive mesh developed by Dorfi & Drury (1987, J. Comp. Phys. 69, 175), which is important to provide the necessary spatial resolution in critical regions like ionization zones and shock waves. Additionally, we employ a second order advection scheme, a time centered temporal discretizaton and an artificial tensor viscosity in order to treat discontinuities. We compute fundamental as well first overtone models of RR Lyrae stars for a grid of stellar parameters both with and without convective energy transport in order to give a detailed picture of the pulsation-convection interaction. In order to investigate the influence of the different features of the convection model calculations with and without overshooting, turbulent pressure and turbulent viscosity are performed and compared with each other. A standard Fourier decomposition is used to confront the resulting light and radial velocity variations with recent observations and we show that the well known RR Lyrae phase discrepancy problem (Simon 1985, ApJ 299, 723) can be resolved with these stellar pulsation computations.

Constructing Integrable High-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibrium Solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

S.R. Hudson; D.A. Monticello; A.H. Reiman

For the (non-axisymmetric) stellarator class of plasma confinement devices to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux surfaces; however, the inherent lack of a continuous symmetry implies that magnetic islands responsible for breaking the smooth topology of the flux surfaces are guaranteed to exist. Thus, the suppression of magnetic islands is a critical issue for stellarator design, particularly for small aspect ratio devices. Pfirsch-Schluter currents, diamagnetic currents, and resonant coil fields contribute to the formation of magnetic islands, and the challenge is to designmore » the plasma and coils such that these effects cancel. Magnetic islands in free-boundary high-pressure full-current stellarator magnetohydrodynamic equilibria are suppressed using a procedure based on the Princeton Iterative Equilibrium Solver [Reiman and Greenside, Comp. Phys. Comm. 43 (1986) 157] which iterate s the equilibrium equations to obtain the plasma equilibrium. At each iteration, changes to a Fourier representation of the coil geometry are made to cancel resonant fields produced by the plasma. The changes are constrained to preserve certain measures of engineering acceptability and to preserve the stability of ideal kink modes. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible, the plasma is stable to ideal kink modes, and the coils satisfy engineering constraints. The method is applied to a candidate plasma and coil design for the National Compact Stellarator Experiment [Reiman, et al., Phys. Plasmas 8 (May 2001) 2083].« less

Quantum Cosmology

NASA Astrophysics Data System (ADS)

Bojowald, Martin

The universe, ultimately, is to be described by quantum theory. Quantum aspects of all there is, including space and time, may not be significant for many purposes, but are crucial for some. And so a quantum description of cosmology is required for a complete and consistent worldview. At any rate, even if we were not directly interested in regimes where quantum cosmology plays a role, a complete physical description could not stop at a stage before the whole universe is reached. Quantum theory is essential in the microphysics of particles, atoms, molecules, solids, white dwarfs and neutron stars. Why should one expect this ladder of scales to end at a certain size? 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Quantum Grav. 17, 1489 (2000). gr-qc/9910103 24.M.Bojowald2002Class. Quantum Grav.19271719081252002CQGra..19.2717B1008.8303710.1088/0264-9381/19/10/313gr-qc/0202077Bojowald, M.: Class. Quantum Grav. 19, 2717 (2002). gr-qc/0202077 25.C.FewsterH.Sahlmann2008Class Quantum Grav2522501524533882008CQGra..25v5015F10.1088/0264-9381/25/22/225015arXiv:0804.2541Fewster, C., Sahlmann, H.: Class Quantum Grav 25, 225015 (2008). arXiv:0804.2541 26.J.M.Velhinho2007Class. Quantum Grav.24374523394202007CQGra..24.3745V1129.8332410.1088/0264-9381/24/14/013arXiv:0704.2397.Velhinho, J.M.: Class. Quantum Grav. 24, 3745 (2007). arXiv:0704.2397. 27.TThiemann1998Class Quantum Grav1583916202091998CQGra..15..839T0956.8301310.1088/0264-9381/15/4/011gr-qc/9606089Thiemann, T.: Class Quantum Grav 15, 839 (1998). gr-qc/9606089 28.T.Thiemann1998Class. Quantum Grav.15128116230751998CQGra..15.1281T0945.8301610.1088/0264-9381/15/5/012gr-qc/9705019Thiemann, T.: Class. Quantum Grav. 15, 1281 (1998). gr-qc/9705019 29.M.Bojowald2001Phys. Rev. D6408401818587272001PhRvD..64h4018B10.1103/PhysRevD.64.084018gr-qc/0105067Bojowald, M.: Phys. Rev. D 64, 084018 (2001). gr-qc/0105067 30.J.BrunnemannT.Thiemann2006Class. Quantum Grav.23139522046892006CQGra..23.1395B1097.8301310.1088/0264-9381/23/5/001gr-qc/0505032Brunnemann, J., Thiemann, T.: Class. Quantum Grav. 23, 1395 (2006). gr-qc/0505032 31.M.Bojowald2006Class. Quantum Grav.2398722029402006CQGra..23..987B1087.8302710.1088/0264-9381/23/3/023gr-qc/0508118Bojowald, M.: Class. Quantum Grav. 23, 987 (2006). gr-qc/0508118 32.J.BrunnemannT.Thiemann2006Class. Quantum Grav.23142922046902006CQGra..23.1429B1089.8301410.1088/0264-9381/23/5/002gr-qc/0505033Brunnemann, J., Thiemann, T.: Class. Quantum Grav. 23, 1429 (2006). gr-qc/0505033 1.W.Unruh1997Time, Gravity, and Quantum MechanicsCambridge University PressCambridge2394Unruh, W.: Time, Gravity, and Quantum Mechanics pp. 23-94. Cambridge University Press, Cambridge (1997) 2.N.Weiss1985Phys Rev D3232288150791985PhRvD..32.3228W10.1103/PhysRevD.32.3228Weiss, N.: Phys. Rev. D 32, 3228 (1985) 3.Jacobson, T.: (2000). hep-th/0001085 4.M.BojowaldP.SinghA.Skirzewski2004Phys. Rev. D7012402221247062004PhRvD..70l4022B10.1103/PhysRevD.70.124022gr-qc/0408094Bojowald, M., Singh, P., Skirzewski, A.: Phys. Rev. D 70, 124022 (2004). gr-qc/0408094 5.C.RovelliL.Smolin1994Phys. Rev. Lett.7244612569161994PhRvL..72..446R0973.8352310.1103/PhysRevLett.72.446gr-qc/9308002Rovelli, C., Smolin, L.: Phys. Rev. Lett. 72, 446 (1994). gr-qc/9308002 6.K.GieselT.Thiemann2007Class Quantum Grav.24246523194272007CQGra..24.2465G1117.8304510.1088/0264-9381/24/10/003gr-qc/0607099Giesel, K., Thiemann, T.: Class Quantum Grav. 24, 2465 (2007). gr-qc/0607099 7.T.Thiemann1998Class Quantum Grav.1583916202091998CQGra..15..839T0956.8301310.1088/0264-9381/15/4/011gr-qc/9606089Thiemann, T.: Class Quantum Grav. 15, 839 (1998). gr-qc/9606089 8.T.Thiemann1998Class Quantum Grav.15128116230751998CQGra..15.1281T0945.8301610.1088/0264-9381/15/5/012gr-qc/9705019Thiemann, T.: Class Quantum Grav. 15, 1281 (1998). gr-qc/9705019 9.T.Thiemann1998Class Quantum Grav.1587516202131998CQGra..15..875T10.1088/0264-9381/15/4/012gr-qc/9606090Thiemann, T.: Class Quantum Grav. 15, 875 (1998). gr-qc/9606090 10.T.Thiemann1996Phys. Lett. B38025713983881996PhLB..380..257T0945.8301310.1016/0370-2693(96)00532-1gr-qc/9606088Thiemann, T.: Phys. Lett. B 380, 257 (1996). gr-qc/9606088 11.J.LewandowskiD.Marolf1998Int. J. Mod. Phys. D729916357561998IJMPD...7..299L0936.8302210.1142/S0218271898000231gr-qc/9710016Lewandowski, J., Marolf, D.: Int. J Mod. Phys. D 7, 299 (1998). gr-qc/9710016 12.R.GambiniJ.LewandowskiD.MarolfJ.Pullin1998Int. J Mod. Phys. D79716250591998IJMPD...7...97G0936.8302110.1142/S0218271898000103gr-qc/9710018Gambini, R., Lewandowski, J., Marolf, D., Pullin, J.: Int. J Mod. Phys. D 7, 97 (1998).gr-qc/9710018 13.A.AshtekarJ.LewandowskiH.Sahlmann2003Class Quantum Grav.20L1119557752003CQGra..20L..11A1025.8350110.1088/0264-9381/20/1/103gr-qc/0211012Ashtekar, A., Lewandowski, J., Sahlmann, H.: Class Quantum Grav. 20, L11 (2003). gr-qc/0211012 14.H.SahlmannT.Thiemann2006Class Quantum Grav.2386722029362006CQGra..23..867S1098.8301410.1088/0264-9381/23/3/019gr-qc/0207030Sahlmann, H., Thiemann, T.: Class Quantum Grav. 23, 867 (2006). gr-qc/0207030 15.M.Bojowald2009

CommWalker: correctly evaluating modules in molecular networks in light of annotation bias.

PubMed

Luecken, M D; Page, M J T; Crosby, A J; Mason, S; Reinert, G; Deane, C M

2018-03-15

Detecting novel functional modules in molecular networks is an important step in biological research. In the absence of gold standard functional modules, functional annotations are often used to verify whether detected modules/communities have biological meaning. However, as we show, the uneven distribution of functional annotations means that such evaluation methods favor communities of well-studied proteins. We propose a novel framework for the evaluation of communities as functional modules. Our proposed framework, CommWalker, takes communities as inputs and evaluates them in their local network environment by performing short random walks. We test CommWalker's ability to overcome annotation bias using input communities from four community detection methods on two protein interaction networks. We find that modules accepted by CommWalker are similarly co-expressed as those accepted by current methods. Crucially, CommWalker performs well not only in well-annotated regions, but also in regions otherwise obscured by poor annotation. CommWalker community prioritization both faithfully captures well-validated communities and identifies functional modules that may correspond to more novel biology. The CommWalker algorithm is freely available at opig.stats.ox.ac.uk/resources or as a docker image on the Docker Hub at hub.docker.com/r/lueckenmd/commwalker/. deane@stats.ox.ac.uk. Supplementary data are available at Bioinformatics online.

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Athanassoulis, Agissilaos

2018-03-01

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

Harmonic maps of S into a complex Grassmann manifold.

PubMed

Chern, S S; Wolfson, J

1985-04-01

Let G(k, n) be the Grassmann manifold of all C(k) in C(n), the complex spaces of dimensions k and n, respectively, or, what is the same, the manifold of all projective spaces P(k-1) in P(n-1), so that G(1, n) is the complex projective space P(n-1) itself. We study harmonic maps of the two-dimensional sphere S(2) into G(k, n). The case k = 1 has been the subject of investigation by several authors [see, for example, Din, A. M. & Zakrzewski, W. J. (1980) Nucl. Phys. B 174, 397-406; Eells, J. & Wood, J. C. (1983) Adv. Math. 49, 217-263; and Wolfson, J. G. Trans. Am. Math. Soc., in press]. The harmonic maps S(2) --> G(2, 4) have been studied by Ramanathan [Ramanathan, J. (1984) J. Differ. Geom. 19, 207-219]. We shall describe all harmonic maps S(2) --> G(2, n). The method is based on several geometrical constructions, which lead from a given harmonic map to new harmonic maps, in which the image projective spaces are related by "fundamental collineations." The key result is the degeneracy of some fundamental collineations, which is a global consequence, following from the fact that the domain manifold is S(2). The method extends to G(k, n).

Coulomb crystallization in classical and quantum systems

NASA Astrophysics Data System (ADS)

Bonitz, Michael

2007-11-01

Coulomb crystallization occurs in one-component plasmas when the average interaction energy exceeds the kinetic energy by about two orders of magnitude. A simple road to reach such strong coupling consists in using external confinement potentials the strength of which controls the density. This has been succsessfully realized with ions in traps and storage rings and also in dusty plasma. Recently a three-dimensional spherical confinement could be created [1] which allows to produce spherical dust crystals containing concentric shells. I will give an overview on our recent results for these ``Yukawa balls'' and compare them to experiments. The shell structure of these systems can be very well explained by using an isotropic statically screened pair interaction. Further, the thermodynamic properties of these systems, such as the radial density distribution are discussed based on an analytical theory [3]. I then will discuss Coulomb crystallization in trapped quantum systems, such as mesoscopic electron and electron hole plasmas in coupled layers [4,5]. These systems show a very rich correlation behavior, including liquid and solid like states and bound states (excitons, biexcitons) and their crystals. On the other hand, also collective quantum and spin effects are observed, including Bose-Einstein condensation and superfluidity of bound electron-hole pairs [4]. Finally, I consider Coulomb crystallization in two-component neutral plasmas in three dimensions. I discuss the necessary conditions for crystals of heavy charges to exist in the presence of a light component which typically is in the Fermi gas or liquid state. It can be shown that their exists a critical ratio of the masses of the species of the order of 80 [5] which is confirmed by Quantum Monte Carlo simulations [6]. Familiar examples are crystals of nuclei in the core of White dwarf stars, but the results also suggest the existence of other crystals, including proton or α-particle crystals in dense matter and of hole crystals in semiconductors. [1] O. Arp, D. Block, A. Piel, and A. Melzer, Phys. Rev. Lett. 93, 165004 (2004). [2] M. Bonitz, D. Block, O. Arp, V. Golubnychiy, H. Baumgartner, P. Ludwig, A. Piel, and A. Filinov, Phys. Rev. Lett. 96, 075001 (2006). [3] C. Henning, H. Baumgartner, A. Piel, P. Ludwig, V. Golubnychiy, M. Bonitz, and D. Block, Phys. Rev. E 74, 056403 (2006) and Phys. Rev. E (2007). [4] A. Filinov, M. Bonitz, and Yu. Lozovik, Phys. Rev. Lett. 86, 3851 (2001). [5] M. Bonitz, V. Filinov, P. Levashov, V. Fortov, and H. Fehske, Phys. Rev. Lett. 95, 235006 (2005) and J. Phys. A: Math. Gen. 39, 4717 (2006). [6] Introduction to Computational Methods for Many-Body Systems, M. Bonitz and D. Semkat (eds.), Rinton Press, Princeton (2006)

Visual Data Comm: A Tool for Visualizing Data Communication in the Multi Sector Planner Study

NASA Technical Reports Server (NTRS)

Lee, Hwasoo Eric

2010-01-01

Data comm is a new technology proposed in future air transport system as a potential tool to provide comprehensive data connectivity. It is a key enabler to manage 4D trajectory digitally, potentially resulting in improved flight times and increased throughput. Future concepts with data comm integration have been tested in a number of human-in-the-loop studies but analyzing the results has proven to be particularly challenging because future traffic environment in which data comm is fully enabled has assumed high traffic density, resulting in data set with large amount of information. This paper describes the motivation, design, current and potential future application of Visual Data Comm (VDC), a tool for visualizing data developed in Java using Processing library which is a tool package designed for interactive visualization programming. This paper includes an example of an application of VDC on data pertaining to the most recent Multi Sector Planner study, conducted at NASA s Airspace Operations Laboratory in 2009, in which VDC was used to visualize and interpret data comm activities

Analytic integrable systems: Analytic normalization and embedding flows

NASA Astrophysics Data System (ADS)

Zhang, Xiang

In this paper we mainly study the existence of analytic normalization and the normal form of finite dimensional complete analytic integrable dynamical systems. More details, we will prove that any complete analytic integrable diffeomorphism F(x)=Bx+f(x) in (Cn,0) with B having eigenvalues not modulus 1 and f(x)=O(|) is locally analytically conjugate to its normal form. Meanwhile, we also prove that any complete analytic integrable differential system x˙=Ax+f(x) in (Cn,0) with A having nonzero eigenvalues and f(x)=O(|) is locally analytically conjugate to its normal form. Furthermore we will prove that any complete analytic integrable diffeomorphism defined on an analytic manifold can be embedded in a complete analytic integrable flow. We note that parts of our results are the improvement of Moser's one in J. Moser, The analytic invariants of an area-preserving mapping near a hyperbolic fixed point, Comm. Pure Appl. Math. 9 (1956) 673-692 and of Poincaré's one in H. Poincaré, Sur l'intégration des équations différentielles du premier order et du premier degré, II, Rend. Circ. Mat. Palermo 11 (1897) 193-239. These results also improve the ones in Xiang Zhang, Analytic normalization of analytic integrable systems and the embedding flows, J. Differential Equations 244 (2008) 1080-1092 in the sense that the linear part of the systems can be nonhyperbolic, and the one in N.T. Zung, Convergence versus integrability in Poincaré-Dulac normal form, Math. Res. Lett. 9 (2002) 217-228 in the way that our paper presents the concrete expression of the normal form in a restricted case.

Direct discontinuous Galerkin method and its variations for second order elliptic equations

DOE PAGES

Huang, Hongying; Chen, Zheng; Li, Jin; ...

2016-08-23

In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Mathmore » 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.« less

Adjunctation and Scalar Product in the Dirac Equation - II

NASA Astrophysics Data System (ADS)

Dima, M.

2017-02-01

Part-I Dima (Int. J. Theor. Phys. 55, 949, 2016) of this paper showed in a representation independent way that γ 0 is the Bergmann-Pauli adjunctator of the Dirac { γ μ } set. The distiction was made between similarity (MATH) transformations and PHYS transformations - related to the (covariant) transformations of physical quantities. Covariance is due solely to the gauging of scalar products between systems of reference and not to the particular action of γ 0 on Lorentz boosts - a matter that in the past led inadvertently to the definition of a second scalar product (the Dirac-bar product). Part-II shows how two scalar products lead to contradictions and eliminates this un-natural duality in favour of the canonical scalar product and its gauge between systems of reference. What constitutes a proper observable is analysed and for instance spin is revealed not to embody one (except as projection on the boost direction - helicity). A thorough investigation into finding a proper-observable current for the theory shows that the Dirac equation does not possess one in operator form. A number of problems with the Dirac current operator are revealed - its Klein-Gordon counterpart being significantly more physical. The alternative suggested is finding a current for the Dirac theory in scalar form j^{μ } = < ρ rangle _{_{ψ }}v^{μ }_{ψ }.

The Fourier transforms for the spatially homogeneous Boltzmann equation and Landau equation

NASA Astrophysics Data System (ADS)

Meng, Fei; Liu, Fang

2018-03-01

In this paper, we study the Fourier transforms for two equations arising in the kinetic theory. The first equation is the spatially homogeneous Boltzmann equation. The Fourier transform of the spatially homogeneous Boltzmann equation has been first addressed by Bobylev (Sov Sci Rev C Math Phys 7:111-233, 1988) in the Maxwellian case. Alexandre et al. (Arch Ration Mech Anal 152(4):327-355, 2000) investigated the Fourier transform of the gain operator for the Boltzmann operator in the cut-off case. Recently, the Fourier transform of the Boltzmann equation is extended to hard or soft potential with cut-off by Kirsch and Rjasanow (J Stat Phys 129:483-492, 2007). We shall first establish the relation between the results in Alexandre et al. (2000) and Kirsch and Rjasanow (2007) for the Fourier transform of the Boltzmann operator in the cut-off case. Then we give the Fourier transform of the spatially homogeneous Boltzmann equation in the non cut-off case. It is shown that our results cover previous works (Bobylev 1988; Kirsch and Rjasanow 2007). The second equation is the spatially homogeneous Landau equation, which can be obtained as a limit of the Boltzmann equation when grazing collisions prevail. Following the method in Kirsch and Rjasanow (2007), we can also derive the Fourier transform for Landau equation.

The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Korhonen, Marko; Lee, Eunghyun

2014-01-15

We treat the N-particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model by Sasamoto and Wadati [“Exact results for one-dimensional totally asymmetric diffusion models,” J. Phys. A 31, 6057–6071 (1998)] or the q-totally asymmetric zero range process (TAZRP) by Borodin and Corwin [“Macdonald processes,” Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle'smore » position at time t. To find the probability for the left-most particle's position we find a new identity corresponding to identity for the asymmetric simple exclusion process by Tracy and Widom [“Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.« less

Conformal invariance of the Lungren-Monin-Novikov equations for vorticity fields in 2D turbulence

NASA Astrophysics Data System (ADS)

Grebenev, V. N.; Wacławczyk, M.; Oberlack, M.

2017-10-01

We study the statistical properties of the vorticity field in two-dimensional turbulence. The field is described in terms of the infinite Lundgren-Monin-Novikov (LMN) chain of equations for multi-point probability density functions (pdf’s) of vorticity. We perform a Lie group analysis of the first equation in this chain using the direct method based on the canonical Lie-Bäcklund transformations devised for integro-differential equations. We analytically show that the conformal group is broken for the first LMN equation i.e. for the 1-point pdf at least for the inviscid case but the equation is still conformally invariant on the associated characteristic with zero-vorticity. Then, we demonstrate that this characteristic is conformally transformed. We find this outcome coincides with the numerical results about the conformal invariance of the statistics of zero-vorticity isolines, see e.g. Falkovich (2007 Russian Math. Surv. 63 497-510). The conformal symmetry can be understood as a ‘local scaling’ and its traces in two-dimensional turbulence were already discussed in the literature, i.e. it was conjectured more than twenty years ago in Polyakov (1993 Nucl. Phys. B 396 367-85) and clearly validated experimentally in Bernard et al (2006 Nat. Phys. 2 124-8).

Direct discontinuous Galerkin method and its variations for second order elliptic equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Hongying; Chen, Zheng; Li, Jin

In this study, we study direct discontinuous Galerkin method (Liu and Yan in SIAM J Numer Anal 47(1):475–698, 2009) and its variations (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010; Vidden and Yan in J Comput Math 31(6):638–662, 2013; Yan in J Sci Comput 54(2–3):663–683, 2013) for 2nd order elliptic problems. A priori error estimate under energy norm is established for all four methods. Optimal error estimate under L 2 norm is obtained for DDG method with interface correction (Liu and Yan in Commun Comput Phys 8(3):541–564, 2010) and symmetric DDG method (Vidden and Yan in J Comput Mathmore » 31(6):638–662, 2013). A series of numerical examples are carried out to illustrate the accuracy and capability of the schemes. Numerically we obtain optimal (k+1)th order convergence for DDG method with interface correction and symmetric DDG method on nonuniform and unstructured triangular meshes. An interface problem with discontinuous diffusion coefficients is investigated and optimal (k+1)th order accuracy is obtained. Peak solutions with sharp transitions are captured well. Highly oscillatory wave solutions of Helmholz equation are well resolved.« less

Development of the LaComm 1.0, A French medical communication analysis software: A study assessing its sensitivity to change.

PubMed

Gibon, Anne-Sophie; Durieux, Jean-François; Merckaert, Isabelle; Delvaux, Nicole; Farvacques, Christine; Libert, Yves; Marchal, Serge; Moucheux, Angélique; Slachmuylder, Jean-Louis; Razavi, Darius

2017-02-01

To test and compare the sensitivity to change of a communication analysis software, the LaComm 1.0, to the CRCWEM's using data from a randomized study assessing the efficacy of a communication skills training program designed for nurses. The program assessment included the recording of two-person simulated interviews at baseline and after training or 3 months later. Interview transcripts were analyzed using the CRCWEM and the LaComm 1.0 tools. One hundred and nine oncology nurses (mainly graduated or certified) were included in the study. The CRCWEM detected 5 changes out of 13 expected changes (38%) (e.g., more open directive questions after training) and the LaComm 1.0, 4 changes out of 7 expected changes (57%) (e.g., more empathic statements after training). For open directive question, the effect sizes of the group-by-time changes were slightly different between tools (CRCWEM: Cohen's d=0.97; LaComm 1.0: Cohen's d=0.67). This study shows that the LaComm 1.0 is sensitive to change. The LaComm 1.0 is a valid method to assess training effectiveness in French. The use of the Lacomm 1.0 in future French communication skills training programs will allow comparisons of studies. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries

NASA Astrophysics Data System (ADS)

Balseiro, Paula; Sansonetto, Nicola

2016-02-01

We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of M-cotangent lift of a vector field on a manifold Q in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fassò F., Ramos A., Sansonetto N., Regul. Chaotic Dyn. 12 (2007), 579-588], and [Fassò F., Giacobbe A., Sansonetto N., Rep. Math. Phys. 62 (2008), 345-367]. Second, we study gauge symmetries and gauge momenta, in the cases in which there are the symmetries that satisfy the so-called vertical symmetry condition. Under such condition we can predict the number of linearly independent first integrals (that are gauge momenta). We illustrate the theory with two examples.

Conformal collineations and anisotropic fluids in general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duggal, K.L.; Sharma, R.

1986-10-01

Recently, Herrera et al. (L. Herrera, J. Jimenez, L. Leal, J. Ponce de Leon, M. Esculpi, and V. Galino, J. Math. Phys. 25, 3274 (1984)) studied the consequences of the existence of a one-parameter group of conformal motions for anisotropic matter. They concluded that for special conformal motions, the stiff equation of state (p = ..mu..) is singled out in a unique way, provided the generating conformal vector field is orthogonal to the four-velocity. In this paper, the same problem is studied by using conformal collineations (which include conformal motions as subgroups). It is shown that, for a special conformalmore » collineation, the stiff equation of state is not singled out. Non-Einstein Ricci-recurrent spaces are considered as physical models for the fluid matter.« less

COMMENT Comment on 'Conservation laws of higher order nonlinear PDEs and the variational conservation laws in the class with mixed derivatives'

NASA Astrophysics Data System (ADS)

Sarlet, W.

2010-11-01

In a recent paper (R Narain and A H Kara 2010 J. Phys. A: Math. Theor. 43 085205), the authors claim to be applying Noether's theorem to higher-order partial differential equations and state that in a large class of examples 'the resultant conserved flows display some previously unknown interesting 'divergence properties' owing to the presence of the mixed derivatives' (citation from their abstract). It turns out that what this obscure sentence is meant to say is that the vector whose divergence must be zero (according to Noether's theorem), turns out to have non-zero divergence and subsequently must be modified to obtain a true conservation law. Clearly this cannot be right: we explain in detail the main source of the error.

Integrability and superintegrability of the generalized n-level many-mode Jaynes-Cummings and Dicke models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skrypnyk, T.

2009-10-15

We analyze symmetries of the integrable generalizations of Jaynes-Cummings and Dicke models associated with simple Lie algebras g and their reductive subalgebras g{sub K}[T. Skrypnyk, 'Generalized n-level Jaynes-Cummings and Dicke models, classical rational r-matrices and nested Bethe ansatz', J. Phys. A: Math. Theor. 41, 475202 (2008)]. We show that their symmetry algebras contain commutative subalgebras isomorphic to the Cartan subalgebras of g, which can be added to the commutative algebras of quantum integrals generated with the help of the quantum Lax operators. We diagonalize additional commuting integrals and constructed with their help the most general integrable quantum Hamiltonian of themore » generalized n-level many-mode Jaynes-Cummings and Dicke-type models using nested algebraic Bethe ansatz.« less

Applicability of modified effective-range theory to positron-atom and positron-molecule scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Idziaszek, Zbigniew; Karwasz, Grzegorz; Instytut Fizyki, Uniwersytet Mikolaja Kopernika, 87-100 Torun

2006-06-15

We analyze low-energy scattering of positrons on Ar atoms and N{sub 2} molecules using the modified effective-range theory (MERT) developed by O'Malley, et al. [J. Math. Phys. 2, 491 (1961)]. We use the formulation of MERT based on exact solutions of the Schroedinger equation with polarization potential rather than low-energy expansions of phase shifts into momentum series. We show that MERT describes the experimental data well, provided that effective-range expansion is performed both for s- and p-wave scattering, which dominate in the considered regime of positron energies (0.4-2 eV). We estimate the values of the s-wave scattering length and themore » effective range for e{sup +}-Ar and e{sup +}-N{sub 2} collisions.« less

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

NASA Astrophysics Data System (ADS)

Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang

2018-05-01

Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.

Decay of Complex-Time Determinantal and Pfaffian Correlation Functionals in Lattices

NASA Astrophysics Data System (ADS)

Aza, N. J. B.; Bru, J.-B.; de Siqueira Pedra, W.

2018-04-01

We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903-931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time correlations. Our proof uses the analyticity of correlation functions via the Hadamard three-line theorem. We show that the dynamical localization for the one-particle system yields the dynamical localization for the many-point fermionic correlation functions, with respect to the Hausdorff distance in the determinantal case. In Sims and Warzel (2016), a stronger notion of decay for many-particle configurations was used but only at dimension one and for real times. Considering determinantal and Pfaffian correlation functionals for complex times is important in the study of weakly interacting fermions.

Presymplectic current and the inverse problem of the calculus of variations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khavkine, Igor, E-mail: i.khavkine@uu.nl

2013-11-15

The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a variational formulation for a subsystem of the given PDE. No constraints on the differential order or number of dependent or independent variables are assumed. The proof follows a recent observation of Bridges, Hydon, and Lawson [Math. Proc. Cambridge Philos. Soc. 148(01), 159–178 (2010)] and generalizes an older result of Henneaux [Ann. Phys. 140(1), 45–64 (1982)]more » from ordinary differential equations (ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.« less

Decay of Complex-Time Determinantal and Pfaffian Correlation Functionals in Lattices

NASA Astrophysics Data System (ADS)

Aza, N. J. B.; Bru, J.-B.; de Siqueira Pedra, W.

2018-06-01

We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903-931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time correlations. Our proof uses the analyticity of correlation functions via the Hadamard three-line theorem. We show that the dynamical localization for the one-particle system yields the dynamical localization for the many-point fermionic correlation functions, with respect to the Hausdorff distance in the determinantal case. In Sims and Warzel (2016), a stronger notion of decay for many-particle configurations was used but only at dimension one and for real times. Considering determinantal and Pfaffian correlation functionals for complex times is important in the study of weakly interacting fermions.

Antihypertensive effects of central ablations in spontaneously hypertensive rats.

PubMed

Moreira, Thiago S; Takakura, Ana C; Colombari, Eduardo; Menani, José V

2009-06-01

Commissural nucleus of the solitary tract (commNTS) lesions transitorily (first 5 days) reduce mean arterial pressure (MAP) in spontaneously hypertensive rats (SHR), and lesions of the tissue surrounding the anteroventral third ventricle (AV3V region) chronically reduce MAP in other models of hypertension. In the present study, we investigated the effects of combined AV3V+commNTS electrolytic lesions on MAP and heart rate (HR) in conscious SHR. Baseline MAP and HR were recorded in male SHR before and for the next 40 days after sham or AV3V lesions combined with sham or commNTS lesions. The AV3V lesions produced no change in MAP in SHR, while commNTS lesions reduced MAP acutely (121 +/- 2 to 127 +/- 3 mmHg in the 1st and 5th days, respectively, vs. prelesion: 192 +/- 4 mmHg) but not chronically (from 10 to 40 days). However, combined AV3V+commNTS lesions reduced MAP of SHR chronically (119 +/- 2 to 161 +/- 4 mmHg, in the 1st and 40th day, respectively, vs. prelesion levels: 186 +/- 4 mmHg) or sham-lesioned SHR (187 +/- 4 to 191 +/- 6 mmHg). Sympathetic and angiotensinergic blockade produced less reduction in MAP in SHR with AV3V+commNTS-lesions, and there was no relationship between changes on water and food intake, body weight, or urinary excretion produced by AV3V+commNTS lesions with the changes in MAP. The present findings suggest that in the absence of the commNTS, the AV3V region contributes to the hypertension observed in SHR by mechanisms that appear to involve enhanced angiotensinergic and sympathetic activity.

Simulation of Noise in a Traveling Wave Tube

NASA Astrophysics Data System (ADS)

Verboncoeur, J. P.; Christenson, P. J.; Smith, H. B.

1999-11-01

Low frequency noise, manifested as close-in sidebands, has long been a significant limit to the performance of many traveling wave tubes. In this study, we investigate oscillations in the gun region due to the presence of plasma formed by electron-impact ionization of a background gas. The gun region of a coupled-cavity traveling wave tube is modeled using the two-dimensional XOOPIC particle-in-cell Monte Carlo collision code (J. P. Verboncoeur et al. Comput. Phys. Comm.) 87, 199-211 (1995). (available via the web: http://ptsg.eecs.berkeley.edu). The beam is 20.5 kV, 2.8 A, in near-confined flow in a solenoidal magnetic field with peak axial value of 0.263 T. Beam scalloping leads to trapping of plasma generated via electron-impact ionization of a background gas. The trapped plasma periodically leaves the system rapidly, and the density begins regenerating at a slow rate, leading to characteristic sawtooth oscillations. Plasma electrons are observed to exit the system axially about 20 ns before the ions exit primarily radially.

Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker's 75th birthday Applications of zeta functions and other spectral functions in mathematics and physics: a special issue in honour of Stuart Dowker's 75th birthday

NASA Astrophysics Data System (ADS)

Dowker, Fay; Elizalde, Emilio; Kirsten, Klaus

2012-09-01

John Stuart Dowker was born in Sheffield, Yorkshire, on 18 March 1937. His life, therefore, was very much influenced by the Second World War. This is evident as his father died on active service in 1945, after being called up in 1941. His grandfather also died shortly afterwards, so he did not know either of them very well. Nevertheless, it seems that he picked up a positive attitude towards natural sciences as both were technically minded. His mother later provided, often from borrowed money, all the necessary intellectual food in forms of chemistry sets, slide rules and other things that a boy needed to develop his interests. Stuart scored excellently in the 11-plus exam, which was used to decide the type of school a pupil should attend after primary school. Although Stuart was generally allowed to do what he wanted, his mother insisted that he chose King Edward VII Grammar School (KES), the top school in Sheffield at the time. KES allowed Stuart to fully develop his intellectual abilities, and after the S-level exam he received a prestigious state scholarship which allowed him to study at any university in the country. He picked Nottingham over other possibilities, mainly because of his interest in electronics and because of the relative proximity to his family. In Nottingham, where he stayed from 1955 to 1958, his research concentration turned out to be mostly solid state physics. But with time on his hands, Stuart raided the library and taught himself things like complex analysis and quantum mechanics, with de Broglie's La mécanique ondulatoire [1] as one of his favorites. Remarkably, this book already contains a discussion of quantization on curved configuration spaces, a setting so relevant in Stuart's later career. Stuart wanted to investigate quantum field theory for his doctoral thesis. So he wrote, among others, to Rudolph Peierls in Birmingham, and, after being interviewed by Peierls himself and J G Valatin, he received an offer of a PhD position. He went to Birmingham in 1958, where his supervisor was Leonardo Castillejo, best known from the Castillejo-Dalitz-Dyson-ambiguity see [2]. His thesis involved stripping theory, and on this topic he wrote his first ever publication [3]. Takeaways from that time were that sometimes one simply has to do what one is told, and even more importantly, sometimes one has to get on with a calculation and 'just roll through it'. It was also around that period that Stuart started to learn quantum field theory properly following the developments of Feynman. After his PhD, it was Peierls who helped him to find a position at the University of Pennsylvania in Philadelphia in 1961, which he accepted before he received an offer from CERN. In retrospect, this was probably fortunate as it is where he met his wife, Pwu Yih, to whom he has been married for nearly 50 years. Scientifically he remained somewhat isolated there and spent much of his time learning more about quantum field theory, for example by reading Bogoliubov and Shirkov [4]. His entry point for general relativity was Eddington's The Mathematical Theory of Relativity [5], which together with the works of Julian Schwinger and Bryce de Witt were the most influential ones at that time. A shift of focus to questions in quantum field theory in curved space time took place. After his stay in Philadelphia, in 1963, helped by connections between Abe Klein and Brian Flowers, he went to the University of Manchester, where he remains to this day. This period was only briefly interrupted by a sabbatical in 1978 to 1979 at Austin following an invitation by Bryce de Witt. Looking back, it seems there were two major driving forces or principles that determined much of Stuart's selection of research projects. One of them is the method of images, about which he says: '...it intrigued me that one problem (charge + plane) could be got from another (just charge) by geometrical reasoning plus uniqueness. Thomson's book [6] took this further. Chapter 5 is devoted to the image and inversion methods and I must have read this closely as there are lots of marginal notes...' The second principle can be read off from the following quote: 'After reading Eddington circa 1960 it was clear to me (and others of course) there is a strong analogy (at least) between gravitation and electromagnetism ... (His work has very strongly influenced me.) So I played a game of asking for the gravitational analogues of existing electromagnetic concepts. The basic analogue is between field strength/charge and curvature/spin... [in that] ...spin, in general relativity, plays the passive role that charge plays in electromagnetism in the sense that it is the spin-curvature coupling that knocks a particle off a geodesic.' It is quite amazing how much of Stuart's work can be traced back to these principles. This is briefly explained in the following by describing some of his most important works. His most cited work [7] fits this bill and can be seen as doing what Julian Schwinger did in [8], for a constant electromagnetic field in the gravitational setting. In more detail he noticed Schulman's work on propagators on the three sphere [9], which he extended to Lie groups; see [10, 11]. He then noticed that having exact propagators, work like Schwinger's could be done and de Sitter space was a natural 'curved' candidate. The paper is best known for the mathematical technique introduced, namely for the zeta function method much used since for the computation of singular quantum field theoretic quantities like effective actions and the Casimir energy. The motivation for introducing this scheme goes back to reading an article of I M Gel'fand about some number theory problem involving zeta functions, image sums, propagators etc. How could an object occurring with other objects physicists were using all the time not be useful? It turned out to be very useful, although in this paper the method was only introduced but actually not used! This is probably the reason that his paper did not receive the same recognition as the one by Hawking [12], where zeta function regularization was mentioned in the title and where it was actually applied to examples in the article. Of course, Stuart's and Raymond's paper hit the pulse of the time in that after Stephen Hawking's announcement about Hawking radiation [13], the quantum field theory in curved space-time frenzy began. He had been interested in that subject for a while, the most important influence being de Witt's Les Houches lectures and also Chris Isham, who introduced him to Dennis Sciama's Oxford group, including Philip Candelas and Derek Raine, in 1973. The project about de Sitter space got somewhat delayed by work on path integrals and the ordering problem until Ray Critchley came by looking for a PhD topic. Several more of his best known papers are in the context of quantum field theory in curved spacetime. In the article [14], conformal transformations play a fundamental role. They are used to transform static manifolds to ultra-static ones where a high-temperature expansion of the effective action can be done. The result has since been rediscovered many times for special cases. In the process they also showed results about the conformal transformation of heat kernel coefficients claimed later on by mathematicians. The paper by Kennedy, Critchley and Dowker [15] belongs in the same context. Deutsch and Candelas had shown the occurrence of non-integrable singularities near boundaries of the Casimir energy densities, which made it impossible to obtain global energies by naively integrating local quantities. To resolve that problem, the needed surface counterterms for an arbitrarily shaped smooth boundary in curved space were computed. How does the paper [16] fit into the general scheme? The seed to considering this topic was probably planted when Yakir Aharonov was visiting Birmingham in 1958. In the Aharonov-Bohm effect we have an electromagnetic field with finite extension that impacts particles never entering that region. What is the gravitational analogue for that situation? The analogue concerns the impact a localized curvature has, and the cone is an excellent example to shed light on that question. Related to the method of images, Stuart has done an enormous amount of work on the influence of topology and curvature on quantum field theory. An example is [17], where the vacuum stress-energy tensor for Clifford-Klein forms of the flat or spherical type were computed. Another strand we would like to mention is Stuart's interest in higher spin equations. In [18], Steven Weinberg wrote down a set of higher spin equations that took his fancy. They involved angular momentum theory, which has always pleased Stuart, and the description was an alternative to Roger Penrose's use of two-spinors. Investigating the inconsistencies that arose on coupling to gauge theories, Stuart extended the classic results in [19], from electromagnetism to gravity in accordance with his general philosophy; see, e.g., [20, 21, 22]. Lately, Stuart is best known for his many applications in the context of zeta function regularization and its applications to quantum field theory under external conditions and spectral theory. He can be considered the world expert on particular case calculations with a knowledge of the literature, old and recent, that is not seen very often and which originated in the many hours spent at different (mostly British) libraries. His attitude towards explicit computations is nicely summarized by himself: 'I have always been interested in exact solutions, even if unphysical, so long as they are pretty. They seem to be working mechanisms that fit together, complete in themselves, like a watch.' The following issue in honour of Stuart's 75th birthday contains contributions that touch upon the various topics he has worked on. References [1] de Broglie L 1928 La mécanique ondulatoire (Paris: Gauthier-Villars) [2] Castillejo L, Dalitz R H and Dyson F J 1956 Low's scattering equation for the charged and neutral scalar theories Phys. Rev. 101 453 [3] Dowker J S 1961 Application of the Chew and Low extrapolation procedure to K- + d → Y + N + π absorption reactions Il Nuovo Cimento 10 182 [4] Bogoliubov N N and Shirkov D V 1959 Introduction to the Theory of Quantized Fields (New York: Interscience) [5] Eddington A S 1923 The Mathematical Theory of Relativity (Cambridge: Cambridge University Press) [6] Thomson J J 1909 Elements of Electricity and Magnetism 4th edn (Cambridge: Cambridge University Press) [7] Dowker J S and Critchley R 1976 Effective Lagrangian and energy momentum tensor in de Sitter space Phys. Rev. D 13 3224 [8] Schwinger J 1951 On gauge invariance and vacuum polarization Phys. Rev. 82 664 [9] Schulman L S 1968 A path integral for spin Phys. Rev. 176 1558 [10] Dowker J S 1970 When is the sum over classical paths exact? J. Phys. A: Math. Gen. 3 451 [11] Dowker J S 1971 Quantum mechanics on group space and Huygens' principle Ann. Phys. 62 361 [12] Hawking S W 1977 Zeta function regularization of path integrals in curved space-time Comm. Math. Phys. 55133 [13] Hawking S W 1974 Black hole explosions Nature 248 30 [14] Dowker J S and Kennedy G 1978 Finite temperature and boundary effects in static space-times J. Phys. A: Math. Gen. 11 895 [15] Kennedy G, Critchley R and Dowker J S 1980 Finite temperature field theory with boundaries: stress tensor and surface action renormalization Ann. Phys. 125 346 [16] Dowker J S 1977 Quantum field theory on a cone J. Phys. A: Math. Gen. 10 115 [17] Dowker J S and Banach R 1978 Quantum field theory on Clifford-Klein space-times. The effective Lagrangian and vacuum stress-energy tensor J. Phys. A: Math. Gen. 11 2255 [18] Weinberg S 1964 Feynman rules for any spin Phys. Rev. 133 B1318 [19] Fierz M and Pauli W 1939 On relativistic wave equations for particles of arbitrary spin in an electromagnetic field Proc. Roy. Soc. A 173 221 [20] Dowker J S and Dowker Y P 1966 Particles of arbitrary spin in curved spaces Proc. Phys. Soc. (Lond.) 87 65 [21] Dowker J S and Dowker Y P 1966 Interactions of massless particles of arbitrary spin Proc. Roy. Soc. A 294 175 [22] Dowker J S 1972 Propagators for arbitrary spin in an Einstein universe Ann. Phys. 71 577

78 FR 61003 - Endangered and Threatened Wildlife and Plants; Endangered Species Status for the Florida Bonneted...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-10-02

..., pers. comm. 2006a). However, four young were noted in 2004 (S. Trokey, pers. comm. 2006a). The capture... cavity as a roost site in Punta Gorda, was a harem group, based on its sex ratio. Belwood (1981, p. 412... individuals, occupying four houses (J. Birchfield, FWC, pers. comm. 2010; Marks and Marks 2012, pp. 12, A61...

Molecular Line Lists for Scandium and Titanium Hydride Using the DUO Program

NASA Astrophysics Data System (ADS)

Lodi, Lorenzo; Yurchenko, Sergei N.; Tennyson, Jonathan

2015-06-01

Transition-metal-containing (TMC) molecules often have very complex electronic spectra because of their large number of low-lying, interacting electronic states, of the large multi-reference character of the electronic states and of the large magnitude of spin-orbit and relativistic effects. As a result, fully ab initio calculations of line positions and intensities of TMC molecules have an accuracy which is considerably worse than the one usually achievable for molecules made up by main-group atoms only. In this presentation we report on new theoretical line lists for scandium hydride ScH and titanium hydride TiH. Scandium and titanium are the lightest transition metal atoms and by virtue of their small number of valence electrons are amenable to high-level electronic-structure treatments and serve as ideal benchmark systems. We report for both systems energy curves, dipole curves and various coupling curves (including spin-orbit) characterising their electronic spectra up to about 20 000 cm-1. Curves were obtained using Internally-Contracted Multi Reference Configuration Interaction (IC-MRCI) as implemented in the quantum chemistry package MOLPRO. The curves where used for the solution of the coupled-surface ro-vibronic problem using the in-house program DUO. DUO is a newly-developed, general program for the spectroscopy of diatomic molecules and its main functionality will be described. The resulting line lists for ScH and TiH are made available as part of the Exomol project. L. Lodi, S. N. Yurchenko and J. Tennyson, Mol. Phys. (Handy special issue) in press. S. N. Yurchenko, L. Lodi, J. Tennyson and A. V. Stolyarov, Computer Phys. Comms., to be submitted.

Damping of microwave induced oscillations in the magneto-resistance of high-mobility 2D electrons: role of disorder

NASA Astrophysics Data System (ADS)

Studenikin, Sergei; Potemski, M.; Coleridge, P. T.; Sachrajda, A.; Zawadzki, P.; Ciorga, M.; Pioro-Landriere, M.; Hilke, M.; Pfeiffer, L. N.; West, K. W.

2004-03-01

Microwave induced resistance oscillations (MIROs), first observed by Zudov et al. [1] and Mani et al. [2] in the longitudinal resistance of high mobility 2DEGs are the subject of extensive theoretical and experimental studies. We have reported recently that MIROs can reveal themselves in the Hall effect as well. [3] In this work we study the waveform and damping of the MIROs as a function of temperature and magnetic field with the purpose of clarifying the role of Landau level broadening. MIROs have been measured on a ˜ 10^7 cm^2/Vs mobility 2DEG GaAs/AlGaAs sample using 50 GHz excitation. To complement these studies, we have also measured the Shubnikov de Haas (SdH) oscillations at low magnetic fields on the same sample at temperatures down to ˜ 30mK. We found that the damping of the MIROs and SdH oscillations is given by a very similar functional dependence, although the MIROs are a more robust phenomena with respect to Landau level broadening and temperature. In both cases the amplitude can be described by ˜ exp(-α kT/ ω_c)exp(-D/ ω_c). In our experiment we found that α _SdH =2π ^2 and α _MIROs.ng 0.7. 1. M.A. Zudov, R.R. Du, J.A. Simmons, and J.L. Reno, Phys. Rev. B Phys. Rev. Lett., 90, 46807 (2003) 2. R.G. Mani, J.H. Smet, K. von Klitzing, V. Narayanamurti,W.B. Johnson, and V. Umansky, Nature 420, 646 (2002) 3. S.A. Studenikin, M. Potemski, P.T. Coleridge, A. Sachrajda, Z.R. Wasilewski, Solid State Comm. 129, 341(2004)

Damping of microwave induced oscillations in the magneto-resistance of high-mobility 2D electrons: role of disorder

NASA Astrophysics Data System (ADS)

Studenikin, Sergei; Potemski, M.; Coleridge, P. T.; Sachrajda, A.; Zawadzki, P.; Ciorga, M.; Pioro-Landriere, M.; Hilke, M.; Pfeiffer, L. N.; West, K. W.

2004-03-01

Microwave induced resistance oscillations (MIROs), first observed by Zudov et al. [1] and Mani et al. [2] in the longitudinal resistance of high mobility 2DEGs are the subject of extensive theoretical and experimental studies. We have reported recently that MIROs can reveal themselves in the Hall effect as well. [3] In this work we study the waveform and damping of the MIROs as a function of temperature and magnetic field with the purpose of clarifying the role of Landau level broadening. MIROs have been measured on a ˜ 10^7 cm^2/Vs mobility 2DEG GaAs/AlGaAs sample using 50 GHz excitation. To complement these studies, we have also measured the Shubnikov de Haas (SdH) oscillations at low magnetic fields on the same sample at temperatures down to ˜ 30mK. We found that the damping of the MIROs and SdH oscillations is given by a very similar functional dependence, although the MIROs are a more robust phenomena with respect to Landau level broadening and temperature. In both cases the amplitude can be described by ˜ exp(-α kT/ ω _c)exp(-D/ ω_c). In our experiment we found that α _SdH =2π ^2 and α _MIROs.ng 0.7. 1. M.A. Zudov, R.R. Du, J.A. Simmons, and J.L. Reno, Phys. Rev. B Phys. Rev. Lett., 90, 46807 (2003) 2. R.G. Mani, J.H. Smet, K. von Klitzing, V. Narayanamurti,W.B. Johnson, and V. Umansky, Nature 420, 646 (2002) 3. S.A. Studenikin, M. Potemski, P.T. Coleridge, A. Sachrajda, Z.R. Wasilewski, Solid State Comm. 129, 341(2004)

Constructing Integrable Full-pressure Full-current Free-boundary Stellarator Magnetohydrodynamic Equilibria

NASA Astrophysics Data System (ADS)

Hudson, S. R.; Monticello, D. A.; Reiman, A. H.; Strickler, D. J.; Hirshman, S. P.

2003-06-01

For the (non-axisymmetric) stellarator class of plasma confinement devices to be feasible candidates for fusion power stations it is essential that, to a good approximation, the magnetic field lines lie on nested flux surfaces; however, the inherent lack of a continuous symmetry implies that magnetic islands are guaranteed to exist. Magnetic islands break the smooth topology of nested flux surfaces and chaotic field lines result when magnetic islands overlap. An analogous case occurs with 11/2-dimension Hamiltonian systems where resonant perturbations cause singularities in the transformation to action-angle coordinates and destroy integrability. The suppression of magnetic islands is a critical issue for stellarator design, particularly for small aspect ratio devices. Techniques for `healing' vacuum fields and fixed-boundary plasma equilibria have been developed, but what is ultimately required is a procedure for designing stellarators such that the self-consistent plasma equilibrium currents and the coil currents combine to produce an integrable magnetic field, and such a procedure is presented here for the first time. Magnetic islands in free-boundary full-pressure full-current stellarator magnetohydrodynamic equilibria are suppressed using a procedure based on the Princeton Iterative Equilibrium Solver [A.H.Reiman & H.S.Greenside, Comp. Phys. Comm., 43:157, 1986.] which iterates the equilibrium equations to obtain the plasma equilibrium. At each iteration, changes to a Fourier representation of the coil geometry are made to cancel resonant fields produced by the plasma. As the iterations continue, the coil geometry and the plasma simultaneously converge to an equilibrium in which the island content is negligible. The method is applied to a candidate plasma and coil design for the National Compact Stellarator eXperiment [G.H.Neilson et.al., Phys. Plas., 7:1911, 2000.].

Why do Scale-Free Networks Emerge in Nature? From Gradient Networks to Transport Efficiency

NASA Astrophysics Data System (ADS)

Toroczkai, Zoltan

2004-03-01

It has recently been recognized [1,2,3] that a large number of complex networks are scale-free (having a power-law degree distribution). Examples include citation networks [4], the internet [5], the world-wide-web [6], cellular metabolic networks [7], protein interaction networks [8], the sex-web [9] and alliance networks in the U.S. biotechnology industry [10]. The existence of scale-free networks in such diverse systems suggests that there is a simple underlying common reason for their development. Here, we propose that scale-free networks emerge because they ensure efficient transport of some entity. We show that for flows generated by gradients of a scalar "potential'' distributed on a network, non scale-free networks, e.g., random graphs [11], will become maximally congested, while scale-free networks will ensure efficient transport in the large network size limit. [1] R. Albert and A.-L. Barabási, Rev.Mod.Phys. 74, 47 (2002). [2] M.E.J. Newman, SIAM Rev. 45, 167 (2003). [3] S.N. Dorogovtsev and J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW, Oxford Univ. Press, Oxford, 2003. [4] S. Redner, Eur.Phys.J. B, 4, 131 (1998). [5] M. Faloutsos, P. Faloutsos and C. Faloutsos Comp.Comm.Rev. 29, 251 (1999). [6] R. Albert, H. Jeong, and A.L. Barabási, Nature 401, 130 (1999). [7] H. Jeong et.al. Nature 407, 651 (2000). [8] H. Jeong, S. Mason, A.-L. Barabási and Z. N. Oltvai, Nature 411, 41 (2001). [9] F. Liljeros et. al. Nature 411 907 (2000). [10] W. W. Powell, D. R. White, K. W. Koput and J. Owen-Smith Am.J.Soc. in press. [11] B. Bollobás, Random Graphs, Second Edition, Cambridge University Press (2001).

KANTBP: A program for computing energy levels, reaction matrix and radial wave functions in the coupled-channel hyperspherical adiabatic approach

NASA Astrophysics Data System (ADS)

Chuluunbaatar, O.; Gusev, A. A.; Abrashkevich, A. G.; Amaya-Tapia, A.; Kaschiev, M. S.; Larsen, S. Y.; Vinitsky, S. I.

2007-10-01

A FORTRAN 77 program is presented which calculates energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on the finite interval with homogeneous boundary conditions of the third type. The resulting system of radial equations which contains the potential matrix elements and first-derivative coupling terms is solved using high-order accuracy approximations of the finite-element method. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 4224 No. of bytes in distributed program, including test data, etc.: 31 232 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Intel Xeon EM64T, Alpha 21264A, AMD Athlon MP, Pentium IV Xeon, Opteron 248, Intel Pentium IV Operating system: OC Linux, Unix AIX 5.3, SunOS 5.8, Solaris, Windows XP RAM: depends on (a) the number of differential equations; (b) the number and order of finite-elements; (c) the number of hyperradial points; and (d) the number of eigensolutions required. Test run requires 30 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [W.H. Press, B.F. Flanery, S.A. Teukolsky, W.T. Vetterley, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986] Nature of problem: In the hyperspherical adiabatic approach [J. Macek, J. Phys. B 1 (1968) 831-843; U. Fano, Rep. Progr. Phys. 46 (1983) 97-165; C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142], a multi-dimensional Schrödinger equation for a two-electron system [A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Comm. 90 (1995) 311-339] or a hydrogen atom in magnetic field [M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352] is reduced by separating the radial coordinate ρ from the angular variables to a system of second-order ordinary differential equations which contain potential matrix elements and first-derivative coupling terms. The purpose of this paper is to present the finite-element method procedure based on the use of high-order accuracy approximations for calculating approximate eigensolutions for such systems of coupled differential equations. Solution method: The boundary problems for coupled differential equations are solved by the finite-element method using high-order accuracy approximations [A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Comm. 85 (1995) 40-64]. The generalized algebraic eigenvalue problem AF=EBF with respect to pair unknowns ( E,F) arising after the replacement of the differential problem by the finite-element approximation is solved by the subspace iteration method using the SSPACE program [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. The generalized algebraic eigenvalue problem (A-EB)F=λDF with respect to pair unknowns (λ,F) arising after the corresponding replacement of the scattering boundary problem in open channels at fixed energy value, E, is solved by the LDL factorization of symmetric matrix and back-substitution methods using the DECOMP and REDBAK programs, respectively [K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982]. As a test desk, the program is applied to the calculation of the energy values and reaction matrix for an exactly solvable 2D-model of three identical particles on a line with pair zero-range potentials described in [Yu. A. Kuperin, P.B. Kurasov, Yu.B. Melnikov, S.P. Merkuriev, Ann. Phys. 205 (1991) 330-361; O. Chuluunbaatar, A.A. Gusev, S.Y. Larsen, S.I. Vinitsky, J. Phys. A 35 (2002) L513-L525; N.P. Mehta, J.R. Shepard, Phys. Rev. A 72 (2005) 032728-1-11; O. Chuluunbaatar, A.A. Gusev, M.S. Kaschiev, V.A. Kaschieva, A. Amaya-Tapia, S.Y. Larsen, S.I. Vinitsky, J. Phys. B 39 (2006) 243-269]. For this benchmark model the needed analytical expressions for the potential matrix elements and first-derivative coupling terms, their asymptotics and asymptotics of radial solutions of the boundary problems for coupled differential equations have been produced with help of a MAPLE computer algebra system. Restrictions: The computer memory requirements depend on: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points; and (d) the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Long Write-Up and listing for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMSC (when solving the scattering problem) that evaluate the asymptotics of the radial wave functions at the right boundary point in case of a boundary condition of the third type, respectively. Running time: The running time depends critically upon: (a) the number of differential equations; (b) the number and order of finite-elements; (c) the total number of hyperradial points on interval [0,ρ]; and (d) the number of eigensolutions required. The test run which accompanies this paper took 28.48 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz.

Implementing Electronic Data Interchange to Provide In-Transit Visibility

DTIC Science & Technology

2000-06-01

As a source system for GTN, DTTS-E will interface with GTN to provide satellite-tracking data from the QualComm Regional Dispatch/Monitor Station...DTTS-E data (subject to data quality constraints and the extent of the QualComm Satellite Tracking application) provides the location of organic...vehicle assets equipped with the European QualComm Satellite Tracking transponders. GATES = Global Air Transportation Execution System (AMC) A

Therapeutic Role of Bmi-1 Inhibitors in Eliminating Prostate Tumor Stem Cells

DTIC Science & Technology

2014-10-01

15 Preprint of Bansal et al., Nature Comm., in revision. (Manuscript, supplemental material and...established, treatment with C-209 resulted in a significant antitumor activity (See Figs. 7 of Bansal et al., Nature Comm. manuscript in revision that is...combination therapy. (See Fig. 7e-g of Bansal et al., Nature Comm. manuscript in revision that is attached in the Appendix). Task #5. We selected

Detecting aberrant opioid behavior in the emergency department: a prospective study using the screener and Opioid Assessment for Patients with Pain-Revised (SOAPP®-R), Current Opioid Misuse Measure (COMM)™, and provider gestalt.

PubMed

Varney, Shawn M; Perez, Crystal A; Araña, Allyson A; Carey, Katherine R; Ganem, Victoria J; Zarzabal, Lee A; Ramos, Rosemarie G; Bebarta, Vikhyat S

2018-03-03

Emergency department (ED) providers have limited time to evaluate patients at risk for opioid misuse. A validated tool to assess the risk for aberrant opioid behavior may mitigate adverse sequelae associated with prescription opioid misuse. We sought to determine if SOAPP-R, COMM, and provider gestalt were able to identify patients at risk for prescription opioid misuse as determined by pharmacy records at 12 months. We conducted a prospective observational study of adult patients in a high volume US ED. Patients completed the SOAPP-R and COMM, and treating EM providers evaluated patients' opioid misuse risk. We performed variable-centered, person-centered, and hierarchical cluster analyses to determine whether provider gestalt, SOAPP-R, or COMM, or a combination, predicted higher misuse risk. The primary outcome was the number of opioid prescriptions at 12 months according to pharmacy records. For 169 patients (mean age 43 years, 51% female, 73% white), correlation analysis showed a strong relationship between SOAPP-R and COMM with predicting the number of opioid prescriptions dispensed at 12 months. Provider scores estimating opioid misuse were not related to SOAPP-R and only weakly associated with COMM. In our adjusted regression models, provider gestalt and SOAPP-R uniquely predicted opioid prescriptions at 6 and 12 months. Using designated cutoff scores, only SOAPP-R detected a difference in the number of opioid prescriptions. Cluster analysis revealed that provider gestalt, SOAPP-R, and COMM scores jointly predicted opioid prescriptions. Provider gestalt and self-report instruments uniquely predicted the number of opioid prescriptions in ED patients. A combination of gestalt and self-assessment scores can be used to identify at-risk patients who otherwise miss the cutoff scores for SOAPP-R and COMM.

Physics Without Physics. The Power of Information-theoretical Principles

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro

2017-01-01

David Finkelstein was very fond of the new information-theoretic paradigm of physics advocated by John Archibald Wheeler and Richard Feynman. Only recently, however, the paradigm has concretely shown its full power, with the derivation of quantum theory (Chiribella et al., Phys. Rev. A 84:012311, 2011; D'Ariano et al., 2017) and of free quantum field theory (D'Ariano and Perinotti, Phys. Rev. A 90:062106, 2014; Bisio et al., Phys. Rev. A 88:032301, 2013; Bisio et al., Ann. Phys. 354:244, 2015; Bisio et al., Ann. Phys. 368:177, 2016) from informational principles. The paradigm has opened for the first time the possibility of avoiding physical primitives in the axioms of the physical theory, allowing a re-foundation of the whole physics over logically solid grounds. In addition to such methodological value, the new information-theoretic derivation of quantum field theory is particularly interesting for establishing a theoretical framework for quantum gravity, with the idea of obtaining gravity itself as emergent from the quantum information processing, as also suggested by the role played by information in the holographic principle (Susskind, J. Math. Phys. 36:6377, 1995; Bousso, Rev. Mod. Phys. 74:825, 2002). In this paper I review how free quantum field theory is derived without using mechanical primitives, including space-time, special relativity, Hamiltonians, and quantization rules. The theory is simply provided by the simplest quantum algorithm encompassing a countable set of quantum systems whose network of interactions satisfies the three following simple principles: homogeneity, locality, and isotropy. The inherent discrete nature of the informational derivation leads to an extension of quantum field theory in terms of a quantum cellular automata and quantum walks. A simple heuristic argument sets the scale to the Planck one, and the currently observed regime where discreteness is not visible is the so-called "relativistic regime" of small wavevectors, which holds for all energies ever tested (and even much larger), where the usual free quantum field theory is perfectly recovered. In the present quantum discrete theory Einstein relativity principle can be restated without using space-time in terms of invariance of the eigenvalue equation of the automaton/walk under change of representations. Distortions of the Poincaré group emerge at the Planck scale, whereas special relativity is perfectly recovered in the relativistic regime. Discreteness, on the other hand, has some plus compared to the continuum theory: 1) it contains it as a special regime; 2) it leads to some additional features with GR flavor: the existence of an upper bound for the particle mass (with physical interpretation as the Planck mass), and a global De Sitter invariance; 3) it provides its own physical standards for space, time, and mass within a purely mathematical adimensional context. The paper ends with the future perspectives of this project, and with an Appendix containing biographic notes about my friendship with David Finkelstein, to whom this paper is dedicated.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li Jibin; Qiao Zhijun

This paper deals with the following equation m{sub t}=(1/2)(1/m{sup k}){sub xxx}-(1/2)(1/m{sup k}){sub x}, which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the casesmore » of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.« less

New class of generalized photon-added coherent states and some of their non-classical properties

NASA Astrophysics Data System (ADS)

Mojaveri, B.; Dehghani, A.; Mahmoodi, S.

2014-08-01

In this paper, we construct a new class of generalized photon added coherent states (GPACSs), |z,m{{\\rangle }_{r}} by excitations on a newly introduced family of generalized coherent states (GCSs) |z{{\\rangle }_{r}} (A Dehghani and B Mojaveri 2012 J. Phys. A: Math. Theor. 45 095304), obtained via generalized hypergeometric type displacement operators acting on the vacuum state of the simple harmonic oscillator. We show that these states realize resolution of the identity property through positive definite measures on the complex plane. Meanwhile, we demonstrate that the introduced states can also be interpreted as nonlinear coherent states (NLCSs), with a spacial nonlinearity function. Finally, some of their non-classical features as well as their quantum statistical properties are compared with Agarwal's photon-added coherent states (PACSs), \\left| z,m \\right\\rangle .

Location of the adsorption transition for lattice polymers

NASA Astrophysics Data System (ADS)

Madras, Neal

2017-02-01

We consider various lattice models of polymers: lattice trees, lattice animals, and self-avoiding walks. The polymer interacts with a surface (hyperplane), receiving an energy reward of β for each site in the surface. It is known that there is an adsorption transition at a critical value of β. We present a new proof of the result of Hammersley et al (1982 J. Phys. A: Math. Gen. 15 539-71) that the transition occurs at a strictly positive value of β when the surface is impenetrable, i.e. when the polymer is restricted to a half-space. In contrast, for a penetrable surface, it is an open problem to prove that the transition occurs at β =0 . We reduce this problem to proving that the fraction of N-site polymers whose span is less than N/{{log}2}N is not too small.

A Hele-Shaw-Cahn-Hilliard Model for Incompressible Two-Phase Flows with Different Densities

NASA Astrophysics Data System (ADS)

Dedè, Luca; Garcke, Harald; Lam, Kei Fong

2017-07-01

Topology changes in multi-phase fluid flows are difficult to model within a traditional sharp interface theory. Diffuse interface models turn out to be an attractive alternative to model two-phase flows. Based on a Cahn-Hilliard-Navier-Stokes model introduced by Abels et al. (Math Models Methods Appl Sci 22(3):1150013, 2012), which uses a volume-averaged velocity, we derive a diffuse interface model in a Hele-Shaw geometry, which in the case of non-matched densities, simplifies an earlier model of Lee et al. (Phys Fluids 14(2):514-545, 2002). We recover the classical Hele-Shaw model as a sharp interface limit of the diffuse interface model. Furthermore, we show the existence of weak solutions and present several numerical computations including situations with rising bubbles and fingering instabilities.

Quantization of systems with temporally varying discretization. II. Local evolution moves

NASA Astrophysics Data System (ADS)

Höhn, Philipp A.

2014-10-01

Several quantum gravity approaches and field theory on an evolving lattice involve a discretization changing dynamics generated by evolution moves. Local evolution moves in variational discrete systems (1) are a generalization of the Pachner evolution moves of simplicial gravity models, (2) update only a small subset of the dynamical data, (3) change the number of kinematical and physical degrees of freedom, and (4) generate a dynamical (or canonical) coarse graining or refining of the underlying discretization. To systematically explore such local moves and their implications in the quantum theory, this article suitably expands the quantum formalism for global evolution moves, constructed in Paper I [P. A. Höhn, "Quantization of systems with temporally varying discretization. I. Evolving Hilbert spaces," J. Math. Phys. 55, 083508 (2014); e-print arXiv:1401.6062 [gr-qc

Analytic model for the long-term evolution of circular Earth satellite orbits including lunar node regression

NASA Astrophysics Data System (ADS)

Zhu, Ting-Lei; Zhao, Chang-Yin; Zhang, Ming-Jiang

2017-04-01

This paper aims to obtain an analytic approximation to the evolution of circular orbits governed by the Earth's J2 and the luni-solar gravitational perturbations. Assuming that the lunar orbital plane coincides with the ecliptic plane, Allan and Cook (Proc. R. Soc. A, Math. Phys. Eng. Sci. 280(1380):97, 1964) derived an analytic solution to the orbital plane evolution of circular orbits. Using their result as an intermediate solution, we establish an approximate analytic model with lunar orbital inclination and its node regression be taken into account. Finally, an approximate analytic expression is derived, which is accurate compared to the numerical results except for the resonant cases when the period of the reference orbit approximately equals the integer multiples (especially 1 or 2 times) of lunar node regression period.

Digging into the Elusive Localised Solutions of (2+1) Dimensional sine-Gordon Equation

NASA Astrophysics Data System (ADS)

Radha, R.; Senthil Kumar, C.

2018-05-01

In this paper, we revisit the (2+1) dimensional sine-Gordon equation analysed earlier [R. Radha and M. Lakshmanan, J. Phys. A Math. Gen. 29, 1551 (1996)] employing the Truncated Painlevé Approach. We then generate the solutions in terms of lower dimensional arbitrary functions of space and time. By suitably harnessing the arbitrary functions present in the closed form of the solution, we have constructed dromion solutions and studied their collisional dynamics. We have also constructed dromion pairs and shown that the dynamics of the dromion pairs can be turned ON or OFF desirably. In addition, we have also shown that the orientation of the dromion pairs can be changed. Apart from the above classes of solutions, we have also generated compactons, rogue waves and lumps and studied their dynamics.

Data Comm Flight Deck Human-in-the-Loop Simulation

NASA Technical Reports Server (NTRS)

Lozito, Sandra; Martin, Lynne Hazel; Sharma, Shivanjli; Kaneshige, John T.; Dulchinos, Victoria

2012-01-01

This presentation discusses an upcoming simulation for data comm in the terminal area. The purpose of the presentation is to provide the REDAC committee with a summary of some of the work in Data Comm that is being sponsored by the FAA. The focus of the simulation is upon flight crew human performance variables, such as crew procedures, timing and errors. The simulation is scheduled to be conducted in Sept 2012.

Dr TIM: Ray-tracer TIM, with additional specialist scientific capabilities

NASA Astrophysics Data System (ADS)

Oxburgh, Stephen; Tyc, Tomáš; Courtial, Johannes

2014-03-01

We describe several extensions to TIM, a raytracing program for ray-optics research. These include relativistic raytracing; simulation of the external appearance of Eaton lenses, Luneburg lenses and generalised focusing gradient-index lens (GGRIN) lenses, which are types of perfect imaging devices; raytracing through interfaces between spaces with different optical metrics; and refraction with generalised confocal lenslet arrays, which are particularly versatile METATOYs. Catalogue identifier: AEKY_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKY_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licencing provisions: GNU General Public License No. of lines in distributed program, including test data, etc.: 106905 No. of bytes in distributed program, including test data, etc.: 6327715 Distribution format: tar.gz Programming language: Java. Computer: Any computer capable of running the Java Virtual Machine (JVM) 1.6. Operating system: Any, developed under Mac OS X Version 10.6 and 10.8.3. RAM: Typically 130 MB (interactive version running under Mac OS X Version 10.8.3) Classification: 14, 18. Catalogue identifier of previous version: AEKY_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183(2012)711 External routines: JAMA [1] (source code included) Does the new version supersede the previous version?: Yes Nature of problem: Visualisation of scenes that include scene objects that create wave-optically forbidden light-ray fields. Solution method: Ray tracing. Reasons for new version: Significant extension of the capabilities (see Summary of revisions), as demanded by our research. Summary of revisions: Added capabilities include the simulation of different types of camera moving at relativistic speeds relative to the scene; visualisation of the external appearance of generalised focusing gradient-index (GGRIN) lenses, including Maxwell fisheye, Eaton and Luneburg lenses; calculation of refraction at the interface between spaces with different optical metrics; and handling of generalised confocal lenslet arrays (gCLAs), a new type of METATOY. Unusual features: Specifically designed to visualise wave-optically forbidden light-ray fields; can visualise ray trajectories and geometric optic transformations; can simulate photos taken with different types of camera moving at relativistic speeds, interfaces between spaces with different optical metrics, the view through METATOYs and generalised focusing gradient-index lenses; can create anaglyphs (for viewing with coloured “3D glasses”), HDMI-1.4a standard 3D images, and random-dot autostereograms of the scene; integrable into web pages. Running time: Problem-dependent; typically seconds for a simple scene. References: [1] JAMA: A Java Matrix Package, http://math.nist.gov/javanumerics/jama/

On the constrained classical capacity of infinite-dimensional covariant quantum channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holevo, A. S.

The additivity of the minimal output entropy and that of the χ-capacity are known to be equivalent for finite-dimensional irreducibly covariant quantum channels. In this paper, we formulate a list of conditions allowing to establish similar equivalence for infinite-dimensional covariant channels with constrained input. This is then applied to bosonic Gaussian channels with quadratic input constraint to extend the classical capacity results of the recent paper [Giovannetti et al., Commun. Math. Phys. 334(3), 1553-1571 (2015)] to the case where the complex structures associated with the channel and with the constraint operator need not commute. In particular, this implies a multimodemore » generalization of the “threshold condition,” obtained for single mode in Schäfer et al. [Phys. Rev. Lett. 111, 030503 (2013)], and the proof of the fact that under this condition the classical “Gaussian capacity” resulting from optimization over only Gaussian inputs is equal to the full classical capacity. Complex structures correspond to different squeezings, each with its own normal modes, vacuum and coherent states, and the gauge. Thus our results apply, e.g., to multimode channels with a squeezed Gaussian noise under the standard input energy constraint, provided the squeezing is not too large as to violate the generalized threshold condition. We also investigate the restrictiveness of the gauge-covariance condition for single- and multimode bosonic Gaussian channels.« less

ComM is a hexameric helicase that promotes branch migration during natural transformation in diverse Gram-negative species.

PubMed

Nero, Thomas M; Dalia, Triana N; Wang, Joseph Che-Yen; Kysela, David T; Bochman, Matthew L; Dalia, Ankur B

2018-05-02

Acquisition of foreign DNA by natural transformation is an important mechanism of adaptation and evolution in diverse microbial species. Here, we characterize the mechanism of ComM, a broadly conserved AAA+ protein previously implicated in homologous recombination of transforming DNA (tDNA) in naturally competent Gram-negative bacterial species. In vivo, we found that ComM was required for efficient comigration of linked genetic markers in Vibrio cholerae and Acinetobacter baylyi, which is consistent with a role in branch migration. Also, ComM was particularly important for integration of tDNA with increased sequence heterology, suggesting that its activity promotes the acquisition of novel DNA sequences. In vitro, we showed that purified ComM binds ssDNA, oligomerizes into a hexameric ring, and has bidirectional helicase and branch migration activity. Based on these data, we propose a model for tDNA integration during natural transformation. This study provides mechanistic insight into the enigmatic steps involved in tDNA integration and uncovers the function of a protein required for this conserved mechanism of horizontal gene transfer.

CommServer: A Communications Manager For Remote Data Sites

NASA Astrophysics Data System (ADS)

Irving, K.; Kane, D. L.

2012-12-01

CommServer is a software system that manages making connections to remote data-gathering stations, providing a simple network interface to client applications. The client requests a connection to a site by name, and the server establishes the connection, providing a bidirectional channel between the client and the target site if successful. CommServer was developed to manage networks of FreeWave serial data radios with multiple data sites, repeaters, and network-accessed base stations, and has been in continuous operational use for several years. Support for Iridium modems using RUDICS will be added soon, and no changes to the application interface are anticipated. CommServer is implemented on Linux using programs written in bash shell, Python, Perl, AWK, under a set of conventions we refer to as ThinObject.

Modular Multi-Function Multi-Band Airborne Radio System (MFBARS). Volume II. Detailed Report.

DTIC Science & Technology

1981-06-01

Three Platforms in a Field of Hyperbolic LOP’s.......................... 187 76 Comparison, MFBARS Versus Baseline .......... 190 77 Program Flow Chart...configure, from a set of common modules, a given total CNI capability on specific platforms for a given mission " the ability to take advantage of...X Comm/Nav GPS L-Band; Spread Spectrum Nay X X SEEK TALK UHF Spread; Spectrum Comm X X SINCGARS VHF; Freq. Hop Comm (some platforms ) AFSATCOM UHF

Mars Comm/Nav MicroSat Network Using the Multi-Mission Bus Launched Piggyback by Ariane 5

NASA Technical Reports Server (NTRS)

Hastrup, R. C.; Cesarone, R. J.; Morabito, D. D.

1999-01-01

Recently, NASA's Jet Propulsion Laboratory completed a Mars Exploration Program Architecture Definition Study with strong international participation. The recommendations of this study include establishment of a low cost in-situ communications and navigation satellite network to provide enabling and enhancing support for the international exploration of Mars. This would be the first step toward establishing a "virtual presence throughout the solar system" as called for in NASA's Strategic Plan. Response to the proposed comm/nav satellite network has been very favorably received, as reflected by the inclusion of a line item in NASA's budget submittal to Congress, which provides funding for implementation of the network with first launch in the 2003 opportunity. Funding has already been provided for a phase A study being conducted this year. This paper presents the planned implementation of the comm/nav network, which will utilize microsats based on a multi-mission spacecraft bus being designed for launch by the Ariane 5 as a secondary payload. A companion paper at this conference, entitled "The Multi-Purpose Mars Micro-Mission System Design Utilizing Ariane 5 Piggyback Launch", describes the multimission bus design. This paper addresses the application of the multi-mission bus to the comm/nav microsat mission. Following an introduction, which provides the background that has led to the proposed comm/nav network, the paper discusses the projected user needs with emphasis on the various possible robotic missions (landers, rovers, ascent vehicles, balloons, aircraft, etc.) progressing toward eventual piloted missions. Next, the paper describes the concept for an evolving network of comm/nav microsats and the expected capability to satisfy the user needs. Results of communications and navigation performance analysis are summarized for attractive satellite constellation configurations. The important comm/nav microsat functional requirements on the multi-mission spacecraft bus are described with discussion of the mission-system tradeoffs for the driving requirements. The functional design of the in-situ communications / navigation package, which constitutes the payload of the microsat, is also described. The paper also includes discussion of technologies which are of specific importance to the implementation of the comm/nav microsat network.

On two parabolic systems: Convergence and blowup

NASA Astrophysics Data System (ADS)

Huang, Yamin

1998-12-01

This dissertation studies two parabolic systems. It consists of two parts. In part one (chapter one), we prove a convergence result, namely, the solution (AK,/ BK) of a system of chemical diffusion-reaction equations (with reaction rate K) converges to the solution (A, B) of a diffusion- instantaneous-reaction equation. To prove our main result, we use some L1 and L2 'energy' estimates and a compactness result due to Aubin (1). As a by-product we also prove that as K approaches infinity, the limit solution exhibits phase separation between A and B. In part two (chapter two), we study the blowup rate for a system of heat equations ut=/Delta u,/ vt=/Delta v in a bounded domain Ωtimes(0,T) coupled in the nonlinear Neumann boundary conditions [/partial u/over/partial n]=vp,/ [/partial v/over/partial n]=uq on ∂Omega×[ 0,T), where p>0,/ q>0,/ pq>1 and n is the exterior normal vector on ∂Omega. Under certain assumptions, we establish exact blowup rate which generalizes the corresponding results of some authors' recent work including Deng (2), Deng-Fila-Levine (3) and Hu-Yin (4). ftn (1) J. P. A scUBIN, Un theoreme de compacite, C. R. Acad. Sci., 256(1963), pp. 5042-5044. (2) K. D scENG, Blow-up rates for parabolic systems, Z. Angew. Math. Phys., 47(1996), No. 1, pp. 132-143. (3) K. D scENG, M. F scILA AND H. A. L scEVINE, On critical exponents for a system of heat equations coupled in the boundary conditions, Acta Math. Univ. Comenian. (N.S.), 36(1994), No. 2, pp. 169-192. (4) B. H scU scAND H. M. Y scIN, The profile near blowup time for solutions of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc., 346(1994), pp. 117-135.

Consortium for Algal Biofuel Commercialization (CAB-COMM) Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mayfield, Stephen P.

The Consortium for Algal Biofuel Commercialization (CAB-Comm) was established in 2010 to conduct research to enable commercial viability of alternative liquid fuels produced from algal biomass. The main objective of CAB-Comm was to dramatically improve the viability of algae as a source of liquid fuels to meet US energy needs, by addressing several significant barriers to economic viability. To achieve this goal, CAB-Comm took a diverse set of approaches on three key aspects of the algal biofuels value chain: crop protection; nutrient utilization and recycling; and the development of genetic tools. These projects have been undertaken as collaboration between sixmore » academic institutions and two industrial partners: University of California, San Diego; Scripps Institution of Oceanography; University of Nebraska, Lincoln; Rutgers University; University of California, Davis; Johns Hopkins University; Sapphire Energy; and Life Technologies.« less

Asymptotic analysis of the narrow escape problem in dendritic spine shaped domain: three dimensions

NASA Astrophysics Data System (ADS)

Li, Xiaofei; Lee, Hyundae; Wang, Yuliang

2017-08-01

This paper deals with the three-dimensional narrow escape problem in a dendritic spine shaped domain, which is composed of a relatively big head and a thin neck. The narrow escape problem is to compute the mean first passage time of Brownian particles traveling from inside the head to the end of the neck. The original model is to solve a mixed Dirichlet-Neumann boundary value problem for the Poisson equation in the composite domain, and is computationally challenging. In this paper we seek to transfer the original problem to a mixed Robin-Neumann boundary value problem by dropping the thin neck part, and rigorously derive the asymptotic expansion of the mean first passage time with high order terms. This study is a nontrivial three-dimensional generalization of the work in Li (2014 J. Phys. A: Math. Theor. 47 505202), where a two-dimensional analogue domain is considered.

Quantum-Like Model for Decision Making Process in Two Players Game. A Non-Kolmogorovian Model

NASA Astrophysics Data System (ADS)

Asano, Masanari; Ohya, Masanori; Khrennikov, Andrei

2011-03-01

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4-17, 2005; Biosystems 84:225-241, 2006; Found. Phys. 35(10):1655-1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105-117, 2009), it was pointed out that statistics collected in such the experiments have "quantum-like" properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33-59, 1999).

Strange quintessence star in Krori-Barua spacetime

NASA Astrophysics Data System (ADS)

Bhar, Piyali

2015-04-01

In the present paper a new model of a compact star is obtained by utilizing the Krori-Barua (KB) ansatz [Krori and Barua in J. Phys. A, Math. Gen. 8:508, 1975] in the presence of a quintessence field characterized by a parameter ω q with . The obtained model of strange stars is singularity free and satisfies all the physical requirements. Our model is stable as well as it is in static equilibrium. The numerical values of the mass of the strange stars 4U1820-30 (radius=10 km), SAX J1808.4-3658(SS1) (radius=7.07 km) and Her X-1 (radius=7.7 km) calculated from our model are very close to the standard data. The interior solution is matched to the exterior Schwarzschild spacetime in the presence of a thin shell where a negative surface pressure is needed to keep the thin shell from collapsing.

Combinatorics of transformations from standard to non-standard bases in Brauer algebras

NASA Astrophysics Data System (ADS)

Chilla, Vincenzo

2007-05-01

Transformation coefficients between standard bases for irreducible representations of the Brauer centralizer algebra \\mathfrak{B}_f(x) and split bases adapted to the \\mathfrak{B}_{f_1} (x) \\times \\mathfrak{B}_{f_2} (x) \\subset \\mathfrak{B}_f (x) subalgebra (f1 + f2 = f) are considered. After providing the suitable combinatorial background, based on the definition of the i-coupling relation on nodes of the subduction grid, we introduce a generalized version of the subduction graph which extends the one given in Chilla (2006 J. Phys. A: Math. Gen. 39 7657) for symmetric groups. Thus, we can describe the structure of the subduction system arising from the linear method and give an outline of the form of the solution space. An ordering relation on the grid is also given and then, as in the case of symmetric groups, the choices of the phases and of the free factors governing the multiplicity separations are discussed.

Derivation of an eigenvalue probability density function relating to the Poincaré disk

NASA Astrophysics Data System (ADS)

Forrester, Peter J.; Krishnapur, Manjunath

2009-09-01

A result of Zyczkowski and Sommers (2000 J. Phys. A: Math. Gen. 33 2045-57) gives the eigenvalue probability density function for the top N × N sub-block of a Haar distributed matrix from U(N + n). In the case n >= N, we rederive this result, starting from knowledge of the distribution of the sub-blocks, introducing the Schur decomposition and integrating over all variables except the eigenvalues. The integration is done by identifying a recursive structure which reduces the dimension. This approach is inspired by an analogous approach which has been recently applied to determine the eigenvalue probability density function for random matrices A-1B, where A and B are random matrices with entries standard complex normals. We relate the eigenvalue distribution of the sub-blocks to a many-body quantum state, and to the one-component plasma, on the pseudosphere.

LETTER TO THE EDITOR: Exact energy distribution function in a time-dependent harmonic oscillator

NASA Astrophysics Data System (ADS)

Robnik, Marko; Romanovski, Valery G.; Stöckmann, Hans-Jürgen

2006-09-01

Following a recent work by Robnik and Romanovski (2006 J. Phys. A: Math. Gen. 39 L35, 2006 Open Syst. Inf. Dyn. 13 197-222), we derive an explicit formula for the universal distribution function of the final energies in a time-dependent 1D harmonic oscillator, whose functional form does not depend on the details of the frequency ω(t) and is closely related to the conservation of the adiabatic invariant. The normalized distribution function is P(x) = \\pi^{-1} (2\\mu^2 - x^2)^{-\\frac{1}{2}} , where x=E_1- \\skew3\\bar{E}_1 ; E1 is the final energy, \\skew3\\bar{E}_1 is its average value and µ2 is the variance of E1. \\skew3\\bar{E}_1 and µ2 can be calculated exactly using the WKB approach to all orders.

Singularity-free anisotropic strange quintessence star

NASA Astrophysics Data System (ADS)

Bhar, Piyali

2015-04-01

Present paper provides a new model of anisotropic strange star corresponding to the exterior Schwarzschild metric. The Einstein field equations have been solved by utilizing the Krori-Barua (KB) ansatz (Krori and Barua in J. Phys. A, Math. Gen. 8:508, 1975) in presence of quintessence field characterized by a parameter ω q with . The obtained solutions are free from central singularity. Our model is potentially stable. The numerical values of mass of the different strange stars SAXJ1808.4-3658(SS1) (radius=7.07 km), 4U1820-30 (radius=10 km), Vela X-12 (radius=9.99 km), PSR J 1614-2230 (radius=10.3 km) obtained from our model is very close to the observational data that confirms the validity of our proposed model. The interior solution is also matched to the exterior Schwarzschild spacetime in presence of thin shell where negative surface pressure is required to hold the thin shell against collapsing.

Linear response formula for piecewise expanding unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Smania, Daniel

2008-04-01

The average R(t)=\\int \\varphi\\,\\rmd \\mu_t of a smooth function phiv with respect to the SRB measure μt of a smooth one-parameter family ft of piecewise expanding interval maps is not always Lipschitz (Baladi 2007 Commun. Math. Phys. 275 839-59, Mazzolena 2007 Master's Thesis Rome 2, Tor Vergata). We prove that if ft is tangent to the topological class of f, and if ∂t ft|t = 0 = X circle f, then R(t) is differentiable at zero, and R'(0) coincides with the resummation proposed (Baladi 2007) of the (a priori divergent) series \\sum_{n=0}^\\infty \\int X(y) \\partial_y (\\varphi \\circ f^n)(y)\\,\\rmd \\mu_0(y) given by Ruelle's conjecture. In fact, we show that t map μt is differentiable within Radon measures. Linear response is violated if and only if ft is transversal to the topological class of f.

Note on a Family of Monotone Quantum Relative Entropies

NASA Astrophysics Data System (ADS)

Deuchert, Andreas; Hainzl, Christian; Seiringer, Robert

2015-10-01

Given a convex function and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691-705, 2014) the relative entropy defined by . Among other things, they prove that the so-defined quantity is monotone if and only if is operator monotone. The monotonicity is then used to properly define for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections with strongly, the limit is shown to exist and to be independent of the sequence of projections . The question whether this sequence converges to its "obvious" limit, namely , has been left open. We answer this question in principle affirmatively and show that . If the operators A and B are regular enough, that is ( A - B), and are trace-class, the identity holds.

13-Moment System with Global Hyperbolicity for Quantum Gas

NASA Astrophysics Data System (ADS)

Di, Yana; Fan, Yuwei; Li, Ruo

2017-06-01

We point out that the quantum Grad's 13-moment system (Yano in Physica A 416:231-241, 2014) is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To remedy this problem, by fully considering Grad's expansion, we split the expansion into the equilibrium part and the non-equilibrium part, and propose a regularization for the system with the help of the new hyperbolic regularization theory developed in Cai et al. (SIAM J Appl Math 75(5):2001-2023, 2015) and Fan et al. (J Stat Phys 162(2):457-486, 2016). This provides us a new model which is hyperbolic for all admissible thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. It should be noted that this procedure is not a trivial application of the hyperbolic regularization theory.

Qualitative analysis of certain generalized classes of quadratic oscillator systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bagchi, Bijan, E-mail: bbagchi123@gmail.com; Ghosh, Samiran, E-mail: sran-g@yahoo.com; Pal, Barnali, E-mail: barrna.roo@gmail.com

2016-02-15

We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis.more » We carry out our study by extending Quesne’s scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term fcosωt.« less

Tightness of the Ising-Kac Model on the Two-Dimensional Torus

NASA Astrophysics Data System (ADS)

Hairer, Martin; Iberti, Massimo

2018-05-01

We consider the sequence of Gibbs measures of Ising models with Kac interaction defined on a periodic two-dimensional discrete torus near criticality. Using the convergence of the Glauber dynamic proven by Mourrat and Weber (Commun Pure Appl Math 70:717-812, 2017) and a method by Tsatsoulis and Weber employed in (arXiv:1609.08447 2016), we show tightness for the sequence of Gibbs measures of the Ising-Kac model near criticality and characterise the law of the limit as the Φ ^4_2 measure on the torus. Our result is very similar to the one obtained by Cassandro et al. (J Stat Phys 78(3):1131-1138, 1995) on Z^2, but our strategy takes advantage of the dynamic, instead of correlation inequalities. In particular, our result covers the whole critical regime and does not require the large temperature/large mass/small coupling assumption present in earlier results.

O'Connell's process as a vicious Brownian motion.

PubMed

Katori, Makoto

2011-12-01

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.

A different Deutsch-Jozsa

NASA Astrophysics Data System (ADS)

Bera, Debajyoti

2015-06-01

One of the early achievements of quantum computing was demonstrated by Deutsch and Jozsa (Proc R Soc Lond A Math Phys Sci 439(1907):553, 1992) regarding classification of a particular type of Boolean functions. Their solution demonstrated an exponential speedup compared to classical approaches to the same problem; however, their solution was the only known quantum algorithm for that specific problem so far. This paper demonstrates another quantum algorithm for the same problem, with the same exponential advantage compared to classical algorithms. The novelty of this algorithm is the use of quantum amplitude amplification, a technique that is the key component of another celebrated quantum algorithm developed by Grover (Proceedings of the twenty-eighth annual ACM symposium on theory of computing, ACM Press, New York, 1996). A lower bound for randomized (classical) algorithms is also presented which establishes a sound gap between the effectiveness of our quantum algorithm and that of any randomized algorithm with similar efficiency.

Subfactors of Index Less Than 5, Part 3: Quadruple Points

NASA Astrophysics Data System (ADS)

Izumi, Masaki; Jones, Vaughan F. R.; Morrison, Scott; Snyder, Noah

2012-12-01

One major obstacle in extending the classification of small index subfactors beyond {3 +sqrt{3}} is the appearance of infinite families of candidate principal graphs with 4-valent vertices (in particular, the "weeds" {{Q}} and {{Q}'} from Part 1 (Morrison and Snyder in Commun. Math. Phys., doi: 10.1007/s00220-012-1426-y, 2012). Thus instead of using triple point obstructions to eliminate candidate graphs, we need to develop new quadruple point obstructions. In this paper we prove two quadruple point obstructions. The first uses quadratic tangles techniques and eliminates the weed {{Q}'} immediately. The second uses connections, and when combined with an additional number theoretic argument it eliminates both weeds {{Q}} and {{Q}'} . Finally, we prove the uniqueness (up to taking duals) of the 3311 Goodman-de la Harpe-Jones subfactor using a combination of planar algebra techniques and connections.

Unstable Mode Solutions to the Klein-Gordon Equation in Kerr-anti-de Sitter Spacetimes

NASA Astrophysics Data System (ADS)

Dold, Dominic

2017-03-01

For any cosmological constant {Λ = -3/ℓ2 < 0} and any {α < 9/4}, we find a Kerr-AdS spacetime {({M}, g_{KAdS})}, in which the Klein-Gordon equation {Box_{g_{KAdS}}ψ + α/ℓ2ψ = 0} has an exponentially growing mode solution satisfying a Dirichlet boundary condition at infinity. The spacetime violates the Hawking-Reall bound {r+2 > |a|ℓ}. We obtain an analogous result for Neumann boundary conditions if {5/4 < α < 9/4}. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses {α} such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result adopts methods of Shlapentokh-Rothman developed in (Commun. Math. Phys. 329:859-891, 2014) and provides the first rigorous construction of a superradiant instability for negative cosmological constant.

Redundant information encoding in QED during decoherence

NASA Astrophysics Data System (ADS)

Tuziemski, J.; Witas, P.; Korbicz, J. K.

2018-01-01

Broadly understood decoherence processes in quantum electrodynamics, induced by neglecting either the radiation [L. Landau, Z. Phys. 45, 430 (1927), 10.1007/BF01343064] or the charged matter [N. Bohr and L. Rosenfeld, K. Danske Vidensk. Selsk, Math.-Fys. Medd. XII, 8 (1933)], have been studied from the dawn of the theory. However, what happens in between, when a part of the radiation may be observed, as is the case in many real-life situations, has not been analyzed yet. We present such an analysis for a nonrelativistic, pointlike charge and thermal radiation. In the dipole approximation, we solve the dynamics and show that there is a regime where, despite the noise, the observed field carries away almost perfect and hugely redundant information about the charge momentum. We analyze a partial charge-field state and show that it approaches a so-called spectrum broadcast structure.

Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence

NASA Astrophysics Data System (ADS)

Aru, Juhan; Huang, Yichao; Sun, Xin

2017-11-01

2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in the realm of probability theory: David et al. (Liouville quantum gravity on the Riemann sphere. Commun Math Phys 342(3):869-907, 2016) and Duplantier et al. (Liouville quantum gravity as a mating of trees. ArXiv e-prints: arXiv:1409.7055, 2014) both provide a probabilistic perspective of the LQG on the 2D sphere. In particular, in each of them one may find a definition of the so-called unit area quantum sphere. We examine these two perspectives and prove their equivalence by showing that the respective unit area quantum spheres are the same. This is done by considering a unified limiting procedure for defining both objects.

A System of ODEs for a Perturbation of a Minimal Mass Soliton

NASA Astrophysics Data System (ADS)

Marzuola, Jeremy L.; Raynor, Sarah; Simpson, Gideon

2010-08-01

We study soliton solutions to the nonlinear Schrödinger equation (NLS) with a saturated nonlinearity. NLS with such a nonlinearity is known to possess a minimal mass soliton. We consider a small perturbation of a minimal mass soliton and identify a system of ODEs extending the work of Comech and Pelinovsky (Commun. Pure Appl. Math. 56:1565-1607, 2003), which models the behavior of the perturbation for short times. We then provide numerical evidence that under this system of ODEs there are two possible dynamical outcomes, in accord with the conclusions of Pelinovsky et al. (Phys. Rev. E 53(2):1940-1953, 1996). Generically, initial data which supports a soliton structure appears to oscillate, with oscillations centered on a stable soliton. For initial data which is expected to disperse, the finite dimensional dynamics initially follow the unstable portion of the soliton curve.

Stability of coefficients in the Kronecker product of a hook and a rectangle

NASA Astrophysics Data System (ADS)

Ballantine, Cristina M.; Hallahan, William T.

2016-02-01

We use recent work of Jonah Blasiak (2012 arXiv:1209.2018) to prove a stability result for the coefficients in the Kronecker product of two Schur functions: one indexed by a hook partition and one indexed by a rectangle partition. We also give nearly sharp bounds for the size of the partition starting with which the Kronecker coefficients are stable. Moreover, we show that once the bound is reached, no new Schur functions appear in the decomposition of Kronecker product. We call this property superstability. Thus, one can recover the Schur decomposition of the Kronecker product from the smallest case in which the superstability holds. The bound for superstability is sharp. Our study of this particular case of the Kronecker product is motivated by its usefulness for the understanding of the quantum Hall effect (Scharf T et al 1994 J. Phys. A: Math. Gen 27 4211-9).

On the plethora of representations arising in noncommutative quantum mechanics and an explicit construction of noncommutative 4-tori

NASA Astrophysics Data System (ADS)

Chowdhury, S. Hasibul Hassan

2017-06-01

We construct a 2-parameter family of unitarily equivalent irreducible representations of the triply extended group GNC of translations of R4 associated with a family of its 4-dimensional coadjoint orbits and show how a continuous 2-parameter family of gauge potentials emerges from these unitarily equivalent representations. We show that the Landau and the symmetric gauges of noncommutative quantum mechanics, widely used in the literature, in fact, belong to this 2-parameter family of gauges. We also provide an explicit construction of noncommutative 4-tori and compute the associated star products using the unitary dual of the group GNC that was studied at length in an earlier paper [S. H. H. Chowdhury and S. T. Ali, J. Phys. A: Math. Theor. 47, 085301 (2014)]. Finally, we construct projective modules over such noncommutative 4-tori and compute constant curvature connections on them using Rieffel's method.

Head-on collisions of localized pressure excitations in derivative cubic relaxing media: dynamical structure survey

NASA Astrophysics Data System (ADS)

Youssoufa, Saliou; Kamgang Kuetche, Victor; Crepin Kofane, Timoleon

2015-02-01

In the wake of the recent derivation of the new cubic nonlinear evolution equation of high-frequency pressure perturbations of a barothropic medium under relaxation (Kuetche V K et al 2014 J. Math. Phys. 55 052702), we closely investigate the head-on collisions of some typical localized waveguide excitations, which are solutions to the previous system. From the viewpoint of Hirota's formalism, we delve into the structural scattering features of the interacting waves mentioned above. As a result, we find that there might exist some ‘characteristic’ amplitude ratio of the interacting waves at which the scattering changes its features. Accordingly, we provide an illustration of the previous result within the depiction of the interactions between three single soliton solutions alongside the phase-shift of each particle. Following these depictions, we address some physical implications of the results as well as the different potential applications.

Generating a New Higher-Dimensional Coupled Integrable Dispersionless System: Algebraic Structures, Bäcklund Transformation and Hidden Structural Symmetries

NASA Astrophysics Data System (ADS)

Souleymanou, Abbagari; Thomas, B. Bouetou; Timoleon, C. Kofane

2013-08-01

The prolongation structure methodologies of Wahlquist—Estabrook [H.D. Wahlquist and F.B. Estabrook, J. Math. Phys. 16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Bäcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2 + 1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.

Almost sure convergence in quantum spin glasses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buzinski, David, E-mail: dab197@case.edu; Meckes, Elizabeth, E-mail: elizabeth.meckes@case.edu

2015-12-15

Recently, Keating, Linden, and Wells [Markov Processes Relat. Fields 21(3), 537-555 (2015)] showed that the density of states measure of a nearest-neighbor quantum spin glass model is approximately Gaussian when the number of particles is large. The density of states measure is the ensemble average of the empirical spectral measure of a random matrix; in this paper, we use concentration of measure and entropy techniques together with the result of Keating, Linden, and Wells to show that in fact the empirical spectral measure of such a random matrix is almost surely approximately Gaussian itself with no ensemble averaging. We alsomore » extend this result to a spherical quantum spin glass model and to the more general coupling geometries investigated by Erdős and Schröder [Math. Phys., Anal. Geom. 17(3-4), 441–464 (2014)].« less

On the energy density of helical proteins.

PubMed

Barros, Manuel; Ferrández, Angel

2014-12-01

We solve the problem of determining the energy actions whose moduli space of extremals contains the class of Lancret helices with a prescribed slope. We first see that the energy density should be linear both in the total bending and in the total twisting, such that the ratio between the weights of them is the prescribed slope. This will give an affirmative answer to the conjecture stated in Barros and Ferrández (J Math Phys 50:103529, 2009). Then, we normalize to get the best choice for the helical energy. It allows us to show that the energy, for instance of a protein chain, does not depend on the slope and is invariant under homotopic changes of the cross section which determines the cylinder where the helix is lying. In particular, the energy of a helix is not arbitrary, but it is given as natural multiples of some basic quantity of energy.

Exploiting the flexibility and the polarization of ferroelectric perovskite surfaces to achieve efficient photochemistry and enantiospecificity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rappe, Andrew

This research project explored the catalytic properties of complex surfaces of functional materials. The PI used first-principles density functional theory (DFT) calculations to explore a tightly integrated set of properties. The physical properties of complex functional materials that influence surface chemistry were explored, including bulk and surface electric dipoles, and surface conductivity. The energetic, compositional, electronic, and chemical properties of the surfaces of these materials were explored in detail, and connections between material properties and chemical reactivity were established. This project led to 28 publications, including Nat. Comm., JACS, 3 PRL, 7 PRB, 2 ACS Nano, 2 Nano Lett., 4more » JPCL, 2 JCP, Chem. Mater., ACS Appl. Mater. Interfaces, Phys. Rev. Appl., and a U.S. Patent on surface catalysts. The key accomplishments in this project involved work in six coordinated areas: pioneering ways to control bulk dipoles in order to dynamically affect catalysis, exploring novel ways of bringing charge to the surface for redox catalysis, nonstoichiometric surfaces offering new sites for heterogeneous catalysis, illustrating how surface catalysis responds to applied pressure, catalytic growth of carbon-based materials, and new computational methods allowing more accurate exploration of molecule-surface interactions« less

TaylUR 3, a multivariate arbitrary-order automatic differentiation package for Fortran 95

NASA Astrophysics Data System (ADS)

von Hippel, G. M.

2010-03-01

This new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives. New version program summaryProgram title: TaylUR Catalogue identifier: ADXR_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXR_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPLv2 No. of lines in distributed program, including test data, etc.: 6750 No. of bytes in distributed program, including test data, etc.: 19 162 Distribution format: tar.gz Programming language: Fortran 95 Computer: Any computer with a conforming Fortran 95 compiler Operating system: Any system with a conforming Fortran 95 compiler Classification: 4.12, 4.14 Catalogue identifier of previous version: ADXR_v2_0 Journal reference of previous version: Comput. Phys. Comm. 176 (2007) 710 Does the new version supersede the previous version?: Yes Nature of problem: Problems that require potentially high orders of partial derivatives with respect to several variables or derivatives of complex-valued functions, such as e.g. momentum or mass expansions of Feynman diagrams in perturbative QFT, and which previous versions of this TaylUR [1,2] cannot handle due to their lack of support for mixed partial derivatives. Solution method: Arithmetic operators and Fortran intrinsics are overloaded to act correctly on objects of a defined type taylor, which encodes a function along with its first few partial derivatives with respect to the user-defined independent variables. Derivatives of products and composite functions are computed using multivariate forms [3] of Leibniz's rule D(fg)=∑{ν!}/{μ!(μ-ν)!}DfDg where ν=(ν,…,ν), |ν|=∑j=1dν, ν!=∏j=1dν!, Df=∂f/(∂x⋯∂x), and μ<ν iff either |μ|<|ν| or |μ|=|ν|,μ=ν,…,μ=ν,μ<ν for some k∈{0,…,d-1}, and of Fàa di Bruno's formula D(f○g)=∑p=1|ν|(f○g)∑s=1|ν|∑,…,k;λ,…,λ)}ν!/(∏j=1sk!λ!)(g)k where the sum is over {(k,…,k;λ,…,λ)∈Z:k>0,0<λ<⋯<λ, ∑i=1sk=p,∑i=1skλ=ν}. An indexed storage system is used to store the higher-order derivative tensors in a one-dimensional array. The relevant indices (k,…,k;λ,…,λ) and the weights occurring in the sums in Leibniz's and Fàa di Bruno's formula are precomputed at startup and stored in static arrays for later use. Reasons for new version: The earlier version lacked support for mixed partial derivatives, but a number of projects of interest required them. Summary of revisions: The internal representation of a taylor object has changed to a one-dimensional array which contains the partial derivatives in ascending order, and in lexicographic order of the corresponding multiindex within the same order. The necessary mappings between multiindices and indices into the taylor objects' internal array are computed at startup. To support the change to a genuinely multivariate taylor type, the DERIVATIVE function is now implemented via an interface that accepts both the older format derivative(f,mu,n)=∂μnf and also a new format derivative(f,mu(:))=Df that allows access to mixed partial derivatives. Another related extension to the functionality of the module is the HESSIAN function that returns the Hessian matrix of second derivatives of its argument. Since the calculation of all mixed partial derivatives can be very costly, and in many cases only some subset is actually needed, a masking facility has been added. Calling the subroutine DEACTIVATE_DERIVATIVE with a multiindex as an argument will deactivate the calculation of the partial derivative belonging to that multiindex, and of all partial derivatives it can feed into. Similarly, calling the subroutine ACTIVATE_DERIVATIVE will activate the calculation of the partial derivative belonging to its argument, and of all partial derivatives that can feed into it. Moreover, it is possible to turn off the computation of mixed derivatives altogether by setting Diagonal_taylors to .TRUE.. It should be noted that any change of Diagonal_taylors or Taylor_order invalidates all existing taylor objects. To aid the better integration of TaylUR into the HPSrc library [4], routines SET_DERIVATIVE and SET_ALL_DERIVATIVES are provided as a means of manually constructing a taylor object with given derivatives. Restrictions: Memory and CPU time constraints may restrict the number of variables and Taylor expansion order that can be achieved. Loss of numerical accuracy due to cancellation may become an issue at very high orders. Unusual features: These are the same as in previous versions, but are enumerated again here for clarity. The complex conjugation operation assumes all independent variables to be real. The functions REAL and AIMAG do not convert to real type, but return a result of type taylor (with the real/imaginary part of each derivative taken) instead. The user-defined functions VALUE, REALVALUE and IMAGVALUE, which return the value of a taylor object as a complex number, and the real and imaginary part of this value, respectively, as a real number are also provided. Fortran 95 intrinsics that are defined only for arguments of real type ( ACOS, AINT, ANINT, ASIN, ATAN, ATAN2, CEILING, DIM, FLOOR, INT, LOG10, MAX, MAXLOC, MAXVAL, MIN, MINLOC, MINVAL, MOD, MODULO, NINT, SIGN) will silently take the real part of taylor-valued arguments unless the module variable Real_args_warn is set to .TRUE., in which case they will return a quiet NaN value (if supported by the compiler) when called with a taylor argument whose imaginary part exceeds the module variable Real_args_tol. In those cases where the derivative of a function becomes undefined at certain points (as for ABS, AINT, ANINT, MAX, MIN, MOD, and MODULO), while the value is well defined, the derivative fields will be filled with quiet NaN values (if supported by the compiler). Additional comments: This version of TaylUR is released under the second version of the GNU General Public License (GPLv2). Therefore anyone is free to use or modify the code for their own calculations. As part of the licensing, it is requested that any publications including results from the use of TaylUR or any modification derived from it cite Refs. [1,2] as well as this paper. Finally, users are also requested to communicate to the author details of such publications, as well as of any bugs found or of required or useful modifications made or desired by them. Running time: The running time of TaylUR operations grows rapidly with both the number of variables and the Taylor expansion order. Judicious use of the masking facility to drop unneeded higher derivatives can lead to significant accelerations, as can activation of the Diagonal_taylors variable whenever mixed partial derivatives are not needed. Acknowledgments: The author thanks Alistair Hart for helpful comments and suggestions. This work is supported by the Deutsche Forschungsgemeinschaft in the SFB/TR 09. References:G.M. von Hippel, TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 174 (2006) 569. G.M. von Hippel, New version announcement for TaylUR, an arbitrary-order diagonal automatic differentiation package for Fortran 95, Comput. Phys. Comm. 176 (2007) 710. G.M. Constantine, T.H. Savits, A multivariate Faa di Bruno formula with applications, Trans. Amer. Math. Soc. 348 (2) (1996) 503. A. Hart, G.M. von Hippel, R.R. Horgan, E.H. Müller, Automated generation of lattice QCD Feynman rules, Comput. Phys. Comm. 180 (2009) 2698, doi:10.1016/j.cpc.2009.04.021, arXiv:0904.0375.

Solitary water wave interactions

NASA Astrophysics Data System (ADS)

Craig, W.; Guyenne, P.; Hammack, J.; Henderson, D.; Sulem, C.

2006-05-01

This article concerns the pairwise nonlinear interaction of solitary waves in the free surface of a body of water lying over a horizontal bottom. Unlike solitary waves in many completely integrable model systems, solitary waves for the full Euler equations do not collide elastically; after interactions, there is a nonzero residual wave that trails the post-collision solitary waves. In this report on new numerical and experimental studies of such solitary wave interactions, we verify that this is the case, both in head-on collisions (the counterpropagating case) and overtaking collisions (the copropagating case), quantifying the degree to which interactions are inelastic. In the situation in which two identical solitary waves undergo a head-on collision, we compare the asymptotic predictions of Su and Mirie [J. Fluid Mech. 98, 509 (1980)] and Byatt-Smith [J. Fluid Mech. 49, 625 (1971)], the wavetank experiments of Maxworthy [J. Fluid Mech. 76, 177 (1976)], and the numerical results of Cooker, Weidman, and Bale [J. Fluid Mech. 342, 141 (1997)] with independent numerical simulations, in which we quantify the phase change, the run-up, and the form of the residual wave and its Fourier signature in both small- and large-amplitude interactions. This updates the prior numerical observations of inelastic interactions in Fenton and Rienecker [J. Fluid Mech. 118, 411 (1982)]. In the case of two nonidentical solitary waves, our precision wavetank experiments are compared with numerical simulations, again observing the run-up, phase lag, and generation of a residual from the interaction. Considering overtaking solitary wave interactions, we compare our experimental observations, numerical simulations, and the asymptotic predictions of Zou and Su [Phys. Fluids 29, 2113 (1986)], and again we quantify the inelastic residual after collisions in the simulations. Geometrically, our numerical simulations of overtaking interactions fit into the three categories of Korteweg-deVries two-soliton solutions defined in Lax [Commun. Pure Appl. Math. 21, 467 (1968)], with, however, a modification in the parameter regime. In all cases we have considered, collisions are seen to be inelastic, although the degree to which interactions depart from elastic is very small. Finally, we give several theoretical results: (i) a relationship between the change in amplitude of solitary waves due to a pairwise collision and the energy carried away from the interaction by the residual component, and (ii) a rigorous estimate of the size of the residual component of pairwise solitary wave collisions. This estimate is consistent with the analytic results of Schneider and Wayne [Commun. Pure Appl. Math. 53, 1475 (2000)], Wright [SIAM J. Math. Anal. 37, 1161 (2005)], and Bona, Colin, and Lannes [Arch. Rat. Mech. Anal. 178, 373 (2005)]. However, in light of our numerical data, both (i) and (ii) indicate a need to reevaluate the asymptotic results in Su and Mirie [J. Fluid Mech. 98, 509 (1980)] and Zou and Su [Phys. Fluids 29, 2113 (1986)].

Improvement of turkey breast meat quality and cooked gel functionality using hot-boning, quarter sectioning, crust-freeze-air-chilling and cold-batter-mincing technologies.

PubMed

Lee, H C; Erasmus, M A; Swanson, J C; Hong, H G; Kang, I

2016-01-01

The effect of rapid carcass chilling on breast meat quality was evaluated using commercial (COMM) and random-bred (RB) turkeys. Immediately after slaughter, 48 turkeys from COMM or RB line were randomly subjected to one of four chilling methods: 1) water-immersion chilling (WIC) of the carcasses at 0°C ice slurry, 2) WIC after temperature abuse (TA) of the carcasses at 40°C for 30 min (TA-WIC), 3) hot-boning, quarter sectioning, and crust-freeze-air-chilling (HB-(1)/4CFAC) of breast fillets at -12°C, and 4) HB-(1)/4CFAC of fillets after TA of carcasses (TA-HB-(1)/4CFAC). The TA increased carcass and fillet temperatures by ∼1.3 and ∼4.1°C, respectively, regardless of turkey line, whereas HB-(1)/4CFAC of fillets required 28 and 33% of carcass chilling time for COMM and RB, respectively. During chilling, COMM breast pH rapidly reduced from 6.04 to 5.82, resulting in a significantly lower pH than RB after chilling (P < 0.05), whereas COMM R-value sharply increased from 1.17 to 1.43, causing no difference from RB (P > 0.05). Significantly higher L* value and cooking yield (P < 0.05) were seen in the samples of TA and WIC than those of no TA and HB-(1)/4CFAC, respectively, with no difference observed between COMM and RB fillets (P > 0.05). Higher values of hardness, gumminess, and chewiness were found for RB, no TA, and HB-(1)/4CFAC gels than COMM, TA, and WIC, respectively. These results generally indicated that protein quality and textural properties of turkey fillets were improved, regardless of strains or temperature abuse, using HB-(1)/4CFAC technology. © 2015 Poultry Science Association Inc.

The PD COMM trial: a protocol for the process evaluation of a randomised trial assessing the effectiveness of two types of SLT for people with Parkinson's disease.

PubMed

Masterson-Algar, Patricia; Burton, Christopher R; Brady, Marian C; Nicoll, Avril; Clarke, Carl E; Rick, Caroline; Hughes, Max; Au, Pui; Smith, Christina H; Sackley, Catherine M

2017-08-29

The PD COMM trial is a phase III multi-centre randomised controlled trial whose aim is to evaluate the effectiveness and cost-effectiveness of two approaches to speech and language therapy (SLT) compared with no SLT intervention (control) for people with Parkinson's disease who have self-reported or carer-reported problems with their speech or voice. Our protocol describes the process evaluation embedded within the outcome evaluation whose aim is to evaluate what happened at the time of the PD COMM intervention implementation and to provide findings that will assist in the interpretation of the PD COMM trial results. Furthermore, the aim of the PD COMM process evaluation is to investigate intervention complexity within a theoretical model of how the trialled interventions might work best and why. Drawing from the Normalization Process Theory and frameworks for implementation fidelity, a mixed method design will be used to address process evaluation research questions. Therapists' and participants' perceptions and experiences will be investigated via in-depth interviews. Critical incident reports, baseline survey data from therapists, treatment record forms and home practice diaries also will be collected at relevant time points throughout the running of the PD COMM trial. Process evaluation data will be analysed independently of the outcome evaluation before the two sets of data are then combined. To date, there are a limited number of published process evaluation protocols, and few are linked to trials investigating rehabilitation therapies. Providing a strong theoretical framework underpinning design choices and being tailored to meet the complex characteristics of the trialled interventions, our process evaluation has the potential to provide valuable insight into which components of the interventions being delivered in PD COMM worked best (and what did not), how they worked well and why. ISRCTN Registry, ISRCTN12421382 . Registered on 18 April 2016.

C++QEDv2 Milestone 10: A C++/Python application-programming framework for simulating open quantum dynamics

NASA Astrophysics Data System (ADS)

Sandner, Raimar; Vukics, András

2014-09-01

The v2 Milestone 10 release of C++QED is primarily a feature release, which also corrects some problems of the previous release, especially as regards the build system. The adoption of C++11 features has led to many simplifications in the codebase. A full doxygen-based API manual [1] is now provided together with updated user guides. A largely automated, versatile new testsuite directed both towards computational and physics features allows for quickly spotting arising errors. The states of trajectories are now savable and recoverable with full binary precision, allowing for trajectory continuation regardless of evolution method (single/ensemble Monte Carlo wave-function or Master equation trajectory). As the main new feature, the framework now presents Python bindings to the highest-level programming interface, so that actual simulations for given composite quantum systems can now be performed from Python. Catalogue identifier: AELU_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELU_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: yes No. of lines in distributed program, including test data, etc.: 492422 No. of bytes in distributed program, including test data, etc.: 8070987 Distribution format: tar.gz Programming language: C++/Python. Computer: i386-i686, x86 64. Operating system: In principle cross-platform, as yet tested only on UNIX-like systems (including Mac OS X). RAM: The framework itself takes about 60MB, which is fully shared. The additional memory taken by the program which defines the actual physical system (script) is typically less than 1MB. The memory storing the actual data scales with the system dimension for state-vector manipulations, and the square of the dimension for density-operator manipulations. This might easily be GBs, and often the memory of the machine limits the size of the simulated system. Classification: 4.3, 4.13, 6.2. External routines: Boost C++ libraries, GNU Scientific Library, Blitz++, FLENS, NumPy, SciPy Catalogue identifier of previous version: AELU_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1381 Does the new version supersede the previous version?: Yes Nature of problem: Definition of (open) composite quantum systems out of elementary building blocks [2,3]. Manipulation of such systems, with emphasis on dynamical simulations such as Master-equation evolution [4] and Monte Carlo wave-function simulation [5]. Solution method: Master equation, Monte Carlo wave-function method Reasons for new version: The new version is mainly a feature release, but it does correct some problems of the previous version, especially as regards the build system. Summary of revisions: We give an example for a typical Python script implementing the ring-cavity system presented in Sec. 3.3 of Ref. [2]: Restrictions: Total dimensionality of the system. Master equation-few thousands. Monte Carlo wave-function trajectory-several millions. Unusual features: Because of the heavy use of compile-time algorithms, compilation of programs written in the framework may take a long time and much memory (up to several GBs). Additional comments: The framework is not a program, but provides and implements an application-programming interface for developing simulations in the indicated problem domain. We use several C++11 features which limits the range of supported compilers (g++ 4.7, clang++ 3.1) Documentation, http://cppqed.sourceforge.net/ Running time: Depending on the magnitude of the problem, can vary from a few seconds to weeks. References: [1] Entry point: http://cppqed.sf.net [2] A. Vukics, C++QEDv2: The multi-array concept and compile-time algorithms in the definition of composite quantum systems, Comp. Phys. Comm. 183(2012)1381. [3] A. Vukics, H. Ritsch, C++QED: an object-oriented framework for wave-function simulations of cavity QED systems, Eur. Phys. J. D 44 (2007) 585. [4] H. J. Carmichael, An Open Systems Approach to Quantum Optics, Springer, 1993. [5] J. Dalibard, Y. Castin, K. Molmer, Wave-function approach to dissipative processes in quantum optics, Phys. Rev. Lett. 68 (1992) 580.

Applications of the First-principles LDA+Usc Method to Spin-crossover Minerals: the NAL Phase and (Mg,Fe)CO3 ferromagnesite

NASA Astrophysics Data System (ADS)

Hsu, H.

2016-12-01

Spin crossover (SCO) in iron-bearing minerals has attracted tremendous attention in recent years, as SCO usually leads to anomalous changes of the elastic, conducting, and thermodynamic properties of these minerals. Possible geophysical effects of SCO have been anticipated as well. With the development of the local density approximation + self-consistent Hubbard U (LDA+Usc) method, first-principles calculations have elucidated SCO in many lower-mantle minerals. The success of LDA+Usc lies in its capability to correctly identify the ground state in a wide pressure range and to accurately determine the mechanism of SCO, including the transition pressure PT. In this talk, two recent LDA+Usc studies of SCO minerals are presented: the "new aluminous (NAL) phase" [1] and (Mg,Fe)CO3 ferromagnesite [2]. The former is considered as a main host of aluminum in the subducted basalt and may be related to the seismic heterogeneities, and the latter is believed to be the major carbon carrier in the Earth's lower mantle and play a key role in the deep carbon cycle. For both minerals, the abrupt change of iron quadrupole splitting and the volume/elastic anomalies accompanying the SCO obtained in our calculations are in great agreement with experiments. Our calculations also suggest that the spin transition pressure PT in the NAL phase is not very sensitive to temperature, due to its nearly degenerate low-spin (LS) states, in contrast with (Mg,Fe)O ferropericlase and (Mg,Fe)CO3 systems, in which PT significantly increases with temperature. By examining the overall performance of the LDA+Usc method in the NAL phase and ferromagnesite, along with our previous calculations for ferropericlase and Fe-bearing MgSiO3 bridgmanite [3-5], we have established LDA+Usc a highly reliable method to study iron-bearing minerals and related materials under high pressure. [1] H. Hsu, in preparation. [2] S.-C. Huang and H. Hsu, Phys. Rev. B (Rapid Comm.), in press. [3] H. Hsu and R. M. Wentzcovitch, Phys. Rev. B 90, 195205 (2014). [4] H. Hsu et al., Earth Planet. Sci. Lett. 359-360, 34 (2012). [5] H. Hsu et al., Phys. Rev. Lett. 106, 118501 (2011).

Direct Images, Fields of Hilbert Spaces, and Geometric Quantization

NASA Astrophysics Data System (ADS)

Lempert, László; Szőke, Róbert

2014-04-01

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H s of Hilbert spaces, and the question arises if the spaces H s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787-902, 1991) and Hitchin (Commun. Math. Phys. 131:347-380, 1990) suggest viewing H s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle along a non-proper map . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Szőke (Bull. Lond. Math. Soc. 44:367-374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.

Tsunami Focusing and Leading Amplitude

NASA Astrophysics Data System (ADS)

Kanoglu, U.

2016-12-01

Tsunamis transform substantially through spatial and temporal spreading from their source region. This substantial spreading might result unique maximum tsunami wave heights which might be attributed to the source configuration, directivity, the waveguide structures of mid-ocean ridges and continental shelves, focusing and defocusing through submarine seamounts, random focusing due to small changes in bathymetry, dispersion, and, most likely, combination of some of these effects. In terms of the maximum tsunami wave height, after Okal and Synolakis (2016 Geophys. J. Int. 204, 719-735), it is clear that dispersion would be one of the reasons to drive the leading wave amplitude in a tsunami wave train. Okal and Synolakis (2016), referring to this phenomenon as sequencing -later waves in the train becoming higher than the leading one, considered Hammack's (1972, Ph.D. Dissertation, Calif. Inst. Tech., 261 pp) formalism, in addition to LeMéhauté and Wang's (1995 Water waves generated by underwater explosion, World Scientific, 367 pp), to evaluate linear dispersive tsunami propagation from a circular plug uplifted on an ocean of constant depth. They identified transition distance, as the second wave being larger, performing parametric study for the radius of the plug and the depth of the ocean. Here, we extend Okal and Synolakis' (2016) analysis to an initial wave field with a finite crest length and, in addition, to a most common tsunami initial wave form of N-wave (Tadepalli and Synolakis, 1994 Proc. R. Soc. A: Math. Phys. Eng. Sci. 445, 99-112). First, we investigate the focusing feature in the leading-depression side, which enhance tsunami wave height as presented by Kanoglu et al. (2013 Proc. R. Soc. A: Math. Phys. Eng. Sci. 469, 20130015). We then discuss the results in terms of leading wave amplitude presenting a parametric study and identify a simple relation for the transition distance. The solution presented here could be used to better analyze dispersive characteristics of shallow water-wave numerical models and for benchmarking, in addition to the benchmark problems in Synolakis et al. (2008 Pure Appl. Geophys. 165(11-12), 2197-2228). This study received funding from project ASTARTE-Assessment Strategy and Risk Reduction for Tsunamis in Europe, a collaborative project Grant 603839, FP7-ENV2013 6.4-3.

Quantum physics with non-Hermitian operators Quantum physics with non-Hermitian operators

NASA Astrophysics Data System (ADS)

Bender, Carl; Fring, Andreas; Günther, Uwe; Jones, Hugh

2012-11-01

The main motivation behind the call for this special issue was to gather recent results, developments and open problems in quantum physics with non-Hermitian operators. There have been previous special issues in this journal [1, 2] and elsewhere on this subject. The intention of this issue is to reflect the current state of this rapidly-developing field. It has therefore been open to all contributions containing new results on non-Hermitian theories that are explicitly PT-symmetric and/or pseudo-Hermitian or quasi-Hermitian. In the last decade these types of systems have proved to be viable self-consistent physical theories with well defined unitary time-evolution and real spectra. As the large number of responses demonstrates, this is a rapidly evolving field of research. A consensus has been reached regarding most of the fundamental problems, and the general ideas and techniques are now readily being employed in many areas of physics. Nonetheless, this issue still contains some treatments of a more general nature regarding the spectral analysis of these models, in particular, the physics of the exceptional points, the breaking of the PT-symmetry, an interpretation of negative energies and the consistent implementation of the WKB analysis. This issue also contains a treatment of a scattering theory associated with these types of systems, weak measurements, coherent states, decoherence, unbounded metric operators and the inclusion of domain issues to obtain well defined self-adjoint theories. Contributions in the form of applications of the general ideas include: studies of classical shock-waves and tunnelling, supersymmetric models, spin chain models, models with ring structure, random matrix models, the Pauli equation, the nonlinear Schrödinger equation, quasi-exactly solvable models, integrable models such as the Calogero model, Bose-Einstein condensates, thermodynamics, nonlinear oligomers, quantum catastrophes, the Landau-Zener problem and pseudo-Fermions. Applications close to experimental realization are proposed in optics, including short light pulse models, waveguides and laser systems, and also in electronics. We hope that this issue will become a valuable reference and inspiration for the broader scientific community working in mathematical and theoretical physics. References [1] Fring A, Jones H F and Znojil M (ed) 2008 J. Phys. A: Math. Theor. 41 240301 [2] Geyer H, Heiss D and Znojil M (ed) 2006 J. Phys. A: Math. Gen. 39 9963

Lessons Learned and Unlearned from the 2004 Great Sumatran Tsunami.

NASA Astrophysics Data System (ADS)

Synolakis, C.; Kanoglu, U.

2014-12-01

Huppert & Sparks (2006 Phil Trans Math Phys Eng Sci) wrote It is likely that in the future, we will experience several disasters per year that kill more than 10,000 people. The 2011 Great East Japan Earthquake Disaster alone resulted in more than 20,000 casualties. Synolakis & Bernard (2006 Phil Trans Math Phys Eng Sci) concluded that Before the next Sumatra-type tsunami strikes, we must resolve to create a world that can coexist with the tsunami hazard. The 2011 Japan tsunami dramatically showed that we are not there yet. Despite substantial advances after the 2004 Boxing Day tsunami, substantial challenges remain for improving tsunami hazard mitigation. If the tsunami community appeared at first perplexed in the aftermath of the 2004 tsunami, it was not due to the failure of recognized hydrodynamic paradigms, much as certain geophysical ones and scaling laws failed, but at the worst surprise, the lack of preparedness and education. Synolakis et al. (2008 Pure Appl Geophys) presented standards for tsunami modeling; for both warnings and inundation maps (IMs). Although at least one forecasting methodology has gone through extensive testing, and is now officially in use by the warning centers (WCs), standards need urgently to be formalized for warnings. In Europe, several WCs have been established, but none has yet to issue an operational warning for a hazardous event. If it happens, there might be confusion with possibly contradictory/competing warnings. Never again should there be a repeat of the TEPCO analysis for the safety of the Fukushima NPP. This was primarily due to lacks of familiarity with the context of numerical predictions and experience with real tsunami. The accident was the result of a cascade of stupid errors, almost impossible to ignore by anyone in the field (Synolakis, 26.03.2011 The New York Times). Current practices in tsunami studies for US NPPs and for IMs do not provide us with optimism that the Fukushima lessons have been absorbed and that bagatellomania is still rabid. What saves human lives is ancestral knowledge and community preparedness, as demonstrated repeatedly. Efforts need to be focused in improving education worldwide in the simple steps they can take. We acknowledge the partial supports from the 7th FP (ASTARTE, Grant 603839), TUBITAK, TR (109Y387) and GSRT, GR (10TUR/1-50-1) projects.

A Solution Space for a System of Null-State Partial Differential Equations: Part 2

NASA Astrophysics Data System (ADS)

Flores, Steven M.; Kleban, Peter

2015-01-01

This article is the second of four that completely and rigorously characterize a solution space for a homogeneous system of 2 N + 3 linear partial differential equations in 2 N variables that arises in conformal field theory (CFT) and multiple Schramm-Löwner evolution (SLE). The system comprises 2 N null-state equations and three conformal Ward identities which govern CFT correlation functions of 2 N one-leg boundary operators. In the first article (Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), we use methods of analysis and linear algebra to prove that dim , with C N the Nth Catalan number. The analysis of that article is complete except for the proof of a lemma that it invokes. The purpose of this article is to provide that proof. The lemma states that if every interval among ( x 2, x 3), ( x 3, x 4),…,( x 2 N-1, x 2 N ) is a two-leg interval of (defined in Flores and Kleban, Commun Math Phys, arXiv:1212.2301, 2012), then F vanishes. Proving this lemma by contradiction, we show that the existence of such a nonzero function implies the existence of a non-vanishing CFT two-point function involving primary operators with different conformal weights, an impossibility. This proof (which is rigorous in spite of our occasional reference to CFT) involves two different types of estimates, those that give the asymptotic behavior of F as the length of one interval vanishes, and those that give this behavior as the lengths of two intervals vanish simultaneously. We derive these estimates by using Green functions to rewrite certain null-state PDEs as integral equations, combining other null-state PDEs to obtain Schauder interior estimates, and then repeatedly integrating the integral equations with these estimates until we obtain optimal bounds. Estimates in which two interval lengths vanish simultaneously divide into two cases: two adjacent intervals and two non-adjacent intervals. The analysis of the latter case is similar to that for one vanishing interval length. In contrast, the analysis of the former case is more complicated, involving a Green function that contains the Jacobi heat kernel as its essential ingredient.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Peng; Department of Physics, Renmin University of China, Beijing 100872; Naidon, Pascal

Most of the current theories on the p-wave superfluid in cold atomic gases are based on the effective-range theory for the two-body scattering, where the low-energy p-wave scattering amplitude f{sub 1}(k) is given by f{sub 1}(k)=-1/[ik+1/(Vk{sup 2})+1/R]. Here k is the incident momentum, V and R are the k-independent scattering volume and effective range, respectively. However, due to the long-range nature of the van der Waals interaction between two colliding ultracold atoms, the p-wave scattering amplitude of the two atoms is not described by the effective-range theory [J. Math. Phys. 4, 54 (1963); Phys. Rev. A 58, 4222 (1998)]. Inmore » this paper we provide an explicit calculation for the p-wave scattering of two ultracold atoms near the p-wave magnetic Feshbach resonance. We show that in this case the low-energy p-wave scattering amplitude f{sub 1}(k)=-1/[ik+1/(V{sup eff}k{sup 2})+1/(S{sup eff}k)+1/R{sup eff}] where V{sup eff}, S{sup eff}, and R{sup eff} are k-dependent parameters. Based on this result, we identify sufficient conditions for the effective-range theory to be a good approximation of the exact scattering amplitude. Using these conditions we show that the effective-range theory is a good approximation for the p-wave scattering in the ultracold gases of {sup 6}Li and {sup 40}K when the scattering volume is enhanced by the resonance.« less

Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks.

PubMed

Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue

2014-11-01

Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011)PLEEE81539-375510.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011)JMBLAJ0303-681210.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.

On the Geometry of the Hamilton-Jacobi Equation and Generating Functions

NASA Astrophysics Data System (ADS)

Ferraro, Sebastián; de León, Manuel; Marrero, Juan Carlos; Martín de Diego, David; Vaquero, Miguel

2017-10-01

In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results about symplectic groupoids, in particular cotangent groupoids, as a keystone for the construction of our framework. Our methodology follows the ambitious program proposed by Weinstein (In Mechanics day (Waterloo, ON, 1992), volume 7 of fields institute communications, American Mathematical Society, Providence, 1996) in order to develop geometric formulations of the dynamical behavior of Lagrangian and Hamiltonian systems on Lie algebroids and Lie groupoids. This procedure allows us to take symmetries into account, and, as a by-product, we recover results from Channell and Scovel (Phys D 50(1):80-88, 1991), Ge (Indiana Univ. Math. J. 39(3):859-876, 1990), Ge and Marsden (Phys Lett A 133(3):134-139, 1988), but even in these situations our approach is new. A theory of generating functions for the Poisson structures considered here is also developed following the same pattern, solving a longstanding problem of the area: how to obtain a generating function for the identity transformation and the nearby Poisson automorphisms of Poisson manifolds. A direct application of our results gives the construction of a family of Poisson integrators, that is, integrators that conserve the underlying Poisson geometry. These integrators are implemented in the paper in benchmark problems. Some conclusions, current and future directions of research are shown at the end of the paper.

Third Bose fugacity coefficient in one dimension, as a function of asymptotic quantities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Amaya-Tapia, A., E-mail: jano@fis.unam.mx; Larsen, S.Y.; Lassaut, M.

2011-02-15

In one of the very few exact quantum mechanical calculations of fugacity coefficients, [L.R. Dodd, A.M. Gibbs. J. Math. Phys. 15 (1974) 41] obtained b{sub 2} and b{sub 3} for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For b{sub 2}, we have shown [A. Amaya-Tapia, S.Y. Larsen, M. Lassaut. Mol. Phys. 103 (2005) 1301-1306. < (arXiv:physics/0405150)>] that Dodd and Gibbs' result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in one dimension. Now, we develop an exact expressionmore » for b{sub 3}-b{sub 3}{sup 0} (where b{sub 3}{sup 0} is the free particle fugacity coefficient) in terms of sums and differences of three-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a Distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the twofold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.« less

Code OK3 - An upgraded version of OK2 with beam wobbling function

NASA Astrophysics Data System (ADS)

Ogoyski, A. I.; Kawata, S.; Popov, P. H.

2010-07-01

For computer simulations on heavy ion beam (HIB) irradiation onto a target with an arbitrary shape and structure in heavy ion fusion (HIF), the code OK2 was developed and presented in Computer Physics Communications 161 (2004). Code OK3 is an upgrade of OK2 including an important capability of wobbling beam illumination. The wobbling beam introduces a unique possibility for a smooth mechanism of inertial fusion target implosion, so that sufficient fusion energy is released to construct a fusion reactor in future. New version program summaryProgram title: OK3 Catalogue identifier: ADST_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADST_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 221 517 No. of bytes in distributed program, including test data, etc.: 2 471 015 Distribution format: tar.gz Programming language: C++ Computer: PC (Pentium 4, 1 GHz or more recommended) Operating system: Windows or UNIX RAM: 2048 MBytes Classification: 19.7 Catalogue identifier of previous version: ADST_v2_0 Journal reference of previous version: Comput. Phys. Comm. 161 (2004) 143 Does the new version supersede the previous version?: Yes Nature of problem: In heavy ion fusion (HIF), ion cancer therapy, material processing, etc., a precise beam energy deposition is essentially important [1]. Codes OK1 and OK2 have been developed to simulate the heavy ion beam energy deposition in three-dimensional arbitrary shaped targets [2, 3]. Wobbling beam illumination is important to smooth the beam energy deposition nonuniformity in HIF, so that a uniform target implosion is realized and a sufficient fusion output energy is released. Solution method: OK3 code works on the base of OK1 and OK2 [2, 3]. The code simulates a multi-beam illumination on a target with arbitrary shape and structure, including beam wobbling function. Reasons for new version: The code OK3 is based on OK2 [3] and uses the same algorithm with some improvements, the most important one is the beam wobbling function. Summary of revisions:In the code OK3, beams are subdivided on many bunches. The displacement of each bunch center from the initial beam direction is calculated. Code OK3 allows the beamlet number to vary from bunch to bunch. That reduces the calculation error especially in case of very complicated mesh structure with big internal holes. The target temperature rises during the time of energy deposition. Some procedures are improved to perform faster. The energy conservation is checked up on each step of calculation process and corrected if necessary. New procedures included in OK3 Procedure BeamCenterRot( ) rotates the beam axis around the impinging direction of each beam. Procedure BeamletRot( ) rotates the beamlet axes that belong to each beam. Procedure Rotation( ) sets the coordinates of rotated beams and beamlets in chamber and pellet systems. Procedure BeamletOut( ) calculates the lost energy of ions that have not impinged on the target. Procedure TargetT( ) sets the temperature of the target layer of energy deposition during the irradiation process. Procedure ECL( ) checks up the energy conservation law at each step of the energy deposition process. Procedure ECLt( ) performs the final check up of the energy conservation law at the end of deposition process. Modified procedures in OK3 Procedure InitBeam( ): This procedure initializes the beam radius and coefficients A1, A2, A3, A4 and A5 for Gauss distributed beams [2]. It is enlarged in OK3 and can set beams with radii from 1 to 20 mm. Procedure kBunch( ) is modified to allow beamlet number variation from bunch to bunch during the deposition. Procedure ijkSp( ) and procedure Hole( ) are modified to perform faster. Procedure Espl( ) and procedure ChechE( ) are modified to increase the calculation accuracy. Procedure SD( ) calculates the total relative root-mean-square (RMS) deviation and the total relative peak-to-valley (PTV) deviation in energy deposition non-uniformity. This procedure is not included in code OK2 because of its limited applications (for spherical targets only). It is taken from code OK1 and modified to perform with code OK3. Running time: The execution time depends on the pellet mesh number and the number of beams in the simulated illumination as well as on the beam characteristics (beam radius on the pellet surface, beam subdivision, projectile particle energy and so on). In almost all of the practical running tests performed, the typical running time for one beam deposition is about 30 s on a PC with a CPU of Pentium 4, 2.4 GHz. References:A.I. Ogoyski, et al., Heavy ion beam irradiation non-uniformity in inertial fusion, Phys. Lett. A 315 (2003) 372-377. A.I. Ogoyski, et al., Code OK1 - Simulation of multi-beam irradiation on a spherical target in heavy ion fusion, Comput. Phys. Comm. 157 (2004) 160-172. A.I. Ogoyski, et al., Code OK2 - A simulation code of ion-beam illumination on an arbitrary shape and structure target, Comput. Phys. Comm. 161 (2004) 143-150.

NextGen Flight Deck Data Comm : Auxiliary Synthetic Speech Phase II

DOT National Transportation Integrated Search

2015-07-01

Data Comma text-based controller-pilot communication systemis expected to yield several NextGen safety and efficiency benefits. With Data Comm, communication becomes a visual task, and may potentially increase head-down time on the flight deck ...

Doping, Strain, Orientation and Disorder of Graphene by Raman Spectroscopy

NASA Astrophysics Data System (ADS)

Ferrari, Andrea C.

2009-03-01

Raman spectroscopy is a fast and non-destructive method for the characterization of carbons [1]. These show two features: the G and D peaks, around 1580 and 1350cm-1 respectively. The G peak corresponds to the doubly degenerate E2g phonon at the Brillouin zone centre. The D peak is due to the breathing modes of sp^2 atoms and requires a defect for its activation [1-5]. It is common for as-prepared graphene not to have enough structural defects for the D peak to be seen [4,6], so that it can only be detected at the edges [6]. The most prominent feature in graphene is the second order 2D peak [6]. This is always seen, since no defects are required for its activation. Its shape distinguishes single and multi-layers [6]. Raman spectroscopy also monitors doping [7-9]. We report the evolution of the Raman spectra of single [7,8] and bi-layer [9] graphene as a function of doping. A Fermi level shift is induced either by applying a bottom gate [7], or by a polymeric top gate [8,9], or naturally happens as a result of charged impurities [10]. This induces a stiffening of the Raman G peak for both hole and electron doping [7]. This is explained including dynamic corrections to the adiabatic Born-Oppenheimer approximation [7]. The phonon renormalization of bilayer graphene has characteristic features compared to single layer. This allows a direct estimation of the interlayer coupling [7-9]. We then consider the effects strain. Uniaxial strain lifts the E2g degeneracy and splits the G peak in two: G^+ and G^-. The peaks downshift as a function of strain allows a direct measurement of the Gruneisen parameter [10]. The polarization dependence of the G^+/G^- modes is a probe of the crystallographic orientation of the sample [10]. Finally, we consider the effect of disorder [3,4,11] and show how to discriminate between disorder, strain and doping [11]. We will also discuss how the D peak is a signature of π electron localisation, and, thus, of gap opening in chemically modified graphene[12]. [4pt] 1. A. C. Ferrari, J. Robertson (eds), Raman spectroscopy in carbons: from nanotubes to diamond, Theme Issue, Phil. Trans. Roy. Soc. 362, 2267 (2004). 2. F. Tuinstra, J.L. Koening, J. Chem. Phys. 53, 1126(1970). 3. A. C. Ferrari, J. Robertson Phys Rev B 61, 14095 (2000); 64, 075414 (2001) 4. A. C. Ferrari Solid State Comm.143, 47 (2007) 5. S. Piscanec et al. Phys. Rev. Lett. 93, 185503 (2004) 6. A. C. Ferrari et al. Phys. Rev. Lett. 97, 187401 (2006) 7. S. Pisana et al. Nature Mater. 6, 198 (2007) 8. A. Das et al, Nature Nano 3, 210 (2008). 9. A. Das et al., arXiv:0807.1631v1 (2008) 10. A. C. Ferrari et al. submitted (2008) 11. C. Casiraghi et al. Appl. Phys Lett. 91, 233108 (2007) 12. Elias et al. arXiv:0810.4706 (2008)

Selection of optimal oligonucleotide probes for microarrays usingmultiple criteria, global alignment and parameter estimation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Xingyuan; He, Zhili; Zhou, Jizhong

2005-10-30

The oligonucleotide specificity for microarray hybridizationcan be predicted by its sequence identity to non-targets, continuousstretch to non-targets, and/or binding free energy to non-targets. Mostcurrently available programs only use one or two of these criteria, whichmay choose 'false' specific oligonucleotides or miss 'true' optimalprobes in a considerable proportion. We have developed a software tool,called CommOligo using new algorithms and all three criteria forselection of optimal oligonucleotide probes. A series of filters,including sequence identity, free energy, continuous stretch, GC content,self-annealing, distance to the 3'-untranslated region (3'-UTR) andmelting temperature (Tm), are used to check each possibleoligonucleotide. A sequence identity is calculated based onmore » gapped globalalignments. A traversal algorithm is used to generate alignments for freeenergy calculation. The optimal Tm interval is determined based on probecandidates that have passed all other filters. Final probes are pickedusing a combination of user-configurable piece-wise linear functions andan iterative process. The thresholds for identity, stretch and freeenergy filters are automatically determined from experimental data by anaccessory software tool, CommOligo_PE (CommOligo Parameter Estimator).The program was used to design probes for both whole-genome and highlyhomologous sequence data. CommOligo and CommOligo_PE are freely availableto academic users upon request.« less

The Impact of Data Communications Messages in the Terminal Area on Flight Crew Workload and Eye Scanning

NASA Technical Reports Server (NTRS)

Comstock, James R., Jr.; Baxley, Brian T.; Norman, Robert M.; Ellis, Kyle K. E.; Adams, Cathy A.; Latorella, Kara A.; Lynn, William A.

2010-01-01

This paper, to accompany a discussion panel, describes a collaborative FAA and NASA research study to determine the effect Data Communications (Data Comm) messages have on flight crew workload and eye scanning behavior in busy terminal area operations. In the Next Generation Air Transportation System Concept of Operations, for the period 2017-2022, the FAA envisions Data Comm between controllers and the flight crew to become the primary means of communicating non-time critical information. Four research conditions were defined that span current day to future equipage levels (Voice with Paper map, Data Comm with Paper map, Data Comm with Moving Map Display with ownship position displayed, Data Comm with Moving Map, ownship and taxi route displayed), and were used to create arrival and departure scenarios at Boston Logan Airport. Preliminary results for workload, situation awareness, and pilot head-up time are presented here. Questionnaire data indicated that pilot acceptability, workload, and situation awareness ratings were favorable for all of the conditions tested. Pilots did indicate that there were times during final approach and landing when they would prefer not to hear the message chime, and would not be able to make a quick response due to high priority tasks in the cockpit.

BSR: B-spline atomic R-matrix codes

NASA Astrophysics Data System (ADS)

Zatsarinny, Oleg

2006-02-01

BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron-atom and electron-ion scattering, and radiative processes such as bound-bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit-Pauli Hamiltonian. New version program summaryTitle of program: BSR Catalogue identifier: ADWY Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWY Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256-512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69 943 No. of bytes in distributed program, including test data, etc.: 746 450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron-atom and electron-ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit-Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput. Phys. Comm. 92 (1995) 290].

3-dimensional indexation of the icosahedral diffraction pattern using the techniques of electron microscopy

NASA Astrophysics Data System (ADS)

Bourdillon, Antony

2012-11-01

The following facts about icosahedra need wider attention. 1) The golden section τ is as fundamental to the icosahedral structure (length /edge) as π is to the sphere (circumference /diameter). 2) The diffraction series are in restricted Fibonacci order because the ratio of adjacent terms fn/fn-1 does not vary, but is the constant τ. The series is therefore geometric. 3) Because of the tetragonal subgroup in the icosahedral point group symmetry, many axes in the icosahedral structure have identical orientation to axes in the face centered cubic matrix of Al6Mn [1] (e.g. [100] and [111]). On these bases, a three dimensional stereographic projection will be presented. 4) A quasi-Bragg law is derived that correctly represents the diffraction series in powers of τ [2]. Furthermore, by employing the normal conventions of electron microscopy, all diffraction patterns are completely indexed in three dimensions. These are the topic of this presentation. Significant consequences will be presented elsewhere: 1) The diffraction pattern intensities near all main axes are correctly simulated, and all atoms are located on a specimen image. 2) The quasi-Bragg law has a special metric. Atomic locations are consistently calculated for the first time. 3) Whereas the Bragg law transforms a crystal lattice in real space into a reciprocal lattice in diffraction space, the quasi-Bragg law transforms a geometric diffraction pattern into a hierarchic structure. 4) Hyperspatial indexation [3] is superceded. [1] Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J.W., Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett., 1984, 53, 1951-3. [2] Bourdillon, A. J., Nearly free electron band structures in a logarithmically periodic solid, Sol. State Comm. 2009, 149, 1221-1225. [3] Duneau, M., and Katz, A., Phys Rev Lett 54, 2688-2691

Excited-State Dynamics in 6-THIOGUANOSINE from Femtosecond to Microsecond Time Scale

NASA Astrophysics Data System (ADS)

Guo, Cao; Reichardt, Christian; Crespo-Hernández, Carlos E.

2011-06-01

6-thioguanine is a widely used pro-drug in which the oxygen atom in the carbonyl group of guanine is replaced by a sulfur atom. Previous studies have shown that patients treated with 6-thioguanine can metabolize and incorporate it in DNA as 6-thioguanosine (6tGuo). These patients show a high incidence of skin cancer when they are exposed to extended periods of sunlight irradiation. In this work, the photodynamics of 6tGuo is investigated by broad band time resolved transient spectroscopy. Similar to previously studied 4-thiothymidine, our results show that excitation of 6tGuo with UVA light at 340 nm results in efficient and ultrafast intersystem crossing to the triplet manifold (τ = 0.31±0.05 ps) and a high triplet quantum yield (φ = 0.8±0.2). The triplet state has a lifetime of 720±10 ns in N2-saturated vs. 460±10 ns in air-saturated aqueous solution. In addition, a minor picosecond deactivation channel (80±15 ps) is observed, which is tentatively assigned to internal conversion from the lowest-energy excited singlet state to the ground state. Quantum chemical calculations support the proposed kinetic model. Based on the high triplet quantum yield measured, it is proposed that the phototoxicity of 6tGuo is due to its ability to photosensitized singlet oxygen, which can result in oxidative damage to DNA. P. O'Donovan, C. M. Perrett, X. Zhang, B. Montaner, Y.-Z. Xu, C. A. Harwood, J. M. McGregor, S. L. Walker, F. Hanaoka, P. Karran, Science 309, 1871 (2005). C. Reichardt, C. Guo, C. E. Crespo-Hernández, J. Phys. Chem. B. in press (2011). C. Reichardt, C. E. Crespo-Hernández, J. Phys. Chem. Lett. 1, 2239 (2010) C. Reichardt, C. E. Crespo-Hernández, Chem. Comm. 46, 5963 (2010).

Pulsed Laser Techniques in Laser Heated Diamond Anvil Cells for Studying Methane (CH4) and Water (H2O) at Extreme Pressures and Temperatures

NASA Astrophysics Data System (ADS)

Holtgrewe, N.; Lobanov, S.; Mahmood, M.; Goncharov, A. F.

2017-12-01

Scientific advancement in the fields of high pressure material synthesis and research on planetary interiors rely heavily on a variety of techniques for probing such extreme conditions, such as laser-heating diamond anvil cells (LHDACs) (Goncharov et al., J. Synch. Rad., 2009) and shock compression (Nellis et al., J. Chem. Phys., 2001/ Armstrong et al., Appl. Phys. Lett., 2008). However, certain chemical properties can create complications in the detection of such extreme states, for example the instability of energetic materials, and detection of these dynamic chemical states by time-resolved methods has proven to be valuable in exploring the kinetics of these materials. Current efforts at the Linac Coherent Light Source (LCLS) for exploring the transitions between different phases of condensed matter (Armstrong et. al., APS Mar. Meeting, 2017/ Radousky et al., APS Mar. Meeting, 2017), and X-ray synchrotron pulsed heating are useful techniques but require large facilities and are not always accessible. Instead, optical properties of materials can serve as a window into the state or structure of species through electronic absorption properties. Pump-probe spectroscopy can be used to detect these electronic properties in time and allow the user to develop a picture of complex dynamic chemical events. Here we present data acquired up to 1.5 megabar (Mbar) pressures and temperatures >3000 K using pulsed transmission/reflective spectroscopy combined with a pulsed LHDAC and time-resolved detection (streak camera) (McWilliams et. al., PNAS, 2015/ McWilliams et al., PRL, 2016). Time-resolved optical properties will be presented on methane (CH4) and water (H2O) at P-T conditions found in icy bodies such as Uranus and Neptune (Lee and Scandolo, Nature Comm., 2011). Our results show that the interiors of Uranus and Neptune are optically opaque at P-T conditions corresponding to the mantles of these icy bodies, which has implications for the unusual magnetic fields of these planets.

Ground-Ground Data Communication-Assisted Planning and Coordination: Shorter Verbal Communications

NASA Technical Reports Server (NTRS)

Kessell, Angela Mary; Lee, Paul U.; Smith, Nancy M.; Lee, Hwasoo Eric

2010-01-01

A human-in-the-loop simulation was conducted to investigate the operational feasibility, technical requirements, and potential improvement in airspace efficiency of adding a Multi-Sector Planner position. A subset of the data from that simulation is analyzed here to determine the impact, if any, of ground-ground data communication (Data Comm) on verbal communication and coordination for multi-sector air traffic management. The results suggest that the use of Data Comm significantly decreases the duration of individual verbal communications. The results also suggest that the use of Data Comm, as instantiated in the current simulation, does not obviate the need for accompanying voice calls.

CompGC: Efficient Offline/Online Semi-Honest Two-Party Computation

DTIC Science & Technology

2017-02-03

κ ∈ N : Pr [ ExptprivA,S(κ) = 1 ] ≤ 1 2 + µ(κ) 4.1. Component-Based Secure Two-Party Compu- tation We now briefly describe how to use component-based...number of classes and “F” is the number of features. Specs. Naive CompGC Bost et al. [BPTG15] Data Set N D Time Time* Comm. Time Time* Comm. Time Comm...Rounds Nursery 4 4 40 0.3 40 0.01 2085 21.6 15 ECG 6 4 40 0.4 40 0.1 8816 29.1 22 (c) Decision tree classifier. “ N ” is the number of internal nodes in

The role of self-math overlap in understanding math anxiety and the relation between math anxiety and performance

PubMed Central

Necka, Elizabeth A.; Sokolowski, H. Moriah; Lyons, Ian M.

2015-01-01

Recent work has demonstrated that math anxiety is more than just the product of poor math skills. Psychosocial factors may play a key role in understanding what it means to be math anxious, and hence may aid in attempts to sever the link between math anxiety and poor math performance. One such factor may be the extent to which individuals integrate math into their sense of self. We adapted a well-established measure of this degree of integration (i.e., self-other overlap) to assess individuals’ self-math overlap. This non-verbal single-item measure showed that identifying oneself with math (having higher self-math overlap) was strongly associated with lower math anxiety (r = -0.610). We also expected that having higher self-math overlap would leave one especially susceptible to the threat of poor math performance to the self. We identified two competing hypotheses regarding how this plays out in terms of math anxiety. Those higher in self-math overlap might be more likely to worry about poor math performance, exacerbating the negative relation between math anxiety and math ability. Alternatively, those higher in self-math overlap might exhibit self-serving biases regarding their math ability, which would instead predict a decoupling of the relation between their perceived and actual math ability, and in turn the relation between their math ability and math anxiety. Results clearly favored the latter hypothesis: those higher in self-math overlap exhibited almost no relation between math anxiety and math ability, whereas those lower in self-math overlap showed a strong negative relation between math anxiety and math ability. This was partially explained by greater self-serving biases among those higher in self-math overlap. In sum, these results reveal that the degree to which one integrates math into one’s self – self-math overlap – may provide insight into how the pernicious negative relation between math anxiety and math ability may be ameliorated. PMID:26528210

The role of self-math overlap in understanding math anxiety and the relation between math anxiety and performance.

PubMed

Necka, Elizabeth A; Sokolowski, H Moriah; Lyons, Ian M

2015-01-01

Recent work has demonstrated that math anxiety is more than just the product of poor math skills. Psychosocial factors may play a key role in understanding what it means to be math anxious, and hence may aid in attempts to sever the link between math anxiety and poor math performance. One such factor may be the extent to which individuals integrate math into their sense of self. We adapted a well-established measure of this degree of integration (i.e., self-other overlap) to assess individuals' self-math overlap. This non-verbal single-item measure showed that identifying oneself with math (having higher self-math overlap) was strongly associated with lower math anxiety (r = -0.610). We also expected that having higher self-math overlap would leave one especially susceptible to the threat of poor math performance to the self. We identified two competing hypotheses regarding how this plays out in terms of math anxiety. Those higher in self-math overlap might be more likely to worry about poor math performance, exacerbating the negative relation between math anxiety and math ability. Alternatively, those higher in self-math overlap might exhibit self-serving biases regarding their math ability, which would instead predict a decoupling of the relation between their perceived and actual math ability, and in turn the relation between their math ability and math anxiety. Results clearly favored the latter hypothesis: those higher in self-math overlap exhibited almost no relation between math anxiety and math ability, whereas those lower in self-math overlap showed a strong negative relation between math anxiety and math ability. This was partially explained by greater self-serving biases among those higher in self-math overlap. In sum, these results reveal that the degree to which one integrates math into one's self - self-math overlap - may provide insight into how the pernicious negative relation between math anxiety and math ability may be ameliorated.

DataComm in Flight Deck Surface Trajectory-Based Operations

NASA Technical Reports Server (NTRS)

Bakowski, Deborah L.; Foyle, David C.; Hooey, Becky L.; Meyer, Glenn R.; Wolter, Cynthia A.

2012-01-01

The purpose of this pilot-in-the-loop aircraft taxi simulation was to evaluate a NextGen concept for surface trajectory-based operations (STBO) in which air traffic control (ATC) issued taxi clearances with a required time of arrival (RTA) by Data Communications (DataComm). Flight deck avionics, driven by an error-nulling algorithm, displayed the speed needed to meet the RTA. To ensure robustness of the algorithm, the ability of 10 two-pilot crews to meet the RTA was tested in nine experimental trials representing a range of realistic conditions including a taxi route change, an RTA change, a departure clearance change, and a crossing traffic hold scenario. In some trials, these DataComm taxi clearances or clearance modifications were accompanied by 'preview' information, in which the airport map display showed a preview of the proposed route changes, including the necessary speed to meet the RTA. Overall, the results of this study show that with the aid of the RTA speed algorithm, pilots were able to meet their RTAs with very little time error in all of the robustness-testing scenarios. Results indicated that when taxi clearance changes were issued by DataComm only, pilots required longer notification distances than with voice communication. However, when the DataComm was accompanied by graphical preview, the notification distance required by pilots was equivalent to that for voice.

DataComm in Flight Deck Surface Trajectory-Based Operations. Chapter 20

NASA Technical Reports Server (NTRS)

Bakowski, Deborah L.; Foyle, David C.; Hooey, Becky L.; Meyer, Glenn R.; Wolter, Cynthia A.

2012-01-01

The purpose of this pilot-in-the-loop aircraft taxi simulation was to evaluate a NextGen concept for surface trajectory-based operations (STBO) in which air traffic control (ATC) issued taxi clearances with a required time of arrival (RTA) by Data Communications (DataComm). Flight deck avionics, driven by an error-nulling algorithm, displayed the speed needed to meet the RTA. To ensure robustness of the algorithm, the ability of 10 two-pilot crews to meet the RTA was tested in nine experimental trials representing a range of realistic conditions including a taxi route change, an RTA change, a departure clearance change, and a crossing traffic hold scenario. In some trials, these DataComm taxi clearances or clearance modifications were accompanied by preview information, in which the airport map display showed a preview of the proposed route changes, including the necessary speed to meet the RTA. Overall, the results of this study show that with the aid of the RTA speed algorithm, pilots were able to meet their RTAs with very little time error in all of the robustness-testing scenarios. Results indicated that when taxi clearance changes were issued by DataComm only, pilots required longer notification distances than with voice communication. However, when the DataComm was accompanied by graphical preview, the notification distance required by pilots was equivalent to that for voice.

Adoption and Usage of mHealth Technology on Quality and Experience of Care Provided by Frontline Workers: Observations From Rural India.

PubMed

Kaphle, Sangya; Chaturvedi, Sharad; Chaudhuri, Indrajit; Krishnan, Ram; Lesh, Neal

2015-05-28

mHealth apps are deployed with the aim of improving access, quality, and experience of health care. It is possible that any mHealth intervention can yield differential impacts for different types of users. Mediating and determining factors, including personal and socioeconomic factors, affect technology adoption, the way health workers leverage and use the technology, and subsequently the quality and experience of care they provide. To develop a framework to assess whether mHealth platforms affect the quality and experience of care provided by frontline workers, and whether these effects on quality and experience are different depending on the level of technology adoption and individual characteristics of the health worker. Literacy, education, age, and previous mobile experience are identified as individual factors that affect technology adoption and use, as well as factors that affect the quality and experience of care directly and via the technology. Formative research was conducted with 15 community health workers (CHWs) using CommCare, an mHealth app for maternal and newborn care, in Bihar, India. CHWs were first classified on the level of CommCare adoption using data from CommCareHQ and were then shadowed on home visits to evaluate their levels of technology proficiency, and the quality and experience of care provided. Regression techniques were employed to test the relationships. Out of all the CHWs, 2 of them refused to participate in the home visits, however, we did have information on their levels of technology adoption and background characteristics, which were included in the analysis as relevant. Level of technology adoption was important for both quality and experience of care. The quality score for high users of CommCare was higher by 33.4% (P=.04), on average, compared to low users of CommCare. Those who scored higher on CommCare proficiency also provided significantly higher quality and experience of care, where an additional point in CommCare proficiency score increased the quality score by around half a point (0.541, P=.07), and experience score by around a third of a point (0.308, P=.03). Age affected CommCare user type negatively, with an increase in age increasing the likelihood of belonging to a lower category of CommCare adoption (-0.105, P=.08). Other individual characteristics did not affect adoption or the predicted values estimating the relationship between adoption and quality and experience of care, although illiteracy was able to affect the relationship negatively. mHealth technology adoption by frontline workers can positively impact the quality and experience of care they provide. Individual characteristics, especially literacy and age, can be important elements affecting technology adoption and the way users leverage the technology for their work. Our formative study provides informed hypotheses and methods for further research.

Adoption and Usage of mHealth Technology on Quality and Experience of Care Provided by Frontline Workers: Observations From Rural India

PubMed Central

Chaturvedi, Sharad; Chaudhuri, Indrajit; Krishnan, Ram; Lesh, Neal

2015-01-01

Background mHealth apps are deployed with the aim of improving access, quality, and experience of health care. It is possible that any mHealth intervention can yield differential impacts for different types of users. Mediating and determining factors, including personal and socioeconomic factors, affect technology adoption, the way health workers leverage and use the technology, and subsequently the quality and experience of care they provide. Objective To develop a framework to assess whether mHealth platforms affect the quality and experience of care provided by frontline workers, and whether these effects on quality and experience are different depending on the level of technology adoption and individual characteristics of the health worker. Literacy, education, age, and previous mobile experience are identified as individual factors that affect technology adoption and use, as well as factors that affect the quality and experience of care directly and via the technology. Methods Formative research was conducted with 15 community health workers (CHWs) using CommCare, an mHealth app for maternal and newborn care, in Bihar, India. CHWs were first classified on the level of CommCare adoption using data from CommCareHQ and were then shadowed on home visits to evaluate their levels of technology proficiency, and the quality and experience of care provided. Regression techniques were employed to test the relationships. Out of all the CHWs, 2 of them refused to participate in the home visits, however, we did have information on their levels of technology adoption and background characteristics, which were included in the analysis as relevant. Results Level of technology adoption was important for both quality and experience of care. The quality score for high users of CommCare was higher by 33.4% (P=.04), on average, compared to low users of CommCare. Those who scored higher on CommCare proficiency also provided significantly higher quality and experience of care, where an additional point in CommCare proficiency score increased the quality score by around half a point (0.541, P=.07), and experience score by around a third of a point (0.308, P=.03). Age affected CommCare user type negatively, with an increase in age increasing the likelihood of belonging to a lower category of CommCare adoption (-0.105, P=.08). Other individual characteristics did not affect adoption or the predicted values estimating the relationship between adoption and quality and experience of care, although illiteracy was able to affect the relationship negatively. Conclusions mHealth technology adoption by frontline workers can positively impact the quality and experience of care they provide. Individual characteristics, especially literacy and age, can be important elements affecting technology adoption and the way users leverage the technology for their work. Our formative study provides informed hypotheses and methods for further research. PMID:26023001

New version of PLNoise: a package for exact numerical simulation of power-law noises

NASA Astrophysics Data System (ADS)

Milotti, Edoardo

2007-08-01

In a recent paper I have introduced a package for the exact simulation of power-law noises and other colored noises [E. Milotti, Comput. Phys. Comm. 175 (2006) 212]: in particular, the algorithm generates 1/f noises with 0<α⩽2. Here I extend the algorithm to generate 1/f noises with 2<α⩽4 (black noises). The method is exact in the sense that it produces a sampled process with a theoretically guaranteed range-limited power-law spectrum for any arbitrary sequence of sampling intervals, i.e. the sampling times may be unevenly spaced. Program summaryTitle of program: PLNoise Catalogue identifier:ADXV_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXV_v2_0.html Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language used: ANSI C Computer: Any computer with an ANSI C compiler: the package has been tested with gcc version 3.2.3 on Red Hat Linux 3.2.3-52 and gcc version 4.0.0 and 4.0.1 on Apple Mac OS X-10.4 Operating system: All operating systems capable of running an ANSI C compiler RAM: The code of the test program is very compact (about 60 Kbytes), but the program works with list management and allocates memory dynamically; in a typical run with average list length 2ṡ10, the RAM taken by the list is 200 Kbytes External routines: The package needs external routines to generate uniform and exponential deviates. The implementation described here uses the random number generation library ranlib freely available from Netlib [B.W. Brown, J. Lovato, K. Russell: ranlib, available from Netlib, http://www.netlib.org/random/index.html, select the C version ranlib.c], but it has also been successfully tested with the random number routines in Numerical Recipes [W.H. Press, S.A. Teulkolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, second ed., Cambridge Univ. Press., Cambridge, 1992, pp. 274-290]. Notice that ranlib requires a pair of routines from the linear algebra package LINPACK, and that the distribution of ranlib includes the C source of these routines, in case LINPACK is not installed on the target machine. No. of lines in distributed program, including test data, etc.:2975 No. of bytes in distributed program, including test data, etc.:194 588 Distribution format:tar.gz Catalogue identifier of previous version: ADXV_v1_0 Journal reference of previous version: Comput. Phys. Comm. 175 (2006) 212 Does the new version supersede the previous version?: Yes Nature of problem: Exact generation of different types of colored noise. Solution method: Random superposition of relaxation processes [E. Milotti, Phys. Rev. E 72 (2005) 056701], possibly followed by an integration step to produce noise with spectral index >2. Reasons for the new version: Extension to 1/f noises with spectral index 2<α⩽4: the new version generates both noises with spectral with spectral index 0<α⩽2 and with 2<α⩽4. Summary of revisions: Although the overall structure remains the same, one routine has been added and several changes have been made throughout the code to include the new integration step. Unusual features: The algorithm is theoretically guaranteed to be exact, and unlike all other existing generators it can generate samples with uneven spacing. Additional comments: The program requires an initialization step; for some parameter sets this may become rather heavy. Running time: Running time varies widely with different input parameters, however in a test run like the one in Section 3 in the long write-up, the generation routine took on average about 75 μs for each sample.

ENVIRONMENTAL TECHNOLOGY VERIFICATION REPORT: COMM ENGINEERING, USA ENVIRONMENTAL VAPOR RECOVERY UNIT (EVRU)

EPA Science Inventory

This report documents the testing of a new technology that recovers and utilizes vapors from crude oil storage tanks employed in the oil production and processing industry. The COMM Engineering, USA Environmental Vapor Recovery Unit (EVRU) is a non-mechanical eductor, or jet pump...

Intergenerational Effects of Parents' Math Anxiety on Children's Math Achievement and Anxiety.

PubMed

Maloney, Erin A; Ramirez, Gerardo; Gunderson, Elizabeth A; Levine, Susan C; Beilock, Sian L

2015-09-01

A large field study of children in first and second grade explored how parents' anxiety about math relates to their children's math achievement. The goal of the study was to better understand why some students perform worse in math than others. We tested whether parents' math anxiety predicts their children's math achievement across the school year. We found that when parents are more math anxious, their children learn significantly less math over the school year and have more math anxiety by the school year's end-but only if math-anxious parents report providing frequent help with math homework. Notably, when parents reported helping with math homework less often, children's math achievement and attitudes were not related to parents' math anxiety. Parents' math anxiety did not predict children's reading achievement, which suggests that the effects of parents' math anxiety are specific to children's math achievement. These findings provide evidence of a mechanism for intergenerational transmission of low math achievement and high math anxiety. © The Author(s) 2015.

PSsolver: A Maple implementation to solve first order ordinary differential equations with Liouvillian solutions

NASA Astrophysics Data System (ADS)

Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.

2012-10-01

We present a set of software routines in Maple 14 for solving first order ordinary differential equations (FOODEs). The package implements the Prelle-Singer method in its original form together with its extension to include integrating factors in terms of elementary functions. The package also presents a theoretical extension to deal with all FOODEs presenting Liouvillian solutions. Applications to ODEs taken from standard references show that it solves ODEs which remain unsolved using Maple's standard ODE solution routines. New version program summary Program title: PSsolver Catalogue identifier: ADPR_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADPR_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 2302 No. of bytes in distributed program, including test data, etc.: 31962 Distribution format: tar.gz Programming language: Maple 14 (also tested using Maple 15 and 16). Computer: Intel Pentium Processor P6000, 1.86 GHz. Operating system: Windows 7. RAM: 4 GB DDR3 Memory Classification: 4.3. Catalogue identifier of previous version: ADPR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 144 (2002) 46 Does the new version supersede the previous version?: Yes Nature of problem: Symbolic solution of first order differential equations via the Prelle-Singer method. Solution method: The method of solution is based on the standard Prelle-Singer method, with extensions for the cases when the FOODE contains elementary functions. Additionally, an extension of our own which solves FOODEs with Liouvillian solutions is included. Reasons for new version: The program was not running anymore due to changes in the latest versions of Maple. Additionally, we corrected/changed some bugs/details that were hampering the smoother functioning of the routines. Summary of revisions: • As time went by, many commands in Maple were deprecated. So, in order to make the program able to run with the newer versions, we have checked and changed some of those. For instance, the command sum had changed, and some program lines were substituted so that the package works properly. • In the old version we must supply the degree of the Darboux polynomials we want to determine. In the present version the user can set the degree by typing Deg = number in the command call (e.g., PSsolve(ode, Deg =3); telling the command PSsolve that it must use Darboux polynomials of degree up to three). If the user does not specify the degree, the routines use, as default, the degree 1. Restrictions: If the integrating factor for the FOODE under consideration has factors of high degree in the dependent and independent variables and in the elementary functions appearing in the FOODE, the package may spend a long time finding the solution. Also, when dealing with FOODEs containing elementary functions, it is essential that the algebraic dependency between them is recognized. If that does not happen, our program can miss some solutions. Unusual features: Our implementation of the Prelle-Singer approach not only solves FOODEs, but can also be used as a research tool that allows the user to follow all the steps of the procedure. For example, the Darboux polynomials (eigenpolynomials) of the D-operator associated with a FOODE (see Section 4) can be calculated. In addition, our package is successful in solving FOODEs that were not solved by some of the most commonly available solvers. Finally, our package implements a theoretical extension (for details, see [1,2]) to the original Prelle-Singer approach that enhances its scope, allowing it to tackle some FOODEs whose solutions involve non-elementary Liouvillian functions. Running time: This depends strongly on the FOODE, but usually under 2 seconds when running our 'arena' test file: The non linear FOODEs presented in the book by Kamke [3]. These times were obtained using an Intel Pentium Processor P6000, 1.86 GHz, with 4 GB RAM. References: [1] M. Singer, Liouvillian first integrals of differential equations, Trans. Amer. Math. Soc. 333 (1992) 673-688. [2] L.G.S. Duarte, S.E.S. Duarte, L.A.C.P. da Mota, J.E.F. Skea, A method to tackle first order ordinary differential equations with Liouvilian functions in the solution, J. Phys. A: Math. Gen. Inglaterra 35 (17) (2002) 3899-3910. [3] E. Kamke, Differentialgleichungen: Lösungsmethoden und Lösungen, Chelsea Publishing Co., New York, 1959.

Implicit constitutive models with a thermodynamic basis: a study of stress concentration

NASA Astrophysics Data System (ADS)

Bridges, C.; Rajagopal, K. R.

2015-02-01

Motivated by the recent generalization of the class of elastic bodies by Rajagopal (Appl Math 48:279-319, 2003), there have been several recent studies that have been carried out within the context of this new class. Rajagopal and Srinivasa (Proc R Soc Ser A 463:357-367, 2007, Proc R Soc Ser A: Math Phys Eng Sci 465:493-500, 2009) provided a thermodynamic basis for such models and appealing to the idea that rate of entropy production ought to be maximized they developed nonlinear rate equations of the form where T is the Cauchy stress and D is the stretching tensor as well as , where S is the Piola-Kirchhoff stress tensor and E is the Green-St. Venant strain tensor. We follow a similar procedure by utilizing the Gibb's potential and the left stretch tensor V from the Polar Decomposition of the deformation gradient, and we show that when the displacement gradient is small one arrives at constitutive relations of the form . This is, of course, in stark contrast to traditional elasticity wherein one obtains a single model, Hooke's law, when the displacement gradient is small. By solving a classical boundary value problem, with a particular form for f( T), we show that when the stresses are small, the strains are also small which is in agreement with traditional elasticity. However, within the context of our model, when the stress blows up the strains remain small, unlike the implications of Hooke's law. We use this model to study boundary value problems in annular domains to illustrate its efficacy.

Parent-child math anxiety and math-gender stereotypes predict adolescents' math education outcomes

PubMed Central

Casad, Bettina J.; Hale, Patricia; Wachs, Faye L.

2015-01-01

Two studies examined social determinants of adolescents' math anxiety including parents' own math anxiety and children's endorsement of math-gender stereotypes. In Study 1, parent-child dyads were surveyed and the interaction between parent and child math anxiety was examined, with an eye to same- and other-gender dyads. Results indicate that parent's math anxiety interacts with daughters' and sons' anxiety to predict math self-efficacy, GPA, behavioral intentions, math attitudes, and math devaluing. Parents with lower math anxiety showed a positive relationship to children's math outcomes when children also had lower anxiety. The strongest relationships were found with same-gender dyads, particularly Mother-Daughter dyads. Study 2 showed that endorsement of math-gender stereotypes predicts math anxiety (and not vice versa) for performance beliefs and outcomes (self-efficacy and GPA). Further, math anxiety fully mediated the relationship between gender stereotypes and math self-efficacy for girls and boys, and for boys with GPA. These findings address gaps in the literature on the role of parents' math anxiety in the effects of children's math anxiety and math anxiety as a mechanism affecting performance. Results have implications for interventions on parents' math anxiety and dispelling gender stereotypes in math classrooms. PMID:26579000

Parent-child math anxiety and math-gender stereotypes predict adolescents' math education outcomes.

PubMed

Casad, Bettina J; Hale, Patricia; Wachs, Faye L

2015-01-01

Two studies examined social determinants of adolescents' math anxiety including parents' own math anxiety and children's endorsement of math-gender stereotypes. In Study 1, parent-child dyads were surveyed and the interaction between parent and child math anxiety was examined, with an eye to same- and other-gender dyads. Results indicate that parent's math anxiety interacts with daughters' and sons' anxiety to predict math self-efficacy, GPA, behavioral intentions, math attitudes, and math devaluing. Parents with lower math anxiety showed a positive relationship to children's math outcomes when children also had lower anxiety. The strongest relationships were found with same-gender dyads, particularly Mother-Daughter dyads. Study 2 showed that endorsement of math-gender stereotypes predicts math anxiety (and not vice versa) for performance beliefs and outcomes (self-efficacy and GPA). Further, math anxiety fully mediated the relationship between gender stereotypes and math self-efficacy for girls and boys, and for boys with GPA. These findings address gaps in the literature on the role of parents' math anxiety in the effects of children's math anxiety and math anxiety as a mechanism affecting performance. Results have implications for interventions on parents' math anxiety and dispelling gender stereotypes in math classrooms.

A collision scheme for hybrid fluid-particle simulation of plasmas

NASA Astrophysics Data System (ADS)

Nguyen, Christine; Lim, Chul-Hyun; Verboncoeur, John

2006-10-01

Desorption phenomena at the wall of a tokamak can lead to the introduction of impurities at the edge of a thermonuclear plasma. In particular, the use of carbon as a constituent of the tokamak wall, as planned for ITER, requires the study of carbon and hydrocarbon transport in the plasma, including understanding of collisional interaction with the plasma. These collisions can result in new hydrocarbons, hydrogen, secondary electrons and so on. Computational modeling is a primary tool for studying these phenomena. XOOPIC [1] and OOPD1 are widely used computer modeling tools for the simulation of plasmas. Both are particle type codes. Particle simulation gives more kinetic information than fluid simulation, but more computation time is required. In order to reduce this disadvantage, hybrid simulation has been developed, and applied to the modeling of collisions. Present particle simulation tools such as XOOPIC and OODP1 employ a Monte Carlo model for the collisions between particle species and a neutral background gas defined by its temperature and pressure. In fluid-particle hybrid plasma models, collisions include combinations of particle and fluid interactions categorized by projectile-target pairing: particle-particle, particle-fluid, and fluid-fluid. For verification of this hybrid collision scheme, we compare simulation results to analytic solutions for classical plasma models. [1] Verboncoeur et al. Comput. Phys. Comm. 87, 199 (1995).

Development of a Grid-Based Gyro-Kinetic Simulation Code

NASA Astrophysics Data System (ADS)

Lapillonne, Xavier; Brunetti, Maura; Tran, Trach-Minh; Brunner, Stephan

2006-10-01

A grid-based semi-Lagrangian code using cubic spline interpolation is being developed at CRPP, for solving the electrostatic drift-kinetic equations [M. Brunetti et. al, Comp. Phys. Comm. 163, 1 (2004)] in a cylindrical system. This 4-dim code, CYGNE, is part of a project with long term aim of studying microturbulence in toroidal fusion devices, in the more general frame of gyro-kinetic equations. Towards their non-linear phase, the simulations from this code are subject to significant overshoot problems, reflected by the development of negative value regions of the distribution function, which leads to bad energy conservation. This has motivated the study of alternative schemes. On the one hand, new time integration algorithms are considered in the semi-Lagrangian frame. On the other hand, fully Eulerian schemes, which separate time and space discretisation (method of lines), are investigated. In particular, the Essentially Non Oscillatory (ENO) approach, constructed so as to minimize the overshoot problem, has been considered. All these methods have first been tested in the simpler case of the 2-dim guiding-center model for the Kelvin-Helmholtz instability, which enables to address the specific issue of the E xB drift also met in the more complex gyrokinetic-type equations. Based on these preliminary studies, the most promising methods are being implemented and tested in CYGNE.

75 FR 4344 - Foreign-Trade Zone 22-Chicago, IL Application for Temporary/Interim Manufacturing Authority LG...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-01-27

... DEPARTMENT OF COMMERCE Foreign-Trade Zones Board [Docket T-1-2010] Foreign-Trade Zone 22--Chicago, IL Application for Temporary/ Interim Manufacturing Authority LG Electronics MobileComm USA, Inc... Electronics MobileComm USA, Inc. (LGEMU) facility, located in Bolingbrook, Illinois. The application was filed...

75 FR 4343 - Foreign-Trade Zone 22-Chicago, IL; Application for Manufacturing Authority; LG Electronics...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-01-27

... DEPARTMENT OF COMMERCE Foreign-Trade Zones Board [Docket 3-2010] Foreign-Trade Zone 22--Chicago, IL; Application for Manufacturing Authority; LG Electronics MobileComm USA, Inc. (Cell Phone Kitting... authority on behalf of LG Electronics MobileComm USA, Inc. (LGEMU), located in Bolingbrook, Illinois. The...

Baltimore Community Schools: Promise & Progress

ERIC Educational Resources Information Center

Durham, Rachel E.; Connolly, Faith

2016-01-01

This report documents the interim progress of the Baltimore Community School (CommSch) strategy by examining outcomes for the 2014-15 school year. Results show that CommSch parents more often reported being connected with community resources by school staff compared to parents at other schools. They also were more likely to report that school…

2005 Unmanned Maritime Vehicle (UMV) Test and Evaluation Conference

DTIC Science & Technology

2005-06-16

it can adapt and reshape itself until the requirements are met. This isn’t commander Cicada – just the Cicada that was handy and happened to be...Comms vs. Speed Results Mode Transition to Comms Chain Swarming Autonomy Benefits 1,000,000,000,000 Cicadas Can’t Be Wrong! Thank you! robert.chalmers

Quantum Gravitational Corrections to the Real Klein-Gordon Field in the Presence of a Minimal Length

NASA Astrophysics Data System (ADS)

Moayedi, S. K.; Setare, M. R.; Moayeri, H.

2010-09-01

The ( D+1)-dimensional ( β, β')-two-parameter Lorentz-covariant deformed algebra introduced by Quesne and Tkachuk (J. Phys., A Math. Gen. 39, 10909, 2006), leads to a nonzero minimal uncertainty in position (minimal length). The Klein-Gordon equation in a (3+1)-dimensional space-time described by Quesne-Tkachuk Lorentz-covariant deformed algebra is studied in the case where β'=2 β up to first order over deformation parameter β. It is shown that the modified Klein-Gordon equation which contains fourth-order derivative of the wave function describes two massive particles with different masses. We have shown that physically acceptable mass states can only exist for β<1/8m^{2c2} which leads to an isotropic minimal length in the interval 10-17 m<(Δ X i )0<10-15 m. Finally, we have shown that the above estimation of minimal length is in good agreement with the results obtained in previous investigations.

Well behaved parametric class of relativistic charged fluid ball in general relativity

NASA Astrophysics Data System (ADS)

Pant, Neeraj

2011-04-01

The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0≤ K≤42) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. Corresponding to K=2 and X=0.30, the maximum mass of the star comes out to be 4.96 M Θ with linear dimension 34.16 km and central redshift and surface redshift 2.1033 and 0.683 respectively. In absence of the charge we are left behind with the well behaved fourth model of Durgapal (J. Phys., A, Math. Gen. 15:2637, 1982).

Double-scaling limits of random matrices and minimal (2m, 1) models: the merging of two cuts in a degenerate case

NASA Astrophysics Data System (ADS)

Marchal, O.; Cafasso, M.

2011-04-01

In this paper, we show that the double-scaling-limit correlation functions of a random matrix model when two cuts merge with degeneracy 2m (i.e. when y ~ x2m for arbitrary values of the integer m) are the same as the determinantal formulae defined by conformal (2m, 1) models. Our approach follows the one developed by Bergère and Eynard in (2009 arXiv:0909.0854) and uses a Lax pair representation of the conformal (2m, 1) models (giving a Painlevé II integrable hierarchy) as suggested by Bleher and Eynard in (2003 J. Phys. A: Math. Gen. 36 3085). In particular we define Baker-Akhiezer functions associated with the Lax pair in order to construct a kernel which is then used to compute determinantal formulae giving the correlation functions of the double-scaling limit of a matrix model near the merging of two cuts.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boche, H., E-mail: boche@tum.de; Janßen, G., E-mail: gisbert.janssen@tum.de

We consider one-way quantum state merging and entanglement distillation under compound and arbitrarily varying source models. Regarding quantum compound sources, where the source is memoryless, but the source state an unknown member of a certain set of density matrices, we continue investigations begun in the work of Bjelaković et al. [“Universal quantum state merging,” J. Math. Phys. 54, 032204 (2013)] and determine the classical as well as entanglement cost of state merging. We further investigate quantum state merging and entanglement distillation protocols for arbitrarily varying quantum sources (AVQS). In the AVQS model, the source state is assumed to vary inmore » an arbitrary manner for each source output due to environmental fluctuations or adversarial manipulation. We determine the one-way entanglement distillation capacity for AVQS, where we invoke the famous robustification and elimination techniques introduced by Ahlswede. Regarding quantum state merging for AVQS we show by example that the robustification and elimination based approach generally leads to suboptimal entanglement as well as classical communication rates.« less

Picosecond timing resolution detection of ggr-photons utilizing microchannel-plate detectors: experimental tests of quantum nonlocality and photon localization

NASA Astrophysics Data System (ADS)

Irby, Victor D.

2004-09-01

The concept and subsequent experimental verification of the proportionality between pulse amplitude and detector transit time for microchannel-plate detectors is presented. This discovery has led to considerable improvement in the overall timing resolution for detection of high-energy ggr-photons. Utilizing a 22Na positron source, a full width half maximum (FWHM) timing resolution of 138 ps has been achieved. This FWHM includes detector transit-time spread for both chevron-stack-type detectors, timing spread due to uncertainties in annihilation location, all electronic uncertainty and any remaining quantum mechanical uncertainty. The first measurement of the minimum quantum uncertainty in the time interval between detection of the two annihilation photons is reported. The experimental results give strong evidence against instantaneous spatial localization of ggr-photons due to measurement-induced nonlocal quantum wavefunction collapse. The experimental results are also the first that imply momentum is conserved only after the quantum uncertainty in time has elapsed (Yukawa H 1935 Proc. Phys. Math. Soc. Japan 17 48).

Resonant Transparency and Non-Trivial Non-Radiating Excitations in Toroidal Metamaterials

PubMed Central

Fedotov, V. A.; Rogacheva, A. V.; Savinov, V.; Tsai, D. P.; Zheludev, N. I.

2013-01-01

Engaging strongly resonant interactions allows dramatic enhancement of functionalities of many electromagnetic devices. However, resonances can be dampened by Joule and radiation losses. While in many cases Joule losses may be minimized by the choice of constituting materials, controlling radiation losses is often a bigger problem. Recent solutions include the use of coupled radiant and sub-radiant modes yielding narrow asymmetric Fano resonances in a wide range of systems, from defect states in photonic crystals and optical waveguides with mesoscopic ring resonators to nanoscale plasmonic and metamaterial systems exhibiting interference effects akin to electromagnetically-induced transparency. Here we demonstrate theoretically and confirm experimentally a new mechanism of resonant electromagnetic transparency, which yields very narrow isolated symmetric Lorentzian transmission lines in toroidal metamaterials. It exploits the long sought non-trivial non-radiating charge-current excitation based on interfering electric and toroidal dipoles that was first proposed by Afanasiev and Stepanovsky in [J. Phys. A Math. Gen. 28, 4565 (1995)]. PMID:24132231

Breakup of Kol'mogorov-Arnol'd-Moser tori of cubic irrational winding number

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mao, J.; Helleman, R.H.G.

1989-01-01

For the special case in which the irrational winding number is the root of a cubic equation, we present numerical evidence for the validity of some form of residue criterion (Greene, J. Math. Phys. 20, 1182 (1979)). This is a criterion for the breakup of Kol'mogorov-Arnol'd-Moser tori in two degrees of freedom. The cubic case is essential for future work on four-dimensional maps. While the residues do approach infinity (respectively, 0) after (respectively, before) the breaking point, it is numerically very difficult to estimate a critical residue value R/sub cr/ for this cubic case (0.15approx. ..infinity, with a ''new'' scalingmore » constant xiapprox. =0.72, where p/sub n//q/sub n/ is the nth rational approximant in the continued-fraction expansion of the cubic irrational. For a quadratic irrational this scaling reduces to the usual power-law scaling approx.delta/sup -//sup n/.« less

Recursion Relations for Double Ramification Hierarchies

NASA Astrophysics Data System (ADS)

Buryak, Alexandr; Rossi, Paolo

2016-03-01

In this paper we study various properties of the double ramification hierarchy, an integrable hierarchy of hamiltonian PDEs introduced in Buryak (CommunMath Phys 336(3):1085-1107, 2015) using intersection theory of the double ramification cycle in the moduli space of stable curves. In particular, we prove a recursion formula that recovers the full hierarchy starting from just one of the Hamiltonians, the one associated to the first descendant of the unit of a cohomological field theory. Moreover, we introduce analogues of the topological recursion relations and the divisor equation both for the Hamiltonian densities and for the string solution of the double ramification hierarchy. This machinery is very efficient and we apply it to various computations for the trivial and Hodge cohomological field theories, and for the r -spin Witten's classes. Moreover, we prove the Miura equivalence between the double ramification hierarchy and the Dubrovin-Zhang hierarchy for the Gromov-Witten theory of the complex projective line (extended Toda hierarchy).

Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion

NASA Astrophysics Data System (ADS)

Hoh, H. J.; Xiao, Z. M.; Luo, J.

2010-09-01

An analytical investigation on the plastic zone size of a crack near a coated circular inclusion under three different loading conditions of uniaxial tension, uniform tension and pure shear was carried out. Both the crack and coated circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small-scale yielding [J. Mech. Phys. Solids 8 (1960) p. 100], two thin strips of yielded plastic zones are introduced at both crack tips. Using the solution for a coated circular inclusion interacting with a single dislocation as the Green's function, the physical problem is formulated into a set of singular integral equations. Using the method of Erdogan and Gupta [Q. J. Appl. Math. 29 (1972) p. 525] and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Law, P.R.

In Matsushita (J. Math. Phys. {bold 22}, 979--982 (1981), {ital ibid}. {bold 24}, 36--40 (1983)), for curvature endomorphisms for the pseudo-Euclidean space {ital R}{sup 2,2}, an analog of the Petrov classification as a basis for applications to neutral Einstein metrics on compact, orientable, four-dimensional manifolds is provided. This paper points out flaws in Matsushita's classification and, moreover, that an error in Chern's ( Pseudo-Riemannian geometry and the Gauss--Bonnet formula,'' Acad. Brasileira Ciencias {bold 35}, 17--26 (1963) and {ital Shiing}-{ital Shen} {ital Chern}: {ital Selected} {ital Papers} (Springer-Verlag, New York, 1978)) Gauss--Bonnet formula for pseudo-Riemannian geometry was incorporated in Matsushita's subsequentmore » analysis. A self-contained account of the subject of the title is presented to correct these errors, including a discussion of the validity of an appropriate analog of the Thorpe--Hitchin inequality of the Riemannian case. When the inequality obtains in the neutral case, the Euler characteristic is nonpositive, in contradistinction to Matsushita's deductions.« less

A characterization of horizontal visibility graphs and combinatorics on words

NASA Astrophysics Data System (ADS)

Gutin, Gregory; Mansour, Toufik; Severini, Simone

2011-06-01

A Horizontal Visibility Graph (HVG) is defined in association with an ordered set of non-negative reals. HVGs realize a methodology in the analysis of time series, their degree distribution being a good discriminator between randomness and chaos Luque et al. [B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: exact results for random time series, Phys. Rev. E 80 (2009), 046103]. We prove that a graph is an HVG if and only if it is outerplanar and has a Hamilton path. Therefore, an HVG is a noncrossing graph, as defined in algebraic combinatorics Flajolet and Noy [P. Flajolet, M. Noy, Analytic combinatorics of noncrossing configurations, Discrete Math., 204 (1999) 203-229]. Our characterization of HVGs implies a linear time recognition algorithm. Treating ordered sets as words, we characterize subfamilies of HVGs highlighting various connections with combinatorial statistics and introducing the notion of a visible pair. With this technique, we determine asymptotically the average number of edges of HVGs.

The algebra of two dimensional generalized Chebyshev-Koornwinder oscillator

NASA Astrophysics Data System (ADS)

Borzov, V. V.; Damaskinsky, E. V.

2014-10-01

In the previous works of Borzov and Damaskinsky ["Chebyshev-Koornwinder oscillator," Theor. Math. Phys. 175(3), 765-772 (2013)] and ["Ladder operators for Chebyshev-Koornwinder oscillator," in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which is bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.

FAST TRACK COMMUNICATION: Superintegrability of the Tremblay-Turbiner-Winternitz quantum Hamiltonians on a plane for odd k

NASA Astrophysics Data System (ADS)

Quesne, C.

2010-02-01

In a recent communication paper by Tremblay et al (2009 J. Phys. A: Math. Theor. 42 205206), it has been conjectured that for any integer value of k, some novel exactly solvable and integrable quantum Hamiltonian Hk on a plane is superintegrable and that the additional integral of motion is a 2kth-order differential operator Y2k. Here we demonstrate the conjecture for the infinite family of Hamiltonians Hk with odd k >= 3, whose first member corresponds to the three-body Calogero-Marchioro-Wolfes model after elimination of the centre-of-mass motion. Our approach is based on the construction of some D2k-extended and invariant Hamiltonian {\\cal H}_k, which can be interpreted as a modified boson oscillator Hamiltonian. The latter is then shown to possess a D2k-invariant integral of motion {\\cal Y}_{2k}, from which Y2k can be obtained by projection in the D2k identity representation space.

Multidimensional entropic uncertainty relation based on a commutator matrix in position and momentum spaces

NASA Astrophysics Data System (ADS)

Hertz, Anaelle; Vanbever, Luc; Cerf, Nicolas J.

2018-01-01

The uncertainty relation for continuous variables due to Byałinicki-Birula and Mycielski [I. Białynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975), 10.1007/BF01608825] expresses the complementarity between two n -tuples of canonically conjugate variables (x1,x2,...,xn) and (p1,p2,...,pn) in terms of Shannon differential entropy. Here we consider the generalization to variables that are not canonically conjugate and derive an entropic uncertainty relation expressing the balance between any two n -variable Gaussian projective measurements. The bound on entropies is expressed in terms of the determinant of a matrix of commutators between the measured variables. This uncertainty relation also captures the complementarity between any two incompatible linear canonical transforms, the bound being written in terms of the corresponding symplectic matrices in phase space. Finally, we extend this uncertainty relation to Rényi entropies and also prove a covariance-based uncertainty relation which generalizes the Robertson relation.

Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra

NASA Astrophysics Data System (ADS)

Yates, L. A.; Jarvis, P. D.

2018-04-01

We analyze the structure of the family of quadratic superalgebras, introduced in Jarvis et al (2011 J. Phys. A: Math. Theor. 44 235205), for the quadratic deformations of N  =  1 space-time conformal supersymmetry. We characterize in particular the ‘zero-step’ modules for this case. In such modules, the odd generators vanish identically, and the quadratic superalgebra is realized on a single irreducible representation of the even subalgebra (which is a Lie algebra). In the case under study, the quadratic deformations of N  =  1 space-time conformal supersymmetry, it is shown that each massless positive energy unitary irreducible representation (in the standard classification of Mack), forms such a zero-step module, for an appropriate parameter choice amongst the quadratic family (with vanishing central charge). For these massless particle multiplets therefore, quadratic supersymmetry is unbroken, in that the supersymmetry generators annihilate all physical states (including the vacuum state), while at the same time, superpartners do not exist.

Particle-like structure of coaxial Lie algebras

NASA Astrophysics Data System (ADS)

Vinogradov, A. M.

2018-01-01

This paper is a natural continuation of Vinogradov [J. Math. Phys. 58, 071703 (2017)] where we proved that any Lie algebra over an algebraically closed field or over R can be assembled in a number of steps from two elementary constituents, called dyons and triadons. Here we consider the problems of the construction and classification of those Lie algebras which can be assembled in one step from base dyons and triadons, called coaxial Lie algebras. The base dyons and triadons are Lie algebra structures that have only one non-trivial structure constant in a given basis, while coaxial Lie algebras are linear combinations of pairwise compatible base dyons and triadons. We describe the maximal families of pairwise compatible base dyons and triadons called clusters, and, as a consequence, we give a complete description of the coaxial Lie algebras. The remarkable fact is that dyons and triadons in clusters are self-organised in structural groups which are surrounded by casings and linked by connectives. We discuss generalisations and applications to the theory of deformations of Lie algebras.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Borzov, V. V., E-mail: borzov.vadim@yandex.ru; Damaskinsky, E. V., E-mail: evd@pdmi.ras.ru

In the previous works of Borzov and Damaskinsky [“Chebyshev-Koornwinder oscillator,” Theor. Math. Phys. 175(3), 765–772 (2013)] and [“Ladder operators for Chebyshev-Koornwinder oscillator,” in Proceedings of the Days on Diffraction, 2013], the authors have defined the oscillator-like system that is associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev-Koornwinder oscillator. In this paper, we study the properties of infinite-dimensional Lie algebra that is analogous to the Heisenberg algebra for the Chebyshev-Koornwinder oscillator. We construct the exact irreducible representation of this algebra in a Hilbert space H of functions that are defined on a region which ismore » bounded by the Steiner hypocycloid. The functions are square-integrable with respect to the orthogonality measure for the Chebyshev-Koornwinder polynomials and these polynomials form an orthonormalized basis in the space H. The generalized oscillator which is studied in the work can be considered as the simplest nontrivial example of multiboson quantum system that is composed of three interacting oscillators.« less

Coarsening dynamics in condensing zero-range processes and size-biased birth death chains

NASA Astrophysics Data System (ADS)

Jatuviriyapornchai, Watthanan; Grosskinsky, Stefan

2016-05-01

Zero-range processes with decreasing jump rates are well known to exhibit a condensation transition under certain conditions on the jump rates, and the dynamics of this transition continues to be a subject of current research interest. Starting from homogeneous initial conditions, the time evolution of the condensed phase exhibits an interesting coarsening phenomenon of mass transport between cluster sites characterized by a power law. We revisit the approach in Godrèche (2003 J. Phys. A: Math. Gen. 36 6313) to derive effective single site dynamics which form a nonlinear birth death chain describing the coarsening behavior. We extend these results to a larger class of parameter values, and introduce a size-biased version of the single site process, which provides an effective tool to analyze the dynamics of the condensed phase without finite size effects and is the main novelty of this paper. Our results are based on a few heuristic assumptions and exact computations, and are corroborated by detailed simulation data.

O'Connell's process as a vicious Brownian motion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Katori, Makoto

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O'Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of themore » quantum Toda lattice in order to analyze a directed polymer model in 1 + 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O'Connell process as a conditional process of the killing Brownian motions to survive forever.« less

On a model of electromagnetic field propagation in ferroelectric media

NASA Astrophysics Data System (ADS)

Picard, Rainer

2007-04-01

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.

The limit distribution in the q-CLT for q\\,\\geqslant \\,1 is unique and can not have a compact support

NASA Astrophysics Data System (ADS)

Umarov, Sabir; Tsallis, Constantino

2016-10-01

In a paper by Umarov et al (2008 Milan J. Math. 76 307-28), a generalization of the Fourier transform, called the q-Fourier transform, was introduced and applied for the proof of a q-generalized central limit theorem (q-CLT). Subsequently, Hilhorst illustrated (2009 Braz. J. Phys. 39 371-9 2010 J. Stat. Mech. P10023) that the q-Fourier transform for q\\gt 1, is not invertible in the space of density functions. Indeed, using an invariance principle, he constructed a family of densities with the same q-Fourier transform and noted that ‘as a consequence, the q-CLT falls short of achieving its stated goal’. The distributions constructed there have compact support. We prove now that the limit distribution in the q-CLT is unique and can not have a compact support. This result excludes all the possible counterexamples which can be constructed using the invariance principle and fills the gap mentioned by Hilhorst.

Lagrangian and Eulerian view of the bursting period

NASA Astrophysics Data System (ADS)

Podvin, Bérengère; Gibson, John; Berkooz, Gal; Lumley, John

1997-02-01

Low-dimensional models for the turbulent wall layer display an intermittent phenomenon with an ejection phase and a sweep phase that strongly resembles the bursting phenomenon observed in experimental flows. The probability distribution of inter-burst times has the observed shape [E. Stone and P. J. Holmes, Physica D 37, 20 (1989); SIAM J. Appl. Math. 50, 726 (1990); Phys. Lett. A 5, 29 (1991); P. J. Holmes and E. Stone, in Studies in Turbulence, edited by T. B. Gatski, S. Sarkar, and C. G. Speziale (Springer, Heidelberg, 1992)]. However, the time scales both for bursts and interburst durations are unrealistically long, a fact that was not appreciated until recently. We believe that the long time scales are due to the model's inclusion of only a single coherent structure, when in fact a succession of quasi-independent structures are being swept past the sensor in an experiment. A simple statistical model of this situation restores the magnitude of the observed bursting period, although there is a great deal of flexibility in the various parameters involved.

Flory Model of Polymer Crystallization, Kauzmann Paradox and Gibbs-DiMarzio Theory of Glass Transition

NASA Astrophysics Data System (ADS)

Corsi, A.; Gujrati, P. D.

2000-03-01

The Flory model of crystallization of polymers is well known and forms the cornerstone of the Gibbs-DiMarzio theory of glass transition. The model has no known exact solution and the original calculation [1] was shown to be incorrect [2]. Still it is interesting to know the order of the phase transition, if it has one. We have studied the thermodynamics of the model in the limit of infinite molecular weight. We have solved it exactly on a recursive lattice with coordination number q=4, relevant for a tetrahedral lattice. Our results show that there is a continuous, i.e. a second-order, transition at which the entropy of the system is continuous. It is finite at all temperatures and approaches 0 as T goes to 0 so that the system is never completely ordered except at T=0. As the temperature is raised above T=0 the system begins to disorder with a degree of disorder that depends on T, which is in accordance with the analysis of Gujrati and Goldstein [2]. Since there is no first order transition there is no Kauzmann paradox. Similarly there is no possible metastable extension in the model which is central to the Gibbs-DiMarzio conjecture for an ideal glass transition. Thus, our solution does not justify their conjecture. [1] P.J. Flory, Proc. R. Soc. London Ser., A234, 60 (1956) [2] P.D. Gujrati, J. Phys. A: Math. Gen., 13, L437 (1980), P.D. Gujrati, M. Goldstein, J. Chem. Phys., 74(4), 2596 (1981)

The Drastic Outcomes from Voting Alliances in Three-Party Democratic Voting (1990 → 2013)

NASA Astrophysics Data System (ADS)

Galam, Serge

2013-04-01

The drastic effect of local alliances in three-party competition is investigated in democratic hierarchical bottom-up voting. The results are obtained analytically using a model which extends a sociophysics frame introduced in 1986 (Galam in J. Math. Phys. 30:426, 1986) and 1990 (Galam in J. Stat. Phys. 61:943, 1990) to study two-party systems and the spontaneous formation of democratic dictatorship. It is worth stressing that the 1990 paper was published in the Journal of Statistical Physics, the first paper of its kind in this journal. It was shown how a minority in power can preserve its leadership using bottom-up democratic elections. However such a bias holds only down to some critical value of minimum support. The results were used latter to explain the sudden collapse of European communist parties in the nineties. The extension to three-party competition reveals the mechanisms by which a very small minority party can get a substantial representation at higher levels of the hierarchy when the other two competing parties are big. Additional surprising results are obtained, which enlighten the complexity of three-party democratic bottom-up voting. In particular, the unexpected outcomes of local voting alliances are singled out. Unbalanced democratic situations are exhibited with strong asymmetries between the actual bottom support of a party and its associated share of power at the top leadership. Subtle strategies are identified for a party to maximize its hold on the top leadership. The results are also valid to describe opinion dynamics with three competing opinions.

Affective and Motivational Factors Mediate the Relation between Math Skills and Use of Math in Everyday Life

PubMed Central

Jansen, Brenda R. J.; Schmitz, Eva A.; van der Maas, Han L. J.

2016-01-01

This study focused on the use of math in everyday life (the propensity to recognize and solve quantitative issues in real life situations). Data from a Dutch nation-wide research on math among adults (N = 521) were used to investigate the question whether math anxiety and perceived math competence mediated the relationship between math skills and use of math in everyday life, taken gender differences into account. Results showed that women reported higher math anxiety, lower perceived math competence, and lower use of math in everyday life, compared to men. Women's skills were estimated at a lower level than men's. For both women and men, higher skills were associated with higher perceived math competence, which in turn was associated with more use of math in everyday life. Only for women, math anxiety also mediated the relation between math skills and use of math in everyday life. PMID:27148122

Working memory, math performance, and math anxiety.

PubMed

Ashcraft, Mark H; Krause, Jeremy A

2007-04-01

The cognitive literature now shows how critically math performance depends on working memory, for any form of arithmetic and math that involves processes beyond simple memory retrieval. The psychometric literature is also very clear on the global consequences of mathematics anxiety. People who are highly math anxious avoid math: They avoid elective coursework in math, both in high school and college, they avoid college majors that emphasize math, and they avoid career paths that involve math. We go beyond these psychometric relationships to examine the cognitive consequences of math anxiety. We show how performance on a standardized math achievement test varies as a function of math anxiety, and that math anxiety compromises the functioning of working memory. High math anxiety works much like a dual task setting: Preoccupation with one's math fears and anxieties functions like a resource-demanding secondary task. We comment on developmental and educational factors related to math and working memory, and on factors that may contribute to the development of math anxiety.

The Photoluminescence Efficiency of Extended Red Emission as a Constraint for Interstellar Dust

NASA Astrophysics Data System (ADS)

Smith, T. L.; Witt, A. N.

1999-12-01

The broad, 60 < FWHM < 100 nm, featureless luminescence band known as extended red emission (ERE) is seen in such diverse dusty astrophysical environments as reflection nebulae 17, planetary nebulae 3, HII regions (Orion) 12, a Nova 11, Galactic cirrus 14, a dark nebula 7, Galaxies 8,6 and the diffuse interstellar medium (ISM) 4. The band is confined between 540-950 nm, but the wavelength of peak emission varies from environment to environment, even within a given object. We have concluded that available data indicate that the wavelength of peak emission is longer and the efficiency of the luminescence is lower, the harder and denser the illuminating radiation field is 13. These general characteristics of ERE constrain the photoluminescence (PL) band and efficiency for laboratory analysis of dust analog materials. We have studied and present the PL band characteristics and efficiencies for a wide variety of dust analogs including hydrogenated amorphous carbon (HAC), Si-HAC alloys, nanodiamonds, silicon carbide nanoparticles, carbon nanoparticles and silicon nanoparticles. The PL efficiencies measured for HAC and Si-HAC alloys are consistent with dust estimates for reflection nebulae and planetary nebulae, but exhibit substantial photoluminescence below 540 nm which is not observed in astrophysical environments. Furthermore, all interstellar grains would need to consist of or be coated with these materials to match the ERE in terms of its quantum efficiency. Only the experimentally confirmed photoluminescence properties of silicon nanoparticles 1,2,5,9,10,15,16 match the ERE photoluminescence band constraints and fulfill the minimum photoluminescence efficiency predicted by Gordon et al. (1998) 4 without introducing unexpected spectral features in the diffuse ISM and without violating the abundance constraints on depleted interstellar silicon 18. This work has been supported by grants from NASA which we acknowledge with gratitude. 1. Credo, G.M., Mason, M.D., & Burrato, S.K. 1999, Appl. Phys. Lett., 74, 1978 2. Ehbrecht, M., Kohn, B., Huisken, F., Laguna, M.A. & Paillard, V. 1997, Phys. Rev. B, 56, 6958 3. Furton, D.G., & Witt, A.N. 1992, ApJ, 386, 587 4. Gordon, K.D., Witt, A.N., & Friedmann, B.C. 1998, ApJ, 498, 522 5. Lockwood, D.J., Lu, Z.H., & Baribeau, J.M. 1996, Phys. Rev. Lett., 76, 539 6. Majeed, A., Witt, A.N., & Boroson, T.A. 1999, Bull. AAS 3,886 7. Mattila, K. 1979, A&A, 78, 253 8. Perrin, J.M., Darbon, S., & Sivan, J.P. 1995, A&A, 304, L21 9. Schuppler, S. et al. 1994, Phys. Rev. B, 56, 6958 10. Schuppler, S. et al. 1995, Phys. Rev. B, 52, 4910 11. Scott, A.D., Evans, A., & Rawlings, J.M.C. 1994, MNRAS, 269, L21 12. Sivan, J.P., & Perrin, J.M. 1993, ApJ, 404, 258 13. Smith, T.L., Witt, A.N. & Gordon, K.D. 1999, BAAS 71.13 14. Szomoru, A., & Guhathakurta, P. 1998, ApJ, 494, L93 15. von Behren, J. van Buuren, T., Zacharias, M., Chimowitz, & E.H. Fauchet,P.M. 1998, Solid State Comm., 105, 317 16. Wilson, W.L., Szajowski, P.F., & Brus, L.E. 1993, Science, 262, 1242 17. Witt, A.N., & Boroson T.A. 1990, ApJ, 355, 182 18. Zubko, V.G. Smith, T.L., & Witt, A.N. 1999, ApJ, 511, L57

Mathematics anxiety: separating the math from the anxiety.

PubMed

Lyons, Ian M; Beilock, Sian L

2012-09-01

Anxiety about math is tied to low math grades and standardized test scores, yet not all math-anxious individuals perform equally poorly in math. We used functional magnetic resonance imaging to separate neural activity during the anticipation of doing math from activity during math performance itself. For higher (but not lower) math-anxious individuals, increased activity in frontoparietal regions when simply anticipating doing math mitigated math-specific performance deficits. This network included bilateral inferior frontal junction, a region involved in cognitive control and reappraisal of negative emotional responses. Furthermore, the relation between frontoparietal anticipatory activity and highly math-anxious individuals' math deficits was fully mediated (or accounted for) by activity in caudate, nucleus accumbens, and hippocampus during math performance. These subcortical regions are important for coordinating task demands and motivational factors during skill execution. Individual differences in how math-anxious individuals recruit cognitive control resources prior to doing math and motivational resources during math performance predict the extent of their math deficits. This work suggests that educational interventions emphasizing control of negative emotional responses to math stimuli (rather than merely additional math training) will be most effective in revealing a population of mathematically competent individuals, who might otherwise go undiscovered.

Female teachers' math anxiety affects girls' math achievement.

PubMed

Beilock, Sian L; Gunderson, Elizabeth A; Ramirez, Gerardo; Levine, Susan C

2010-02-02

People's fear and anxiety about doing math--over and above actual math ability--can be an impediment to their math achievement. We show that when the math-anxious individuals are female elementary school teachers, their math anxiety carries negative consequences for the math achievement of their female students. Early elementary school teachers in the United States are almost exclusively female (>90%), and we provide evidence that these female teachers' anxieties relate to girls' math achievement via girls' beliefs about who is good at math. First- and second-grade female teachers completed measures of math anxiety. The math achievement of the students in these teachers' classrooms was also assessed. There was no relation between a teacher's math anxiety and her students' math achievement at the beginning of the school year. By the school year's end, however, the more anxious teachers were about math, the more likely girls (but not boys) were to endorse the commonly held stereotype that "boys are good at math, and girls are good at reading" and the lower these girls' math achievement. Indeed, by the end of the school year, girls who endorsed this stereotype had significantly worse math achievement than girls who did not and than boys overall. In early elementary school, where the teachers are almost all female, teachers' math anxiety carries consequences for girls' math achievement by influencing girls' beliefs about who is good at math.

An Analysis of Manpower Requirements for the United States Marine Corps Tiers II and III Unmanned Aerial Systems Family of Systems Program

DTIC Science & Technology

2007-06-01

Organizational Automotive Mechanic ( MVM ) 1141 Electrician (EL) 0651 Data Network Specialist (COMM) 6072 Aircraft Support Equipment (SE)/hydraulic/Pneumatic...units reside, is cultural and not structural. Table 8. UAV Outsourcing Manpower Requirements MVO MVM EL COMM AVSE AVORD TOTALS PCS-1 0 0 0 0

Frozen Egg Products for Air Force Missile Sites

DTIC Science & Technology

1974-01-01

Freeze at -29*C (.20*F) and store at -18’C (0*F). Reheating: Air convection oven: Place frozen slices on cooky sheet and heat in oven (204°C, 400°F...Residual 40 .1028 French toast (comm.) Scrambled eggs (comm. ) French toast (sour dough ) Western egg &ham, dry minced onion 6 mo. Puffy omelet

2006 Combat Vehicles Conference

DTIC Science & Technology

2006-10-25

stressed or worn out beyond economic repair due to combat operations by repairing, rebuilding, or procuring replacement equipment. These...lives Vehicle Hardening Logistics Solutions for the Warfighter • Unique and economical surge capability • Support in coordination with op tempo...Speed, • Diagnostics Indicators – DECU Health Check Indicator, Utility Bus Comm Failure, 1553 Bus Comm Failure; MPU Critical Failure, Cautions and

Universals and Specifics of Math Self-Concept, Math Self-Efficacy, and Math Anxiety across 41 PISA 2003 Participating Countries

ERIC Educational Resources Information Center

Lee, Jihyun

2009-01-01

The overarching goal of the present study is to investigate the factorial structure of three closely related constructs: math self-concept, math self-efficacy, and math anxiety. The factorial structure consisting of three factors, each representing math self-concept, math self-efficacy, and math anxiety, is supported in all 41 countries employed…

Simulation of n-qubit quantum systems. IV. Parametrizations of quantum states, matrices and probability distributions

NASA Astrophysics Data System (ADS)

Radtke, T.; Fritzsche, S.

2008-11-01

Entanglement is known today as a key resource in many protocols from quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. The investigation of these and related questions often requires a search or optimization over the set of quantum states and, hence, a parametrization of them and various other objects. To facilitate this kind of studies in quantum information theory, here we present an extension of the FEYNMAN program that was developed during recent years as a toolbox for the simulation and analysis of quantum registers. In particular, we implement parameterizations of hermitian and unitary matrices (of arbitrary order), pure and mixed quantum states as well as separable states. In addition to being a prerequisite for the study of many optimization problems, these parameterizations also provide the necessary basis for heuristic studies which make use of random states, unitary matrices and other objects. Program summaryProgram title: FEYNMAN Catalogue identifier: ADWE_v4_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v4_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 231 No. of bytes in distributed program, including test data, etc.: 1 416 085 Distribution format: tar.gz Programming language: Maple 11 Computer: Any computer with Maple software installed Operating system: Any system that supports Maple; program has been tested under Microsoft Windows XP, Linux Classification: 4.15 Does the new version supersede the previous version?: Yes Nature of problem: During the last decades, quantum information science has contributed to our understanding of quantum mechanics and has provided also new and efficient protocols, based on the use of entangled quantum states. To determine the behavior and entanglement of n-qubit quantum registers, symbolic and numerical simulations need to be applied in order to analyze how these quantum information protocols work and which role the entanglement plays hereby. Solution method: Using the computer algebra system Maple, we have developed a set of procedures that support the definition, manipulation and analysis of n-qubit quantum registers. These procedures also help to deal with (unitary) logic gates and (nonunitary) quantum operations that act upon the quantum registers. With the parameterization of various frequently-applied objects, that are implemented in the present version, the program now facilitates a wider range of symbolic and numerical studies. All commands can be used interactively in order to simulate and analyze the evolution of n-qubit quantum systems, both in ideal and noisy quantum circuits. Reasons for new version: In the first version of the FEYNMAN program [1], we implemented the data structures and tools that are necessary to create, manipulate and to analyze the state of quantum registers. Later [2,3], support was added to deal with quantum operations (noisy channels) as an ingredient which is essential for studying the effects of decoherence. With the present extension, we add a number of parametrizations of objects frequently utilized in decoherence and entanglement studies, such that as hermitian and unitary matrices, probability distributions, or various kinds of quantum states. This extension therefore provides the basis, for example, for the optimization of a given function over the set of pure states or the simple generation of random objects. Running time: Most commands that act upon quantum registers with five or less qubits take ⩽10 seconds of processor time on a Pentium 4 processor with ⩾2GHz or newer, and about 5-20 MB of working memory (in addition to the memory for the Maple environment). Especially when working with symbolic expressions, however, the requirements on CPU time and memory critically depend on the size of the quantum registers, owing to the exponential growth of the dimension of the associated Hilbert space. For example, complex (symbolic) noise models, i.e. with several symbolic Kraus operators, result for multi-qubit systems often in very large expressions that dramatically slow down the evaluation of e.g. distance measures or the final-state entropy, etc. In these cases, Maple's assume facility sometimes helps to reduce the complexity of the symbolic expressions, but more often only a numerical evaluation is possible eventually. Since the complexity of the various commands of the FEYNMAN program and the possible usage scenarios can be very different, no general scaling law for CPU time or the memory requirements can be given. References: [1] T. Radtke, S. Fritzsche, Comput. Phys. Comm. 173 (2005) 91. [2] T. Radtke, S. Fritzsche, Comput. Phys. Comm. 175 (2006) 145. [3] T. Radtke, S. Fritzsche, Comput. Phys. Comm. 176 (2007) 617.

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayissi, Raoul Domingo, E-mail: raoulayissi@yahoo.fr; Noutchegueme, Norbert, E-mail: nnoutch@yahoo.fr

Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academymore » of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the global in time existence and uniqueness of a regular solution to the Einstein-Maxwell-Boltzmann system with the cosmological constant. We define and we use the weighted Sobolev separable spaces for the Boltzmann equation; some special spaces for the Einstein equations, then we clearly display all the proofs leading to the global existence theorems.« less

Bianchi type-I magnetized cosmological models for the Einstein-Boltzmann equation with the cosmological constant

NASA Astrophysics Data System (ADS)

Ayissi, Raoul Domingo; Noutchegueme, Norbert

2015-01-01

Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the global in time existence and uniqueness of a regular solution to the Einstein-Maxwell-Boltzmann system with the cosmological constant. We define and we use the weighted Sobolev separable spaces for the Boltzmann equation; some special spaces for the Einstein equations, then we clearly display all the proofs leading to the global existence theorems.

On the relationship between math anxiety and math achievement in early elementary school: The role of problem solving strategies.

PubMed

Ramirez, Gerardo; Chang, Hyesang; Maloney, Erin A; Levine, Susan C; Beilock, Sian L

2016-01-01

Even at young ages, children self-report experiencing math anxiety, which negatively relates to their math achievement. Leveraging a large dataset of first and second grade students' math achievement scores, math problem solving strategies, and math attitudes, we explored the possibility that children's math anxiety (i.e., a fear or apprehension about math) negatively relates to their use of more advanced problem solving strategies, which in turn relates to their math achievement. Our results confirm our hypothesis and, moreover, demonstrate that the relation between math anxiety and math problem solving strategies is strongest in children with the highest working memory capacity. Ironically, children who have the highest cognitive capacity avoid using advanced problem solving strategies when they are high in math anxiety and, as a result, underperform in math compared with their lower working memory peers. Copyright © 2015 Elsevier Inc. All rights reserved.

Is Math Anxiety Always Bad for Math Learning? The Role of Math Motivation.

PubMed

Wang, Zhe; Lukowski, Sarah L; Hart, Sara A; Lyons, Ian M; Thompson, Lee A; Kovas, Yulia; Mazzocco, Michèle M M; Plomin, Robert; Petrill, Stephen A

2015-12-01

The linear relations between math anxiety and math cognition have been frequently studied. However, the relations between anxiety and performance on complex cognitive tasks have been repeatedly demonstrated to follow a curvilinear fashion. In the current studies, we aimed to address the lack of attention given to the possibility of such complex interplay between emotion and cognition in the math-learning literature by exploring the relations among math anxiety, math motivation, and math cognition. In two samples-young adolescent twins and adult college students-results showed inverted-U relations between math anxiety and math performance in participants with high intrinsic math motivation and modest negative associations between math anxiety and math performance in participants with low intrinsic math motivation. However, this pattern was not observed in tasks assessing participants' nonsymbolic and symbolic number-estimation ability. These findings may help advance the understanding of mathematics-learning processes and provide important insights for treatment programs that target improving mathematics-learning experiences and mathematical skills. © The Author(s) 2015.

Principals in Partnership with Math Coaches

ERIC Educational Resources Information Center

Grant, Catherine Miles; Davenport, Linda Ruiz

2009-01-01

One of the most promising developments in math education is the fact that many districts are hiring math coaches--also called math resource teachers, math facilitators, math lead teachers, or math specialists--to assist elementary-level teachers with math instruction. What must not be lost, however, is that principals play an essential role in…

When math hurts: math anxiety predicts pain network activation in anticipation of doing math.

PubMed

Lyons, Ian M; Beilock, Sian L

2012-01-01

Math can be difficult, and for those with high levels of mathematics-anxiety (HMAs), math is associated with tension, apprehension, and fear. But what underlies the feelings of dread effected by math anxiety? Are HMAs' feelings about math merely psychological epiphenomena, or is their anxiety grounded in simulation of a concrete, visceral sensation - such as pain - about which they have every right to feel anxious? We show that, when anticipating an upcoming math-task, the higher one's math anxiety, the more one increases activity in regions associated with visceral threat detection, and often the experience of pain itself (bilateral dorso-posterior insula). Interestingly, this relation was not seen during math performance, suggesting that it is not that math itself hurts; rather, the anticipation of math is painful. Our data suggest that pain network activation underlies the intuition that simply anticipating a dreaded event can feel painful. These results may also provide a potential neural mechanism to explain why HMAs tend to avoid math and math-related situations, which in turn can bias HMAs away from taking math classes or even entire math-related career paths.

Is Mathematical Anxiety Always Bad for Math Learning: The Role of Math Motivation

PubMed Central

Wang, Zhe; Lukowski, Sarah L.; Hart, Sara Ann; Lyons, Ian M.; Thompson, Lee A.; Kovas, Yulia; Mazzocco, Michèle M.; Plomin, Robert; Petrill, Stephen A.

2015-01-01

The linear relations between math anxiety and math cognition have been frequently studied. However, the relations between anxiety and performance on complex cognitive tasks have been repeatedly demonstrated to follow a curvilinear fashion. Given the lack of attention to the possibility of such complex interplay between emotion and cognition in the math learning literature, the current study aimed to address this gap via exploring the relations between math anxiety, math motivation, and math cognition. The current study consisted of two samples. One sample included 262 pairs of young adolescent twins and the other included 237 adult college students. Participants self-reported their math anxiety and math motivation. Math cognition was assessed using a comprehensive battery of mathematics tasks. In both samples, results showed inverted-U relations between math anxiety and math performance in students with high intrinsic math motivation, and modest negative associations between math anxiety and math performance in students with low intrinsic math motivation. However, this pattern was not observed in tasks assessing student’s nonsymbolic and symbolic number estimation. These findings may help advance our understanding of mathematics learning processes and may provide important insights for treatment programs that target improving mathematics learning experiences and mathematical skills. PMID:26518438

When approximate number acuity predicts math performance: The moderating role of math anxiety

PubMed Central

Libertus, Melissa E.

2018-01-01

Separate lines of research suggest that people who are better at estimating numerical quantities using the approximate number system (ANS) have better math performance, and that people with high levels of math anxiety have worse math performance. Only a handful of studies have examined both ANS acuity and math anxiety in the same participants and those studies report contradictory results. To address these inconsistencies, in the current study 87 undergraduate students completed assessments of ANS acuity, math anxiety, and three different measures of math. We considered moderation models to examine the interplay of ANS acuity and math anxiety on different aspects of math performance. Math anxiety and ANS acuity were both unique significant predictors of the ability to automatically recall basic number facts. ANS acuity was also a unique significant predictor of the ability to solve applied math problems, and this relation was further qualified by a significant interaction with math anxiety: the positive association between ANS acuity and applied problem solving was only present in students with high math anxiety. Our findings suggest that ANS acuity and math anxiety are differentially related to various aspects of math and should be considered together when examining their respective influences on math ability. Our findings also raise the possibility that good ANS acuity serves as a protective factor for highly math-anxious students on certain types of math assessments. PMID:29718939

Math anxiety and math performance in children: The mediating roles of working memory and math self-concept.

PubMed

Justicia-Galiano, M José; Martín-Puga, M Eva; Linares, Rocío; Pelegrina, Santiago

2017-12-01

Numerous studies, most of them involving adolescents and adults, have evidenced a moderate negative relationship between math anxiety and math performance. There are, however, a limited number of studies that have addressed the mechanisms underlying this relation. This study aimed to investigate the role of two possible mediational mechanisms between math anxiety and math performance. Specifically, we sought to test the simultaneous mediating role of working memory and math self-concept. A total of 167 children aged 8-12 years participated in this study. Children completed a set of questionnaires used to assess math and trait anxiety, math self-concept as well as measures of math fluency and math problem-solving. Teachers were asked to rate each student's math achievement. As measures of working memory, two backward span tasks were administered to the children. A series of multiple mediation analyses were conducted. Results indicated that both mediators (working memory and math self-concept) contributed to explaining the relationship between math anxiety and math achievement. Results suggest that working memory and self-concept could be worth considering when designing interventions aimed at helping students with math anxiety. Longitudinal designs could also be used to better understand the mediational mechanisms that may explain the relationship between math anxiety and math performance. © 2017 The British Psychological Society.

When approximate number acuity predicts math performance: The moderating role of math anxiety.

PubMed

Braham, Emily J; Libertus, Melissa E

2018-01-01

Separate lines of research suggest that people who are better at estimating numerical quantities using the approximate number system (ANS) have better math performance, and that people with high levels of math anxiety have worse math performance. Only a handful of studies have examined both ANS acuity and math anxiety in the same participants and those studies report contradictory results. To address these inconsistencies, in the current study 87 undergraduate students completed assessments of ANS acuity, math anxiety, and three different measures of math. We considered moderation models to examine the interplay of ANS acuity and math anxiety on different aspects of math performance. Math anxiety and ANS acuity were both unique significant predictors of the ability to automatically recall basic number facts. ANS acuity was also a unique significant predictor of the ability to solve applied math problems, and this relation was further qualified by a significant interaction with math anxiety: the positive association between ANS acuity and applied problem solving was only present in students with high math anxiety. Our findings suggest that ANS acuity and math anxiety are differentially related to various aspects of math and should be considered together when examining their respective influences on math ability. Our findings also raise the possibility that good ANS acuity serves as a protective factor for highly math-anxious students on certain types of math assessments.

Development and validation of the Current Opioid Misuse Measure.

PubMed

Butler, Stephen F; Budman, Simon H; Fernandez, Kathrine C; Houle, Brian; Benoit, Christine; Katz, Nathaniel; Jamison, Robert N

2007-07-01

Clinicians recognize the importance of monitoring aberrant medication-related behaviors of chronic pain patients while being prescribed opioid therapy. The purpose of this study was to develop and validate the Current Opioid Misuse Measure (COMM) for those pain patients already on long-term opioid therapy. An initial pool of 177 items was developed with input from 26 pain management and addiction specialists. Concept mapping identified six primary concepts underlying medication misuse, which were used to develop an initial item pool. Twenty-two pain and addiction specialists rated the items on importance and relevance, resulting in selection of a 40-item alpha COMM. Final item selection was based on empirical evaluation of items with patients taking opioids for chronic, noncancer pain (N=227). One-week test-retest reliability was examined with 55 participants. All participants were administered the alpha version of the COMM, the Prescription Drug Use Questionnaire (PDUQ) interview, and submitted a urine sample for toxicology screening. Physician ratings of patient aberrant behaviors were also obtained. Of the 40 items, 17 items appeared to adequately measure aberrant behavior, demonstrating excellent internal consistency and test-retest reliability. Cutoff scores were examined using ROC curve analysis and reasonable sensitivity and specificity were established. To evaluate the COMM's ability to capture change in patient status, it was tested on a subset of patients (N=86) that were followed and reassessed three months later. The COMM was found to have promise as a brief, self-report measure of current aberrant drug-related behavior. Further cross-validation and replication of these preliminary results is pending.

Measurement of math beliefs and their associations with math behaviors in college students.

PubMed

Hendy, Helen M; Schorschinsky, Nancy; Wade, Barbara

2014-12-01

Our purpose in the present study was to expand understanding of math beliefs in college students by developing 3 new psychometrically tested scales as guided by expectancy-value theory, self-efficacy theory, and health belief model. Additionally, we identified which math beliefs (and which theory) best explained variance in math behaviors and performance by college students and which students were most likely to have problematic math beliefs. Study participants included 368 college math students who completed questionnaires to report math behaviors (attending class, doing homework, reading textbooks, asking for help) and used a 5-point rating scale to indicate a variety of math beliefs. For a subset of 84 students, math professors provided final math grades. Factor analyses produced a 10-item Math Value Scale with 2 subscales (Class Devaluation, No Future Value), a 7-item single-dimension Math Confidence Scale, and an 11-item Math Barriers Scale with 2 subscales (Math Anxiety, Discouraging Words). Hierarchical multiple regression revealed that high levels of the newly discovered class devaluation belief (guided by expectancy-value theory) were most consistently associated with poor math behaviors in college students, with high math anxiety (guided by health belief model) and low math confidence (guided by self-efficacy theory) also found to be significant. Analyses of covariance revealed that younger and male students were at increased risk for class devaluation and older students were at increased risk for poor math confidence. (c) 2014 APA, all rights reserved.

Weberized Mumford-Shah Model with Bose-Einstein Photon Noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen Jianhong, E-mail: jhshen@math.umn.edu; Jung, Yoon-Mo

Human vision works equally well in a large dynamic range of light intensities, from only a few photons to typical midday sunlight. Contributing to such remarkable flexibility is a famous law in perceptual (both visual and aural) psychology and psychophysics known as Weber's Law. The current paper develops a new segmentation model based on the integration of Weber's Law and the celebrated Mumford-Shah segmentation model (Comm. Pure Appl. Math., vol. 42, pp. 577-685, 1989). Explained in detail are issues concerning why the classical Mumford-Shah model lacks light adaptivity, and why its 'weberized' version can more faithfully reflect human vision's superiormore » segmentation capability in a variety of illuminance conditions from dawn to dusk. It is also argued that the popular Gaussian noise model is physically inappropriate for the weberization procedure. As a result, the intrinsic thermal noise of photon ensembles is introduced based on Bose and Einstein's distributions in quantum statistics, which turns out to be compatible with weberization both analytically and computationally. The current paper focuses on both the theory and computation of the weberized Mumford-Shah model with Bose-Einstein noise. In particular, Ambrosio-Tortorelli's {gamma}-convergence approximation theory is adapted (Boll. Un. Mat. Ital. B, vol. 6, pp. 105-123, 1992), and stable numerical algorithms are developed for the associated pair ofnonlinear Euler-Lagrange PDEs.« less

When Math Hurts: Math Anxiety Predicts Pain Network Activation in Anticipation of Doing Math

PubMed Central

Lyons, Ian M.; Beilock, Sian L.

2012-01-01

Math can be difficult, and for those with high levels of mathematics-anxiety (HMAs), math is associated with tension, apprehension, and fear. But what underlies the feelings of dread effected by math anxiety? Are HMAs’ feelings about math merely psychological epiphenomena, or is their anxiety grounded in simulation of a concrete, visceral sensation – such as pain – about which they have every right to feel anxious? We show that, when anticipating an upcoming math-task, the higher one’s math anxiety, the more one increases activity in regions associated with visceral threat detection, and often the experience of pain itself (bilateral dorso-posterior insula). Interestingly, this relation was not seen during math performance, suggesting that it is not that math itself hurts; rather, the anticipation of math is painful. Our data suggest that pain network activation underlies the intuition that simply anticipating a dreaded event can feel painful. These results may also provide a potential neural mechanism to explain why HMAs tend to avoid math and math-related situations, which in turn can bias HMAs away from taking math classes or even entire math-related career paths. PMID:23118929

A latent profile analysis of math achievement, numerosity, and math anxiety in twins

PubMed Central

Hart, Sara A.; Logan, Jessica A.R.; Thompson, Lee; Kovas, Yulia; McLoughlin, Gráinne; Petrill, Stephen A.

2015-01-01

Underperformance in math is a problem with increasing prevalence, complex etiology, and severe repercussions. This study examined the etiological heterogeneity of math performance in a sample of 264 pairs of 12-year-old twins assessed on measures of math achievement, numerosity and math anxiety. Latent profile analysis indicated five groupings of individuals representing different patterns of math achievement, numerosity and math anxiety, coupled with differing degrees of familial transmission. These results suggest that there may be distinct profiles of math achievement, numerosity and anxiety; particularly for students who struggle in math. PMID:26957650

A latent profile analysis of math achievement, numerosity, and math anxiety in twins.

PubMed

Hart, Sara A; Logan, Jessica A R; Thompson, Lee; Kovas, Yulia; McLoughlin, Gráinne; Petrill, Stephen A

2016-02-01

Underperformance in math is a problem with increasing prevalence, complex etiology, and severe repercussions. This study examined the etiological heterogeneity of math performance in a sample of 264 pairs of 12-year-old twins assessed on measures of math achievement, numerosity and math anxiety. Latent profile analysis indicated five groupings of individuals representing different patterns of math achievement, numerosity and math anxiety, coupled with differing degrees of familial transmission. These results suggest that there may be distinct profiles of math achievement, numerosity and anxiety; particularly for students who struggle in math.

The Effects of the Elevate Math Summer Program on Math Achievement and Algebra Readiness. REL 2015-096

ERIC Educational Resources Information Center

Snipes, Jason; Huang, Chun-Wei; Jaquet, Karina; Finkelstein, Neal

2015-01-01

The Effects of the Elevate Math summer program on math achievement and algebra readiness: This randomized trial examined the effects of the Elevate Math summer program on math achievement and algebra readiness, as well as math interest and self-efficacy, among rising 8th grade students in California's Silicon Valley. The Elevate Math summer math…

tweezercalib 2.0: Faster version of MatLab package for precise calibration of optical tweezers

NASA Astrophysics Data System (ADS)

Hansen, Poul Martin; Tolić-Nørrelykke, Iva Marija; Flyvbjerg, Henrik; Berg-Sørensen, Kirstine

2006-03-01

We present a vectorized version of the MatLab (MathWorks Inc.) package tweezercalib for calibration of optical tweezers with precision. The calibration is based on the power spectrum of the Brownian motion of a dielectric bead trapped in the tweezers. Precision is achieved by accounting for a number of factors that affect this power spectrum, as described in vs. 1 of the package [I.M. Tolić-Nørrelykke, K. Berg-Sørensen, H. Flyvbjerg, Matlab program for precision calibration of optical tweezers, Comput. Phys. Comm. 159 (2004) 225-240]. The graphical user interface allows the user to include or leave out each of these factors. Several "health tests" are applied to the experimental data during calibration, and test results are displayed graphically. Thus, the user can easily see whether the data comply with the theory used for their interpretation. Final calibration results are given with statistical errors and covariance matrix. New version program summaryTitle of program: tweezercalib Catalogue identifier: ADTV_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTV_v2_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Reference in CPC to previous version: I.M. Tolić-Nørrelykke, K. Berg-Sørensen, H. Flyvbjerg, Comput. Phys. Comm. 159 (2004) 225 Catalogue identifier of previous version: ADTV Does the new version supersede the original program: Yes Computer for which the program is designed and others on which it has been tested: General computer running MatLab (Mathworks Inc.) Operating systems under with the program has been tested: Windows2000, Windows-XP, Linux Programming language used: MatLab (Mathworks Inc.), standard license Memory required to execute with typical data: Of order four times the size of the data file High speed storage required: none No. of lines in distributed program, including test data, etc.: 135 989 No. of bytes in distributed program, including test data, etc.: 1 527 611 Distribution format: tar. gz Nature of physical problem: Calibrate optical tweezers with precision by fitting theory to experimental power spectrum of position of bead doing Brownian motion in incompressible fluid, possibly near microscope cover slip, while trapped in optical tweezers. Thereby determine spring constant of optical trap and conversion factor for arbitrary-units-to-nanometers for detection system. Method of solution: Elimination of cross-talk between quadrant photo-diode's output channels for positions (optional). Check that distribution of recorded positions agrees with Boltzmann distribution of bead in harmonic trap. Data compression and noise reduction by blocking method applied to power spectrum. Full accounting for hydrodynamic effects: Frequency-dependent drag force and interaction with nearby cover slip (optional). Full accounting for electronic filters (optional), for "virtual filtering" caused by detection system (optional). Full accounting for aliasing caused by finite sampling rate (optional). Standard non-linear least-squares fitting. Statistical support for fit is given, with several plots facilitating inspection of consistency and quality of data and fit. Summary of revisions: A faster fitting routine, adapted from [J. Nocedal, Y.x. Yuan, Combining trust region and line search techniques, Technical Report OTC 98/04, Optimization Technology Center, 1998; W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes. The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986], is applied. It uses fewer function evaluations, and the remaining function evaluations have been vectorized. Calls to routines in Toolboxes not included with a standard MatLab license have been replaced by calls to routines that are included in the present package. Fitting parameters are rescaled to ensure that they are all of roughly the same size (of order 1) while being fitted. Generally, the program package has been updated to comply with MatLab, vs. 7.0, and optimized for speed. Restrictions on the complexity of the problem: Data should be positions of bead doing Brownian motion while held by optical tweezers. For high precision in final results, data should be time series measured over a long time, with sufficiently high experimental sampling rate: The sampling rate should be well above the characteristic frequency of the trap, the so-called corner frequency. Thus, the sampling frequency should typically be larger than 10 kHz. The Fast Fourier Transform used works optimally when the time series contain 2 data points, and long measurement time is obtained with n>12-15. Finally, the optics should be set to ensure a harmonic trapping potential in the range of positions visited by the bead. The fitting procedure checks for harmonic potential. Typical running time: Seconds Unusual features of the program: None References: The theoretical underpinnings for the procedure are found in [K. Berg-Sørensen, H. Flyvbjerg, Power spectrum analysis for optical tweezers, Rev. Sci. Ins. 75 (2004) 594-612].

On the Aharonov-Bohm Operators with Varying Poles: The Boundary Behavior of Eigenvalues

NASA Astrophysics Data System (ADS)

Noris, Benedetta; Nys, Manon; Terracini, Susanna

2015-11-01

We consider a magnetic Schrödinger operator with magnetic field concentrated at one point (the pole) of a domain and half integer circulation, and we focus on the behavior of Dirichlet eigenvalues as functions of the pole. Although the magnetic field vanishes almost everywhere, it is well known that it affects the operator at the spectral level (the Aharonov-Bohm effect, Phys Rev (2) 115:485-491, 1959). Moreover, the numerical computations performed in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010) show a rather complex behavior of the eigenvalues as the pole varies in a planar domain. In this paper, in continuation of the analysis started in (Bonnaillie-Noël et al., Anal PDE 7(6):1365-1395, 2014; Noris and Terracini, Indiana Univ Math J 59(4):1361-1403, 2010), we analyze the relation between the variation of the eigenvalue and the nodal structure of the associated eigenfunctions. We deal with planar domains with Dirichlet boundary conditions and we focus on the case when the singular pole approaches the boundary of the domain: then, the operator loses its singular character and the k-th magnetic eigenvalue converges to that of the standard Laplacian. We can predict both the rate of convergence and whether the convergence happens from above or from below, in relation with the number of nodal lines of the k-th eigenfunction of the Laplacian. The proof relies on the variational characterization of eigenvalues, together with a detailed asymptotic analysis of the eigenfunctions, based on an Almgren-type frequency formula for magnetic eigenfunctions and on the blow-up technique.

Beyond the excised ensemble: modelling elliptic curve L-functions with random matrices

NASA Astrophysics Data System (ADS)

Cooper, I. A.; Morris, Patrick W.; Snaith, N. C.

2016-02-01

The ‘excised ensemble’, a random matrix model for the zeros of quadratic twist families of elliptic curve L-functions, was introduced by Dueñez et al (2012 J. Phys. A: Math. Theor. 45 115207) The excised model is motivated by a formula for central values of these L-functions in a paper by Kohnen and Zagier (1981 Invent. Math. 64 175-98). This formula indicates that for a finite set of L-functions from a family of quadratic twists, the central values are all either zero or are greater than some positive cutoff. The excised model imposes this same condition on the central values of characteristic polynomials of matrices from {SO}(2N). Strangely, the cutoff on the characteristic polynomials that results in a convincing model for the L-function zeros is significantly smaller than that which we would obtain by naively transferring Kohnen and Zagier’s cutoff to the {SO}(2N) ensemble. In this current paper we investigate a modification to the excised model. It lacks the simplicity of the original excised ensemble, but it serves to explain the reason for the unexpectedly low cutoff in the original excised model. Additionally, the distribution of central L-values is ‘choppier’ than the distribution of characteristic polynomials, in the sense that it is a superposition of a series of peaks: the characteristic polynomial distribution is a smooth approximation to this. The excised model did not attempt to incorporate these successive peaks, only the initial cutoff. Here we experiment with including some of the structure of the L-value distribution. The conclusion is that a critical feature of a good model is to associate the correct mass to the first peak of the L-value distribution.

Stability of Nonlinear Wave Patterns to the Bipolar Vlasov-Poisson-Boltzmann System

NASA Astrophysics Data System (ADS)

Li, Hailiang; Wang, Yi; Yang, Tong; Zhong, Mingying

2018-04-01

The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction waves for the bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in Liu and Yu (Commun Math Phys 246:133-179, 2004) and Liu et al. (Physica D 188:178-192, 2004), we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction waves are proved for the 1D bipolar VPB system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of the rarefaction wave fan to compressible Euler equations is proved for the 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in Li et al. (Indiana Univ Math J 65(2):665-725, 2016) sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

On the M-function and Borg-Marchenko theorems for vector-valued Sturm-Liouville equations

NASA Astrophysics Data System (ADS)

Andersson, E.

2003-12-01

We will consider a vector-valued Sturm-Liouville equation of the form R[U]≔-(PU')'+QU=λWU, x∈[0,b), with P-1, W, Q∈Lloc1([0,b))m×m being Hermitian and under some additional conditions on P-1 and W. We give an elementary deduction of the leading order term asymptotics for the Titchmarsh-Weyl M-function corresponding to this equation. In the special case of P=W=I, Q∈L1([0,∞))m×m and the Neumann boundary conditions at 0, we will also prove that M=(1/√-λ )(I+R)(I-R)-1, where R=limn→∞ Rn=∑n=1∞Qn, for recursively defined sequences {Rn} and {Qn}. If Q∈Lloc1([0,b))m×m, 0

Identifying Maths Anxiety in Student Nurses and Focusing Remedial Work

ERIC Educational Resources Information Center

Bull, Heather

2009-01-01

Maths anxiety interferes with maths cognition and thereby increases the risk of maths errors. To initiate strategies for preventing anxiety-related errors progressing into nursing practice, this study explored the hypothesis that student nurses experience high maths anxiety in association with poor maths performance, and that high maths anxiety is…

The Strategic Nature of the Tactical Satellite. Part 2

DTIC Science & Technology

2006-08-13

hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and...constellation orbiting at 100 NM. The curves represent data for three mission types: SIGINT (solid), comm/BFT (dashed), and imagery (dotted). Two panes...persistent constellation orbiting at 500 km. The curves represent data for three mission types: SIGINT (solid), comm/BFT (dashed), and imagery (dotted

Evaluation des Connaissances-Attitudes-Pratiques des populations des districts sanitaires de Benoye, Laoukassy, Moundou et N’Djaména Sud sur la rage canine au Tchad

PubMed Central

Mindekem, Rolande; Lechenne, Monique; Alfaroukh, Idriss Oumar; Moto, Daugla Doumagoum; Zinsstag, Jakob; Ouedraogo, Laurent Tinoaga; Salifou, Sahidou

2017-01-01

Introduction La rage canine demeure une préoccupation en Afrique comme au Tchad. La présente étude vise à évaluer les Connaissances-Attitudes-Pratiques des populations pour la prise en charge appropriée des personnes exposées et une lutte efficace. Méthodes C’était une étude transversale descriptive réalisée en juillet et septembre dans quatre districts sanitaires au Tchad en 2015. Les données ont été collectées à l’aide d’un questionnaire auprès des ménages recrutés suivant un sondage aléatoire à 3 degrés. Résultats C’était 2428 personnes enquêtées avec un niveau maximum primaire (54,12%). L’âge moyen était de 36 ± 13,50 ans. Ils étaient cultivateurs (35,17%), commerçants (18,04%), ménagères (12,81%). La rage était définie comme une maladie transmise du chien à l’homme (41,43%), une altération du cerveau (41,27%), une sous-alimentation (10,26%). Le chat était faiblement connu réservoir (13,84%) et vecteur (19,77%) ainsi que la griffure comme moyen de transmission (4,61%) et la vaccination du chat comme mesure préventive (0,49%). Les premiers soins en cas de morsure à domicile étaient les pratiques traditionnelles (47,69%), le lavage des plaies (19,48%) ou aucune action entreprise (20,43%). Les ménages consultaient la santé humaine (78,50%), la santé animale (5,35%) et les guérisseurs traditionnels (27%). Conclusion La communication en rapport avec des premiers soins à la maison en cas de morsure, la connaissance du chat comme réservoir et vecteur, celle de la griffure comme moyen de transmission et la promotion de la consultation des services vétérinaires en cas de morsure sont nécessaires. PMID:28761600

Math Anxiety in Second and Third Graders and Its Relation to Mathematics Achievement

PubMed Central

Wu, Sarah S.; Barth, Maria; Amin, Hitha; Malcarne, Vanessa; Menon, Vinod

2012-01-01

Although the detrimental effects of math anxiety in adults are well understood, few studies have examined how it affects younger children who are beginning to learn math in a formal academic setting. Here, we examine the relationship between math anxiety and math achievement in second and third graders. In response to the need for a grade-appropriate measure of assessing math anxiety in this group we first describe the development of Scale for Early Mathematics Anxiety (SEMA), a new measure for assessing math anxiety in second and third graders that is based on the Math Anxiety Rating Scale. We demonstrate the construct validity and reliability of the SEMA and use it to characterize the effect of math anxiety on standardized measures of math abilities, as assessed using the Mathematical Reasoning and Numerical Operations subtests of the Wechsler Individual Achievement Test (WIAT-II). Math achievement, as measured by the WIAT-II Math Composite score, was significantly and negatively correlated with SEMA but not with trait anxiety scores. Additional analyses showed that SEMA scores were strongly correlated with Mathematical Reasoning scores, which involves more complex verbal problem solving. SEMA scores were weakly correlated with Numerical Operations which assesses basic computation skills, suggesting that math anxiety has a pronounced effect on more demanding calculations. We also found that math anxiety has an equally detrimental impact on math achievement regardless of whether children have an anxiety related to numbers or to the situational and social experience of doing math. Critically, these effects were unrelated to trait anxiety, providing the first evidence that the specific effects of math anxiety can be detected in the earliest stages of formal math learning in school. Our findings provide new insights into the developmental origins of math anxiety, and further underscore the need to remediate math anxiety and its deleterious effects on math achievement in young children. PMID:22701105

Math anxiety in second and third graders and its relation to mathematics achievement.

PubMed

Wu, Sarah S; Barth, Maria; Amin, Hitha; Malcarne, Vanessa; Menon, Vinod

2012-01-01

Although the detrimental effects of math anxiety in adults are well understood, few studies have examined how it affects younger children who are beginning to learn math in a formal academic setting. Here, we examine the relationship between math anxiety and math achievement in second and third graders. In response to the need for a grade-appropriate measure of assessing math anxiety in this group we first describe the development of Scale for Early Mathematics Anxiety (SEMA), a new measure for assessing math anxiety in second and third graders that is based on the Math Anxiety Rating Scale. We demonstrate the construct validity and reliability of the SEMA and use it to characterize the effect of math anxiety on standardized measures of math abilities, as assessed using the Mathematical Reasoning and Numerical Operations subtests of the Wechsler Individual Achievement Test (WIAT-II). Math achievement, as measured by the WIAT-II Math Composite score, was significantly and negatively correlated with SEMA but not with trait anxiety scores. Additional analyses showed that SEMA scores were strongly correlated with Mathematical Reasoning scores, which involves more complex verbal problem solving. SEMA scores were weakly correlated with Numerical Operations which assesses basic computation skills, suggesting that math anxiety has a pronounced effect on more demanding calculations. We also found that math anxiety has an equally detrimental impact on math achievement regardless of whether children have an anxiety related to numbers or to the situational and social experience of doing math. Critically, these effects were unrelated to trait anxiety, providing the first evidence that the specific effects of math anxiety can be detected in the earliest stages of formal math learning in school. Our findings provide new insights into the developmental origins of math anxiety, and further underscore the need to remediate math anxiety and its deleterious effects on math achievement in young children.

Math anxiety differentially affects WAIS-IV arithmetic performance in undergraduates.

PubMed

Buelow, Melissa T; Frakey, Laura L

2013-06-01

Previous research has shown that math anxiety can influence the math performance level; however, to date, it is unknown whether math anxiety influences performance on working memory tasks during neuropsychological evaluation. In the present study, 172 undergraduate students completed measures of math achievement (the Math Computation subtest from the Wide Range Achievement Test-IV), math anxiety (the Math Anxiety Rating Scale-Revised), general test anxiety (from the Adult Manifest Anxiety Scale-College version), and the three Working Memory Index tasks from the Wechsler Adult Intelligence Scale-IV Edition (WAIS-IV; Digit Span [DS], Arithmetic, Letter-Number Sequencing [LNS]). Results indicated that math anxiety predicted performance on Arithmetic, but not DS or LNS, above and beyond the effects of gender, general test anxiety, and math performance level. Our findings suggest that math anxiety can negatively influence WAIS-IV working memory subtest scores. Implications for clinical practice include the utilization of LNS in individuals expressing high math anxiety.

Self-Regulation and Math Attitudes: Effects on Academic Performance in Developmental Math Courses at a Community College

ERIC Educational Resources Information Center

Otts, Cynthia D.

2010-01-01

The purpose of the study was to investigate the relationship among math attitudes, self-regulated learning, and course outcomes in developmental math. Math attitudes involved perceived usefulness of math and math anxiety. Self-regulated learning represented the ability of students to control cognitive, metacognitive, and behavioral aspects of…

College Math Assessment: SAT Scores vs. College Math Placement Scores

ERIC Educational Resources Information Center

Foley-Peres, Kathleen; Poirier, Dawn

2008-01-01

Many colleges and university's use SAT math scores or math placement tests to place students in the appropriate math course. This study compares the use of math placement scores and SAT scores for 188 freshman students. The student's grades and faculty observations were analyzed to determine if the SAT scores and/or college math assessment scores…

Mathematical learning instruction and teacher motivation factors affecting science technology engineering and math (STEM) major choices in 4-year colleges and universities: Multilevel structural equation modeling

NASA Astrophysics Data System (ADS)

Lee, Ahlam

2011-12-01

Using the Educational Longitudinal Study of 2002/06, this study examined the effects of the selected mathematical learning and teacher motivation factors on graduates' science, technology, engineering, and math (STEM) related major choices in 4-year colleges and universities, as mediated by math performance and math self-efficacy. Using multilevel structural equation modeling, I analyzed: (1) the association between mathematical learning instruction factors (i.e., computer, individual, and lecture-based learning activities in mathematics) and students' STEM major choices in 4-year colleges and universities as mediated by math performance and math self-efficacy and (2) the association between school factor, teacher motivation and students' STEM major choices in 4-year colleges and universities via mediators of math performance and math self-efficacy. The results revealed that among the selected learning experience factors, computer-based learning activities in math classrooms yielded the most positive effects on math self-efficacy, which significantly predicted the increase in the proportion of students' STEM major choice as mediated by math self-efficacy. Further, when controlling for base-year math Item Response Theory (IRT) scores, a positive relationship between individual-based learning activities in math classrooms and the first follow-up math IRT scores emerged, which related to the high proportion of students' STEM major choices. The results also indicated that individual and lecture-based learning activities in math yielded positive effects on math self-efficacy, which related to STEM major choice. Concerning between-school levels, teacher motivation yielded positive effects on the first follow up math IRT score, when controlling for base year IRT score. The results from this study inform educators, parents, and policy makers on how mathematics instruction can improve student math performance and encourage more students to prepare for STEM careers. Students should receive all possible opportunities to use computers to enhance their math self-efficacy, be encouraged to review math materials, and concentrate on listening to math teachers' lectures. While all selected math-learning activities should be embraced in math instruction, computer and individual-based learning activities, which reflect student-driven learning, should be emphasized in the high school instruction. Likewise, students should be encouraged to frequently engage in individual-based learning activities to improve their math performance.

Is math anxiety in the secondary classroom limiting physics mastery? A study of math anxiety and physics performance

NASA Astrophysics Data System (ADS)

Mercer, Gary J.

This quantitative study examined the relationship between secondary students with math anxiety and physics performance in an inquiry-based constructivist classroom. The Revised Math Anxiety Rating Scale was used to evaluate math anxiety levels. The results were then compared to the performance on a physics standardized final examination. A simple correlation was performed, followed by a multivariate regression analysis to examine effects based on gender and prior math background. The correlation showed statistical significance between math anxiety and physics performance. The regression analysis showed statistical significance for math anxiety, physics performance, and prior math background, but did not show statistical significance for math anxiety, physics performance, and gender.

Math practice and its influence on math skills and executive functions in adolescents with mild to borderline intellectual disability.

PubMed

Jansen, Brenda R J; De Lange, Eva; Van der Molen, Mariët J

2013-05-01

Adolescents with mild to borderline intellectual disability (MBID) often complete schooling without mastering basic math skills, even though basic math is essential for math-related challenges in everyday life. Limited attention to cognitive skills and low executive functioning (EF) may cause this delay. We aimed to improve math skills in an MBID-sample using computerized math training. Also, it was investigated whether EF and math performance were related and whether computerized math training had beneficial effects on EF. The sample consisted of a total of 58 adolescents (12-15 years) from special education. Participants were randomly assigned to either the experimental group or a treatment as usual (TAU) group. In the experimental condition, participants received 5 weeks of training. Math performance and EF were assessed before and after the training period. Math performance improved equally in both groups. However, frequently practicing participants improved more than participants in the control group. Visuo-spatial memory skills were positively related to addition and subtraction skills. Transfer effects from math training to EF were absent. It is concluded that math skills may increase if a reasonable effort in practicing math skills is made. The relation between visuo-spatial memory skills provides opportunities for improving math performance. Copyright © 2013 Elsevier Ltd. All rights reserved.

Math anxiety in Thai early adolescents: a cognitive-behavioral perspective.

PubMed

Wangsiriwech, Tawatchai; Pisitsungkagarn, Kullaya; Jarukasemthawee, Somboon

2017-08-29

With its high prevalence and debilitating impact on students, math anxiety is well studied within the educational context. However, the problem has yet to be examined from the psychological perspective, which is necessary in order to produce a more comprehensive perspective and to pave the way for therapeutic intervention. The current study, therefore, was conducted to identify cognitive and behavioral factors relevant to the occurrence and maintenance of math anxiety. Data were collected from 300 grade 9 students (150 females and 150 males) from public and private schools in Bangkok, Thailand. Participants responded to the measures of math anxiety, negative math beliefs, negative math appraisals and math avoidance. Structural equation modeling was conducted. Model fit indices obtained consistently suggested the good fitness of the model to the data [e.g. χ2/df = 0.42, root mean square error of approximation (RMSEA) = 0.00]. Negative math beliefs, negative math appraisals and math avoidance had a significant direct effect on math anxiety. Additionally, the indirect effect of negative math appraisal was observed between negative math beliefs and math anxiety. In summary, the proposed model accounted for 84.5% of the variance in the anxiety. The findings are discussed with particular focus on implications for therapeutic intervention for math anxiety.

Simulating economic effects of disruptions in the telecommunications infrastructure.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cox, Roger Gary; Barton, Dianne Catherine; Reinert, Rhonda K.

2004-01-01

CommAspen is a new agent-based model for simulating the interdependent effects of market decisions and disruptions in the telecommunications infrastructure on other critical infrastructures in the U.S. economy such as banking and finance, and electric power. CommAspen extends and modifies the capabilities of Aspen-EE, an agent-based model previously developed by Sandia National Laboratories to analyze the interdependencies between the electric power system and other critical infrastructures. CommAspen has been tested on a series of scenarios in which the communications network has been disrupted, due to congestion and outages. Analysis of the scenario results indicates that communications networks simulated by themore » model behave as their counterparts do in the real world. Results also show that the model could be used to analyze the economic impact of communications congestion and outages.« less

Rigidity of quantum steering and one-sided device-independent verifiable quantum computation

NASA Astrophysics Data System (ADS)

Gheorghiu, Alexandru; Wallden, Petros; Kashefi, Elham

2017-02-01

The relationship between correlations and entanglement has played a major role in understanding quantum theory since the work of Einstein et al (1935 Phys. Rev. 47 777-80). Tsirelson proved that Bell states, shared among two parties, when measured suitably, achieve the maximum non-local correlations allowed by quantum mechanics (Cirel’son 1980 Lett. Math. Phys. 4 93-100). Conversely, Reichardt et al showed that observing the maximal correlation value over a sequence of repeated measurements, implies that the underlying quantum state is close to a tensor product of maximally entangled states and, moreover, that it is measured according to an ideal strategy (Reichardt et al 2013 Nature 496 456-60). However, this strong rigidity result comes at a high price, requiring a large number of entangled pairs to be tested. In this paper, we present a significant improvement in terms of the overhead by instead considering quantum steering where the device of the one side is trusted. We first demonstrate a robust one-sided device-independent version of self-testing, which characterises the shared state and measurement operators of two parties up to a certain bound. We show that this bound is optimal up to constant factors and we generalise the results for the most general attacks. This leads us to a rigidity theorem for maximal steering correlations. As a key application we give a one-sided device-independent protocol for verifiable delegated quantum computation, and compare it to other existing protocols, to highlight the cost of trust assumptions. Finally, we show that under reasonable assumptions, the states shared in order to run a certain type of verification protocol must be unitarily equivalent to perfect Bell states.

Casimir effect due to a single boundary as a manifestation of the Weyl problem

NASA Astrophysics Data System (ADS)

Kolomeisky, Eugene B.; Straley, Joseph P.; Langsjoen, Luke S.; Zaidi, Hussain

2010-09-01

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases, the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary, we explore the relationship between such approaches, with the goal of better understanding of the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978 J. Phys. A: Math. Gen. 11 895) and Deutsch and Candelas (1979 Phys. Rev. D 20 3063) that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases, the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having a geometrical origin, and an 'intrinsic' term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff and a non-geometrical intrinsic term. As by-products, we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.

Squirmers with swirl: a model for Volvox swimming.

PubMed

Pedley, T J; Brumley, D R; Goldstein, R E

2016-07-10

Colonies of the green alga Volvox are spheres that swim through the beating of pairs of flagella on their surface somatic cells. The somatic cells themselves are mounted rigidly in a polymeric extracellular matrix, fixing the orientation of the flagella so that they beat approximately in a meridional plane, with axis of symmetry in the swimming direction, but with a roughly [Formula: see text] azimuthal offset which results in the eponymous rotation of the colonies about a body-fixed axis. Experiments on colonies of Volvox carteri held stationary on a micropipette show that the beating pattern takes the form of a symplectic metachronal wave (Brumley  et al.   Phys. Rev. Lett. , vol. 109, 2012, 268102). Here we extend the Lighthill/Blake axisymmetric, Stokes-flow model of a free-swimming spherical squirmer (Lighthill  Commun. Pure Appl. Maths , vol. 5, 1952, pp. 109-118; Blake  J. Fluid Mech. , vol. 46, 1971 b , pp. 199-208) to include azimuthal swirl. The measured kinematics of the metachronal wave for 60 different colonies are used to calculate the coefficients in the eigenfunction expansions and hence predict the mean swimming speeds and rotation rates, proportional to the square of the beating amplitude, as functions of colony radius. As a test of the squirmer model, the results are compared with measurements (Drescher  et al.   Phys. Rev. Lett. , vol. 102, 2009, 168101) of the mean swimming speeds and angular velocities of a different set of 220 colonies, also given as functions of colony radius. The predicted variation with radius is qualitatively correct, but the model underestimates both the mean swimming speed and the mean angular velocity unless the amplitude of the flagellar beat is taken to be larger than previously thought. The reasons for this discrepancy are discussed.

Does Math Self-Efficacy Mediate the Effect of the Perceived Classroom Environment on Standardized Math Test Performance?

ERIC Educational Resources Information Center

Fast, Lisa A.; Lewis, James L.; Bryant, Michael J.; Bocian, Kathleen A.; Cardullo, Richard A.; Rettig, Michael; Hammond, Kimberly A.

2010-01-01

We examined the effect of the perceived classroom environment on math self-efficacy and the effect of math self-efficacy on standardized math test performance. Upper elementary school students (N = 1,163) provided self-reports of their perceived math self-efficacy and the degree to which their math classroom environment was mastery oriented,…

The role of expressive writing in math anxiety.

PubMed

Park, Daeun; Ramirez, Gerardo; Beilock, Sian L

2014-06-01

Math anxiety is a negative affective reaction to situations involving math. Previous work demonstrates that math anxiety can negatively impact math problem solving by creating performance-related worries that disrupt the working memory needed for the task at hand. By leveraging knowledge about the mechanism underlying the math anxiety-performance relationship, we tested the effectiveness of a short expressive writing intervention that has been shown to reduce intrusive thoughts and improve working memory availability. Students (N = 80) varying in math anxiety were asked to sit quietly (control group) prior to completing difficulty-matched math and word problems or to write about their thoughts and feelings regarding the exam they were about to take (expressive writing group). For the control group, high math-anxious individuals (HMAs) performed significantly worse on the math problems than low math-anxious students (LMAs). In the expressive writing group, however, this difference in math performance across HMAs and LMAs was significantly reduced. Among HMAs, the use of words related to anxiety, cause, and insight in their writing was positively related to math performance. Expressive writing boosts the performance of anxious students in math-testing situations. PsycINFO Database Record (c) 2014 APA, all rights reserved.

Understanding the Home Math Environment and Its Role in Predicting Parent Report of Children's Math Skills.

PubMed

Hart, Sara A; Ganley, Colleen M; Purpura, David J

2016-01-01

There is a growing literature concerning the role of the home math environment in children's math development. In this study, we examined the relation between these constructs by specifically addressing three goals. The first goal was to identify the measurement structure of the home math environment through a series of confirmatory factor analyses. The second goal was to examine the role of the home math environment in predicting parent report of children's math skills. The third goal was to test a series of potential alternative explanations for the relation between the home math environment and parent report of children's skills, specifically the direct and indirect role of household income, parent math anxiety, and parent math ability as measured by their approximate number system performance. A final sample of 339 parents of children aged 3 through 8 drawn from Mechanical Turk answered a questionnaire online. The best fitting model of the home math environment was a bifactor model with a general factor representing the general home math environment, and three specific factors representing the direct numeracy environment, the indirect numeracy environment, and the spatial environment. When examining the association of the home math environment factors to parent report of child skills, the general home math environment factor and the spatial environment were the only significant predictors. Parents who reported doing more general math activities in the home reported having children with higher math skills, whereas parents who reported doing more spatial activities reported having children with lower math skills.

Math anxiety and its relationship with basic arithmetic skills among primary school children.

PubMed

Sorvo, Riikka; Koponen, Tuire; Viholainen, Helena; Aro, Tuija; Räikkönen, Eija; Peura, Pilvi; Dowker, Ann; Aro, Mikko

2017-09-01

Children have been found to report and demonstrate math anxiety as early as the first grade. However, previous results concerning the relationship between math anxiety and performance are contradictory, with some studies establishing a correlation between them while others do not. These contradictory results might be related to varying operationalizations of math anxiety. In this study, we aimed to examine the prevalence of math anxiety and its relationship with basic arithmetic skills in primary school children, with explicit focus on two aspects of math anxiety: anxiety about failure in mathematics and anxiety in math-related situations. The participants comprised 1,327 children at grades 2-5. Math anxiety was assessed using six items, and basic arithmetic skills were assessed using three assessment tasks. Around one-third of the participants reported anxiety about being unable to do math, one-fifth about having to answer teachers' questions, and one tenth about having to do math. Confirmatory factor analysis indicated that anxiety about math-related situations and anxiety about failure in mathematics are separable aspects of math anxiety. Structural equation modelling suggested that anxiety about math-related situations was more strongly associated with arithmetic fluency than anxiety about failure. Anxiety about math-related situations was most common among second graders and least common among fifth graders. As math anxiety, particularly about math-related situations, was related to arithmetic fluency even as early as the second grade, children's negative feelings and math anxiety should be identified and addressed from the early primary school years. © 2017 The British Psychological Society.

Understanding the Home Math Environment and Its Role in Predicting Parent Report of Children’s Math Skills

PubMed Central

Ganley, Colleen M.; Purpura, David J.

2016-01-01

There is a growing literature concerning the role of the home math environment in children’s math development. In this study, we examined the relation between these constructs by specifically addressing three goals. The first goal was to identify the measurement structure of the home math environment through a series of confirmatory factor analyses. The second goal was to examine the role of the home math environment in predicting parent report of children’s math skills. The third goal was to test a series of potential alternative explanations for the relation between the home math environment and parent report of children’s skills, specifically the direct and indirect role of household income, parent math anxiety, and parent math ability as measured by their approximate number system performance. A final sample of 339 parents of children aged 3 through 8 drawn from Mechanical Turk answered a questionnaire online. The best fitting model of the home math environment was a bifactor model with a general factor representing the general home math environment, and three specific factors representing the direct numeracy environment, the indirect numeracy environment, and the spatial environment. When examining the association of the home math environment factors to parent report of child skills, the general home math environment factor and the spatial environment were the only significant predictors. Parents who reported doing more general math activities in the home reported having children with higher math skills, whereas parents who reported doing more spatial activities reported having children with lower math skills. PMID:28005925

Enjoying mathematics or feeling competent in mathematics? Reciprocal effects on mathematics achievement and perceived math effort expenditure.

PubMed

Pinxten, Maarten; Marsh, Herbert W; De Fraine, Bieke; Van Den Noortgate, Wim; Van Damme, Jan

2014-03-01

The multidimensionality of the academic self-concept in terms of domain specificity has been well established in previous studies, whereas its multidimensionality in terms of motivational functions (the so-called affect-competence separation) needs further examination. This study aims at exploring differential effects of enjoyment and competence beliefs on two external validity criteria in the field of mathematics. Data analysed in this study were part of a large-scale longitudinal research project. Following a five-wave design, math enjoyment, math competence beliefs, math achievement, and perceived math effort expenditure measures were repeatedly collected from a cohort of 4,724 pupils in Grades 3-7. Confirmatory factor analysis (CFA) was used to test the internal factor structure of the math self-concept. Additionally, a series of nested models was tested using structural equation modelling to examine longitudinal reciprocal interrelations between math competence beliefs and math enjoyment on the one hand and math achievement and perceived math effort expenditure on the other. Our results showed that CFA models with separate factors for math enjoyment and math competence beliefs fit the data substantially better than models without it. Furthermore, differential relationships between both constructs and the two educational outcomes were observed. Math competence beliefs had positive effects on math achievement and negative effects on perceived math effort expenditure. Math enjoyment had (mild) positive effects on subsequent perceived effort expenditure and math competence beliefs. This study provides further support for the affect-competence separation. Theoretical issues regarding adequate conceptualization and practical consequences for practitioners are discussed. © 2013 The British Psychological Society.

Neural correlates of math anxiety - an overview and implications.

PubMed

Artemenko, Christina; Daroczy, Gabriella; Nuerk, Hans-Christoph

2015-01-01

Math anxiety is a common phenomenon which can have a negative impact on numerical and arithmetic performance. However, so far little is known about the underlying neurocognitive mechanisms. This mini review provides an overview of studies investigating the neural correlates of math anxiety which provide several hints regarding its influence on math performance: while behavioral studies mostly observe an influence of math anxiety on difficult math tasks, neurophysiological studies show that processing efficiency is already affected in basic number processing. Overall, the neurocognitive literature suggests that (i) math anxiety elicits emotion- and pain-related activation during and before math activities, (ii) that the negative emotional response to math anxiety impairs processing efficiency, and (iii) that math deficits triggered by math anxiety may be compensated for by modulating the cognitive control or emotional regulation network. However, activation differs strongly between studies, depending on tasks, paradigms, and samples. We conclude that neural correlates can help to understand and explore the processes underlying math anxiety, but the data are not very consistent yet.

Neural correlates of math anxiety – an overview and implications

PubMed Central

Artemenko, Christina; Daroczy, Gabriella; Nuerk, Hans-Christoph

2015-01-01

Math anxiety is a common phenomenon which can have a negative impact on numerical and arithmetic performance. However, so far little is known about the underlying neurocognitive mechanisms. This mini review provides an overview of studies investigating the neural correlates of math anxiety which provide several hints regarding its influence on math performance: while behavioral studies mostly observe an influence of math anxiety on difficult math tasks, neurophysiological studies show that processing efficiency is already affected in basic number processing. Overall, the neurocognitive literature suggests that (i) math anxiety elicits emotion- and pain-related activation during and before math activities, (ii) that the negative emotional response to math anxiety impairs processing efficiency, and (iii) that math deficits triggered by math anxiety may be compensated for by modulating the cognitive control or emotional regulation network. However, activation differs strongly between studies, depending on tasks, paradigms, and samples. We conclude that neural correlates can help to understand and explore the processes underlying math anxiety, but the data are not very consistent yet. PMID:26388824

A Review of Communications Satellites and Related Spacecraft for Factors Influencing Mission Success. Volume 2

DTIC Science & Technology

1975-11-17

and control (subsystem) COMM., comm AEC Atomic Energy Commission comsat AFB Air Force Base COMSTAR ACE A-hr aerospace ground equipment ampere...array TDA Satellite Assembly Building TDAL Space and Missile Systems Organization (U.S. Air Force) TDM THIR satellite communications system TI...Satellite Control Facility (U.S. Air Force) TIROS selective chopper radiometer TLM, T/M surface composition mapping radiometer TOS TRUST

Nonlinear Optics Technology. Volume 2. Phase Conjugated Optical Communication Link. Phase 3

DTIC Science & Technology

1991-01-12

who performed the mission analysis, Mr. Larry A. Dozal whose laboratory assistance was vital to both the comm link experiments and mechanical design of...further the understanding of FWM PC comm link physics and to determine design requirements for a fieldable system. The system model demonstrated that...neterodyne receiver using photorefractive iaterial was also designed , fabricated, and characterized. The efficiency o heterodyne mixing of an aberrated

The Sum of All Fears: The Effects of Math Anxiety on Math Achievement in Fifth Grade Students and the Implications for School Counselors

ERIC Educational Resources Information Center

Ruff, Sarah E.; Boes, Susan R.

2014-01-01

Low math achievement is a recurring weakness in many students. Math anxiety is a persistent and significant theme to math avoidance and low achievement. Causes for math anxiety include social, cognitive, and academic factors. Interventions to reduce math anxiety are limited as they exclude the expert skills of professional school counselors to…

A Study of Perceptions of Math Mindset, Math Anxiety, and View of Math by Young Adults

ERIC Educational Resources Information Center

Hocker, Tami

2017-01-01

This study's purpose was to determine whether instruction in growth math mindset led to change in perceptions of 18-22-year-old at-risk students in math mindset, math anxiety, and view of math. The experimental curriculum was created by the researcher with the guidance of experts in mathematics and education and focused on the impact of brain…

Errors in Multi-Digit Arithmetic and Behavioral Inattention in Children With Math Difficulties

PubMed Central

Raghubar, Kimberly; Cirino, Paul; Barnes, Marcia; Ewing-Cobbs, Linda; Fletcher, Jack; Fuchs, Lynn

2009-01-01

Errors in written multi-digit computation were investigated in children with math difficulties. Third-and fourth-grade children (n = 291) with coexisting math and reading difficulties, math difficulties, reading difficulties, or no learning difficulties were compared. A second analysis compared those with severe math learning difficulties, low average achievement in math, and no learning difficulties. Math fact errors were related to the severity of the math difficulties, not to reading status. Contrary to predictions, children with poorer reading, regardless of math achievement, committed more visually based errors. Operation switch errors were not systematically related to group membership. Teacher ratings of behavioral inattention were related to accuracy, math fact errors, and procedural bugs. The findings are discussed with respect to hypotheses about the cognitive origins of arithmetic errors and in relation to current discussions about how to conceptualize math disabilities. PMID:19380494