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.

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.

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.

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.

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.

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.

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.

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

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.

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).

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.

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.

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.

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.

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)].

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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

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.

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

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.

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.

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).

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

Dietary Regulation of PTEN Signaling and Mammary Tumor Initiating Cells: Implications for Breast Cancer Prevention

DTIC Science & Technology

2012-07-01

1999 Paradoxical decrease of an adipose-specific protein, adiponectin, in obesity. Biochem Bio- phys Res Commun 257:79–83 10. Barb D, Pazaitou...Y, Pecquery R 2006 Adiponectin mediates antiproliferative and ap- optotic responses in human MCF7 breast cancer cells. Biochem Bio- phys Res Commun ...Noorden S, Wahlstrom T, Coombes RC, Warner M, Gustafsson JA 2002 Estrogen receptor in breast cancer. Endocr Relat Cancer 9:1–13 29. Esslimani-Sahla M

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.

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.

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.

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.

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.

Dietary Regulation of PTEN Signaling and Mammary Tumor Initiating Cells: Implications for Breast Cancer Prevention

DTIC Science & Technology

2012-01-01

adiponectin, in obesity. Biochem Bio- phys Res Commun 257:79–83 10. Barb D, Pazaitou-Panayiotou K, Mantzoros CS 2006 Adiponectin: a link between obesity and...optotic responses in human MCF7 breast cancer cells. Biochem Bio- phys Res Commun 345:271–279 17. Liu J, Lam JB, Chow KH, Xu A, Lam KS, Moon RT...220 28. Palmieri C, Cheng GJ, Saji S, Zelada-Hedman M, Wärri A, Weihua Z, Van Noorden S, Wahlstrom T, Coombes RC, Warner M, Gustafsson JA 2002

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).

ERRATUM: Papers published in incorrect sections

NASA Astrophysics Data System (ADS)

2004-04-01

A number of J. Phys. A: Math. Gen. articles have mistakenly been placed in the wrong subject section in recent issues of the journal. We would like to apologize to the authors of these articles for publishing their papers in the Fluid and Plasma Theory section. The correct section for each article is given below. Statistical Physics Issue 4: Microcanonical entropy for small magnetizations Behringer H 2004 J. Phys. A: Math. Gen. 37 1443 Mathematical Physics Issue 9: On the solution of fractional evolution equations Kilbas A A, Pierantozzi T, Trujillo J J and Vázquez L 2004 J. Phys. A: Math. Gen. 37 3271 Quantum Mechanics and Quantum Information Theory Issue 6: New exactly solvable isospectral partners for PT-symmetric potentials Sinha A and Roy P 2004 J. Phys. A: Math. Gen. 37 2509 Issue 9: Symplectically entangled states and their applications to coding Vourdas A 2004 J. Phys. A: Math. Gen. 37 3305 Classical and Quantum Field Theory Issue 6: Pairing of parafermions of order 2: seniority model Nelson C A 2004 J. Phys. A: Math. Gen. 37 2497 Issue 7: Jordan-Schwinger map, 3D harmonic oscillator constants of motion, and classical and quantum parameters characterizing electromagnetic wave polarization Mota R D, Xicoténcatl M A and Granados V D 2004 J. Phys. A: Math. Gen. 37 2835 Issue 9: Could only fermions be elementary? Lev F M 2004 J. Phys. A: Math. Gen. 37 3285

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.

Impurity and Defect Characterization in Epitaxial GaAs, InP and the Ternary and Quaternary Compound Semiconductors.

DTIC Science & Technology

1982-11-02

Wolfe, Phys. Rev. Lett. 27, 988 (1971). 5. H.R. Fetterman , D.M. Larsen, G.E. Stillman, P.E. Tannenwald, and J. Waldman, Phys.Rev. Lett. 26. 975(1971). 6...Kirkman, P.E. Simmonds, and R.A. Stradling, J. Phys. C., Solid State Phys. 8, 530 (1975). 18. H.R. Fetterman , J. Waldman and C.M. Wolfe, Solid State Commun

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.

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.

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.

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.

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

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.

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.

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.

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

Electronic Promoters and Semiconductor Oxidation: Alkali Metals on Si(111) Surfaces.

DTIC Science & Technology

1986-04-25

SPAS, Caiimissariate a’ l’Energie Atctmique, CEN Saclay, France. 1. T. Narusawa, S. Komiya, and A. Hiraki , Appi. Phys. Lett. 20, 272 (1972). 2. J...Raisanen, and N. Troullier, Phys. Rev. B (in press). 10. K. Okuno, T. Ito, M. Iwami, and A. Hiraki , Sol. State Commun. 34, 493 (1980) and references

Inner-shell photoionization of atomic chlorine near the 2p-1 edge: a Breit-Pauli R-matrix calculation

NASA Astrophysics Data System (ADS)

Felfli, Z.; Deb, N. C.; Manson, S. T.; Hibbert, A.; Msezane, A. Z.

2009-05-01

An R-matrix calculation which takes into account relativistic effects via the Breit-Pauli (BP) operator is performed for photoionization cross sections of atomic Cl near the 2p threshold. The wavefunctions are constructed with orbitals generated from a careful large scale configuration interaction (CI) calculation with relativistic corrections using the CIV3 code of Hibbert [1] and Glass and Hibbert [2]. The results are contrasted with the calculation of Martins [3], which uses a CI with relativistic corrections, and compared with the most recent measurements [4]. [1] A. Hibbert, Comput. Phys. Commun. 9, 141 (1975) [2] R. Glass and A. Hibbert, Comput. Phys. Commun. 16, 19 (1978) [3] M. Martins, J. Phys. B 34, 1321 (2001) [4] D. Lindle et al (private communication) Research supported by U.S. DOE, Division of Chemical Sciences, NSF and CAU CFNM, NSF-CREST Program. Computing facilities at Queen's University of Belfast, UK and of DOE Office of Science, NERSC are appreciated.

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).

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.

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)].

Creating Extended and Dense Plasma Channels in Air by Using Spatially and Temporally Shaped Ultra-Intense Laser Pulses

DTIC Science & Technology

2011-08-16

Wolf, Phys. Rev. Lett. 104, 103903 (2010). 6. M. Aközbek, M. Scalora , C. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001). 7. A. Couairon, Phys...Aközbek, M. Scalora , C. Bowden, and S. L. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in

Influence of the parallel nonlinearity on zonal flows and heat transport in global gyrokinetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Jolliet, S.; McMillan, B. F.; Vernay, T.; Villard, L.; Hatzky, R.; Bottino, A.; Angelino, P.

2009-07-01

In this paper, the influence of the parallel nonlinearity on zonal flows and heat transport in global particle-in-cell ion-temperature-gradient simulations is studied. Although this term is in theory orders of magnitude smaller than the others, several authors [L. Villard, P. Angelino, A. Bottino et al., Plasma Phys. Contr. Fusion 46, B51 (2004); L. Villard, S. J. Allfrey, A. Bottino et al., Nucl. Fusion 44, 172 (2004); J. C. Kniep, J. N. G. Leboeuf, and V. C. Decyck, Comput. Phys. Commun. 164, 98 (2004); J. Candy, R. E. Waltz, S. E. Parker et al., Phys. Plasmas 13, 074501 (2006)] found different results on its role. The study is performed using the global gyrokinetic particle-in-cell codes TORB (theta-pinch) [R. Hatzky, T. M. Tran, A. Könies et al., Phys. Plasmas 9, 898 (2002)] and ORB5 (tokamak geometry) [S. Jolliet, A. Bottino, P. Angelino et al., Comput. Phys. Commun. 177, 409 (2007)]. In particular, it is demonstrated that the parallel nonlinearity, while important for energy conservation, affects the zonal electric field only if the simulation is noise dominated. When a proper convergence is reached, the influence of parallel nonlinearity on the zonal electric field, if any, is shown to be small for both the cases of decaying and driven turbulence.

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

Parallel filtering in global gyrokinetic simulations

NASA Astrophysics Data System (ADS)

Jolliet, S.; McMillan, B. F.; Villard, L.; Vernay, T.; Angelino, P.; Tran, T. M.; Brunner, S.; Bottino, A.; Idomura, Y.

2012-02-01

In this work, a Fourier solver [B.F. McMillan, S. Jolliet, A. Bottino, P. Angelino, T.M. Tran, L. Villard, Comp. Phys. Commun. 181 (2010) 715] is implemented in the global Eulerian gyrokinetic code GT5D [Y. Idomura, H. Urano, N. Aiba, S. Tokuda, Nucl. Fusion 49 (2009) 065029] and in the global Particle-In-Cell code ORB5 [S. Jolliet, A. Bottino, P. Angelino, R. Hatzky, T.M. Tran, B.F. McMillan, O. Sauter, K. Appert, Y. Idomura, L. Villard, Comp. Phys. Commun. 177 (2007) 409] in order to reduce the memory of the matrix associated with the field equation. This scheme is verified with linear and nonlinear simulations of turbulence. It is demonstrated that the straight-field-line angle is the coordinate that optimizes the Fourier solver, that both linear and nonlinear turbulent states are unaffected by the parallel filtering, and that the k∥ spectrum is independent of plasma size at fixed normalized poloidal wave number.

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

NASA Astrophysics Data System (ADS)

Wang, Y.; Xiao, J.

2017-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2} . An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

A Liouville Problem for the Stationary Fractional Navier-Stokes-Poisson System

NASA Astrophysics Data System (ADS)

Wang, Y.; Xiao, J.

2018-06-01

This paper deals with a Liouville problem for the stationary fractional Navier-Stokes-Poisson system whose special case k=0 covers the compressible and incompressible time-independent fractional Navier-Stokes systems in R^{N≥2}. An essential difficulty raises from the fractional Laplacian, which is a non-local operator and thus makes the local analysis unsuitable. To overcome the difficulty, we utilize a recently-introduced extension-method in Wang and Xiao (Commun Contemp Math 18(6):1650019, 2016) which develops Caffarelli-Silvestre's technique in Caffarelli and Silvestre (Commun Partial Diff Equ 32:1245-1260, 2007).

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.

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.

Fractional quiver W-algebras

NASA Astrophysics Data System (ADS)

Kimura, Taro; Pestun, Vasily

2018-04-01

We introduce quiver gauge theory associated with the non-simply laced type fractional quiver and define fractional quiver W-algebras by using construction of Kimura and Pestun (Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1072-1; Lett Math Phys, 2018. https://doi.org/10.1007/s11005-018-1073-0) with representation of fractional quivers.

A Note on ;New Hierarchies of Integrable Lattice Equations and Associated Properties: Darboux Transformation Conservation Laws and Integrable Coupling; [Rep. Math. Phys. 67 (2011), 259

NASA Astrophysics Data System (ADS)

Xu, Xi-Xiang

2016-12-01

We prove that two new hierarchies of integrable lattice equations in [Rep. Math. Phys.67 (2011), 259] can be respectively changed into the famous relativistic Toda lattice hierarchies in the polynomial and the rational forms by means of a simple transformation.

On Non-Linear Sensitivity of Marine Biological Models to Parameter Variations

DTIC Science & Technology

2007-01-01

M.B., 2002. Understanding uncertain enviromental systems. In: Grasman, J., van Straten, G. (Eds.), Predictability and Nonlinear Modelling in Natural...model evaluations to compute sensitivity indices. Comput. Phys. Commun. 145, 280–297. Saltelli, A., Andres, T.H., Homma, T., 1993. Some new techniques

Dust Cloud Combustion for Defeat of Airborne Bio-WMD

DTIC Science & Technology

2017-12-01

Explosibility of metal powders,” DTIC Document, Report, (1964). [7] J. H. Burgoyne and L. Cohen, Proc. R. Soc. London. Ser. A. Math . Phys. Sci., 225...London. A. Math . Phys. Sci., 385, (1983), 21–51. [13] J. Sun, R. Dobashi, and T. Hirano, J. Loss Prev. Process Ind., 14, (2001), 463–467. [14] J.-H. Sun...J. Sung, Combust. Flame, 124, (2001), 35– 49. [27] B. Matkowsky and G. Sivashinsky, SIAM J. Appl. Math ., 35, (1978), 465–478. [28] G. Jomaas, J. K

Chaotic attractors and physical measures for some density dependent Leslie population models

NASA Astrophysics Data System (ADS)

Ugarcovici, Ilie; Weiss, Howard

2007-12-01

Following ecologists' discoveries, mathematicians have begun studying extensions of the ubiquitous age structured Leslie population model that allow some survival probabilities and/or fertility rates to depend on population densities. These nonlinear extensions commonly exhibit very complicated dynamics: through computer studies, some authors have discovered robust Hénon-like strange attractors in several families. Population biologists and demographers frequently wish to average a function over many generations and conclude that the average is independent of the initial population distribution. This type of 'ergodicity' seems to be a fundamental tenet in population biology. In this paper we develop the first rigorous ergodic theoretic framework for density dependent Leslie population models. We study two generation models with Ricker and Hassell (recruitment type) fertility terms. We prove that for some parameter regions these models admit a chaotic (ergodic) attractor which supports a unique physical probability measure. This physical measure, having full Lebesgue measure basin, satisfies in the strongest possible sense the population biologist's requirement for ergodicity in their population models. We use the celebrated work of Wang and Young 2001 Commun. Math. Phys. 218 1-97, and our results are the first applications of their method to biology, ecology or demography.

On the Electrostatic Born-Infeld Equation with Extended Charges

NASA Astrophysics Data System (ADS)

Bonheure, Denis; d'Avenia, Pietro; Pomponio, Alessio

2016-09-01

In this paper, we deal with the electrostatic Born-Infeld equation -operatorname{div} (nablaφ/√{1-|nabla φ|^2} )= ρ quad{in} {R}^N, lim_{|x|to ∞} φ(x)= 0,. quad quad quad quad ({{BI}}) where {ρ} is an assigned extended charge density. We are interested in the existence and uniqueness of the potential {φ} and finiteness of the energy of the electrostatic field {-nabla φ}. We first relax the problem and treat it with the direct method of the Calculus of Variations for a broad class of charge densities. Assuming {ρ} is radially distributed, we recover the weak formulation of {({{BI}})} and the regularity of the solution of the Poisson equation (under the same smoothness assumptions). In the case of a locally bounded charge, we also recover the weak formulation without assuming any symmetry. The solution is even classical if {ρ} is smooth. Then we analyze the case where the density {ρ} is a superposition of point charges and discuss the results in (Kiessling, Commun Math Phys 314:509-523, 2012). Other models are discussed, as for instance a system arising from the coupling of the nonlinear Klein-Gordon equation with the Born-Infeld theory.

Comment on "Classification of Lie point symmetries for quadratic Liénard type equation x ̈ + f ( x ) x ˙ 2 + g ( x ) = 0 " [J. Math. Phys. 54, 053506 (2013)] and its erratum [J. Math. Phys. 55, 059901 (2014)

NASA Astrophysics Data System (ADS)

Paliathanasis, A.; Leach, P. G. L.

2016-02-01

We demonstrate a simplification of some recent works on the classification of the Lie symmetries for a quadratic equation of Liénard type. We observe that the problem could have been resolved more simply.

Comment on “Maxwell's equations and electromagnetic Lagrangian density in fractional form” [J. Math. Phys. 53, 033505 (2012)

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

Rabei, Eqab M.; Al-Jamel, A.; Widyan, H.

In a recent paper, Jaradat et al. [J. Math. Phys. 53, 033505 (2012)] have presented the fractional form of the electromagnetic Lagrangian density within the Riemann-Liouville fractional derivative. They claimed that the Agrawal procedure [O. P. Agrawal, J. Math. Anal. Appl. 272, 368 (2002)] is used to obtain Maxwell's equations in the fractional form, and the Hamilton's equations of motion together with the conserved quantities obtained from fractional Noether's theorem are reported. In this comment, we draw the attention that there are some serious steps of the procedure used in their work are not applicable even though their final resultsmore » are correct. Their work should have been done based on a formulation as reported by Baleanu and Muslih [Phys. Scr. 72, 119 (2005)].« less

Multi-Party Quantum Private Comparison Protocol Based on Entanglement Swapping of Bell Entangled States

NASA Astrophysics Data System (ADS)

Ye, Tian-Yu

2016-09-01

Recently, Liu et al. proposed a two-party quantum private comparison (QPC) protocol using entanglement swapping of Bell entangled state (Commun. Theor. Phys. 57 (2012) 583). Subsequently Liu et al. pointed out that in Liu et al.'s protocol, the TP can extract the two users' secret inputs without being detected by launching the Bell-basis measurement attack, and suggested the corresponding improvement to mend this loophole (Commun. Theor. Phys. 62 (2014) 210). In this paper, we first point out the information leakage problem toward TP existing in both of the above two protocols, and then suggest the corresponding improvement by using the one-way hash function to encrypt the two users' secret inputs. We further put forward the three-party QPC protocol also based on entanglement swapping of Bell entangled state, and then validate its output correctness and its security in detail. Finally, we generalize the three-party QPC protocol into the multi-party case, which can accomplish arbitrary pair's comparison of equality among K users within one execution. Supported by the National Natural Science Foundation of China under Grant No. 61402407

GRILLIX: a 3D turbulence code based on the flux-coordinate independent approach

NASA Astrophysics Data System (ADS)

Stegmeir, Andreas; Coster, David; Ross, Alexander; Maj, Omar; Lackner, Karl; Poli, Emanuele

2018-03-01

The GRILLIX code is presented with which plasma turbulence/transport in various geometries can be simulated in 3D. The distinguishing feature of the code is that it is based on the flux-coordinate independent approach (FCI) (Hariri and Ottaviani 2013 Comput. Phys. Commun. 184 2419; Stegmeir et al 2016 Comput. Phys. Commun. 198 139). Cylindrical or Cartesian grids are used on which perpendicular operators are discretised via standard finite difference methods and parallel operators via a field line tracing and interpolation procedure (field line map). This offers a very high flexibility with respect to geometry, especially a separatrix with X-point(s) or a magnetic axis can be treated easily in contrast to approaches which are based on field aligned coordinates and suffer from coordinate singularities. Aiming finally for simulation of edge and scrape-off layer (SOL) turbulence, an isothermal electrostatic drift-reduced Braginskii model (Zeiler et al 1997 Phys. Plasmas 4 2134) has been implemented in GRILLIX. We present the numerical approach, which is based on a toroidally staggered formulation of the FCI, we show verification of the code with the method of manufactured solutions and show a benchmark based on a TORPEX blob experiment, previously performed by several edge/SOL codes (Riva et al 2016 Plasma Phys. Control. Fusion 58 044005). Examples for slab, circular, limiter and diverted geometry are presented. Finally, the results show that the FCI approach in general and GRILLIX in particular are viable approaches in order to tackle simulation of edge/SOL turbulence in diverted geometry.

Convergence of Mayer and Virial expansions and the Penrose tree-graph identity

NASA Astrophysics Data System (ADS)

Procacci, Aldo; Yuhjtman, Sergio A.

2017-01-01

We establish new lower bounds for the convergence radius of the Mayer series and the Virial series of a continuous particle system interacting via a stable and tempered pair potential. Our bounds considerably improve those given by Penrose (J Math Phys 4:1312, 1963) and Ruelle (Ann Phys 5:109-120, 1963) for the Mayer series and by Lebowitz and Penrose (J Math Phys 7:841-847, 1964) for the Virial series. To get our results, we exploit the tree-graph identity given by Penrose (Statistical mechanics: foundations and applications. Benjamin, New York, 1967) using a new partition scheme based on minimum spanning trees.

Boundary Layers for the Navier-Stokes Equations Linearized Around a Stationary Euler Flow

NASA Astrophysics Data System (ADS)

Gie, Gung-Min; Kelliher, James P.; Mazzucato, Anna L.

2018-03-01

We study the viscous boundary layer that forms at small viscosity near a rigid wall for the solution to the Navier-Stokes equations linearized around a smooth and stationary Euler flow (LNSE for short) in a smooth bounded domain Ω \\subset R^3 under no-slip boundary conditions. LNSE is supplemented with smooth initial data and smooth external forcing, assumed ill-prepared, that is, not compatible with the no-slip boundary condition. We construct an approximate solution to LNSE on the time interval [0, T], 0

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).

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

Single top quark photoproduction at the LHC

NASA Astrophysics Data System (ADS)

de Favereau de Jeneret, J.; Ovyn, S.

2008-08-01

High-energy photon-proton interactions at the LHC offer interesting possibilities for the study of the electroweak sector up to TeV scale and searches for processes beyond the Standard Model. An analysis of the W associated single top photoproduction has been performed using the adapted MadGraph/MadEvent [F. Maltoni and T. Stelzer, JHEP 0302, (2003) 027; T. Stelzer and W.F. Long, Phys. Commun. 81, (1994) 357-371] and CalcHEP [A. Pukhov, Nucl. Inst. Meth A 502, (2003) 596-598] programs interfaced to the Pythia [T. Sjöstrand et al., Comput. Phys. Commun. 135, (2001) 238] generator and a fast detector simulation program. Event selection and suppression of main backgrounds have been studied. A comparable sensitivity to |V| to those obtained using the standard single top production in pp collisions has been achieved already for 10 fb of integrated luminosity. Photoproduction at the LHC provides also an attractive framework for observation of the anomalous production of single top due to Flavour-Changing Neutral Currents. The sensitivity to anomalous coupling parameters, k and k is presented and indicates that stronger limits can be placed on anomalous couplings after 1 fb.

On relativistic spin network vertices

NASA Astrophysics Data System (ADS)

Reisenberger, Michael P.

1999-04-01

Barrett and Crane have proposed a model of simplicial Euclidean quantum gravity in which a central role is played by a class of Spin(4) spin networks called "relativistic spin networks" which satisfy a series of physically motivated constraints. Here a proof is presented that demonstrates that the intertwiner of a vertex of such a spin network is uniquely determined, up to normalization, by the representations on the incident edges and the constraints. Moreover, the constraints, which were formulated for four valent spin networks only, are extended to networks of arbitrary valence, and the generalized relativistic spin networks proposed by Yetter are shown to form the entire solution set (mod normalization) of the extended constraints. Finally, using the extended constraints, the Barrett-Crane model is generalized to arbitrary polyhedral complexes (instead of just simplicial complexes) representing space-time. It is explained how this model, like the Barret-Crane model can be derived from BF theory, a simple topological field theory [G. Horowitz, Commun. Math. Phys. 125, 417 (1989)], by restricting the sum over histories to ones in which the left-handed and right-handed areas of any 2-surface are equal. It is known that the solutions of classical Euclidean general relativity form a branch of the stationary points of the BF action with respect to variations preserving this condition.

Regularity criterion for solutions of the three-dimensional Cahn-Hilliard-Navier-Stokes equations and associated computations.

PubMed

Gibbon, John D; Pal, Nairita; Gupta, Anupam; Pandit, Rahul

2016-12-01

We consider the three-dimensional (3D) Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter ϕ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the 3D incompressible Euler equations [J. T. Beale, T. Kato, and A. J. Majda, Commun. Math. Phys. 94, 61 (1984)CMPHAY0010-361610.1007/BF01212349]. By taking an L^{∞} norm of the energy of the full binary system, designated as E_{∞}, we have shown that ∫_{0}^{t}E_{∞}(τ)dτ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs) of the 3D CHNS equations for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with 128^{3} to 512^{3} collocation points and over the duration of our DNSs confirm that E_{∞} remains bounded as far as our computations allow.

Global Well-Posedness and Decay Rates of Strong Solutions to a Non-Conservative Compressible Two-Fluid Model

NASA Astrophysics Data System (ADS)

Evje, Steinar; Wang, Wenjun; Wen, Huanyao

2016-09-01

In this paper, we consider a compressible two-fluid model with constant viscosity coefficients and unequal pressure functions {P^+neq P^-}. As mentioned in the seminal work by Bresch, Desjardins, et al. (Arch Rational Mech Anal 196:599-629, 2010) for the compressible two-fluid model, where {P^+=P^-} (common pressure) is used and capillarity effects are accounted for in terms of a third-order derivative of density, the case of constant viscosity coefficients cannot be handled in their settings. Besides, their analysis relies on a special choice for the density-dependent viscosity [refer also to another reference (Commun Math Phys 309:737-755, 2012) by Bresch, Huang and Li for a study of the same model in one dimension but without capillarity effects]. In this work, we obtain the global solution and its optimal decay rate (in time) with constant viscosity coefficients and some smallness assumptions. In particular, capillary pressure is taken into account in the sense that {Δ P=P^+ - P^-=fneq 0} where the difference function {f} is assumed to be a strictly decreasing function near the equilibrium relative to the fluid corresponding to {P^-}. This assumption plays an key role in the analysis and appears to have an essential stabilization effect on the model in question.

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.

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

A general Kastler-Kalau-Walze type theorem for manifolds with boundary

NASA Astrophysics Data System (ADS)

Wang, Jian; Wang, Yong

2016-11-01

In this paper, we establish a general Kastler-Kalau-Walze type theorem for any dimensional manifolds with boundary which generalizes the results in [Y. Wang, Lower-dimensional volumes and Kastler-Kalau-Walze type theorem for manifolds with boundary, Commun. Theor. Phys. 54 (2010) 38-42]. This solves a problem of the referee of [J. Wang and Y. Wang, A Kastler-Kalau-Walze type theorem for five-dimensional manifolds with boundary, Int. J. Geom. Meth. Mod. Phys. 12(5) (2015), Article ID: 1550064, 34 pp.], which is a general expression of the lower dimensional volumes in terms of the geometric data on the manifold.

Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq Equations

NASA Astrophysics Data System (ADS)

Brenier, Yann

2009-10-01

We establish a connection between optimal transport theory (see Villani in Topics in optimal transportation. Graduate studies in mathematics, vol. 58, AMS, Providence, 2003, for instance) and classical convection theory for geophysical flows (Pedlosky, in Geophysical fluid dynamics, Springer, New York, 1979). Our starting point is the model designed few years ago by Angenent, Haker, and Tannenbaum (SIAM J. Math. Anal. 35:61-97, 2003) to solve some optimal transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized hydrostatic-Boussinesq equations) to various models involving optimal transport (and the related Monge-Ampère equation, Brenier in Commun. Pure Appl. Math. 64:375-417, 1991; Caffarelli in Commun. Pure Appl. Math. 45:1141-1151, 1992). This includes the 2D semi-geostrophic equations (Hoskins in Annual review of fluid mechanics, vol. 14, pp. 131-151, Palo Alto, 1982; Cullen et al. in SIAM J. Appl. Math. 51:20-31, 1991, Arch. Ration. Mech. Anal. 185:341-363, 2007; Benamou and Brenier in SIAM J. Appl. Math. 58:1450-1461, 1998; Loeper in SIAM J. Math. Anal. 38:795-823, 2006) and some fully nonlinear versions of the so-called high-field limit of the Vlasov-Poisson system (Nieto et al. in Arch. Ration. Mech. Anal. 158:29-59, 2001) and of the Keller-Segel for Chemotaxis (Keller and Segel in J. Theor. Biol. 30:225-234, 1971; Jäger and Luckhaus in Trans. Am. Math. Soc. 329:819-824, 1992; Chalub et al. in Mon. Math. 142:123-141, 2004). Mathematically speaking, we establish some existence theorems for local smooth, global smooth or global weak solutions of the different models. We also justify that the inertia terms can be rigorously neglected under appropriate scaling assumptions in the generalized Navier-Stokes-Boussinesq equations. Finally, we show how a “stringy” generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology (see Arnold and Khesin in Topological methods in hydrodynamics. Applied mathematical sciences, vol. 125, Springer, Berlin, 1998; Moffatt in J. Fluid Mech. 159:359-378, 1985, Topological aspects of the dynamics of fluids and plasmas. NATO adv. sci. inst. ser. E, appl. sci., vol. 218, Kluwer, Dordrecht, 1992; Schonbek in Theory of the Navier-Stokes equations, Ser. adv. math. appl. sci., vol. 47, pp. 179-184, World Sci., Singapore, 1998; Vladimirov et al. in J. Fluid Mech. 390:127-150, 1999; Nishiyama in Bull. Inst. Math. Acad. Sin. (N.S.) 2:139-154, 2007).

Global Well-Posedness of the Incompressible Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Cai, Yuan; Lei, Zhen

2018-06-01

This paper studies the Cauchy problem of the incompressible magnetohydro dynamic systems with or without viscosity ν. Under the assumption that the initial velocity field and the displacement of the initialmagnetic field froma non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all ν ≧ 0 and all spaces with dimension n ≧ 2. Such a result holds true uniformly in nonnegative viscosity parameters. The proof is based on the inherent strong null structure of the systems introduced by Lei (Commun Pure Appl Math 69(11):2072-2106, 2016) and the ghost weight technique introduced by Alinhac (Invent Math 145(3):597-618, 2001).

On the zero-Rossby limit for the primitive equations of the atmosphere*

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang; Zhang, Ping

2001-09-01

The zero-Rossby limit for the primitive equations governing atmospheric motions is analysed. The limit is important in geophysics for large-scale models (cf Lions 1996 Int. Conf. IAM 95 (Hamburg 1995) (Math. Res. vol 87) (Berlin: Akademie) pp 177-212) and is in the level of the zero relaxation limit for nonlinear partial differential equations (cf Chen et al 1994 Commun. Pure Appl. Math. 47 787-830). It is proved that, if the initial data appropriately approximate data of geostrophic type, the corresponding solutions of the simplified primitive equations approximate the solutions of the quasigeostrophic equations with order ɛ accuracy as the Rossby number ɛ goes to zero.

Boron Nitride Substrates for High Mobility Chemical Vapor Deposited Graphene

DTIC Science & Technology

2011-06-13

Hone, H. L. Stormer , and P. Kim, Phys. Rev. Lett. 101, 096802 2008. 5K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and...H. L. Stormer , Solid State Commun. 146, 351 2008. 6S. Berciaud, S. Ryu, L. E. Brus, and T. F. Heinz, Nano Lett. 9, 346 2009. 7S. Bae, H. Kim, Y

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.

PIES applications to NCSX

NASA Astrophysics Data System (ADS)

Monticello, D. A.; Pomphrey, N.; Reiman, A. H.

1999-11-01

The PIES ( Reiman, A. H., Greenside, H. S., Compt. Phys. Commun. 43), (1986) code will be used to evaluate the flux surface quality of NCSX. In addition, we have generalized the Cary-Hanson technique for minimizing vacuum islands to the case where finite pressure and current exist in the plasma. We will use this technique to develop trim coils and other methods for repairing broken flux surfaces if they are found in NCSX.

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.

Effects of finite poloidal gyroradius, shaping, and collisions on the zonal flow residuala)

NASA Astrophysics Data System (ADS)

Xiao, Yong; Catto, Peter J.; Dorland, William

2007-05-01

Zonal flow helps reduce and regulate the turbulent transport level in tokamaks. Rosenbluth and Hinton have shown that zonal flow damps to a nonvanishing residual level in collisionless [M. Rosenbluth and F. Hinton, Phys. Rev. Lett. 80, 724 (1998)] and collisional [F. Hinton and M. Rosenbluth, Plasma Phys. Control. Fusion 41, A653 (1999)] banana regime plasmas. Recent zonal flow advances are summarized including the evaluation of the effects on the zonal flow residual by plasma cross-section shaping, shorter wavelengths including those less than an electron gyroradius, and arbitrary ion collisionality relative to the zonal low frequency. In addition to giving a brief summary of these new developments, the analytic results are compared with GS2 numerical simulations [M. Kotschenreuther, G. Rewoldt, and W. Tang, Comput. Phys. Commun. 88, 128 (1991)] to demonstrate their value as benchmarks for turbulence codes.

Parton distribution functions with QED corrections in the valon model

NASA Astrophysics Data System (ADS)

Mottaghizadeh, Marzieh; Taghavi Shahri, Fatemeh; Eslami, Parvin

2017-10-01

The parton distribution functions (PDFs) with QED corrections are obtained by solving the QCD ⊗QED DGLAP evolution equations in the framework of the "valon" model at the next-to-leading-order QCD and the leading-order QED approximations. Our results for the PDFs with QED corrections in this phenomenological model are in good agreement with the newly related CT14QED global fits code [Phys. Rev. D 93, 114015 (2016), 10.1103/PhysRevD.93.114015] and APFEL (NNPDF2.3QED) program [Comput. Phys. Commun. 185, 1647 (2014), 10.1016/j.cpc.2014.03.007] in a wide range of x =[10-5,1 ] and Q2=[0.283 ,108] GeV2 . The model calculations agree rather well with those codes. In the latter, we proposed a new method for studying the symmetry breaking of the sea quark distribution functions inside the proton.

PIES free boundary stellarator equilibria with improved initial conditions

NASA Astrophysics Data System (ADS)

Drevlak, M.; Monticello, D.; Reiman, A.

2005-07-01

The MFBE procedure developed by Strumberger (1997 Nucl. Fusion 37 19) is used to provide an improved starting point for free boundary equilibrium computations in the case of W7-X (Nührenberg and Zille 1986 Phys. Lett. A 114 129) using the Princeton iterative equilibrium solver (PIES) code (Reiman and Greenside 1986 Comput. Phys. Commun. 43 157). Transferring the consistent field found by the variational moments equilibrium code (VMEC) (Hirshmann and Whitson 1983 Phys. Fluids 26 3553) to an extended coordinate system using the VMORPH code, a safe margin between plasma boundary and PIES domain is established. The new EXTENDER_P code implements a generalization of the virtual casing principle, which allows field extension both for VMEC and PIES equilibria. This facilitates analysis of the 5/5 islands of the W7-X standard case without including them in the original PIES computation.

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.

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’.

Fine Resolution Imaging of Space Objects.

DTIC Science & Technology

1982-02-01

Figur einschliesst," J. reine agnew. Math. 123, 241 (1901). 5. J. Christou, "Imaging of Star Clusters from Speckle Inter- ferometry," Opt. Commun...Also, at any point x, by definition g.+,(x) is the near- est value to gMx ) that satisfies the object-domain constraints. Therefore, at all...the point gk(x) rather than from g^(x) since presumably gMx ) is closer to the solution than gk(x). After using Eq. (40), one would employ Eq. (35

Separated Component-Based Restoration of Speckled SAR Images

DTIC Science & Technology

2013-01-01

unsupervised change detection from SAR amplitude imagery,” IEEE Trans. Geosci. Remote Sens., vol. 44, no. 10, pp. 2972–2982, Oct. 2006. [5] F. Argenti , T...Sens., vol. 40, no. 10, pp. 2196–2212, Oct. 2002. [13] F. Argenti and L. Alparone, “Speckle removal from SAR images in the undecimated wavelet domain...iterative thresh- olding algorithm for linear inverse problems with a sparsity con- straint,” Commun . Pure Appl. Math., vol. 57, no. 11, pp. 1413

Designing for Compressive Sensing: Compressive Art, Camouflage, Fonts, and Quick Response Codes

DTIC Science & Technology

2018-01-01

an example where the signal is non-sparse in the standard basis, but sparse in the discrete cosine basis . The top plot shows the signal from the...previous example, now used as sparse discrete cosine transform (DCT) coefficients . The next plot shows the non-sparse signal in the standard...Romberg JK, Tao T. Stable signal recovery from incomplete and inaccurate measurements. Commun Pure Appl Math . 2006;59(8):1207–1223. 3. Donoho DL

Characteristic operator functions for quantum input-plant-output models and coherent control

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

Gough, John E.

We introduce the characteristic operator as the generalization of the usual concept of a transfer function of linear input-plant-output systems to arbitrary quantum nonlinear Markovian input-output models. This is intended as a tool in the characterization of quantum feedback control systems that fits in with the general theory of networks. The definition exploits the linearity of noise differentials in both the plant Heisenberg equations of motion and the differential form of the input-output relations. Mathematically, the characteristic operator is a matrix of dimension equal to the number of outputs times the number of inputs (which must coincide), but with entriesmore » that are operators of the plant system. In this sense, the characteristic operator retains details of the effective plant dynamical structure and is an essentially quantum object. We illustrate the relevance to model reduction and simplification definition by showing that the convergence of the characteristic operator in adiabatic elimination limit models requires the same conditions and assumptions appearing in the work on limit quantum stochastic differential theorems of Bouten and Silberfarb [Commun. Math. Phys. 283, 491-505 (2008)]. This approach also shows in a natural way that the limit coefficients of the quantum stochastic differential equations in adiabatic elimination problems arise algebraically as Schur complements and amounts to a model reduction where the fast degrees of freedom are decoupled from the slow ones and eliminated.« less

Logarithmic violation of scaling in strongly anisotropic turbulent transfer of a passive vector field

NASA Astrophysics Data System (ADS)

Antonov, N. V.; Gulitskiy, N. M.

2015-01-01

Inertial-range asymptotic behavior of a vector (e.g., magnetic) field, passively advected by a strongly anisotropic turbulent flow, is studied by means of the field-theoretic renormalization group and the operator product expansion. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝δ (t -t') /k⊥d -1 +ξ , where k⊥=|k⊥| and k⊥ is the component of the wave vector, perpendicular to the distinguished direction ("direction of the flow")—the d -dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131, 381 (1990), 10.1007/BF02161420]. The stochastic advection-diffusion equation for the transverse (divergence-free) vector field includes, as special cases, the kinematic dynamo model for magnetohydrodynamic turbulence and the linearized Navier-Stokes equation. In contrast to the well-known isotropic Kraichnan's model, where various correlation functions exhibit anomalous scaling behavior with infinite sets of anomalous exponents, here the dependence on the integral turbulence scale L has a logarithmic behavior: Instead of powerlike corrections to ordinary scaling, determined by naive (canonical) dimensions, the anomalies manifest themselves as polynomials of logarithms of L . The key point is that the matrices of scaling dimensions of the relevant families of composite operators appear nilpotent and cannot be diagonalized. The detailed proof of this fact is given for the correlation functions of arbitrary order.

Non-Markovian quantum feedback networks II: Controlled flows

NASA Astrophysics Data System (ADS)

Gough, John E.

2017-06-01

The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering. In this paper, we build on the ideas presented by Bouten and van Handel [Quantum Stochastics and Information: Statistics, Filtering and Control (World Scientific, 2008)] and develop a general theory of quantum feedback. We elucidate the relationship between the controlling processes, Z, and the measured processes, Y, and to this end we make a distinction between what we call the input picture and the output picture. We should note that the input-output relations for the noise fields have additional terms not present in the standard theory but that the relationship between the control processes and measured processes themselves is internally consistent—we do this for the two main cases of quadrature measurement and photon-counting measurement. The theory is general enough to include a modulating filter which post-processes the measurement readout Y before returning to the system. This opens up the prospect of applying very general engineering feedback control techniques to open quantum systems in a systematic manner, and we consider a number of specific modulating filter problems. Finally, we give a brief argument as to why most of the rules for making instantaneous feedback connections [J. Gough and M. R. James, Commun. Math. Phys. 287, 1109 (2009)] ought to apply for controlled dynamical networks as well.

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.

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.

Singular Instantons and Painlevé VI

NASA Astrophysics Data System (ADS)

Muñiz Manasliski, Richard

2016-06-01

We consider a two parameter family of instantons, which is studied in [Sadun L., Comm. Math. Phys. 163 (1994), 257-291], invariant under the irreducible action of SU_2 on S^4, but which are not globally defined. We will see that these instantons produce solutions to a one parameter family of Painlevé VI equations (P_VI}) and we will give an explicit expression of the map between instantons and solutions to P_{VI}. The solutions are algebraic only for that values of the parameters which correspond to the instantons that can be extended to all of S^4. This work is a generalization of [Muñiz Manasliski R., Contemp. Math., Vol. 434, Amer. Math. Soc., Providence, RI, 2007, 215-222] and [Muñiz Manasliski R., J. Geom. Phys. 59 (2009), 1036-1047, arXiv:1602.07221], where instantons without singularities are studied.

One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative p^{-2} U(1) Gauge Model

NASA Astrophysics Data System (ADS)

Blaschke, Daniel N.; Rofner, Arnold; Sedmik, René I. P.

2010-05-01

This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θ-deformed non-commutative p-2 model originally introduced by Gurau et al. [Comm. Math. Phys. 287 (2009), 275-290]. It is shown that breaking terms of the form used by Vilar et al. [J. Phys. A: Math. Theor. 43 (2010), 135401, 13 pages] and ourselves [Eur. Phys. J. C: Part. Fields 62 (2009), 433-443] to localize the BRST covariant operator (D2θ2D2)-1 lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.

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

Research in Electronics - JSEP.

DTIC Science & Technology

1981-03-01

17. H . Helvajian and C. Wittig, "Collisional Quenching of HgBr(B 2 4i/2), Opt. Commun. 30, 189 (1979). 18. H . Reisler and C. Wittig, "Electronic...Luminescence Resulting from IR Multiple Photon Excitation, " in ’Photoselective Chemistry, Part I,’ J. Jortner ed., Wiley, 1981. 19. H . Helvajian , M...to Intramolecular V E coupling in IR Laser Excited Polyatomics, " J. Chem. Phys., in press. 22. H . Helvajian and C. Wittig, "Vibrational Quenching 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.

A Proof of Friedman's Ergosphere Instability for Scalar Waves

NASA Astrophysics Data System (ADS)

Moschidis, Georgios

2018-03-01

Let {(M^{3+1},g)} be a real analytic, stationary and asymptotically flat spacetime with a non-empty ergoregion E and no future event horizon H}^{+. In Friedman (Commun Math Phys 63(3):243-255, 1978), Friedman observed that, on such spacetimes, there exist solutions φ to the wave equation \\squaregφ=0 such that their local energy does not decay to 0 as time increases. In addition, Friedman provided a heuristic argument that the energy of such solutions actually grows to +∞. In this paper, we provide a rigorous proof of Friedman's instability. Our setting is, in fact, more general. We consider smooth spacetimes {(M^{d+1},g)}, for any {d≥2}, not necessarily globally real analytic. We impose only a unique continuation condition for the wave equation across the boundary partial{E} of E on a small neighborhood of a point p\\inpartialE. This condition always holds if {(M,g)} is analytic in that neighborhood of p, but it can also be inferred in the case when {(M,g)} possesses a second Killing field {Φ} such that the span of {Φ} and the stationary Killing field T is timelike on partial{E}. We also allow the spacetimes {(M,g)} under consideration to possess a (possibly empty) future event horizon H}^{+, such that, however, {H+\\cap E=\\emptyset} (excluding, thus, the Kerr exterior family). As an application of our theorem, we infer an instability result for the acoustical wave equation on the hydrodynamic vortex, a phenomenon first investigated numerically by Oliveira et al. in (Phys Rev D 89(12):124008, 2014). Furthermore, as a side benefit of our proof, we provide a derivation, based entirely on the vector field method, of a Carleman-type estimate on the exterior of the ergoregion for a general class of stationary and asymptotically flat spacetimes. Applications of this estimate include a Morawetz-type bound for solutions φ of \\squaregφ=0 with frequency support bounded away from {{ω}=0} and {{ω}=±∞}.

Quantum-tunneling isotope-exchange reaction H2+D-→HD +H-

NASA Astrophysics Data System (ADS)

Yuen, Chi Hong; Ayouz, Mehdi; Endres, Eric S.; Lakhamanskaya, Olga; Wester, Roland; Kokoouline, Viatcheslav

2018-02-01

The tunneling reaction H2+D-→HD +H- was studied in a recent experimental work at low temperatures (10, 19, and 23 K) by Endres et al. [Phys. Rev. A 95, 022706 (2017), 10.1103/PhysRevA.95.022706]. An upper limit of the rate coefficient was found to be about 10-18cm3 /s. In the present study, reaction probabilities are determined using the ABC program developed by Skouteris et al. [Comput. Phys. Commun. 133, 128 (2000), 10.1016/S0010-4655(00)00167-3]. The probabilities for ortho-H2 and para-H2 in their ground rovibrational states are obtained numerically at collision energies above 50 meV with the total angular momentum J =0 -15 and extrapolated below 50 meV using a WKB approach. Thermally averaged rate coefficients for ortho- and para-H2 are obtained; the largest one, for ortho-H2, is about 3.1 ×10-20cm3 /s, which agrees with the experimental results.

Cryptanalysis on a scheme to share information via employing a discrete algorithm to quantum states

NASA Astrophysics Data System (ADS)

Amellal, H.; Meslouhi, A.; El Baz, M.; Hassouni, Y.; El Allati, A.

2017-03-01

Recently, Yang and Hwang [Int. J. Theor. Phys. 53, 224 (2014)] demonstrated that the scheme to share information via employing discrete algorithm to quantum states presented by Kang and Fang [Commun. Theor. Phys. 55, 239 (2011)] suffers from a major vulnerability allowing an eavesdropper to perform a measurement and resend attack. By introducing an additional checking state framework, the authors have proposed an improved protocol to overcome this weakness. This work calls into question the invoked vulnerability in order to clarify a misinterpretation in the same protocol stages also introduce a possible leakage information strategy, known as a faked state attack, despite the proposed improvement, which means that the same security problem may persist. Finally, an upgrading technic was introduced in order to enhance the security transmission.

New Optical Field Generated by Partial Tracing Over Two-Mode Squeezing-Rotating Entangled Vacuum State ^{{*}}

NASA Astrophysics Data System (ADS)

Ren, Gang; Du, Jian-ming; Zhang, Wen-Hai

2018-05-01

Based on the two-mode squeezing-rotating entangled vacuum state (Fan and Fan in Commun Theor Phys 33:701-704, 2000), we obtained a new quantum state by using partial tracing method. This new state can be considered as a real chaotic field. We also studied its squeezing properties and quantum statistical properties by giving the analytic results and exact numerical results. It was established that the rotation angle's parameter plays an important role in this new optical field.

RETRACTION (G' / G)-expansion method equivalent to the extended tanh-function method

NASA Astrophysics Data System (ADS)

El-Wakil, S. A.; Abdou, M. A.; El-Shewy, E. K.; Hendi, A.; Abdelwahed, H. G.

2010-10-01

This paper has been formally retracted on ethical grounds due to the similarity in content, presentation and style to another article published by Liu Chun-Ping in the journal Communications in Theoretical Physics (Chun-Ping 2009 Commun. Theor. Phys. 51 985). It is unfortunate that this was not detected before going to press. Our thanks go to the original author for bringing this fact to our attention. Corrections were made to this article on 22 October 2010.

New version: GRASP2K relativistic atomic structure package

NASA Astrophysics Data System (ADS)

Jönsson, P.; Gaigalas, G.; Bieroń, J.; Fischer, C. Froese; Grant, I. P.

2013-09-01

A revised version of GRASP2K [P. Jönsson, X. He, C. Froese Fischer, I.P. Grant, Comput. Phys. Commun. 177 (2007) 597] is presented. It supports earlier non-block and block versions of codes as well as a new block version in which the njgraf library module [A. Bar-Shalom, M. Klapisch, Comput. Phys. Commun. 50 (1988) 375] has been replaced by the librang angular package developed by Gaigalas based on the theory of [G. Gaigalas, Z.B. Rudzikas, C. Froese Fischer, J. Phys. B: At. Mol. Phys. 30 (1997) 3747, G. Gaigalas, S. Fritzsche, I.P. Grant, Comput. Phys. Commun. 139 (2001) 263]. Tests have shown that errors encountered by njgraf do not occur with the new angular package. The three versions are denoted v1, v2, and v3, respectively. In addition, in v3, the coefficients of fractional parentage have been extended to j=9/2, making calculations feasible for the lanthanides and actinides. Changes in v2 include minor improvements. For example, the new version of rci2 may be used to compute quantum electrodynamic (QED) corrections only from selected orbitals. In v3, a new program, jj2lsj, reports the percentage composition of the wave function in LSJ and the program rlevels has been modified to report the configuration state function (CSF) with the largest coefficient of an LSJ expansion. The bioscl2 and bioscl3 application programs have been modified to produce a file of transition data with one record for each transition in the same format as in ATSP2K [C. Froese Fischer, G. Tachiev, G. Gaigalas, M.R. Godefroid, Comput. Phys. Commun. 176 (2007) 559], which identifies each atomic state by the total energy and a label for the CSF with the largest expansion coefficient in LSJ intermediate coupling. All versions of the codes have been adapted for 64-bit computer architecture. Program SummaryProgram title: GRASP2K, version 1_1 Catalogue identifier: ADZL_v1_1 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZL_v1_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.: 730252 No. of bytes in distributed program, including test data, etc.: 14808872 Distribution format: tar.gz Programming language: Fortran. Computer: Intel Xeon, 2.66 GHz. Operating system: Suse, Ubuntu, and Debian Linux 64-bit. RAM: 500 MB or more Classification: 2.1. Catalogue identifier of previous version: ADZL_v1_0 Journal reference of previous version: Comput. Phys. Comm. 177 (2007) 597 Does the new version supersede the previous version?: Yes Nature of problem: Prediction of atomic properties — atomic energy levels, oscillator strengths, radiative decay rates, hyperfine structure parameters, Landé gJ-factors, and specific mass shift parameters — using a multiconfiguration Dirac-Hartree-Fock approach. Solution method: The computational method is the same as in the previous GRASP2K [1] version except that for v3 codes the njgraf library module [2] for recoupling has been replaced by librang [3,4]. Reasons for new version: New angular libraries with improved performance are available. Also methodology for transforming from jj- to LSJ-coupling has been developed. Summary of revisions: New angular libraries where the coefficients of fractional parentage have been extended to j=9/2, making calculations feasible for the lanthanides and actinides. Inclusion of a new program jj2lsj, which reports the percentage composition of the wave function in LSJ. Transition programs have been modified to produce a file of transition data with one record for each transition in the same format as Atsp2K [C. Froese Fischer, G. Tachiev, G. Gaigalas and M.R. Godefroid, Comput. Phys. Commun. 176 (2007) 559], which identifies each atomic state by the total energy and a label for the CSF with the largest expansion coefficient in LSJ intermediate coupling. Updated to 64-bit architecture. A comprehensive user manual in pdf format for the program package has been added. Restrictions: The packing algorithm restricts the maximum number of orbitals to be ≤214. The tables of reduced coefficients of fractional parentage used in this version are limited to subshells with j≤9/2 [5]; occupied subshells with j>9/2 are, therefore, restricted to a maximum of two electrons. Some other parameters, such as the maximum number of subshells of a CSF outside a common set of closed shells are determined by a parameter.def file that can be modified prior to compile time. Unusual features: The bioscl3 program reports transition data in the same format as in Atsp2K [6], and the data processing program tables of the latter package can be used. The tables program takes a name.lsj file, usually a concatenated file of all the .lsj transition files for a given atom or ion, and finds the energy structure of the levels and the multiplet transition arrays. The tables posted at the website http://atoms.vuse.vanderbilt.edu are examples of tables produced by the tables program. With the extension of coefficients of fractional parentage to j=9/2, calculations for the lanthanides and actinides become possible. Running time: CPU time required to execute test cases: 70.5 s.

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.

Bilinear covariants and spinor fields duality in quantum Clifford algebras

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

Abłamowicz, Rafał, E-mail: rablamowicz@tntech.edu; Gonçalves, Icaro, E-mail: icaro.goncalves@ufabc.edu.br; Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto'smore » spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.« less

Discrete diffraction managed solitons: Threshold phenomena and rapid decay for general nonlinearities

NASA Astrophysics Data System (ADS)

Choi, Mi-Ran; Hundertmark, Dirk; Lee, Young-Ran

2017-10-01

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of nonlinearities; they are, for example, allowed to change sign, and the weakest possible condition, it only has to be locally integrable, on the local diffraction profile. The solutions are found as minimizers of a nonlinear and nonlocal variational problem which is translation invariant. There exists a critical threshold λcr such that minimizers for this variational problem exist if their power is bigger than λcr and no minimizers exist with power less than the critical threshold. We also give simple criteria for the finiteness and strict positivity of the critical threshold. Our proof of existence of minimizers is rather direct and avoids the use of Lions' concentration compactness argument. Furthermore, we give precise quantitative lower bounds on the exponential decay rate of the diffraction management solitons, which confirm the physical heuristic prediction for the asymptotic decay rate. Moreover, for ground state solutions, these bounds give a quantitative lower bound for the divergence of the exponential decay rate in the limit of vanishing average diffraction. For zero average diffraction, we prove quantitative bounds which show that the solitons decay much faster than exponentially. Our results considerably extend and strengthen the results of Hundertmark and Lee [J. Nonlinear Sci. 22, 1-38 (2012) and Commun. Math. Phys. 309(1), 1-21 (2012)].

Oscillatory Critical Amplitudes in Hierarchical Models and the Harris Function of Branching Processes

NASA Astrophysics Data System (ADS)

Costin, Ovidiu; Giacomin, Giambattista

2013-02-01

Oscillatory critical amplitudes have been repeatedly observed in hierarchical models and, in the cases that have been taken into consideration, these oscillations are so small to be hardly detectable. Hierarchical models are tightly related to iteration of maps and, in fact, very similar phenomena have been repeatedly reported in many fields of mathematics, like combinatorial evaluations and discrete branching processes. It is precisely in the context of branching processes with bounded off-spring that T. Harris, in 1948, first set forth the possibility that the logarithm of the moment generating function of the rescaled population size, in the super-critical regime, does not grow near infinity as a power, but it has an oscillatory prefactor (the Harris function). These oscillations have been observed numerically only much later and, while the origin is clearly tied to the discrete character of the iteration, the amplitude size is not so well understood. The purpose of this note is to reconsider the issue for hierarchical models and in what is arguably the most elementary setting—the pinning model—that actually just boils down to iteration of polynomial maps (and, notably, quadratic maps). In this note we show that the oscillatory critical amplitude for pinning models and the Harris function coincide. Moreover we make explicit the link between these oscillatory functions and the geometry of the Julia set of the map, making thus rigorous and quantitative some ideas set forth in Derrida et al. (Commun. Math. Phys. 94:115-132, 1984).

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)].

Tuning Rashba spin-orbit coupling in homogeneous semiconductor nanowires

NASA Astrophysics Data System (ADS)

Wójcik, Paweł; Bertoni, Andrea; Goldoni, Guido

2018-04-01

We use k .p theory to estimate the Rashba spin-orbit coupling (SOC) in large semiconductor nanowires. We specifically investigate GaAs- and InSb-based devices with different gate configurations to control symmetry and localization of the electron charge density. We explore gate-controlled SOC for wires of different size and doping, and we show that in high carrier density SOC has a nonlinear electric field susceptibility, due to large reshaping of the quantum states. We analyze recent experiments with InSb nanowires in light of our calculations. Good agreement is found with the SOC coefficients reported in Phys. Rev. B 91, 201413(R) (2015), 10.1103/PhysRevB.91.201413, but not with the much larger values reported in Nat. Commun. 8, 478 (2017), 10.1038/s41467-017-00315-y. We discuss possible origins of this discrepancy.

Global two-fluid simulations of geodesic acoustic modes in strongly shaped tight aspect ratio tokamak plasmas

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

Robinson, J. R.; Hnat, B.; Thyagaraja, A.

2013-05-15

Following recent observations suggesting the presence of the geodesic acoustic mode (GAM) in ohmically heated discharges in the Mega Amp Spherical Tokamak (MAST) [J. R. Robinson et al., Plasma Phys. Controlled Fusion 54, 105007 (2012)], the behaviour of the GAM is studied numerically using the two fluid, global code CENTORI [P. J. Knight et al. Comput. Phys. Commun. 183, 2346 (2012)]. We examine mode localisation and effects of magnetic geometry, given by aspect ratio, elongation, and safety factor, on the observed frequency of the mode. An excellent agreement between simulations and experimental data is found for simulation plasma parameters matchedmore » to those of MAST. Increasing aspect ratio yields good agreement between the GAM frequency found in the simulations and an analytical result obtained for elongated large aspect ratio plasmas.« less

Synthesis of Si Nanowires for an Anode Material of Li Batteries

DTIC Science & Technology

2007-12-04

Zhou, H. Li, H.P. Sun , D.P. Yu, Y.Q. Wang, X.J. Huang, L.Q. Chen, Z. Zhang, Appl. Phys. Lett. 75 (16) (1999) 2447 6. A.M. Wilson, B.M. Way, J.R. Dahn...Y. Liu, Electrochem. Commun. 5 (2003) 165 12. Tatsuo Umeno, Kenji Fukuda, Hongyu Wang, Nikolay Dimov, Takashi Iwao, Masaki Yoshio, Chem. Lett...Hansu Kim, Junghee Choi, Hun-Joon Sohn and Tak Kang, J. Electrochem. Soc. 146 (12) (1999) 4401 18. G.X. Wang, L. Sun , D.H. Bradhurst, S. Zhong, S.X. Dou

New Metrics from a Fractional Gravitational Field

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2017-09-01

Agop et al. proved in Commun. Theor. Phys. (2008) that, a Reissner-Nordstrom type metric is obtained, if gauge gravitational field in a fractal spacetime is constructed by means of concepts of scale relativity. We prove in this short communication that similar result is obtained if gravity in D-spacetime dimensions is fractionalized by means of the Glaeske-Kilbas-Saigo fractional. Besides, non-singular gravitational fields are obtained without using extra-dimensions. We present few examples to show that these gravitational fields hold a number of motivating features in spacetime physics.

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…

Surfing surface gravity waves

NASA Astrophysics Data System (ADS)

Pizzo, Nick

2017-11-01

A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497-503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.

Singularity formations for a surface wave model

NASA Astrophysics Data System (ADS)

Castro, Angel; Córdoba, Diego; Gancedo, Francisco

2010-11-01

In this paper we study the Burgers equation with a nonlocal term of the form Hu where H is the Hilbert transform. This system has been considered as a quadratic approximation for the dynamics of a free boundary of a vortex patch (see Biello and Hunter 2010 Commun. Pure Appl. Math. LXIII 0303-36 Marsden and Weinstein 1983 Physica D 7 305-23). We prove blowup in finite time for a large class of initial data with finite energy. Considering a more general nonlocal term, of the form ΛαHu for 0 < α < 1, finite time singularity formation is also shown.

Finite Beta Boundary Magnetic Fields of NCSX

NASA Astrophysics Data System (ADS)

Grossman, A.; Kaiser, T.; Mioduszewski, P.

2004-11-01

The magnetic field between the plasma surface and wall of the National Compact Stellarator (NCSX), which uses quasi-symmetry to combine the best features of the tokamak and stellarator in a configuration of low aspect ratio is mapped via field line tracing in a range of finite beta in which part of the rotational transform is generated by the bootstrap current. We adopt the methodology developed for W7-X, in which an equilibrium solution is computed by an inverse equilibrium solver based on an energy minimizing variational moments code, VMEC2000[1], which solves directly for the shape of the flux surfaces given the external coils and their currents as well as a bootstrap current provided by a separate transport calculation. The VMEC solution and the Biot-Savart vacuum fields are coupled to the magnetic field solver for finite-beta equilibrium (MFBE2001)[2] code to determine the magnetic field on a 3D grid over a computational domain. It is found that the edge plasma is more stellarator-like, with a complex 3D structure, and less like the ordered 2D symmetric structure of a tokamak. The field lines make a transition from ergodically covering a surface to ergodically covering a volume, as the distance from the last closed magnetic surface is increased. The results are compared with the PIES[3] calculations. [1] S.P. Hirshman et al. Comput. Phys. Commun. 43 (1986) 143. [2] E. Strumberger, et al. Nucl. Fusion 42 (2002) 827. [3] A.H. Reiman and H.S. Greenside, Comput. Phys. Commun. 43, 157 (1986).

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.

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

GENXICC2.1: An improved version of GENXICC for hadronic production of doubly heavy baryons

NASA Astrophysics Data System (ADS)

Wang, Xian-You; Wu, Xing-Gang

2013-03-01

We present an improved version of GENXICC, which is a generator for hadronic production of the doubly heavy baryons Ξcc, Ξbc and Ξbb and has been introduced by C.H. Chang, J.X. Wang and X.G. Wu [Comput. Phys. Commun. 177 (2007) 467; Comput. Phys. Commun. 181 (2010) 1144]. In comparison with the previous GENXICC versions, we update the program in order to generate the unweighted baryon events more effectively under various simulation environments, whose distributions are now generated according to the probability proportional to the integrand. One Les Houches Event (LHE) common block has been added to produce a standard LHE data file that contains useful information of the doubly heavy baryon and its accompanying partons. Such LHE data can be conveniently imported into PYTHIA to do further hadronization and decay simulation, especially, the color-flow problem can be solved with PYTHIA8.0. NEW VERSION PROGRAM SUMMARYTitle of program: GENXICC2.1 Program obtained from: CPC Program Library Reference to original program: GENXICC Reference in CPC: Comput. Phys. Commun. 177, 467 (2007); Comput. Phys. Commun. 181, 1144 (2010) Does the new version supersede the old program: No Computer: Any LINUX based on PC with FORTRAN 77 or FORTRAN 90 and GNU C compiler as well Operating systems: LINUX Programming language used: FORTRAN 77/90 Memory required to execute with typical data: About 2.0 MB No. of bytes in distributed program: About 2 MB, including PYTHIA6.4 Distribution format: .tar.gz Nature of physical problem: Hadronic production of doubly heavy baryons Ξcc, Ξbc and Ξbb. Method of solution: The upgraded version with a proper interface to PYTHIA can generate full production and decay events, either weighted or unweighted, conveniently and effectively. Especially, the unweighted events are generated by using an improved hit-and-miss approach. Reasons for new version: Responding to the feedback from users of CMS and LHCb groups at the Large Hadron Collider, and based on the recent improvements of PYTHIA on the color-flow problem, we improve the efficiency for generating the unweighted events, and also improve the color-flow part for further hadronization. Especially, an interface has been added to import the output production events into a suitable form for PYTHIA8.0 simulation, in which the color-flow during the simulation can be correctly set. Typical running time: It depends on which option is chosen to match PYTHIA when generating the full events and also on which mechanism is chosen to generate the events. Typically, for the dominant gluon-gluon fusion mechanism to generate the mixed events via the intermediate diquarks in (cc)[3S1]3¯ and (cc)[1S0]6 states, setting IDWTUP=3 and unwght =.true., it takes 30 min to generate 105 unweighted events on a 2.27 GHz Intel Xeon E5520 processor machine; setting IDWTUP=3 and unwght =.false. or IDWTUP=1 and IGENERATE=0, it only needs 2 min to generate the 105 baryon events (the fastest way, for theoretical purposes only). As a comparison, for previous GENXICC versions, if setting IDWTUP=1 and IGENERATE=1, it takes about 22 hours to generate 1000 unweighted events. Keywords: Event generator; Doubly heavy baryons; Hadronic production. Summary of the changes (improvements): (1) The scheme for generating unweighted events has been improved; (2) One Les Houches Event (LHE) common block has been added to record the standard LHE data in order to be the correct input for PYTHIA8.0 for later simulation; (3) We present the code for connecting GENXICC to PYTHIA8.0, where three color-flows have to be correctly set for later simulation. More specifically, we present the changes together with their detailed explanations in the following:

Non-CMC solutions to the Einstein constraint equations on asymptotically Euclidean manifolds with apparent horizon boundaries

NASA Astrophysics Data System (ADS)

Holst, Michael; Meier, Caleb

2015-01-01

In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary Σ. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show the existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on Σ, similar to those analyzed previously by Dain (2004 Class. Quantum Grav. 21 555-73), by Maxwell (2004, 2005 Commun. Math. Phys. 253 561-83), and by Holst and Tsogtgerel (2013 Class. Quantum Grav. 30 205011) as a model of black holes in various CMC settings, and by Holst et al (2013 Non-CMC solutions to the einstein constraint equations with apparent horizon boundaries arXiv:1310.2302v1) in the setting of far-from-CMC solutions on compact manifolds with boundary. These ‘marginally trapped surface’ Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region Σ are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assuming a suitable form of weak cosmic censorship, the results presented in this article guarantee the existence of initial data that will evolve into a space-time containing an arbitrary number of black holes. A particularly important feature of our results are the minimal restrictions we place on the mean curvature, giving both near- and far-from-CMC results that are new.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2018-03-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2}). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3}) and the level sets of the Gaussian free field ({d≥ 3}). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

Quenched Large Deviations for Simple Random Walks on Percolation Clusters Including Long-Range Correlations

NASA Astrophysics Data System (ADS)

Berger, Noam; Mukherjee, Chiranjib; Okamura, Kazuki

2017-12-01

We prove a quenched large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster (SRWPC) on {Z^d} ({d ≥ 2} ). The models under interest include classical Bernoulli bond and site percolation as well as models that exhibit long range correlations, like the random cluster model, the random interlacement and the vacant set of random interlacements (for {d ≥ 3} ) and the level sets of the Gaussian free field ({d≥ 3} ). Inspired by the methods developed by Kosygina et al. (Commun Pure Appl Math 59:1489-1521, 2006) for proving quenched LDP for elliptic diffusions with a random drift, and by Yilmaz (Commun Pure Appl Math 62(8):1033-1075, 2009) and Rosenbluth (Quenched large deviations for multidimensional random walks in a random environment: a variational formula. Ph.D. thesis, NYU, arXiv:0804.1444v1) for similar results regarding elliptic random walks in random environment, we take the point of view of the moving particle and prove a large deviation principle for the quenched distribution of the pair empirical measures of the environment Markov chain in the non-elliptic case of SRWPC. Via a contraction principle, this reduces easily to a quenched LDP for the distribution of the mean velocity of the random walk and both rate functions admit explicit variational formulas. The main difficulty in our set up lies in the inherent non-ellipticity as well as the lack of translation-invariance stemming from conditioning on the fact that the origin belongs to the infinite cluster. We develop a unifying approach for proving quenched large deviations for SRWPC based on exploiting coercivity properties of the relative entropies in the context of convex variational analysis, combined with input from ergodic theory and invoking geometric properties of the supercritical percolation cluster.

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.

CFEL-ASG Software Suite (CASS): usage for free-electron laser experiments with biological focus.

PubMed

Foucar, Lutz

2016-08-01

CASS [Foucar et al. (2012). Comput. Phys. Commun. 183 , 2207-2213] is a well established software suite for experiments performed at any sort of light source. It is based on a modular design and can easily be adapted for use at free-electron laser (FEL) experiments that have a biological focus. This article will list all the additional functionality and enhancements of CASS for use with FEL experiments that have been introduced since the first publication. The article will also highlight some advanced experiments with biological aspects that have been performed.

Low Mach number fluctuating hydrodynamics of multispecies liquid mixtures

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

Donev, Aleksandar, E-mail: donev@courant.nyu.edu; Bhattacharjee, Amit Kumar; Nonaka, Andy

We develop a low Mach number formulation of the hydrodynamic equations describing transport of mass and momentum in a multispecies mixture of incompressible miscible liquids at specified temperature and pressure, which generalizes our prior work on ideal mixtures of ideal gases [Balakrishnan et al., “Fluctuating hydrodynamics of multispecies nonreactive mixtures,” Phys. Rev. E 89 013017 (2014)] and binary liquid mixtures [Donev et al., “Low mach number fluctuating hydrodynamics of diffusively mixing fluids,” Commun. Appl. Math. Comput. Sci. 9(1), 47-105 (2014)]. In this formulation, we combine and extend a number of existing descriptions of multispecies transport available in the literature. Themore » formulation applies to non-ideal mixtures of arbitrary number of species, without the need to single out a “solvent” species, and includes contributions to the diffusive mass flux due to gradients of composition, temperature, and pressure. Momentum transport and advective mass transport are handled using a low Mach number approach that eliminates fast sound waves (pressure fluctuations) from the full compressible system of equations and leads to a quasi-incompressible formulation. Thermal fluctuations are included in our fluctuating hydrodynamics description following the principles of nonequilibrium thermodynamics. We extend the semi-implicit staggered-grid finite-volume numerical method developed in our prior work on binary liquid mixtures [Nonaka et al., “Low mach number fluctuating hydrodynamics of binary liquid mixtures,” http://arxiv.org/abs/1410.2300 (2015)] and use it to study the development of giant nonequilibrium concentration fluctuations in a ternary mixture subjected to a steady concentration gradient. We also numerically study the development of diffusion-driven gravitational instabilities in a ternary mixture and compare our numerical results to recent experimental measurements [Carballido-Landeira et al., “Mixed-mode instability of a miscible interface due to coupling between Rayleigh–Taylor and double-diffusive convective modes,” Phys. Fluids 25, 024107 (2013)] in a Hele-Shaw cell. We find that giant nonequilibrium fluctuations can trigger the instability but are eventually dominated by the deterministic growth of the unstable mode, in both quasi-two-dimensional (Hele-Shaw) and fully three-dimensional geometries used in typical shadowgraph experiments.« less

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.

Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities

NASA Astrophysics Data System (ADS)

Adamović, Dražen; Lin, Xianzu; Milas, Antun

2015-03-01

We consider AD-type orbifolds of the triplet vertex algebras W(p) extending the well-known c=1 orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras A(W(p)^{A_m}) and A(W(p)^{D_m}), where A_m and D_m are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible W(p)^Γ-modules is developed, which relies on a family of constant term identities and properties of certain polynomials based on constant terms. All these properties can be checked for small values of m and p with a computer software. As a result, we argue that if certain constant term properties hold, the irreducible modules constructed in [Commun. Contemp. Math. 15 (2013), 1350028, 30 pages; Internat. J. Math. 25 (2014), 1450001, 34 pages] provide a complete list of irreducible W(p)^{A_m} and W(p)^{D_m}-modules. This paper is a continuation of our previous work on the ADE subalgebras of the triplet vertex algebra W(p).

KANTBP 2.0: New version of 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.; Vinitsky, S. I.; Abrashkevich, A. G.

2008-11-01

A FORTRAN 77 program for calculating energy values, reaction matrix and corresponding radial wave functions in a coupled-channel approximation of the hyperspherical adiabatic approach is presented. In this approach, a multi-dimensional Schrödinger equation is reduced to a system of the coupled second-order ordinary differential equations on a finite interval with homogeneous boundary conditions: (i) the Dirichlet, Neumann and third type at the left and right boundary points for continuous spectrum problem, (ii) the Dirichlet and Neumann type conditions at left boundary point and Dirichlet, Neumann and third type at the right boundary point for the discrete spectrum problem. The resulting system of radial equations containing 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 reaction matrix and radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field. This version extends the previous version 1.0 of the KANTBP program [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]. Program summaryProgram title: KANTBP Catalogue identifier: ADZH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZH_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.: 20 403 No. of bytes in distributed program, including test data, etc.: 147 563 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: This depends on the number of differential equations; the number and order of finite elements; the number of hyperradial points; and the number of eigensolutions required. The test run requires 2 MB Classification: 2.1, 2.4 External routines: GAULEG and GAUSSJ [2] Nature of problem: In the hyperspherical adiabatic approach [3-5], a multidimensional Schrödinger equation for a two-electron system [6] or a hydrogen atom in magnetic field [7-9] is reduced by separating radial coordinate ρ from the angular variables to a system of the second-order ordinary differential equations containing the 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 of the continuum spectrum for such systems of coupled differential equations on finite intervals of the radial variable ρ∈[ρ,ρ]. This approach can be used in the calculations of effects of electron screening on low-energy fusion cross sections [10-12]. Solution method: The boundary problems for the coupled second-order differential equations are solved by the finite element method using high-order accuracy approximations [13]. 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 [14]. 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 [14]. As a test desk, the program is applied to the calculation of the reaction matrix and corresponding radial wave functions for 3D-model of a hydrogen-like atom in a homogeneous magnetic field described in [9] on finite intervals of the radial variable ρ∈[ρ,ρ]. For this benchmark model the required analytical expressions for asymptotics of the potential matrix elements and first-derivative coupling terms, and also 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: the number of differential equations; the number and order of finite elements; the total number of hyperradial points; and the number of eigensolutions required. Restrictions due to dimension sizes may be easily alleviated by altering PARAMETER statements (see Section 3 and [1] for details). The user must also supply subroutine POTCAL for evaluating potential matrix elements. The user should also supply subroutines ASYMEV (when solving the eigenvalue problem) or ASYMS0 and ASYMSC (when solving the scattering problem) which evaluate asymptotics of the radial wave functions at left and right boundary points in case of a boundary condition of the third type for the above problems. Running time: The running time depends critically upon: the number of differential equations; the number and order of finite elements; the total number of hyperradial points on interval [ ρ,ρ]; and the number of eigensolutions required. The test run which accompanies this paper took 2 s without calculation of matrix potentials on the Intel Pentium IV 2.4 GHz. References: [1] 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; http://cpc.cs.qub.ac.uk/summaries/ADZHv10.html. [2] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press, Cambridge, 1986. [3] J. Macek, J. Phys. B 1 (1968) 831-843. [4] U. Fano, Rep. Progr. Phys. 46 (1983) 97-165. [5] C.D. Lin, Adv. Atom. Mol. Phys. 22 (1986) 77-142. [6] A.G. Abrashkevich, D.G. Abrashkevich, M. Shapiro, Comput. Phys. Commun. 90 (1995) 311-339. [7] M.G. Dimova, M.S. Kaschiev, S.I. Vinitsky, J. Phys. B 38 (2005) 2337-2352. [8] 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. [9] 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. Commun. 178 (2007) 301 330; http://cpc.cs.qub.ac.uk/summaries/AEAAv10.html. [10] H.J. Assenbaum, K. Langanke, C. Rolfs, Z. Phys. A 327 (1987) 461-468. [11] V. Melezhik, Nucl. Phys. A 550 (1992) 223-234. [12] L. Bracci, G. Fiorentini, V.S. Melezhik, G. Mezzorani, P. Pasini, Phys. Lett. A 153 (1991) 456-460. [13] A.G. Abrashkevich, D.G. Abrashkevich, M.S. Kaschiev, I.V. Puzynin, Comput. Phys. Commun. 85 (1995) 40-64. [14] K.J. Bathe, Finite Element Procedures in Engineering Analysis, Englewood Cliffs, Prentice-Hall, New York, 1982.

Global stability of steady states in the classical Stefan problem for general boundary shapes

PubMed Central

Hadžić, Mahir; Shkoller, Steve

2015-01-01

The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady-state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of such steady states, assuming a sufficient degree of smoothness on the initial domain, but without any a priori restriction on the convexity properties of the initial shape. This is an extension of our previous result (Hadžić & Shkoller 2014 Commun. Pure Appl. Math. 68, 689–757 (doi:10.1002/cpa.21522)) in which we studied nearly spherical shapes. PMID:26261359

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

Hora, H.; Korn, G.; Eliezer, S.

Measured highly elevated gains of proton–boron (HB11) fusion (Picciottoet al., Phys. Rev. X4, 031030 (2014)) confirmed the exceptional avalanche reaction process (Lalousiset al., Laser Part. Beams 32, 409 (2014); Horaet al., Laser Part. Beams33, 607 (2015)) for the combination of the non-thermal block ignition using ultrahigh intensity laser pulses of picoseconds duration. The ultrahigh accelerationabovemore » $$10^{20}~\\text{cm}~\\text{s}^{-2}$$ for plasma blocks was theoretically and numerically predicted since 1978 (Hora,Physics of Laser Driven Plasmas(Wiley, 1981), pp. 178 and 179) and measured (Sauerbrey, Phys. Plasmas3, 4712 (1996)) in exact agreement (Horaet al., Phys. Plasmas14, 072701 (2007)) when the dominating force was overcoming thermal processes. This is based on Maxwell’s stress tensor by the dielectric properties of plasma leading to the nonlinear (ponderomotive) force $$f_{\\text{NL}}$$ resulting in ultra-fast expanding plasma blocks by a dielectric explosion. Combining this with measured ultrahigh magnetic fields and the avalanche process opens an option for an environmentally absolute clean and economic boron fusion power reactor. Finally, this is supported also by other experiments with very high HB11 reactions under different conditions (Labauneet al., Nature Commun.4, 2506 (2013)).« less

Simulation of n-qubit quantum systems. V. Quantum measurements

NASA Astrophysics Data System (ADS)

Radtke, T.; Fritzsche, S.

2010-02-01

The FEYNMAN program has been developed during the last years to support case studies on the dynamics and entanglement of n-qubit quantum registers. Apart from basic transformations and (gate) operations, it currently supports a good number of separability criteria and entanglement measures, quantum channels as well as the parametrizations of various frequently applied objects in quantum information theory, such as (pure and mixed) quantum states, hermitian and unitary matrices or classical probability distributions. With the present update of the FEYNMAN program, we provide a simple access to (the simulation of) quantum measurements. This includes not only the widely-applied projective measurements upon the eigenspaces of some given operator but also single-qubit measurements in various pre- and user-defined bases as well as the support for two-qubit Bell measurements. In addition, we help perform generalized and POVM measurements. Knowing the importance of measurements for many quantum information protocols, e.g., one-way computing, we hope that this update makes the FEYNMAN code an attractive and versatile tool for both, research and education. New version program summaryProgram title: FEYNMAN Catalogue identifier: ADWE_v5_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v5_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.: 27 210 No. of bytes in distributed program, including test data, etc.: 1 960 471 Distribution format: tar.gz Programming language: Maple 12 Computer: Any computer with Maple software installed Operating system: Any system that supports Maple; the program has been tested under Microsoft Windows XP and Linux Classification: 4.15 Catalogue identifier of previous version: ADWE_v4_0 Journal reference of previous version: Comput. Phys. Commun. 179 (2008) 647 Does the new version supersede the previous version?: Yes Nature of problem: During the last decade, the field of quantum information science has largely contributed to our understanding of quantum mechanics, and has provided also new and efficient protocols that are used on quantum entanglement. To further analyze the amount and transfer of entanglement in n-qubit quantum protocols, symbolic and numerical simulations need to be handled efficiently. Solution method: Using the computer algebra system Maple, we developed a set of procedures in order to 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 and measurements that act upon the quantum registers. All commands are organized in a hierarchical order and 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: Until the present, the FEYNMAN program supported the basic data structures and operations of n-qubit quantum registers [1], a good number of separability and entanglement measures [2], quantum operations (noisy channels) [3] as well as the parametrizations of various frequently applied objects, such as (pure and mixed) quantum states, hermitian and unitary matrices or classical probability distributions [4]. With the current extension, we here add all necessary features to simulate quantum measurements, including the projective measurements in various single-qubit and the two-qubit Bell basis, and POVM measurements. Together with the previously implemented functionality, this greatly enhances the possibilities of analyzing quantum information protocols in which measurements play a central role, e.g., one-way computation. Running time: Most commands require ⩽10 seconds of processor time on a Pentium 4 processor with ⩾2 GHz RAM or newer, if they work with quantum registers with five or less qubits. Moreover, about 5-20 MB of working memory is typically needed (in addition to the memory for the Maple environment itself). However, especially when working with symbolic expressions, the requirements on the 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 Kraus operators, may result 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 than not only a numerical evaluation is feasible. Since the various commands can be applied to quite different scenarios, no general scaling rule can be given for the CPU time or the request of memory. References:[1] T. Radtke, S. Fritzsche, Comput. Phys. Commun. 173 (2005) 91.[2] T. Radtke, S. Fritzsche, Comput. Phys. Commun. 175 (2006) 145.[3] T. Radtke, S. Fritzsche, Comput. Phys. Commun. 176 (2007) 617.[4] T. Radtke, S. Fritzsche, Comput. Phys. Commun. 179 (2008) 647.

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.

Families of quantum fingerprinting protocols

NASA Astrophysics Data System (ADS)

Lovitz, Benjamin; Lütkenhaus, Norbert

2018-03-01

We introduce several families of quantum fingerprinting protocols to evaluate the equality function on two n -bit strings in the simultaneous message passing model. The original quantum fingerprinting protocol uses a tensor product of a small number of O (logn ) -qubit high-dimensional signals [H. Buhrman et al., Phys. Rev. Lett. 87, 167902 (2001), 10.1103/PhysRevLett.87.167902], whereas a recently proposed optical protocol uses a tensor product of O (n ) single-qubit signals, while maintaining the O (logn ) information leakage of the original protocol [J. M. Arazola and N. Lütkenhaus, Phys. Rev. A 89, 062305 (2014), 10.1103/PhysRevA.89.062305]. We find a family of protocols which interpolate between the original and optical protocols while maintaining the O (logn ) information leakage, thus demonstrating a tradeoff between the number of signals sent and the dimension of each signal. There has been interest in experimental realization of the recently proposed optical protocol using coherent states [F. Xu et al., Nat. Commun. 6, 8735 (2015), 10.1038/ncomms9735; J.-Y. Guan et al., Phys. Rev. Lett. 116, 240502 (2016), 10.1103/PhysRevLett.116.240502], but as the required number of laser pulses grows linearly with the input size n , eventual challenges for the long-time stability of experimental setups arise. We find a coherent state protocol which reduces the number of signals by a factor 1/2 while also reducing the information leakage. Our reduction makes use of a simple modulation scheme in optical phase space, and we find that more complex modulation schemes are not advantageous. Using a similar technique, we improve a recently proposed coherent state protocol for evaluating the Euclidean distance between two real unit vectors [N. Kumar et al., Phys. Rev. A 95, 032337 (2017), 10.1103/PhysRevA.95.032337] by reducing the number of signals by a factor 1/2 and also reducing the information leakage.

First Measurements of Deuterium-Tritium and Deuterium-Deuterium Fusion Reaction Yields in Ignition-Scalable Direct-Drive Implosions

NASA Astrophysics Data System (ADS)

Forrest, C. J.; Radha, P. B.; Knauer, J. P.; Glebov, V. Yu.; Goncharov, V. N.; Regan, S. P.; Rosenberg, M. J.; Sangster, T. C.; Shmayda, W. T.; Stoeckl, C.; Gatu Johnson, M.

2017-03-01

The deuterium-tritium (D-T) and deuterium-deuterium neutron yield ratio in cryogenic inertial confinement fusion (ICF) experiments is used to examine multifluid effects, traditionally not included in ICF modeling. This ratio has been measured for ignition-scalable direct-drive cryogenic DT implosions at the Omega Laser Facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997), 10.1016/S0030-4018(96)00325-2] using a high-dynamic-range neutron time-of-flight spectrometer. The experimentally inferred yield ratio is consistent with both the calculated values of the nuclear reaction rates and the measured preshot target-fuel composition. These observations indicate that the physical mechanisms that have been proposed to alter the fuel composition, such as species separation of the hydrogen isotopes [D. T. Casey et al., Phys. Rev. Lett. 108, 075002 (2012), 10.1103/PhysRevLett.108.075002], are not significant during the period of peak neutron production in ignition-scalable cryogenic direct-drive DT implosions.

Finite-beta equilibria for Wendelstein 7-X configurations using the Princeton Iterative Equilibrium Solver code

NASA Astrophysics Data System (ADS)

Arndt, S.; Merkel, P.; Monticello, D. A.; Reiman, A. H.

1999-04-01

Fixed- and free-boundary equilibria for Wendelstein 7-X (W7-X) [W. Lotz et al., Plasma Physics and Controlled Nuclear Fusion Research 1990 (Proc. 13th Int. Conf. Washington, DC, 1990), (International Atomic Energy Agency, Vienna, 1991), Vol. 2, p. 603] configurations are calculated using the Princeton Iterative Equilibrium Solver (PIES) [A. H. Reiman et al., Comput. Phys. Commun., 43, 157 (1986)] to deal with magnetic islands and stochastic regions. Usually, these W7-X configurations require a large number of iterations for PIES convergence. Here, two methods have been successfully tested in an attempt to decrease the number of iterations needed for convergence. First, periodic sequences of different blending parameters are used. Second, the initial guess is vastly improved by using results of the Variational Moments Equilibrium Code (VMEC) [S. P. Hirshmann et al., Phys. Fluids 26, 3553 (1983)]. Use of these two methods have allowed verification of the Hamada condition and tendency of "self-healing" of islands has been observed.

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])

Free-boundary PIES Calculations

NASA Astrophysics Data System (ADS)

Monticello, D. A.; Reiman, A. H.; Arndt, S. C.; Merkel, P. K.

1998-11-01

A new formulation of the free boundary problem for general three-dimensional configurations has been formulated for the PIES( Reiman, A. H., Greenside, H. S., Compt. Phys. Commun. 43), (1986). code. The new formulation is more flexible and is faster that the original formulation described in Merkel et al(Merkel, P., Johnson, J. L., Monticello, D.A., et al., Proceedings of the Fourteenth International Conference on Plasma Physics and Controlled Nuclear Fusion Research paper IAEA-CN-60 | D-P-II-10) (1994) . These advantages will be described and first results of the application of this new algorithm to W7-X and NCSX (National Compact Stellarator Experiment) configurations will be presented.

The Dielectric Permittivity of Crystals in the Reduced Hartree-Fock Approximation

NASA Astrophysics Data System (ADS)

Cancès, Éric; Lewin, Mathieu

2010-07-01

In a recent article (Cancès et al. in Commun Math Phys 281:129-177, 2008), we have rigorously derived, by means of bulk limit arguments, a new variational model to describe the electronic ground state of insulating or semiconducting crystals in the presence of local defects. In this so-called reduced Hartree-Fock model, the ground state electronic density matrix is decomposed as {γ = γ^0_per + Q_{ν,\\varepsilon_F}}, where {γ^0_per} is the ground state density matrix of the host crystal and {Q_{ν,\\varepsilon_F}} the modification of the electronic density matrix generated by a modification ν of the nuclear charge of the host crystal, the Fermi level ɛ F being kept fixed. The purpose of the present article is twofold. First, we study in more detail the mathematical properties of the density matrix {Q_{ν,\\varepsilon_F}} (which is known to be a self-adjoint Hilbert-Schmidt operator on {L^2(mathbb{R}^3)}). We show in particular that if {int_{mathbb{R}^3} ν neq 0, Q_{ν,\\varepsilon_F}} is not trace-class. Moreover, the associated density of charge is not in {L^1(mathbb{R}^3)} if the crystal exhibits anisotropic dielectric properties. These results are obtained by analyzing, for a small defect ν, the linear and nonlinear terms of the resolvent expansion of {Q_{ν,\\varepsilon_F}}. Second, we show that, after an appropriate rescaling, the potential generated by the microscopic total charge (nuclear plus electronic contributions) of the crystal in the presence of the defect converges to a homogenized electrostatic potential solution to a Poisson equation involving the macroscopic dielectric permittivity of the crystal. This provides an alternative (and rigorous) derivation of the Adler-Wiser formula.

Conserved Quantities in General Relativity: From the Quasi-Local Level to Spatial Infinity

NASA Astrophysics Data System (ADS)

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

2015-08-01

We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in Wang and Yau (Commun Math Phys 288(3):919-942, 2009) to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group is assigned. Quasi-local angular momentum and quasi-local center of mass correspond to pairing this element with rotation Killing fields and boost Killing fields, respectively. They obey classical transformation laws under the action of the Poincaré group. We further justify these definitions by considering their limits as the total angular momentum and the total center of mass of an isolated system. These expressions were derived from the Hamilton-Jacobi analysis of the gravitational action and thus satisfy conservation laws. As a result, we obtained an invariant total angular momentum theorem in the Kerr spacetime. For a vacuum asymptotically flat initial data set of order 1, it is shown that the limits are always finite without any extra assumptions. We also study these total conserved quantities on a family of asymptotically flat initial data sets evolving by the vacuum Einstein evolution equation. It is shown that the total angular momentum is conserved under the evolution. For the total center of mass, the classical dynamical formula relating the center of mass, energy, and linear momentum is recovered, in the nonlinear context of initial data sets evolving by the vacuum Einstein evolution equation. The definition of quasi-local angular momentum provides an answer to the second problem in classical general relativity on Penrose's list (Proc R Soc Lond Ser A 381(1780):53-63, 1982).

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

NASA Astrophysics Data System (ADS)

Chiodaroli, Elisabetta; Kreml, Ondřej

2018-04-01

We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157–90), and based on the techniques of De Lellis and Székelyhidi (2010 Arch. Ration. Mech. Anal. 195 225–60), we extend the results of Chiodaroli and Kreml (2014 Arch. Ration. Mech. Anal. 214 1019–49) and prove that it is possible to characterize a set of Riemann data, giving rise to a self-similar solution consisting of one admissible shock and one rarefaction wave, for which the problem also admits infinitely many admissible weak solutions.

Optimal ancilla-free Pauli+V circuits for axial rotations

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

Blass, Andreas; Bocharov, Alex; Gurevich, Yuri

We address the problem of optimal representation of single-qubit rotations in a certain unitary basis consisting of the so-called V gates and Pauli matrices. The V matrices were proposed by Lubotsky, Philips, and Sarnak [Commun. Pure Appl. Math. 40, 401–420 (1987)] as a purely geometric construct in 1987 and recently found applications in quantum computation. They allow for exceptionally simple quantum circuit synthesis algorithms based on quaternionic factorization. We adapt the deterministic-search technique initially proposed by Ross and Selinger to synthesize approximating Pauli+V circuits of optimal depth for single-qubit axial rotations. Our synthesis procedure based on simple SL{sub 2}(ℤ) geometrymore » is almost elementary.« less

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.

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].

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?”.

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.

Avalanche boron fusion by laser picosecond block ignition with magnetic trapping for clean and economic reactor

DOE PAGES

Hora, H.; Korn, G.; Eliezer, S.; ...

2016-10-11

Measured highly elevated gains of proton–boron (HB11) fusion (Picciottoet al., Phys. Rev. X4, 031030 (2014)) confirmed the exceptional avalanche reaction process (Lalousiset al., Laser Part. Beams 32, 409 (2014); Horaet al., Laser Part. Beams33, 607 (2015)) for the combination of the non-thermal block ignition using ultrahigh intensity laser pulses of picoseconds duration. The ultrahigh accelerationabovemore » $$10^{20}~\\text{cm}~\\text{s}^{-2}$$ for plasma blocks was theoretically and numerically predicted since 1978 (Hora,Physics of Laser Driven Plasmas(Wiley, 1981), pp. 178 and 179) and measured (Sauerbrey, Phys. Plasmas3, 4712 (1996)) in exact agreement (Horaet al., Phys. Plasmas14, 072701 (2007)) when the dominating force was overcoming thermal processes. This is based on Maxwell’s stress tensor by the dielectric properties of plasma leading to the nonlinear (ponderomotive) force $$f_{\\text{NL}}$$ resulting in ultra-fast expanding plasma blocks by a dielectric explosion. Combining this with measured ultrahigh magnetic fields and the avalanche process opens an option for an environmentally absolute clean and economic boron fusion power reactor. Finally, this is supported also by other experiments with very high HB11 reactions under different conditions (Labauneet al., Nature Commun.4, 2506 (2013)).« less

Well-posedness of the Cauchy problem for models of large amplitude internal waves

NASA Astrophysics Data System (ADS)

Guyenne, Philippe; Lannes, David; Saut, Jean-Claude

2010-02-01

We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1-36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587-641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538-66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensional interfaces, this system is of hyperbolic type and its local well-posedness does not raise serious difficulties, although other issues (blow-up, loss of hyperbolicity, etc) turn out to be delicate. For two-dimensional interfaces, the system is nonlocal. Nevertheless, we prove that it conserves some properties of 'hyperbolic type' and show that the associated Cauchy problem is locally well posed in suitable Sobolev classes provided some natural restrictions are imposed on the data. These results are illustrated by numerical simulations with emphasis on the formation of shock waves.

Sublimation of amino acids with enantiomeric excess amplification

NASA Astrophysics Data System (ADS)

Guillemin, Jean-Claude; Guillemin, Jean-Claude; Bellec, Aurelien

The notion of chirality was first reported in 1848 by Pasteur, when he mechanically separated the two enantiomers of tartrate salts.[1] Amino acids are considered as the most important building blocks of life with sugars. On the Earth, the living systems are only composed of L- amino acids and D-sugars. Nowadays, the origin of homochirality on Earth is still unknown, and there are many theories trying to explain this phenomenon. Recently Cooks [2] and Feringa [3] reported that the sublimation of small amounts of L and D amino acid mixtures containing an excess of one of them leads to a huge enantiomeric excess (ee) enhancement of the sublimate. We reinvestigated these experiments to determine the rules leading to this enhancement. Starting from mixtures of L- and DL leucine we observed increasing and decreasing of the ee in function of the starting ratios. By the use of 13C derivatives, the origin of the sublimed enantiomers has been precised. Various parameters (L and D, or L and DL mixtures, dissolution in water before sublimation, . . . ) were studied. We also took into consideration the recently proposed hypothesis of the role played by the eutectic ee in the sublimation. [4] The application of these results to find an explanation of the enantiomeric excess in meteorites or in the Primitive Earth scenarios will be discussed. 1 Pasteur, L. Ann. Phys., 1848, 24, 442. 2 R. H. Perry, C. Wu, M. Nefliu, R. G. Cooks, Chem. Commun., 2007, 1071-1073. 3 S. P. Fletcher, R. B. C. Jagt, B. L. Feringa, Chem. Commun., 2007, 2578-2580. 4 D. G. Blackmond, M. Klussmannb Chem. Commun., 2007, 3990-3996.

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.

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.

A Priori Bound on the Velocity in Axially Symmetric Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Lei, Zhen; Navas, Esteban A.; Zhang, Qi S.

2016-01-01

Let v be the velocity of Leray-Hopf solutions to the axially symmetric three-dimensional Navier-Stokes equations. Under suitable conditions for initial values, we prove the following a priori bound |v(x, t)| ≤ C |ln r|^{1/2}/r^2, qquad 0 < r ≤ 1/2, where r is the distance from x to the z axis, and C is a constant depending only on the initial value. This provides a pointwise upper bound (worst case scenario) for possible singularities, while the recent papers (Chiun-Chuan et al., Commun PDE 34(1-3):203-232, 2009; Koch et al., Acta Math 203(1):83-105, 2009) gave a lower bound. The gap is polynomial order 1 modulo a half log term.

Quasistatic Evolution in Perfect Plasticity for General Heterogeneous Materials

NASA Astrophysics Data System (ADS)

Solombrino, Francesco

2014-04-01

Inspired by some recent developments in the theory of small-strain heterogeneous elastoplasticity, we both revisit and generalize the formulation of the quasistatic evolutionary problem in perfect plasticity given by Francfort and Giacomini (Commun Pure Appl Math, 65:1185-1241, 2012). We show that their definition of the plastic dissipation measure is equivalent to an abstract one, where it is defined as the supremum of the dualities between the deviatoric parts of admissible stress fields and the plastic strains. By means of this abstract definition, a viscoplastic approximation and variational techniques from the theory of rate-independent processes give the existence of an evolution satisfying an energy-dissipation balance and consequently Hill's maximum plastic work principle for an abstract and very large class of yield conditions.

On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions.

PubMed

Gerencsér, Máté; Jentzen, Arnulf; Salimova, Diyora

2017-11-01

In a recent article (Jentzen et al. 2016 Commun. Math. Sci. 14 , 1477-1500 (doi:10.4310/CMS.2016.v14.n6.a1)), it has been established that, for every arbitrarily slow convergence speed and every natural number d ∈{4,5,…}, there exist d -dimensional stochastic differential equations with infinitely often differentiable and globally bounded coefficients such that no approximation method based on finitely many observations of the driving Brownian motion can converge in absolute mean to the solution faster than the given speed of convergence. In this paper, we strengthen the above result by proving that this slow convergence phenomenon also arises in two ( d =2) and three ( d =3) space dimensions.

Temperature dependence of the A, B, and C excitons in ZnO over 5-400 K: A modulated reflectivity study.

NASA Astrophysics Data System (ADS)

Tsoi, S.; Cardona, M.; Lauck, R.; Alawadhi, H.; Lu, X.; Grimsditch, M.; Ramdas, A. K.

2005-03-01

Optical properties of ZnO, a wide gap semiconductor with wurtzite structure, have generated renewed interest in the material in the context of opto-electronic phenomena and applications. The A, B, and C excitons of ZnO, arising from the combined effects of crystal field and spin-orbit splittings of the valence band, are investigated in the temperature range 5- 400 K, exploiting electro-, photo-, and wavelength-modulated reflectivity. The specimens studied have natural isotopic composition. The temperature dependence of the A, B, and C excitonic band gaps, fitted with a two harmonic oscillator modelootnotetextM. Cardona, Phys. Status. Solidi b 220, 5 (2000); R. Pä'ssler, J. Appl. Phys. 89, 6235 (2001) following Manj'on et al.ootnotetextF. J. Manj'on et al., Solid State Commun. 128, 35 (2003), yields the magnitudes of the zero-point renormalizations 262 meV (A), 227 meV (B), and 249 meV (C), respectively. Isotopically controlled ZnO is currently being investigated to determine the isotopic mass dependence of the zero-point renormalizations.

A novel feedback algorithm for simulating controlled dynamics and confinement in the advanced reversed-field pinch

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

Dahlin, J.-E.; Scheffel, J.

2005-06-15

In the advanced reversed-field pinch (RFP), the current density profile is externally controlled to diminish tearing instabilities. Thus the scaling of energy confinement time with plasma current and density is improved substantially as compared to the conventional RFP. This may be numerically simulated by introducing an ad hoc electric field, adjusted to generate a tearing mode stable parallel current density profile. In the present work a current profile control algorithm, based on feedback of the fluctuating electric field in Ohm's law, is introduced into the resistive magnetohydrodynamic code DEBSP [D. D. Schnack and D. C. Baxter, J. Comput. Phys. 55,more » 485 (1984); D. D. Schnack, D. C. Barnes, Z. Mikic, D. S. Marneal, E. J. Caramana, and R. A. Nebel, Comput. Phys. Commun. 43, 17 (1986)]. The resulting radial magnetic field is decreased considerably, causing an increase in energy confinement time and poloidal {beta}. It is found that the parallel current density profile spontaneously becomes hollow, and that a formation, being related to persisting resistive g modes, appears close to the reversal surface.« less

Testing the Porcelli Sawtooth Trigger Module

NASA Astrophysics Data System (ADS)

Bateman, G.; Nave, M. F. F.; Parail, V.

2005-10-01

The Porcelli sawtooth trigger model [1] is implemented as a module for the National Transport Code Collaboration Module Library [2] and is tested using BALDUR and JETTO integrated modeling simulations of JET and other tokamak discharges. Statistical techniques are used to compute the average sawtooth period and the random scatter in sawtooth periods obtained during selected time intervals in the simulations compared with the corresponding statistical measures obtained from experimental data. It is found that the results are affected systematically by the fraction of magnetic reconnection during each sawtooth crash and by the model that is used for transport within the sawtooth mixing region. The physical processes that affect the sawtooth cycle in the simulations are found to involve an interaction among magnetic diffusion, reheating within the sawtooth mixing region, the instabilities that trigger a sawtooth crash in the Porcelli model, and the magnetic reconnection produced by each sawtooth crash. [1] F. Porcelli, et al., Plasma Phys. Contol. Fusion 38 (1996) 2163. [2] A.H. Kritz, et al., Comput. Phys. Commun. 164 (2004) 108; http://w3.pppl.gov/NTCC. Supported by DOE DE-FG02-92-ER-54141.

First Measurements of Deuterium-Tritium and Deuterium-Deuterium Fusion Reaction Yields in Ignition-Scalable Direct-Drive Implosions.

PubMed

Forrest, C J; Radha, P B; Knauer, J P; Glebov, V Yu; Goncharov, V N; Regan, S P; Rosenberg, M J; Sangster, T C; Shmayda, W T; Stoeckl, C; Gatu Johnson, M

2017-03-03

The deuterium-tritium (D-T) and deuterium-deuterium neutron yield ratio in cryogenic inertial confinement fusion (ICF) experiments is used to examine multifluid effects, traditionally not included in ICF modeling. This ratio has been measured for ignition-scalable direct-drive cryogenic DT implosions at the Omega Laser Facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)OPCOB80030-401810.1016/S0030-4018(96)00325-2] using a high-dynamic-range neutron time-of-flight spectrometer. The experimentally inferred yield ratio is consistent with both the calculated values of the nuclear reaction rates and the measured preshot target-fuel composition. These observations indicate that the physical mechanisms that have been proposed to alter the fuel composition, such as species separation of the hydrogen isotopes [D. T. Casey et al., Phys. Rev. Lett. 108, 075002 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.075002], are not significant during the period of peak neutron production in ignition-scalable cryogenic direct-drive DT implosions.

Investigation of the chiral antiferromagnetic Heisenberg model using projected entangled pair states

NASA Astrophysics Data System (ADS)

Poilblanc, Didier

2017-09-01

A simple spin-1/2 frustrated antiferromagnetic Heisenberg model (AFHM) on the square lattice—including chiral plaquette cyclic terms—was argued [A. E. B. Nielsen, G. Sierra, and J. I. Cirac, Nat. Commun. 4, 2864 (2013), 10.1038/ncomms3864] to host a bosonic Kalmeyer-Laughlin (KL) fractional quantum Hall ground state [V. Kalmeyer and R. B. Laughlin, Phys. Rev. Lett. 59, 2095 (1987), 10.1103/PhysRevLett.59.2095]. Here, we construct generic families of chiral projected entangled pair states (chiral PEPS) with low bond dimension (D =3 ,4 ,5 ) which, upon optimization, provide better variational energies than the KL Ansatz. The optimal D =3 PEPS exhibits chiral edge modes described by the Wess-Zumino-Witten SU(2) 1 model, as expected for the KL spin liquid. However, we find evidence that, in contrast to the KL state, the PEPS spin liquids have power-law dimer-dimer correlations and exhibit a gossamer long-range tail in the spin-spin correlations. We conjecture that these features are genuine to local chiral AFHM on bipartite lattices.

Theory-based transport simulations of TFTR L-mode temperature profiles

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

Bateman, G.

1992-03-01

The temperature profiles from a selection of Tokamak Fusion Test Reactor (TFTR) L-mode discharges (17{ital th} {ital European} {ital Conference} {ital on} {ital Controlled} {ital Fusion} {ital and} {ital Plasma} {ital Heating}, Amsterdam, 1990 (EPS, Petit-Lancy, Switzerland, 1990, p. 114)) are simulated with the 1 (1)/(2) -D baldur transport code (Comput. Phys. Commun. {bold 49}, 275 (1988)) using a combination of theoretically derived transport models, called the Multi-Mode Model (Comments Plasma Phys. Controlled Fusion {bold 11}, 165 (1988)). The present version of the Multi-Mode Model consists of effective thermal diffusivities resulting from trapped electron modes and ion temperature gradient ({eta}{submore » {ital i}}) modes, which dominate in the core of the plasma, together with resistive ballooning modes, which dominate in the periphery. Within the context of this transport model and the TFTR simulations reported here, the scaling of confinement with heating power comes from the temperature dependence of the {eta}{sub {ital i}} and trapped electron modes, while the scaling with current comes mostly from resistive ballooning modes.« less

X-ray continuum as a measure of pressure and fuel–shell mix in compressed isobaric hydrogen implosion cores

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

Epstein, R.; Goncharov, V. N.; Marshall, F. J.

Pressure, by definition, characterizes the conditions within an isobaric implosion core at peak compression [Gus'kov et al., Nucl. Fusion 16, 957 (1976); Betti et al., Phys. Plasmas 8, 5257 (2001)] and is a key parameter in quantifying its near-ignition performance [Lawson, Proc. Phys. Soc. London, B 70, 6 (1957); Betti et al., Phys. Plasmas 17, 058102 (2010); Goncharov et al., Phys. Plasmas 21, 056315 (2014); and Glenzer et al., Phys. Plasmas 19, 056318 (2012)]. At high spectral energy, where the x-ray emission from an imploded hydrogen core is optically thin, the emissivity profile can be inferred from the spatially resolvedmore » core emission. This emissivity, which can be modeled accurately under hot-core conditions, is dependent almost entirely on the pressure when measured within a restricted spectral range matched to the temperature range anticipated for the emitting volume. In this way, the hot core pressure at the time of peak emission can be inferred from the measured free-free emissivity profile. The pressure and temperature dependences of the x-ray emissivity and the neutron-production rate explain a simple scaling of the total filtered x-ray emission as a constant power of the total neutron yield for implosions of targets of similar design over a broad range of shell implosion isentropes. This scaling behavior has been seen in implosion simulations and is confirmed by measurements of high-isentrope implosions [Sangster et al., Phys. Plasmas 20, 056317 (2013)] on the OMEGA laser system [Boehly et al., Opt. Commun. 133, 495 (1997)]. Attributing the excess emission from less-stable, low-isentrope implosions, above the level expected from this neutron-yield scaling, to the higher emissivity of shell carbon mixed into the implosion's central hot spot, the hot-spot “fuel–shell” mix mass can be inferred.« less

X-ray continuum as a measure of pressure and fuel–shell mix in compressed isobaric hydrogen implosion cores

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

Epstein, R.; Goncharov, V. N.; Marshall, F. J.

Pressure, by definition, characterizes the conditions within an isobaric implosion core at peak compression [Gus’kov et al., Nucl. Fusion 16, 957 (1976); Betti et al., Phys. Plasmas 8, 5257 (2001)] and is a key parameter in quantifying its near-ignition performance [Lawson, Proc. Phys. Soc. London, B 70, 6 (1957); Betti et al., Phys. Plasmas 17, 058102 (2010); Goncharov et al., Phys. Plasmas 21, 056315 (2014); and Glenzer et al., Phys. Plasmas 19, 056318 (2012)]. At high spectral energy, where the x-ray emission from an imploded hydrogen core is optically thin, the emissivity profile can be inferred from the spatially resolvedmore » core emission. This emissivity, which can be modeled accurately under hot-core conditions, is dependent almost entirely on the pressure when measured within a restricted spectral range matched to the temperature range anticipated for the emitting volume. In this way, the hot core pressure at the time of peak emission can be inferred from the measured free-free emissivity profile. The pressure and temperature dependences of the x-ray emissivity and the neutron-production rate explain a simple scaling of the total filtered x-ray emission as a constant power of the total neutron yield for implosions of targets of similar design over a broad range of shell implosion isentropes. This scaling behavior has been seen in implosion simulations and is confirmed by measurements of high-isentrope implosions [Sangster et al., Phys. Plasmas 20, 056317 (2013)] on the OMEGA laser system [Boehly et al., Opt. Commun. 133, 495 (1997)]. Attributing the excess emission from less-stable, low-isentrope implosions, above the level expected from this neutron-yield scaling, to the higher emissivity of shell carbon mixed into the implosion’s central hot spot, the hot-spot “fuel–shell” mix mass can be inferred.« less

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).

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.

Stress formulation in the all-electron full-potential linearized augmented plane wave method

NASA Astrophysics Data System (ADS)

Nagasako, Naoyuki; Oguchi, Tamio

2012-02-01

Stress formulation in the linearlized augmented plane wave (LAPW) method has been proposed in 2002 [1] as an extension of the force formulation in the LAPW method [2]. However, pressure calculations only for Al and Si were reported in Ref.[1] and even now stress calculations have not yet been fully established in the LAPW method. In order to make it possible to efficiently relax lattice shape and atomic positions simultaneously and to precisely evaluate the elastic constants in the LAPW method, we reformulate stress formula in the LAPW method with the Soler-Williams representation [3]. Validity of the formulation is tested by comparing the pressure obtained as the trace of stress tensor with that estimated from total energies for a wide variety of material systems. Results show that pressure is estimated within the accuracy of less than 0.1 GPa. Calculations of the shear elastic constant show that the shear components of the stress tensor are also precisely computed with the present formulation [4].[4pt] [1] T. Thonhauser et al., Solid State Commun. 124, 275 (2002).[0pt] [2] R. Yu et al., Phys. Rev. B 43, 6411 (1991).[0pt] [3] J. M. Soler and A. R. Williams, Phys. Rev. B 40, 1560 (1989).[0pt] [4] N. Nagasako and T. Oguchi, J. Phys. Soc. Jpn. 80, 024701 (2011).

Effects of alpha stopping power modelling on the ignition threshold in a directly-driven inertial confinement fusion capsule

NASA Astrophysics Data System (ADS)

Temporal, Mauro; Canaud, Benoit; Cayzac, Witold; Ramis, Rafael; Singleton, Robert L.

2017-05-01

The alpha-particle energy deposition mechanism modifies the ignition conditions of the thermonuclear Deuterium-Tritium fusion reactions, and constitutes a key issue in achieving high gain in Inertial Confinement Fusion implosions. One-dimensional hydrodynamic calculations have been performed with the code Multi-IFE [R. Ramis, J. Meyer-ter-Vehn, Comput. Phys. Commun. 203, 226 (2016)] to simulate the implosion of a capsule directly irradiated by a laser beam. The diffusion approximation for the alpha energy deposition has been used to optimize three laser profiles corresponding to different implosion velocities. A Monte-Carlo package has been included in Multi-IFE to calculate the alpha energy transport, and in this case the energy deposition uses both the LP [C.K. Li, R.D. Petrasso, Phys. Rev. Lett. 70, 3059 (1993)] and the BPS [L.S. Brown, D.L. Preston, R.L. Singleton Jr., Phys. Rep. 410, 237 (2005)] stopping power models. Homothetic transformations that maintain a constant implosion velocity have been used to map out the transition region between marginally-igniting and high-gain configurations. The results provided by the two models have been compared and it is found that - close to the ignition threshold - in order to produce the same fusion energy, the calculations performed with the BPS model require about 10% more invested energy with respect to the LP model.

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.

Numerical solution of a spatio-temporal gender-structured model for hantavirus infection in rodents.

PubMed

Bürger, Raimund; Chowell, Gerardo; Gavilán, Elvis; Mulet, Pep; Villada, Luis M

2018-02-01

In this article we describe the transmission dynamics of hantavirus in rodents using a spatio-temporal susceptible-exposed-infective-recovered (SEIR) compartmental model that distinguishes between male and female subpopulations [L.J.S. Allen, R.K. McCormack and C.B. Jonsson, Bull. Math. Biol. 68 (2006), 511--524]. Both subpopulations are assumed to differ in their movement with respect to local variations in the densities of their own and the opposite gender group. Three alternative models for the movement of the male individuals are examined. In some cases the movement is not only directed by the gradient of a density (as in the standard diffusive case), but also by a non-local convolution of density values as proposed, in another context, in [R.M. Colombo and E. Rossi, Commun. Math. Sci., 13 (2015), 369--400]. An efficient numerical method for the resulting convection-diffusion-reaction system of partial differential equations is proposed. This method involves techniques of weighted essentially non-oscillatory (WENO) reconstructions in combination with implicit-explicit Runge-Kutta (IMEX-RK) methods for time stepping. The numerical results demonstrate significant differences in the spatio-temporal behavior predicted by the different models, which suggest future research directions.

Dissipative behavior of some fully non-linear KdV-type equations

NASA Astrophysics Data System (ADS)

Brenier, Yann; Levy, Doron

2000-03-01

The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

Optimal Time-decay Estimates for the Compressible Navier-Stokes Equations in the Critical L p Framework

NASA Astrophysics Data System (ADS)

Danchin, Raphaël; Xu, Jiang

2017-04-01

The global existence issue for the isentropic compressible Navier-Stokes equations in the critical regularity framework was addressed in Danchin (Invent Math 141(3):579-614, 2000) more than 15 years ago. However, whether (optimal) time-decay rates could be shown in critical spaces has remained an open question. Here we give a positive answer to that issue not only in the L 2 critical framework of Danchin (Invent Math 141(3):579-614, 2000) but also in the general L p critical framework of Charve and Danchin (Arch Ration Mech Anal 198(1):233-271, 2010), Chen et al. (Commun Pure Appl Math 63(9):1173-1224, 2010), Haspot (Arch Ration Mech Anal 202(2):427-460, 2011): we show that under a mild additional decay assumption that is satisfied if, for example, the low frequencies of the initial data are in {L^{p/2}(Rd)}, the L p norm (the slightly stronger dot B^0_{p,1} norm in fact) of the critical global solutions decays like t^{-d(1/p - 1/4} for {tto+∞,} exactly as firstly observed by Matsumura and Nishida in (Proc Jpn Acad Ser A 55:337-342, 1979) in the case p = 2 and d = 3, for solutions with high Sobolev regularity. Our method relies on refined time weighted inequalities in the Fourier space, and is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics.

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

Sublayer of Prandtl Boundary Layers

NASA Astrophysics Data System (ADS)

Grenier, Emmanuel; Nguyen, Toan T.

2018-03-01

The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit {ν \\to 0} . In Grenier (Commun Pure Appl Math 53(9):1067-1091, 2000), one of the authors proved that there exists no asymptotic expansion involving one of Prandtl's boundary layer, with thickness of order {√{ν}} , which describes the inviscid limit of Navier-Stokes equations. The instability gives rise to a viscous boundary sublayer whose thickness is of order {ν^{3/4}} . In this paper, we point out how the stability of the classical Prandtl's layer is linked to the stability of this sublayer. In particular, we prove that the two layers cannot both be nonlinearly stable in L^∞. That is, either the Prandtl's layer or the boundary sublayer is nonlinearly unstable in the sup norm.

Poincaré chaos and unpredictable functions

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2017-07-01

The results of this study are continuation of the research of Poincaré chaos initiated in the papers (M. Akhmet and M.O. Fen, Commun Nonlinear Sci Numer Simulat 40 (2016) 1-5; M. Akhmet and M.O. Fen, Turk J Math, doi:10.3906/mat-1603-51, in press). We focus on the construction of an unpredictable function, continuous on the real axis. As auxiliary results, unpredictable orbits for the symbolic dynamics and the logistic map are obtained. By shaping the unpredictable function as well as Poisson function we have performed the first step in the development of the theory of unpredictable solutions for differential and discrete equations. The results are preliminary ones for deep analysis of chaos existence in differential and hybrid systems. Illustrative examples concerning unpredictable solutions of differential equations are provided.

Applications and Implications of Fractional Dynamics for Dielectric Relaxation

NASA Astrophysics Data System (ADS)

Hilfer, R.

This article summarizes briefly the presentation given by the author at the NATO Advanced Research Workshop on "Broadband Dielectric Spectroscopy and its Advanced Technological Applications", held in Perpignan, France, in September 2011. The purpose of the invited presentation at the workshop was to review and summarize the basic theory of fractional dynamics (Hilfer, Phys Rev E 48:2466, 1993; Hilfer and Anton, Phys Rev E Rapid Commun 51:R848, 1995; Hilfer, Fractals 3(1):211, 1995; Hilfer, Chaos Solitons Fractals 5:1475, 1995; Hilfer, Fractals 3:549, 1995; Hilfer, Physica A 221:89, 1995; Hilfer, On fractional diffusion and its relation with continuous time random walks. In: Pekalski et al. (eds) Anomalous diffusion: from basis to applications. Springer, Berlin, p 77, 1999; Hilfer, Fractional evolution equations and irreversibility. In: Helbing et al. (eds) Traffic and granular flow'99. Springer, Berlin, p 215, 2000; Hilfer, Fractional time evolution. In: Hilfer (ed) Applications of fractional calculus in physics. World Scientific, Singapore, p 87, 2000; Hilfer, Remarks on fractional time. In: Castell and Ischebeck (eds) Time, quantum and information. Springer, Berlin, p 235, 2003; Hilfer, Physica A 329:35, 2003; Hilfer, Threefold introduction to fractional derivatives. In: Klages et al. (eds) Anomalous transport: foundations and applications. Wiley-VCH, Weinheim, pp 17-74, 2008; Hilfer, Foundations of fractional dynamics: a short account. In: Klafter et al. (eds) Fractional dynamics: recent advances. World Scientific, Singapore, p 207, 2011) and demonstrate its relevance and application to broadband dielectric spectroscopy (Hilfer, J Phys Condens Matter 14:2297, 2002; Hilfer, Chem Phys 284:399, 2002; Hilfer, Fractals 11:251, 2003; Hilfer et al., Fractional Calc Appl Anal 12:299, 2009). It was argued, that broadband dielectric spectroscopy might be useful to test effective field theories based on fractional dynamics.

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.

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.

Atomic data from the IRON project. LXVI. Electron impact excitation of Fe18+

NASA Astrophysics Data System (ADS)

Butler, K.; Badnell, N. R.

2008-10-01

Context: Accurate electron collisional data are required for the analysis of the Fe xix astrophysical spectrum, in particular in the sun. Such an analysis can provide information on the physical characteristics of the coronal plasma. Aims: An extensive target is used in an R-matrix scattering calculation to provide the necessary data for Fe18+. The use of the R-matrix method includes the resonance contribution lacking in the distorted wave approach and the large target improves the accuracy of the close-coupling approximation. Methods: The R-Matrix package described by Berrington et al. (1995, Comput. Phys. Commun., 92, 290) as provided by the UK RmaX project has been used to calculate electron collisional data among 342 levels of Fe18+. We have used the intermediate-coupling frame-transformation (ICFT) method (Griffin et al. 1998, J. Phys. B: At. Mol. Opt. Phys., 31, 3713) to transform data obtained in a 166 term LS-coupling calculation. Contributions from the mass and Darwin interactions have also been included in the Hamiltonian. Results: Collision stengths for all transitions between the 342 levels of Fe18+ are presented. They are tabulated over a wide range of electron temperatures of astrophysical interest. The results are compared with the earlier Iron Project work of Butler & Zeippen (2001, A&A, 372, 1083) and also with that of McLaughlin et al. (2001, J. Phys. B: At. Mol. Opt. Phys., 34, 4521) and Landi & Gu (2006, ApJ, 640, 1171). The agreement is reasonable for the low-lying transitions. Larger differences are found for the more highly excited states. Full Table 4 is only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/489/1369

Progress in Direct-Drive Inertial Confinement Fusion

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

McCrory, R.L.; Meyerhofer, D.D.; Betti, R.

Significant progress in direct-drive inertial confinement fusion (ICF) research has been made since the completion of the 60-beam, 30-kJ UV OMEGA Laser System [T. R. Boehly, Opt. Commun. 133, 495 (1997)] in 1995. A theory of ignition requirements, applicable to any ICF concept, has been developed. Detailed understanding of laser-plasma coupling, electron thermal transport, and hot-electron preheating has lead to the measurement of neutron-averaged areal densities of ~200 mg/cm^2 in cryogenic target implosions. These correspond to an estimated peak fuel density in excess of 100 g/cm^3 and are in good agreement with hydrodynamic simulations. The implosions were performed using anmore » 18-kJ drive pulse designed to put the converging fuel on an adiabat of two. The polar-drive concept will allow direct-drive-ignition research on the National Ignition Facility while it is configured for indirect drive. Advanced ICF ignition concepts—fast ignition [Tabak et al., Phys. Plasmas 1, 1626 (1994)] and shock ignition [R. Betti et al., Phys. Rev. Lett. 98, 155001 (2007)]—have the potential to significantly reduce ignition driver energies and/or provide higher target gain.« less

Progress in direct-drive inertial confinement fusion

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

McCrory, R. L.; Meyerhofer, D. D.; Betti, R.

Significant progress in direct-drive inertial confinement fusion (ICF) research has been made since the completion of the 60-beam, 30-kJ{sub UV} OMEGA Laser System [Boehly, Opt. Commun. 133, 495 (1997)] in 1995. A theory of ignition requirements, applicable to any ICF concept, has been developed. Detailed understanding of laser-plasma coupling, electron thermal transport, and hot-electron preheating has lead to the measurement of neutron-averaged areal densities of {approx}200 mg/cm{sup 2} in cryogenic target implosions. These correspond to an estimated peak fuel density in excess of 100 g/cm{sup 3} and are in good agreement with hydrodynamic simulations. The implosions were performed using anmore » 18-kJ drive pulse designed to put the converging fuel on an adiabat of two. The polar-drive concept will allow direct-drive-ignition research on the National Ignition Facility while it is configured for indirect drive. Advanced ICF ignition concepts - fast ignition [Tabak et al., Phys. Plasmas 1, 1626 (1994)] and shock ignition [Betti et al., Phys. Rev. Lett. 98, 155001 (2007)] - have the potential to significantly reduce ignition driver energies and/or provide higher target gain.« less

Ion temperature gradient driven transport in tokamaks with square shaping

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

Joiner, N.; Dorland, W.

2010-06-15

Advanced tokamak schemes which may offer significant improvement to plasma confinement on the usual large aspect ratio Dee-shaped flux surface configuration are of great interest to the fusion community. One possibility is to introduce square shaping to the flux surfaces. The gyrokinetic code GS2[Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1996)] is used to study linear stability and the resulting nonlinear thermal transport of the ion temperature gradient driven (ITG) mode in tokamak equilibria with square shaping. The maximum linear growth rate of ITG modes is increased by negative squareness (diamond shaping) and reduced by positive values (square shaping).more » The dependence of thermal transport produced by saturated ITG instabilities on squareness is not as clear. The overall trend follows that of the linear instability, heat and particle fluxes increase with negative squareness and decrease with positive squareness. This is contradictory to recent experimental results [Holcomb et al., Phys. Plasmas 16, 056116 (2009)] which show a reduction in transport with negative squareness. This may be reconciled as a reduction in transport (consistent with the experiment) is observed at small negative values of the squareness parameter.« less

Study of Second Stability for Global ITG Modes in MHD-stable Equilibria

NASA Astrophysics Data System (ADS)

Fivaz, Mathieu; Sauter, Olivier; Appert, Kurt; Tran, Trach-Minh; Vaclavik, Jan

1997-11-01

We study finite pressure effects on the Ion Temperature Gradient (ITG) instabilities; these modes are stabilized when the magnetic field gradient is reversed at high β [1]. This second stability regime for ITG modes is studied in details with a global linear gyrokinetic Particle-In-Cell code which takes the full toroidal MHD equilibrium data from the equilibrium solver CHEASE [2]. Both the trapped-ion and the toroidal ITG regimes are explored. In contrast to second stability for MHD ballooning modes, low magnetic shear and high values of the safety factor do not facilitate strongly the access to the second-stable ITG regime. The consequences for anomalous ion heat transport in tokamaks are explored. We use the results to find optimized configurations that are stable to ideal MHD modes for both the long (kink) and short (ballooning) wavelengths and where the ITG modes are stable or have very low growth rates; such configurations might present very low level of anomalous transport. [1] M. Fivaz, T.M. Tran, K. Appert, J. Vaclavik and S. E. Parker, Phys. Rev. Lett. 78, 1997, p. 3471 [2] H. Lütjens, A. Bondeson and O. Sauter, Comput. Phys. Commun. 97, 1996, p. 219

Magnetism and transport properties of layered rare-earth cobaltates Ln{sub 0.3}CoO{sub 2}

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

Knížek, K., E-mail: knizek@fzu.cz; Novák, P.; Jirák, Z.

2015-05-07

The ab-initio (GGA+U) electronic structure calculations of layered cobaltates Ln{sub 0.3}CoO{sub 2} (Ln = La, Pr, Nd) prepared by ionic exchange from Na{sub 0.90}CoO{sub 2} precursors have been performed. The data are used for numerical modeling of Seebeck coefficient within Boltzmann transport theory using BoltzTraP program [G. K. H. Madsen and D. J. Singh, Comput. Phys. Commun. 175, 67 (2006)], as well as for determination of the crystal field split levels of rare-earth ions using a method based on a transformation of Bloch states into the basis of Wannier functions [P. Novák et al., Phys. Rev. B 87, 205139 (2013)]. An overallmore » agreement with observed magnetism and transport properties is obtained. In particular, the high p-type thermopower is well reproduced in a broad temperature range, but instead of theoretical linear decrease down to the lowest temperatures, the real systems exhibit an anomalous change of Seebeck sign, which might be related to the change of bare metallic carriers into the polaronic ones.« less

Finite-beta equilibria for Wendelstein 7-X configurations using the Princeton Iterative Equilibrium Solver code

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

Arndt, S.; Merkel, P.; Monticello, D.A.

Fixed- and free-boundary equilibria for Wendelstein 7-X (W7-X) [W. Lotz {ital et al.}, {ital Plasma Physics and Controlled Nuclear Fusion Research 1990} (Proc. 13th Int. Conf. Washington, DC, 1990), (International Atomic Energy Agency, Vienna, 1991), Vol. 2, p. 603] configurations are calculated using the Princeton Iterative Equilibrium Solver (PIES) [A. H. Reiman {ital et al.}, Comput. Phys. Commun., {bold 43}, 157 (1986)] to deal with magnetic islands and stochastic regions. Usually, these W7-X configurations require a large number of iterations for PIES convergence. Here, two methods have been successfully tested in an attempt to decrease the number of iterations neededmore » for convergence. First, periodic sequences of different blending parameters are used. Second, the initial guess is vastly improved by using results of the Variational Moments Equilibrium Code (VMEC) [S. P. Hirshmann {ital et al.}, Phys. Fluids {bold 26}, 3553 (1983)]. Use of these two methods have allowed verification of the Hamada condition and tendency of {open_quotes}self-healing{close_quotes} of islands has been observed. {copyright} {ital 1999 American Institute of Physics.}« less

First-Principles Calculations of Lattice Dynamics in La_2CuO_4

NASA Astrophysics Data System (ADS)

Wang, C.-Z.; Yu, Rici; Krakauer, Henry

1998-03-01

To investigate wavevector-dependent lattice vibrational properties of the high-temperature cuprate superconductor La_2-xSr_xCuO_4, we have performed first principles calculations for tetragonal I4/mmm La_2CuO_4, using the linear response LAPW method(R. Yu and H. Krakauer, Phys. Rev. B 49), 4467 (1994). Phonon frequencies and polarization vectors are obtained throughout the Brillouin zone. Generally good agreement is obtained with experiment, but we underestimate the frequencies of the low lying modes, which involve either motions of the apical oxygen atoms parallel to the CuO2 planes or motions of the plane O atoms along the c-axis. The discrepancy may be due to anharmonic coupling of these modes(R. Cohen, W. Pickett, and H. Krakauer, Phys. Rev. Lett. 62), 831 (1989)^,(D. J. Singh, Solid State Commun. 98), 575 (1996). The X point tilt phonon mode is found to be the most unstable mode, consistent with previous frozen phonon calculations^3 and the observed phase transition to the orthorhombic structure at low temperature. The results will be discussed in comparison with previous calculations^3,4 and experiment.

Effects of plasma shaping on nonlinear gyrokinetic turbulence

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

Belli, E. A.; Hammett, G. W.; Dorland, W.

The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the GS2 code [M. Kotschenreuther, G. Rewoldt, and W. M. Tang, Comput. Phys. Commun. 88, 128 (1995); W. Dorland, F. Jenko, M. Kotschenreuther, and B. N. Rogers, Phys. Rev. Lett. 85, 5579 (2000)]. Studies of the scaling of nonlinear turbulence with shaping parameters are performed using analytic equilibria based on interpolations of representative shapes of the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)]. High shaping is found to be a stabilizing influence on bothmore » the linear ion-temperature-gradient (ITG) instability and the nonlinear ITG turbulence. For the parameter regime studied here, a scaling of the heat flux with elongation of {chi}{approx}{kappa}{sup -1.5} or {kappa}{sup -2.0}, depending on the triangularity, is observed at fixed average temperature gradient. While this is not as strong as empirical elongation scalings, it is also found that high shaping results in a larger Dimits upshift of the nonlinear critical temperature gradient due to an enhancement of the Rosenbluth-Hinton residual zonal flows.« less

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

Oscillatory system I-, H2O2, HClO4: the modified form of the Bray-Liebhafsky reaction.

PubMed

Olexová, Anna; Mrákavová, Marta; Melichercík, Milan; Treindl, L'udovít

2010-07-08

The kinetics of iodide ions oxidation with hydrogen peroxide in solutions of perchloric acid at temperature of 60 degrees C has been studied in detail. We have found conditions under which this reaction proceeds oscillatory. The Bray-Liebhafsky (BL) oscillatory reaction started by the oxidation of iodide ions with hydrogen peroxide is described for the first time. The described results support our assumption (Olexová, A.; Mrákavová, M.; Melichercík, M.; Treindl, L. Collect. Czech. Chem. Commun. 2006, 71, 91-106) that singlet oxygen ((1)O(2)) is an important intermediate of the BL oscillatory reaction in the sense of the Noyes-Treindl (N-T) skeleton mechanism (Treindl, L.; Noyes, R.M. J. Phys. Chem. 1993, 97, 11354-11362).

Boundary modelling of the stellarator Wendelstein 7-X

NASA Astrophysics Data System (ADS)

Renner, H.; Strumberger, E.; Kisslinger, J.; Nührenberg, J.; Wobig, H.

1997-02-01

To justify the design of the divertor plates in W7-X the magnetic fields of finite-β HELIAS equilibria for the so-called high-mirror case have been computed for various average β-values up to < β > = 0.04 with the NEMEC free-boundary equilibrium code [S.P. Hirshman, W.I. van Rij and W.I. Merkel, Comput. Phys. Commun. 43 (1986) 143] in combination with the newly developed MFBE (magnetic field solver for finite-beta equilibria) code. In a second study the unloading of the target plates by radiation was investigated. The B2 code [B.J. Braams, Ph.D. Thesis, Rijksuniversiteit Utrecht (1986)] was applied for the first time to stellarators to provide of a self-consistent modelling of the SOL including effects of neutrals and impurities.

Differentiability of energy functionals in spin-density-functional theory

NASA Astrophysics Data System (ADS)

Gál, Tamás

2007-06-01

Recently, nonuniqueness of external electrostatic and magnetic fields yielding a given many-electron ground state has been pointed out [K. Capelle and G. Vignale, Phys. Rev. Lett. 86, 5546 (2001); H. Eschrig and W. E. Pickett, Solid State Commun. 118, 123 (2001)], implying the nondifferentiability of the ground-state energy functional of spin-density-functional theory (SDFT), on the basis of which the applicability of widely used DFT methods in SDFT has been put into question and the need for a critical reexamination of those applications has been concluded. Here it is shown, for collinear magnetic fields, that the nonuniqueness of the external potentials in SDFT does not imply the nonexistence of number-conserving functional derivatives as well, with the use of which therefore problems arising from the nondifferentiability are avoided.

Anomalous diffusion in the evolution of soccer championship scores: Real data, mean-field analysis, and an agent-based model

NASA Astrophysics Data System (ADS)

da Silva, Roberto; Vainstein, Mendeli H.; Gonçalves, Sebastián; Paula, Felipe S. F.

2013-08-01

Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva , Comput. Phys. Commun.CPHCBZ0010-465510.1016/j.cpc.2012.10.030 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.

Log-gamma directed polymer with fixed endpoints via the replica Bethe Ansatz

NASA Astrophysics Data System (ADS)

Thiery, Thimothée; Le Doussal, Pierre

2014-10-01

We study the model of a discrete directed polymer (DP) on a square lattice with homogeneous inverse gamma distribution of site random Boltzmann weights, introduced by Seppalainen (2012 Ann. Probab. 40 19-73). The integer moments of the partition sum, \\overline{Z^n} , are studied using a transfer matrix formulation, which appears as a generalization of the Lieb-Liniger quantum mechanics of bosons to discrete time and space. In the present case of the inverse gamma distribution the model is integrable in terms of a coordinate Bethe Ansatz, as discovered by Brunet. Using the Brunet-Bethe eigenstates we obtain an exact expression for the integer moments of \\overline{Z^n} for polymers of arbitrary lengths and fixed endpoint positions. Although these moments do not exist for all integer n, we are nevertheless able to construct a generating function which reproduces all existing integer moments and which takes the form of a Fredholm determinant (FD). This suggests an analytic continuation via a Mellin-Barnes transform and we thereby propose a FD ansatz representation for the probability distribution function (PDF) of Z and its Laplace transform. In the limit of a very long DP, this ansatz yields that the distribution of the free energy converges to the Gaussian unitary ensemble (GUE) Tracy-Widom distribution up to a non-trivial average and variance that we calculate. Our asymptotic predictions coincide with a result by Borodin et al (2013 Commun. Math. Phys. 324 215-32) based on a formula obtained by Corwin et al (2011 arXiv:1110.3489) using the geometric Robinson-Schensted-Knuth (gRSK) correspondence. In addition we obtain the dependence on the endpoint position and the exact elastic coefficient at a large time. We argue the equivalence between our formula and that of Borodin et al. As we will discuss, this provides a connection between quantum integrability and tropical combinatorics.

First passage times for a tracer particle in single file diffusion and fractional Brownian motion.

PubMed

Sanders, Lloyd P; Ambjörnsson, Tobias

2012-05-07

We investigate the full functional form of the first passage time density (FPTD) of a tracer particle in a single-file diffusion (SFD) system whose population is: (i) homogeneous, i.e., all particles having the same diffusion constant and (ii) heterogeneous, with diffusion constants drawn from a heavy-tailed power-law distribution. In parallel, the full FPTD for fractional Brownian motion [fBm-defined by the Hurst parameter, H ∈ (0, 1)] is studied, of interest here as fBm and SFD systems belong to the same universality class. Extensive stochastic (non-Markovian) SFD and fBm simulations are performed and compared to two analytical Markovian techniques: the method of images approximation (MIA) and the Willemski-Fixman approximation (WFA). We find that the MIA cannot approximate well any temporal scale of the SFD FPTD. Our exact inversion of the Willemski-Fixman integral equation captures the long-time power-law exponent, when H ≥ 1/3, as predicted by Molchan [Commun. Math. Phys. 205, 97 (1999)] for fBm. When H < 1/3, which includes homogeneous SFD (H = 1/4), and heterogeneous SFD (H < 1/4), the WFA fails to agree with any temporal scale of the simulations and Molchan's long-time result. SFD systems are compared to their fBm counter parts; and in the homogeneous system both scaled FPTDs agree on all temporal scales including also, the result by Molchan, thus affirming that SFD and fBm dynamics belong to the same universality class. In the heterogeneous case SFD and fBm results for heterogeneity-averaged FPTDs agree in the asymptotic time limit. The non-averaged heterogeneous SFD systems display a lack of self-averaging. An exponential with a power-law argument, multiplied by a power-law pre-factor is shown to describe well the FPTD for all times for homogeneous SFD and sub-diffusive fBm systems.

Bipolar Spintronics: From magnetic diodes to magnetic bipolar transistors

NASA Astrophysics Data System (ADS)

Zutic, Igor

2004-03-01

We develop a theory of bipolar (electrons and holes) spin-polarized transport [1,2] in semiconductors and discuss its implications for spintronic devices [3]. In our proposal for magnetic bipolar transistors [4,5] we show how bipolar spintronics can lead to spin and magnetic field controlled active devices, not limited by the magnetoresistive effects used in all-metallic structures [3]. We focus on magnetic p-n diodes [1,2] with spatially dependent spin splitting (Zeeman or exchange) of carrier bands. An exchange splitting can be provided by ferromagnetic semiconductors [6], while a large Zeeman splitting can be realized in the presence of magnetic field in magnetically doped or narrow band gap semiconductors [3]. Our theory of magnetic diodes [1,2] can be directly applied to magnetic bipolar transistors--the three-terminal devices which consist of two magnetic p-n diodes connected in series [4,5]. Predictions of exponentially large magnetoresistance [1] and a strong coupling between the spin and charge transport leading to the spin-voltaic effect [1,7] for magnetic diodes are also relevant for magnetic bipolar transistors. In particular, in n-p-n transistors, we show the importance of considering the nonequilibrium spin leading to the spin-voltaic effect. In addition to the applied magnetic filed, the injected nonequilibrium spin can be used to dynamically control the current amplification (gain). Recent experimental progress [8,9] supports the viability of our theoretical proposals. [1] I. Zutic, J. Fabian, S. Das Sarma, Phys. Rev. Lett. 88, 066603 (2002). [2] J. Fabian, I. Zutic, S. Das Sarma, Phys. Rev. B 66, 165301 (2002). [3] I. Zutic, J. Fabian, S. Das Sarma, Rev. Mod. Phys., in press. [4] J. Fabian, I. Zutic, S. Das Sarma, cond-mat/0211639; cond-mat/0307014, Appl. Phys. Lett., in press. [5] J. Fabian and I. Zutic, cond-mat/0311456. [6] H. Ohno, Science 281, 951 (1998). [7] I. Zutic, J. Fabian, S. Das Sarma, Appl. Phys. Lett. 82, 221 (2003). [8] N. Samarth, S. H. Chun, K. C. Ku, S. J. Potashnik, P. Schiffer, Solid State Commun. 127, 173 (2003). [9] F. Tsui, L. Ma, L. He, Appl. Phys. 83, 954 (2003).

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.

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.

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

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

NASA Astrophysics Data System (ADS)

Na, D.-Y.; Moon, H.; Omelchenko, Y. A.; Teixeira, F. L.

2018-01-01

Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

Hohlraum-driven mid-Z (SiO2) double-shell implosions on the omega laser facility and their scaling to NIF.

PubMed

Robey, H F; Amendt, P A; Milovich, J L; Park, H-S; Hamza, A V; Bono, M J

2009-10-02

High-convergence, hohlraum-driven implosions of double-shell capsules using mid-Z (SiO2) inner shells have been performed on the OMEGA laser facility [T. R. Boehly, Opt. Commun. 133, 495 (1997)]. These experiments provide an essential extension of the results of previous low-Z (CH) double-shell implosions [P. A. Amendt, Phys. Rev. Lett. 94, 065004 (2005)] to materials of higher density and atomic number. Analytic modeling, supported by highly resolved 2D numerical simulations, is used to account for the yield degradation due to interfacial atomic mixing. This extended experimental database from OMEGA enables a validation of the mix model, and provides a means for quantitatively assessing the prospects for high-Z double-shell implosions on the National Ignition Facility [Paisner, Laser Focus World 30, 75 (1994)].

A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials

NASA Astrophysics Data System (ADS)

Deift, P.; Kriecherbauer, T.; McLaughlin, K. T.-R.; Venakides, S.; Zhou, X.

2001-08-01

A few years ago the authors introduced a new approach to study asymptotic questions for orthogonal polynomials. In this paper we give an overview of our method and review the results which have been obtained in Deift et al. (Internat. Math. Res. Notices (1997) 759, Comm. Pure Appl. Math. 52 (1999) 1491, 1335), Deift (Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes, Vol. 3, New York University, 1999), Kriecherbauer and McLaughlin (Internat. Math. Res. Notices (1999) 299) and Baik et al. (J. Amer. Math. Soc. 12 (1999) 1119). We mainly consider orthogonal polynomials with respect to weights on the real line which are either (1) Freud-type weights d[alpha](x)=e-Q(x) dx (Q polynomial or Q(x)=x[beta], [beta]>0), or (2) varying weights d[alpha]n(x)=e-nV(x) dx (V analytic, limx-->[infinity] V(x)/logx=[infinity]). We obtain Plancherel-Rotach-type asymptotics in the entire complex plane as well as asymptotic formulae with error estimates for the leading coefficients, for the recurrence coefficients, and for the zeros of the orthogonal polynomials. Our proof starts from an observation of Fokas et al. (Comm. Math. Phys. 142 (1991) 313) that the orthogonal polynomials can be determined as solutions of certain matrix valued Riemann-Hilbert problems. We analyze the Riemann-Hilbert problems by a steepest descent type method introduced by Deift and Zhou (Ann. Math. 137 (1993) 295) and further developed in Deift and Zhou (Comm. Pure Appl. Math. 48 (1995) 277) and Deift et al. (Proc. Nat. Acad. Sci. USA 95 (1998) 450). A crucial step in our analysis is the use of the well-known equilibrium measure which describes the asymptotic distribution of the zeros of the orthogonal polynomials.

Effective aperture of X-ray compound refractive lenses.

PubMed

Kohn, V G

2017-05-01

A new definition of the effective aperture of the X-ray compound refractive lens (CRL) is proposed. Both linear (one-dimensional) and circular (two-dimensional) CRLs are considered. It is shown that for a strongly absorbing CRL the real aperture does not influence the focusing properties and the effective aperture is determined by absorption. However, there are three ways to determine the effective aperture in terms of transparent CRLs. In the papers by Kohn [(2002). JETP Lett. 76, 600-603; (2003). J. Exp. Theor. Phys. 97, 204-215; (2009). J. Surface Investig. 3, 358-364; (2012). J. Synchrotron Rad. 19, 84-92; Kohn et al. (2003). Opt. Commun. 216, 247-260; (2003). J. Phys. IV Fr, 104, 217-220], the FWHM of the X-ray beam intensity just behind the CRL was used. In the papers by Lengeler et al. [(1999). J. Synchrotron Rad. 6, 1153-1167; (1998). J. Appl. Phys. 84, 5855-5861], the maximum intensity value at the focus was used. Numerically, these two definitions differ by 50%. The new definition is based on the integral intensity of the beam behind the CRL over the real aperture. The integral intensity is the most physical value and is independent of distance. The new definition gives a value that is greater than that of the Kohn definition by 6% and less than that of the Lengeler definition by 41%. A new approximation for the aperture function of a two-dimensional CRL is proposed which allows one to calculate the two-dimensional CRL through the one-dimensional CRL and to obtain an analytical solution for a complex system of many CRLs.

Fermi-surface reconstruction by stripe order in cuprate superconductors

NASA Astrophysics Data System (ADS)

Laliberté, Francis

2012-02-01

The origin of pairing in a superconductor resides in the underlying normal state. In the cuprate high-temperature superconductor YBCO, application of a magnetic field to suppress superconductivity reveals a ground state that appears to break the translational symmetry of the lattice, pointing to some density-wave order [1,2,3]. In another cuprate, Eu-LSCO, the onset of stripe order - a modulation of spin and charge densities - at low temperature is well established [4]. By a comparative study of thermoelectric transport in the cuprates YBCO and Eu-LSCO, we show that the two materials exhibit a very similar process of Fermi-surface reconstruction as a function of temperature and doping [5,6]. This strongly suggests that Fermi-surface reconstruction is caused by stripe order in both cases, compelling evidence that stripe order is a generic tendency of hole-doped cuprates.[4pt] Work done in collaboration with J. Chang, N. Doiron-Leyraud, E. Hassinger, R. Daou, D. LeBoeuf, M. Rondeau, B. J. Ramshaw, R. Liang, D. A. Bonn, W. N. Hardy, S. Pyon, T. Takayama, H. Takagi, I. Sheikin, L. Malone, C. Proust, K. Behnia and L. Taillefer.[4pt] [1] N. Doiron-Leyraud et al., Nature 447, 565 (2007).[0pt] [2] D. LeBoeuf et al., Nature 450, 533 (2007).[0pt] [3] D. LeBoeuf et al., Phys. Rev. B 83, 054506 (2011).[0pt] [4] J. Fink et al., Phys. Rev. B 83, 092503 (2011).[0pt] [5] J. Chang et al., Phys. Rev. Lett. 104, 057005 (2010).[0pt] [6] F. Lalibert'e et al., Nat. Commun. 2, 432 (2011).

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.

On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation

NASA Astrophysics Data System (ADS)

Sarna, Neeraj; Torrilhon, Manuel

2018-01-01

We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331-407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.

Kinetic approach to relativistic dissipation

NASA Astrophysics Data System (ADS)

Gabbana, A.; Mendoza, M.; Succi, S.; Tripiccione, R.

2017-08-01

Despite a long record of intense effort, the basic mechanisms by which dissipation emerges from the microscopic dynamics of a relativistic fluid still elude complete understanding. In particular, several details must still be finalized in the pathway from kinetic theory to hydrodynamics mainly in the derivation of the values of the transport coefficients. In this paper, we approach the problem by matching data from lattice-kinetic simulations with analytical predictions. Our numerical results provide neat evidence in favor of the Chapman-Enskog [The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, U.K., 1970)] procedure as suggested by recent theoretical analyses along with qualitative hints at the basic reasons why the Chapman-Enskog expansion might be better suited than Grad's method [Commun. Pure Appl. Math. 2, 331 (1949), 10.1002/cpa.3160020403] to capture the emergence of dissipative effects in relativistic fluids.

EXAFS and XANES investigation of the ETS-10 microporous titanosilicate.

PubMed

Prestipino, C; Solari, P L; Lamberti, C

2005-07-14

In this work, we report state-of-the-art analysis of both Ti K-edge high-resolution XANES and EXAFS data collected on the ETS-10 molecular sieve at the GILDA BM8 beamline of the ESRF facility. The interatomic distances and the angles obtained in our EXAFS study are in fair agreement with the single-crystal XRD data of Wang and Jacobson (Chem. Commun. 1999, 973) and with the recent ab initio periodic study of Damin et al. (J. Phys. Chem. B 2004, 108, 1328) Differently from previous EXAFS work (J. Phys. Chem. 1996, 100, 449), our study supports a model of ETS-10 where the Ti atoms are bonded with two equivalent axial oxygen atoms. This model is also able to reproduce the edge and the post-edge region of the XANES spectrum. Conversely, the weak but well-defined pre-edge peak at 4971.3 eV can be explained only by assuming that a fraction of Ti atoms are in a local geometry similar to that of the pentacoordinated Ti sites in the ETS-4 structure. These Ti atoms in ETS-10 should be the terminal of the -Ti-O-Ti-O-Ti- chains, of which the actual number is strongly increased by the high crystal defectivity (Ti vacancies).

Anomalous yield reduction in direct-drive deuterium/tritium implosions due to 3He addition

NASA Astrophysics Data System (ADS)

Herrmann, H. W.; Langenbrunner, J. R.; Mack, J. M.; Cooley, J. H.; Wilson, D. C.; Evans, S. C.; Sedillo, T. J.; Kyrala, G. A.; Caldwell, S. E.; Young, C. S.; Nobile, A.; Wermer, J.; Paglieri, S.; McEvoy, A. M.; Kim, Y.; Batha, S. H.; Horsfield, C. J.; Drew, D.; Garbett, W.; Rubery, M.; Glebov, V. Yu.; Roberts, S.; Frenje, J. A.

2009-05-01

Glass capsules were imploded in direct drive on the OMEGA laser [Boehly et al., Opt. Commun. 133, 495 (1997)] to look for anomalous degradation in deuterium/tritium (DT) yield and changes in reaction history with H3e addition. Such anomalies have previously been reported for D/H3e plasmas but had not yet been investigated for DT/H3e. Anomalies such as these provide fertile ground for furthering our physics understanding of inertial confinement fusion implosions and capsule performance. Anomalous degradation in the compression component of yield was observed, consistent with the "factor of 2" degradation previously reported by Massachusetts Institute of Technology (MIT) at a 50% H3e atom fraction in D2 using plastic capsules [Rygg, Phys. Plasmas 13, 052702 (2006)]. However, clean calculations (i.e., no fuel-shell mixing) predict the shock component of yield quite well, contrary to the result reported by MIT but consistent with Los Alamos National Laboratory results in D2/H3e [Wilson et al., J. Phys.: Conf. Ser. 112, 022015 (2008)]. X-ray imaging suggests less-than-predicted compression of capsules containing H3e. Leading candidate explanations are poorly understood equation of state for gas mixtures and unanticipated particle pressure variation with increasing H3e addition.

Theoretical quantification of shock-timing sensitivities for direct-drive inertial confinement fusion implosions on OMEGA

NASA Astrophysics Data System (ADS)

Cao, D.; Boehly, T. R.; Gregor, M. C.; Polsin, D. N.; Davis, A. K.; Radha, P. B.; Regan, S. P.; Goncharov, V. N.

2018-05-01

Using temporally shaped laser pulses, multiple shocks can be launched in direct-drive inertial confinement fusion implosion experiments to set the shell on a desired isentrope or adiabat. The velocity of the first shock and the times at which subsequent shocks catch up to it are measured through the velocity interferometry system for any reflector diagnostic [T. R. Boehly et al., Phys. Plasmas 18, 092706 (2011)] on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. Simulations reproduce these velocity and shock-merger time measurements when using laser pulses designed for setting mid-adiabat (α ˜ 3) implosions, but agreement degrades for lower-adiabat (α ˜ 1) designs. Simulation results indicate that the shock timing discrepancy is most sensitive to details of the density and temperature profiles in the coronal plasma, which influences the laser energy coupled into the target, and only marginally sensitive to the target offset and beam power imbalance. To aid in verifying the coronal profile's influence, a new technique under development to infer coronal profiles using x-ray self-emission imaging [A. K. Davis et al., Bull. Am. Phys. Soc. 61, BAPS.2016.DPP.NO8.7 (2016)] can be applied to the pulse shapes used in shock-timing experiments.

Unconventional superconductivity and surface pairing symmetry in half-Heusler compounds

NASA Astrophysics Data System (ADS)

Wang, Qing-Ze; Yu, Jiabin; Liu, Chao-Xing

2018-06-01

Signatures of nodal line/point superconductivity [Kim et al., Sci. Adv. 4, eaao4513 (2018), 10.1126/sciadv.aao4513; Brydon et al., Phys. Rev. Lett. 116, 177001 (2016), 10.1103/PhysRevLett.116.177001] have been observed in half-Heusler compounds, such as LnPtBi (Ln = Y, Lu). Topologically nontrivial band structures, as well as topological surface states, have also been confirmed by angular-resolved photoemission spectroscopy in these compounds [Liu et al., Nat. Commun. 7, 12924 (2016), 10.1038/ncomms12924]. In this paper, we present a systematical classification of possible gap functions of bulk states and surface states in half-Heusler compounds and the corresponding topological properties based on the representations of crystalline symmetry group. Different from all the previous studies based on the four band Luttinger model, our study starts with the six-band Kane model, which involves both four p-orbital type of Γ8 bands and two s-orbital type of Γ6 bands. Although the Γ6 bands are away from the Fermi energy, our results reveal the importance of topological surface states, which originate from the band inversion between Γ6 and Γ8 bands, in determining surface properties of these compounds in the superconducting regime by combining topological bulk state picture and nontrivial surface state picture.

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

Hydrogen adsorption strength and sites in the metal organic framework MOF5: Comparing experiment and model calculations

NASA Astrophysics Data System (ADS)

Mulder, F. M.; Dingemans, T. J.; Schimmel, H. G.; Ramirez-Cuesta, A. J.; Kearley, G. J.

2008-07-01

Hydrogen adsorption in porous, high surface area, and stable metal organic frameworks (MOF's) appears a novel route towards hydrogen storage materials [N.L. Rosi, J. Eckert, M. Eddaoudi, D.T. Vodak, J. Kim, M. O'Keeffe, O.M. Yaghi, Science 300 (2003) 1127; J.L.C. Rowsell, A.R. Millward, K. Sung Park, O.M. Yaghi, J. Am. Chem. Soc. 126 (2004) 5666; G. Ferey, M. Latroche, C. Serre, F. Millange, T. Loiseau, A. Percheron-Guegan, Chem. Commun. (2003) 2976; T. Loiseau, C. Serre, C. Huguenard, G. Fink, F. Taulelle, M. Henry, T. Bataille, G. Férey, Chem. Eur. J. 10 (2004) 1373]. A prerequisite for such materials is sufficient adsorption interaction strength for hydrogen adsorbed on the adsorption sites of the material because this facilitates successful operation under moderate temperature and pressure conditions. Here we report detailed information on the geometry of the hydrogen adsorption sites, based on the analysis of inelastic neutron spectroscopy (INS). The adsorption energies for the metal organic framework MOF5 equal about 800 K for part of the different sites, which is significantly higher than for nanoporous carbon materials (˜550 K) [H.G. Schimmel, G.J. Kearley, M.G. Nijkamp, C.T. Visser, K.P. de Jong, F.M. Mulder, Chem. Eur. J. 9 (2003) 4764], and is in agreement with what is found in first principles calculations [T. Sagara, J. Klassen, E. Ganz, J. Chem. Phys. 121 (2004) 12543; F.M. Mulder, T.J. Dingemans, M. Wagemaker, G.J. Kearley, Chem. Phys. 317 (2005) 113]. Assignments of the INS spectra is realized using comparison with independently published model calculations [F.M. Mulder, T.J. Dingemans, M. Wagemaker, G.J. Kearley, Chem. Phys. 317 (2005) 113] and structural data [T. Yildirim, M.R. Hartman, Phys. Rev. Lett. 95 (2005) 215504].

Soliton Resolution for the Derivative Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Jenkins, Robert; Liu, Jiaqi; Perry, Peter; Sulem, Catherine

2018-05-01

We study the derivative nonlinear Schrödinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou (Commun Pure Appl Math 56:1029-1077, 2003) revisited by the {\\overline{partial}} -analysis of McLaughlin and Miller (IMRP Int Math Res Pap 48673:1-77, 2006) and Dieng and McLaughlin (Long-time asymptotics for the NLS equation via dbar methods. Preprint, arXiv:0805.2807, 2008), and complemented by the recent work of Borghese et al. (Ann Inst Henri Poincaré Anal Non Linéaire, https://doi.org/10.1016/j.anihpc.2017.08.006, 2017) on soliton resolution for the focusing nonlinear Schrödinger equation. Our results imply that N-soliton solutions of the derivative nonlinear Schrödinger equation are asymptotically stable.

Coupling of PIES 3-D Equilibrium Code and NIFS Bootstrap Code with Applications to the Computation of Stellarator Equilibria

NASA Astrophysics Data System (ADS)

Monticello, D. A.; Reiman, A. H.; Watanabe, K. Y.; Nakajima, N.; Okamoto, M.

1997-11-01

The existence of bootstrap currents in both tokamaks and stellarators was confirmed, experimentally, more than ten years ago. Such currents can have significant effects on the equilibrium and stability of these MHD devices. In addition, stellarators, with the notable exception of W7-X, are predicted to have such large bootstrap currents that reliable equilibrium calculations require the self-consistent evaluation of bootstrap currents. Modeling of discharges which contain islands requires an algorithm that does not assume good surfaces. Only one of the two 3-D equilibrium codes that exist, PIES( Reiman, A. H., Greenside, H. S., Compt. Phys. Commun. 43), (1986)., can easily be modified to handle bootstrap current. Here we report on the coupling of the PIES 3-D equilibrium code and NIFS bootstrap code(Watanabe, K., et al., Nuclear Fusion 35) (1995), 335.

Confinement and Diffusion Effects in Dynamical Nuclear Polarization in Low Dimensional Nanostructures

NASA Astrophysics Data System (ADS)

Henriksen, Dan; Tifrea, Ionel

2012-02-01

We investigate the dynamic nuclear polarization as it results from the hyperfine coupling between nonequilibrium electronic spins and nuclear spins in semiconductor nanostructures. The natural confinement provided by low dimensional nanostructures is responsible for an efficient nuclear spin - electron spin hyperfine coupling [1] and for a reduced value of the nuclear spin diffusion constant [2]. In the case of optical pumping, the induced nuclear spin polarization is position dependent even in the presence of nuclear spin diffusion. This effect should be measurable via optically induced nuclear magnetic resonance or time-resolved Faraday rotation experiments. We discuss the implications of our calculations for the case of GaAs quantum well structures.[4pt] [1] I. Tifrea and M. E. Flatt'e, Phys. Rev. B 84, 155319 (2011).[0pt] [2] A. Malinowski and R. T. Harley, Solid State Commun. 114, 419 (2000).

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.

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.

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.

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (III) HFBTHO (v3.00): A new version of the program

NASA Astrophysics Data System (ADS)

Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.

2017-11-01

We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton intrinsic densities. In the present version of HFBTHO, the energy density derives either from the zero-range Skyrme or the finite-range Gogny effective two-body interaction between nucleons. Nuclear super-fluidity is treated at the Hartree-Fock-Bogolyubov (HFB) approximation. Constraints on the nuclear shape allows probing the potential energy surface of the nucleus as needed e.g., for the description of shape isomers or fission. The implementation of a local scale transformation of the single-particle basis in which the HFB solutions are expanded provide a tool to properly compute the structure of weakly-bound nuclei. Solution method: The program uses the axial Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogolyubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions or the finite-range Gogny force until a self-consistent solution is found. A previous version of the program was presented in M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013) 1592-1604 with much of the formalism presented in the original paper M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Additional comments: The user must have access to (i) the LAPACK subroutines DSYEEVR, DSYEVD, DSYTRF and DSYTRI, and their dependencies, which compute eigenvalues and eigenfunctions of real symmetric matrices, (ii) the LAPACK subroutines DGETRI and DGETRF, which invert arbitrary real matrices, and (iii) the BLAS routines DCOPY, DSCAL, DGEMM and DGEMV for double-precision linear algebra (or provide another set of subroutines that can perform such tasks). The BLAS and LAPACK subroutines can be obtained from the Netlib Repository at the University of Tennessee, Knoxville: http://netlib2.cs.utk.edu/.

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.

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

Self-consistent gyrokinetic modeling of neoclassical and turbulent impurity transport

NASA Astrophysics Data System (ADS)

Estève, D.; Sarazin, Y.; Garbet, X.; Grandgirard, V.; Breton, S.; Donnel, P.; Asahi, Y.; Bourdelle, C.; Dif-Pradalier, G.; Ehrlacher, C.; Emeriau, C.; Ghendrih, Ph.; Gillot, C.; Latu, G.; Passeron, C.

2018-03-01

Trace impurity transport is studied with the flux-driven gyrokinetic GYSELA code (Grandgirard et al 2016 Comput. Phys. Commun. 207 35). A reduced and linearized multi-species collision operator has been recently implemented, so that both neoclassical and turbulent transport channels can be treated self-consistently on an equal footing. In the Pfirsch-Schlüter regime that is probably relevant for tungsten, the standard expression for the neoclassical impurity flux is shown to be recovered from gyrokinetics with the employed collision operator. Purely neoclassical simulations of deuterium plasma with trace impurities of helium, carbon and tungsten lead to impurity diffusion coefficients, inward pinch velocities due to density peaking, and thermo-diffusion terms which quantitatively agree with neoclassical predictions and NEO simulations (Belli et al 2012 Plasma Phys. Control. Fusion 54 015015). The thermal screening factor appears to be less than predicted analytically in the Pfirsch-Schlüter regime, which can be detrimental to fusion performance. Finally, self-consistent nonlinear simulations have revealed that the tungsten impurity flux is not the sum of turbulent and neoclassical fluxes computed separately, as is usually assumed. The synergy partly results from the turbulence-driven in-out poloidal asymmetry of tungsten density. This result suggests the need for self-consistent simulations of impurity transport, i.e. including both turbulence and neoclassical physics, in view of quantitative predictions for ITER.

Improving cryogenic deuterium–tritium implosion performance on OMEGA

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

Sangster, T. C.; Goncharov, V. N.; Betti, R.

2013-05-15

A flexible direct-drive target platform is used to implode cryogenic deuterium–tritium (DT) capsules on the OMEGA laser [Boehly et al., Opt. Commun. 133, 495 (1997)]. The goal of these experiments is to demonstrate ignition hydrodynamically equivalent performance where the laser drive intensity, the implosion velocity, the fuel adiabat, and the in-flight aspect ratio (IFAR) are the same as those for a 1.5-MJ target [Goncharov et al., Phys. Rev. Lett. 104, 165001 (2010)] designed to ignite on the National Ignition Facility [Hogan et al., Nucl. Fusion 41, 567 (2001)]. The results from a series of 29 cryogenic DT implosions are presented.more » The implosions were designed to span a broad region of design space to study target performance as a function of shell stability (adiabat) and implosion velocity. Ablation-front perturbation growth appears to limit target performance at high implosion velocities. Target outer-surface defects associated with contaminant gases in the DT fuel are identified as the dominant perturbation source at the ablation surface; performance degradation is confirmed by 2D hydrodynamic simulations that include these defects. A trend in the value of the Lawson criterion [Betti et al., Phys. Plasmas 17, 058102 (2010)] for each of the implosions in adiabat–IFAR space suggests the existence of a stability boundary that leads to ablator mixing into the hot spot for the most ignition-equivalent designs.« less

Improving cryogenic deuterium tritium implosion performance on OMEGA

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

Sangster, T. C.; Goncharov, V. N.; Betti, R.

2013-01-01

A flexible direct-drive target platform is used to implode cryogenic deuterium–tritium (DT) capsules on the OMEGA laser [Boehly et al., Opt. Commun. 133, 495 (1997)]. The goal of these experiments is to demonstrate ignition hydrodynamically equivalent performance where the laser drive intensity, the implosion velocity, the fuel adiabat, and the in-flight aspect ratio (IFAR) are the same as those for a 1.5-MJ target [Goncharov et al., Phys. Rev. Lett. 104, 165001 (2010)] designed to ignite on the National Ignition Facility [Hogan et al., Nucl. Fusion 41, 567 (2001)]. The results from a series of 29 cryogenic DT implosions are presented.more » The implosions were designed to span a broad region of design space to study target performance as a function of shell stability (adiabat) and implosion velocity. Ablation-front perturbation growth appears to limit target performance at high implosion velocities. Target outer-surface defects associated with contaminant gases in the DT fuel are identified as the dominant perturbation source at the ablation surface; performance degradation is confirmed by 2D hydrodynamic simulations that include these defects. A trend in the value of the Lawson criterion [Betti et al., Phys. Plasmas 17, 058102 (2010)] for each of the implosions in adiabat–IFAR space suggests the existence of a stability boundary that leads to ablator mixing into the hot spot for the most ignition-equivalent designs.« less

Explicit Lower and Upper Bounds on the Entangled Value of Multiplayer XOR Games

NASA Astrophysics Data System (ADS)

Briët, Jop; Vidick, Thomas

2013-07-01

The study of quantum-mechanical violations of Bell inequalities is motivated by the investigation, and the eventual demonstration, of the nonlocal properties of entanglement. In recent years, Bell inequalities have found a fruitful re-formulation using the language of multiplayer games originating from Computer Science. This paper studies the nonlocal properties of entanglement in the context of the simplest such games, called XOR games. When there are two players, it is well known that the maximum bias—the advantage over random play—of players using entanglement can be at most a constant times greater than that of classical players. Recently, Pérez-García et al. (Commun. Mathe. Phys. 279:455, 2008) showed that no such bound holds when there are three or more players: the use of entanglement can provide an unbounded advantage, and scale with the number of questions in the game. Their proof relies on non-trivial results from operator space theory, and gives a non-explicit existence proof, leading to a game with a very large number of questions and only a loose control over the local dimension of the players' shared entanglement. We give a new, simple and explicit (though still probabilistic) construction of a family of three-player XOR games which achieve a large quantum-classical gap (QC-gap). This QC-gap is exponentially larger than the one given by Pérez-García et. al. in terms of the size of the game, achieving a QC-gap of order {√{N}} with N 2 questions per player. In terms of the dimension of the entangled state required, we achieve the same (optimal) QC-gap of {√{N}} for a state of local dimension N per player. Moreover, the optimal entangled strategy is very simple, involving observables defined by tensor products of the Pauli matrices. Additionally, we give the first upper bound on the maximal QC-gap in terms of the number of questions per player, showing that our construction is only quadratically off in that respect. Our results rely on probabilistic estimates on the norm of random matrices and higher-order tensors which may be of independent interest.

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.

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.

Kinetic models of opinion formation in the presence of personal conviction

NASA Astrophysics Data System (ADS)

Brugna, Carlo; Toscani, Giuseppe

2015-11-01

We consider a nonlinear kinetic equation of Boltzmann type, which takes into account the influence of conviction during the formation of opinion in a system of agents, which interact through the binary exchanges, introduced by Toscani [G. Toscani, Commun. Math. Sci. 4, 481 (2006), 10.4310/CMS.2006.v4.n3.a1]. The original exchange mechanism, which is based on the human tendency to compromise and change of opinion through self-thinking, is here modified in the parameters of the compromise and diffusion terms, which now are assumed to depend on the personal degree of conviction. The numerical simulations show that the presence of conviction has the potential to break symmetry, and to produce clusters of opinions. The model is partially inspired by the recent work [L. Pareschi and G. Toscani, Phil. Trans. R. Soc. A 372, 20130396 (2014), 10.1098/rsta.2013.0396], in which the role of knowledge in the formation of wealth distribution has been investigated.

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.

L{sup 2}-stability of the Vlasov-Maxwell-Boltzmann system near global Maxwellians

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

Ha, Seung-Yeal, E-mail: syha@snu.ac.kr; Xiao, Qinghua, E-mail: pdexqh@hotmail.com; Xiong, Linjie, E-mail: xlj@whu.edu.cn

2013-12-15

We present a L{sup 2}-stability theory of the Vlasov-Maxwell-Boltzmann system for the two-species collisional plasma. We show that in a perturbative regime of a global Maxwellian, the L{sup 2}-distance between two strong solutions can be controlled by that between initial data in a Lipschitz manner. Our stability result extends earlier results [Ha, S.-Y. and Xiao, Q.-H., “A revisiting to the L{sup 2}-stability theory of the Boltzmann equation near global Maxwellians,” (submitted) and Ha, S.-Y., Yang, X.-F., and Yun, S.-B., “L{sup 2} stability theory of the Boltzmann equation near a global Maxwellian,” Arch. Ration. Mech. Anal. 197, 657–688 (2010)] on themore » L{sup 2}-stability of the Boltzmann equation to the Boltzmann equation coupled with self-consistent external forces. As a direct application of our stability result, we show that classical solutions in Duan et al. [“Optimal large-time behavior of the Vlasov-Maxwell-Boltzmann system in the whole space,” Commun. Pure Appl. Math. 24, 1497–1546 (2011)] and Guo [“The Vlasov-Maxwell-Boltzmann system near Maxwellians,” Invent. Math. 153(3), 593–630 (2003)] satisfy a uniform L{sup 2}-stability estimate. This is the first result on the L{sup 2}-stability of the Boltzmann equation coupled with self-consistent field equations in three dimensions.« less

Transport and Dynamics in Toroidal Fusion Systems

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

Sovinec, Carl

The study entitled, "Transport and Dynamics in Toroidal Fusion Systems," (TDTFS) applied analytical theory and numerical computation to investigate topics of importance to confining plasma, the fourth state of matter, with magnetic fields. A central focus of the work is how non-thermal components of the ion particle distribution affect the "sawtooth" collective oscillation in the core of the tokamak magnetic configuration. Previous experimental and analytical research had shown and described how the oscillation frequency decreases and amplitude increases, leading to "monster" or "giant" sawteeth, when the non-thermal component is increased by injecting particle beams or by exciting ions with imposedmore » electromagnetic waves. The TDTFS study applied numerical computation to self-consistently simulate the interaction between macroscopic collective plasma dynamics and the non-thermal particles. The modeling used the NIMROD code [Sovinec, Glasser, Gianakon, et al., J. Comput. Phys. 195, 355 (2004)] with the energetic component represented by simulation particles [Kim, Parker, Sovinec, and the NIMROD Team, Comput. Phys. Commun. 164, 448 (2004)]. The computations found decreasing growth rates for the instability that drives the oscillations, but they were ultimately limited from achieving experimentally relevant parameters due to computational practicalities. Nonetheless, this effort provided valuable lessons for integrated simulation of macroscopic plasma dynamics. It also motivated an investigation of the applicability of fluid-based modeling to the ion temperature gradient instability, leading to the journal publication [Schnack, Cheng, Barnes, and Parker, Phys. Plasmas 20, 062106 (2013)]. Apart from the tokamak-specific topics, the TDTFS study also addressed topics in the basic physics of magnetized plasma and in the dynamics of the reversed-field pinch (RFP) configuration. The basic physics work contributed to a study of two-fluid effects on interchange dynamics, where "two-fluid" refers to modeling independent dynamics of electron and ion species without full kinetic effects. In collaboration with scientist Ping Zhu, who received separate support, it was found that the rule-of-thumb criteria on stabilizing interchange has caveats that depend on the plasma density and temperature profiles. This work was published in [Zhu, Schnack, Ebrahimi, et al., Phys. Rev. Lett. 101, 085005 (2008)]. An investigation of general nonlinear relaxation with fluid models was partially supported by the TDTFS study and led to the publication [Khalzov, Ebrahimi, Schnack, and Mirnov, Phys. Plasmas 19, 012111 (2012)]. Work specific to the RFP included an investigation of interchange at large plasma pressure and support for applications [for example, Scheffel, Schnack, and Mirza, Nucl. Fusion 53, 113007 (2013)] of the DEBS code [Schnack, Barnes, Mikic, Harned, and Caramana, J. Comput. Phys. 70, 330 (1987)]. Finally, the principal investigator over most of the award period, Dalton Schnack, supervised a numerical study of modeling magnetic island suppression [Jenkins, Kruger, Hegna, Schnack, and Sovinec, Phys. Plasmas 17, 12502 (2010)].« less

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.

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).

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!!!

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

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.

Land bidding game with conflicting interest and its quantum solution

NASA Astrophysics Data System (ADS)

Situ, Haozhen; Alonso-Sanz, Ramón; Li, Lvzhou; Zhang, Cai

Recently, the first conflicting interest quantum game based on the nonlocality property of quantum mechanics has been introduced in A. Pappa, N. Kumar, T. Lawson, M. Santha, S. Y. Zhang, E. Diamanti and I. Kerenidis, Phys. Rev. Lett. 114 (2015) 020401. Several quantum games of the same genre have also been proposed subsequently. However, these games are constructed from some well-known Bell inequalities, thus are quite abstract and lack of realistic interpretations. In the present paper, we modify the common interest land bidding game introduced in N. Brunner and N. Linden, Nat. Commun. 4 (2013) 2057, which is also based on nonlocality and can be understood as two companies collaborating in developing a project. The modified game has conflicting interest and reflects the free rider problem in economics. Then we show that it has a fair quantum solution that leads to better outcome. Finally, we study how several types of paradigmatic noise affect the outcome of this game.

BPS algebras, genus zero and the heterotic Monster

NASA Astrophysics Data System (ADS)

Paquette, Natalie M.; Persson, Daniel; Volpato, Roberto

2017-10-01

In this note, we expand on some technical issues raised in (Paquette et al 2016 Commun. Number Theory Phys. 10 433-526) by the authors, as well as providing a friendly introduction to and summary of our previous work. We construct a set of heterotic string compactifications to 0  +  1 dimensions intimately related to the Monstrous moonshine module of Frenkel, Lepowsky, and Meurman (and orbifolds thereof). Using this model, we review our physical interpretation of the genus zero property of Monstrous moonshine. Furthermore, we show that the space of (second-quantized) BPS-states forms a module over the Monstrous Lie algebras mg —some of the first and most prominent examples of Generalized Kac-Moody algebras—constructed by Borcherds and Carnahan. In particular, we clarify the structure of the module present in the second-quantized string theory. We also sketch a proof of our methods in the language of vertex operator algebras, for the interested mathematician.

Universal exchange-driven phonon splitting

NASA Astrophysics Data System (ADS)

Deisenhofer, Joachim; Kant, Christian; Schmidt, Michael; Wang, Zhe; Mayr, Franz; Tsurkan, Vladimir; Loidl, Alois

2012-02-01

We report on a linear dependence of the phonon splitting on the non-dominant exchange coupling Jnd in the antiferromagnetic monoxides MnO, Fe0.92O, CoO and NiO, and in the highly frustrated antiferromagnetic spinels CdCr2O4, MgCr2O4 and ZnCr2O4. For the monoxides our results directly confirm the theoretical prediction of a predominantly exchange induced splitting of the zone-centre optical phonon [1,2]. We find the linear relation δφ= βJndS^2 with slope β = 3.7. This relation also holds for a very different class of systems, namely the highly frustrated chromium spinels. Our finding suggests a universal dependence of the exchange-induced phonon splitting at the antiferromagnetic transition on the non-dominant exchange coupling [3].[4pt] [1] S. Massidda et al., Phys. Rev. Lett. 82, 430 (1999).[0pt] [2] W. Luo et al., Solid State Commun. 142, 504 (2007).[0pt] [3] Ch. Kant et al., arxiv:1109.4809.

Scaling of Energy Deposition in Fast Ignition Targets

NASA Astrophysics Data System (ADS)

Campbell, R. B.; Welch, Dale

2005-10-01

We examine the scaling to ignition of the energy deposition of laser generated electrons in compressed fast ignition cores. Relevant cores have densities of several hundred g/cm^3, with a few keV initial temperature. As the laser intensities increase approaching ignition systems, on the order of a few 10^21W/cm^2, the hot electron energies expected to approach 100MeV[1]. Most certainly anomalous processes must play a role in the energy transfer, but the exact nature of these processes, as well as a practical way to model them, remain open issues. Traditional PIC explicit methods are limited to low densities on current and anticipated computing platforms, so the study of relevant parameter ranges has received so far little attention. We use LSP[2] to examine a relativistic electron beam (presumed generated from a laser plasma interaction) of legislated energy and angular distribution is injected into a 3D block of compressed DT. Collective effects will determine the stopping, most likely driven by magnetic field filamentation. The scaling of the stopping as a function of block density and temperature, as well as hot electron current and laser intensity is presented. Sub-grid models may be profitably used and degenerate effects included in the solution of this problem. Sandia is operated by Sandia Corporation, for the USDOE. [1] A. Pukhov, et. al., Phys. Plas. 6, p2847 (1999) [2] D. R. Welch et al., Comput. Phys.Commun. 164, p183 (2004).

Comment on "Peres experiment using photons: No test for hypercomplex (quaternionic) quantum theories"

NASA Astrophysics Data System (ADS)

Procopio, Lorenzo M.; Rozema, Lee A.; Dakić, Borivoje; Walther, Philip

2017-09-01

In his recent article [Phys. Rev. A 95, 060101(R) (2017), 10.1103/PhysRevA.95.060101], Adler questions the usefulness of the bound found in our experimental search for genuine effects of hypercomplex quantum mechanics [Nat. Commun. 8, 15044 (2017), 10.1038/ncomms15044]. Our experiment was performed using a black-box (instrumentalist) approach to generalized probabilistic theories; therefore, it does not assume a priori any particular underlying mechanism. From that point of view our experimental results do indeed place meaningful bounds on the possible effects of "postquantum theories," including quaternionic quantum mechanics. In his article, Adler compares our experiment to nonrelativistic and Möller formal scattering theories within quaternionic quantum mechanics. With a particular set of assumptions, he finds that quaternionic effects would likely not manifest themselves in general. Although these assumptions are justified in the nonrelativistic case, a proper calculation for relativistic particles is still missing. Here, we provide a concrete relativistic example of Klein-Gordon scattering wherein the quaternionic effects persist. We note that when the Klein-Gordon equation is formulated using a Hamiltonian formalism it displays a so-called "indefinite metric," a characteristic feature of relativistic quantum wave equations. In Adler's example this is directly forbidden by his assumptions, and therefore our present example is not in contradiction to his work. In complex quantum mechanics this problem of an indefinite metric is solved in a second quantization. Unfortunately, there is no known algorithm for canonical field quantization in quaternionic quantum mechanics.

Anomalous yield reduction in direct-drive DT implosions due to 3He addition

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

Herrmann, Hans W; Langenbrunner, James R; Mack, Joseph M

2008-01-01

Glass capsules were imploded in direct drive on the OMEGA laser [T. R. Boehly et aI., Opt. Commun. 133, 495, 1997] to look for anomalous degradation in deuterium/tritium (DT) yield (i.e., beyond what is predicted) and changes in reaction history with {sup 3}He addition. Such anomalies have previously been reported for D/{sup 3}He plasmas, but had not yet been investigated for DT/{sup 3}He. Anomalies such as these provide fertile ground for furthering our physics understanding of ICF implosions and capsule performance. A relatively short laser pulse (600 ps) was used to provide some degree of temporal separation between shock andmore » compression yield components for analysis. Anomalous degradation in the compression component of yield was observed, consistent with the 'factor of two' degradation previously reported by MIT at a 50% {sup 3}He atom fraction in D{sub 2} using plastic capsules [Rygg et aI., Phys. Plasmas 13, 052702 (2006)]. However, clean calculations (i.e., no fuel-shell mixing) predict the shock component of yield quite well, contrary to the result reported by MIT, but consistent with LANL results in D{sub 2}/{sup 3}He [Wilson, et aI., lml Phys: Conf Series 112, 022015 (2008)]. X-ray imaging suggests less-than-predicted compression ofcapsules containing {sup 3}He. Leading candidate explanations are poorly understood Equation-of-State (EOS) for gas mixtures, and unanticipated particle pressure variation with increasing {sup 3}He addition.« less

Indirect drive ablative Rayleigh-Taylor experiments with rugby hohlraums on OMEGA

NASA Astrophysics Data System (ADS)

Casner, A.; Galmiche, D.; Huser, G.; Jadaud, J.-P.; Liberatore, S.; Vandenboomgaerde, M.

2009-09-01

Results of ablative Rayleigh-Taylor instability growth experiments performed in indirect drive on the OMEGA laser facility [T. R. Boehly, D. L. Brown, S. Craxton et al., Opt. Commun. 133, 495 (1997)] are reported. These experiments aim at benchmarking hydrocodes simulations and ablator instabilities growth in conditions relevant to ignition in the framework of the Laser MégaJoule [C. Cavailler, Plasma Phys. Controlled Fusion 47, 389 (2005)]. The modulated samples under study were made of germanium-doped plastic (CHGe), which is the nominal ablator for future ignition experiments. The incident x-ray drive was provided using rugby-shaped hohlraums [M. Vandenboomgaerde, J. Bastian, A. Casner et al., Phys. Rev. Lett. 99, 065004 (2007)] and was characterized by means of absolute time-resolved soft x-ray power measurements through a dedicated diagnostic hole, shock breakout data and one-dimensional and two-dimensional (2D) side-on radiographies. All these independent x-ray drive diagnostics lead to an actual on-foil flux that is about 50% smaller than laser-entrance-hole measurements. The experimentally inferred flux is used to simulate experimental optical depths obtained from face-on radiographies for an extensive set of initial conditions: front-side single-mode (wavelength λ =35, 50, and 70 μm) and two-mode perturbations (wavelength λ =35 and 70 μm, in phase or in opposite phase). Three-dimensional pattern growth is also compared with the 2D case. Finally the case of the feedthrough mechanism is addressed with rear-side modulated foils.

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)

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.

Rational solutions of CYBE for simple compact real Lie algebras

NASA Astrophysics Data System (ADS)

Pop, Iulia; Stolin, Alexander

2007-04-01

In [A.A. Stolin, On rational solutions of Yang-Baxter equation for sl(n), Math. Scand. 69 (1991) 57-80; A.A. Stolin, On rational solutions of Yang-Baxter equation. Maximal orders in loop algebra, Comm. Math. Phys. 141 (1991) 533-548; A. Stolin, A geometrical approach to rational solutions of the classical Yang-Baxter equation. Part I, in: Walter de Gruyter & Co. (Ed.), Symposia Gaussiana, Conf. Alg., Berlin, New York, 1995, pp. 347-357] a theory of rational solutions of the classical Yang-Baxter equation for a simple complex Lie algebra g was presented. We discuss this theory for simple compact real Lie algebras g. We prove that up to gauge equivalence all rational solutions have the form X(u,v)={Ω}/{u-v}+t1∧t2+⋯+t∧t2n, where Ω denotes the quadratic Casimir element of g and {ti} are linearly independent elements in a maximal torus t of g. The quantization of these solutions is also emphasized.

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

Edge localized linear ideal magnetohydrodynamic instability studies in an extended-magnetohydrodynamic code

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

Burke, B. J.; Kruger, S. E.; Hegna, C. C.

A linear benchmark between the linear ideal MHD stability codes ELITE [H. R. Wilson et al., Phys. Plasmas 9, 1277 (2002)], GATO [L. Bernard et al., Comput. Phys. Commun. 24, 377 (1981)], and the extended nonlinear magnetohydrodynamic (MHD) code, NIMROD [C. R. Sovinec et al.., J. Comput. Phys. 195, 355 (2004)] is undertaken for edge-localized (MHD) instabilities. Two ballooning-unstable, shifted-circle tokamak equilibria are compared where the stability characteristics are varied by changing the equilibrium plasma profiles. The equilibria model an H-mode plasma with a pedestal pressure profile and parallel edge currents. For both equilibria, NIMROD accurately reproduces the transition tomore » instability (the marginally unstable mode), as well as the ideal growth spectrum for a large range of toroidal modes (n=1-20). The results use the compressible MHD model and depend on a precise representation of 'ideal-like' and 'vacuumlike' or 'halo' regions within the code. The halo region is modeled by the introduction of a Lundquist-value profile that transitions from a large to a small value at a flux surface location outside of the pedestal region. To model an ideal-like MHD response in the core and a vacuumlike response outside the transition, separate criteria on the plasma and halo Lundquist values are required. For the benchmarked equilibria the critical Lundquist values are 10{sup 8} and 10{sup 3} for the ideal-like and halo regions, respectively. Notably, this gives a ratio on the order of 10{sup 5}, which is much larger than experimentally measured values using T{sub e} values associated with the top of the pedestal and separatrix. Excellent agreement with ELITE and GATO calculations are made when sharp boundary transitions in the resistivity are used and a small amount of physical dissipation is added for conditions very near and below marginal ideal stability.« less

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.

Ground-state Properties of Inhomogeneous Graphene Sheets

NASA Astrophysics Data System (ADS)

Polini, Marco

2009-03-01

When inter-valley scattering is weak and gauge fields due to e.g. ripples are neglected, doped and gated graphene sheets can be described using an envelope-function Hamiltonian with a new sublattice pseudospin degree-of freedom, an ultrarelativistic massless-Dirac free-fermion term, a pseudospin scalar disorder potential, and a non-relativistic instantaneous Coulombic interaction term. There is considerable evidence from experiment that this simplified description of a honeycomb lattice of Carbon atoms is usually a valid starting point for theories of those observables that depend solely on the electronic properties of π-electrons near the graphene Dirac point [1]. Although the use of this model simplifies the physics considerably it still leaves us with a many-body problem without translational invariance, which we do not know how to solve. In this talk we present a Kohn-Sham-Dirac density-functional-theory (DFT) scheme for graphene sheets that treats slowly-varying inhomogeneous scalar external potentials and electron-electron interactions on an equal footing [2]. The theory is able to account for the unusual property that the exchange-correlation contribution to chemical potential increases with carrier density in graphene [3,4]. Consequences of this property, and advantages and disadvantages of using the DFT approach to describe it, are discussed. The approach is illustrated by solving the Kohn-Sham-Dirac equations self-consistently for a model random potential describing charged point-like impurities located close to the graphene plane. The influence of electron-electron interactions on these non-linear screening calculations is discussed at length, in the light of recent experiments [5,6] reporting evidence for the presence of electron-hole puddles in nearly-neutral graphene sheets. [4pt] [1] A.K. Geim and K.S. Novoselov, Nature Mater. 6, 183 (2007); A.K. Geim and A.H. MacDonald, Phys. Today 60, 35 (2007); A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, arXiv:0709.1163v2 (2007).[0pt] [2] M. Polini, A. Tomadin, R. Asgari, and A.H. MacDonald, Phys. Rev. B 78, 115426 (2008).[0pt] [3] Y. Barlas, T. Pereg-Barnea, M. Polini, R. Asgari, and A.H. MacDonald, Phys. Rev. Lett. 98, 236601 (2007); M. Polini, R. Asgari, Y. Barlas, T. Pereg-Barnea, and A.H. MacDonald, Solid State Commun. 143, 58 (2007). [0pt] [4] E.H. Hwang, B.Y.-K. Hu, and S. Das Sarma, Phys. Rev. Lett. 99, 226801 (2007).[0pt] [5] J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J.H. Smet, K. von Klitzing, and A. Yacoby, Nature Phys. 4, 144 (2008).[0pt] [6] V.W. Brar, Y. Zhang, C. Girit, F. Wang, A. Zettl, and M. Crommie, Bull. Am. Phys. Soc. 53 (2), 443 (2008).

Extreme events as foundation of Lévy walks with varying velocity

NASA Astrophysics Data System (ADS)

Kutner, Ryszard

2002-11-01

In this work we study the role of extreme events [E.W. Montroll, B.J. West, in: J.L. Lebowitz, E.W. Montrell (Eds.), Fluctuation Phenomena, SSM, vol. VII, North-Holland, Amsterdam, 1979, p. 63; J.-P. Bouchaud, M. Potters, Theory of Financial Risks from Statistical Physics to Risk Management, Cambridge University Press, Cambridge, 2001; D. Sornette, Critical Phenomena in Natural Sciences. Chaos, Fractals, Selforganization and Disorder: Concepts and Tools, Springer, Berlin, 2000] in determining the scaling properties of Lévy walks with varying velocity. This model is an extension of the well-known Lévy walks one [J. Klafter, G. Zumofen, M.F. Shlesinger, in M.F. Shlesinger, G.M. Zaslavsky, U. Frisch (Eds.), Lévy Flights and Related Topics ion Physics, Lecture Notes in Physics, vol. 450, Springer, Berlin, 1995, p. 196; G. Zumofen, J. Klafter, M.F. Shlesinger, in: R. Kutner, A. Pȩkalski, K. Sznajd-Weron (Eds.), Anomalous Diffusion. From Basics to Applications, Lecture Note in Physics, vol. 519, Springer, Berlin, 1999, p. 15] introduced in the context of chaotic dynamics where a fixed value of the walker velocity is assumed for simplicity. Such an extension seems to be necessary when the open and/or complex system is studied. The model of Lévy walks with varying velocity is spanned on two coupled velocity-temporal hierarchies: the first one consisting of velocities and the second of corresponding time intervals which the walker spends between the successive turning points. Both these hierarchical structures are characterized by their own self-similar dimensions. The extreme event, which can appear within a given time interval, is defined as a single random step of the walker having largest length. By finding power-laws which describe the time-dependence of this displacement and its statistics we obtained two independent diffusion exponents, which are related to the above-mentioned dimensions and which characterize the extreme event kinetics. In this work we show the principal influence of extreme events on the basic quantities (one-step distributions and moments as well as two-step correlation functions) of the continuous-time random walk formalism. Besides, we construct both the waiting-time distribution and sojourn probability density directly in a real space and time in the scaling form by proper component analysis which takes into account all possible fluctuations of the walker steps in contrast to the extreme event analysis. In this work we pay our attention to the basic quantities, since the summarized multi-step ones were already discussed earlier [Physica A 264 (1999) 107; Comp. Phys. Commun. 147 (2002) 565]. Moreover, we study not only the scaling phenomena but also, assuming a finite number of hierarchy levels, the breaking of scaling and its dependence on control parameters. This seems to be important for studying empirical systems the more so as there are still no closed formulae describing this phenomenon except the one for truncated Lévy flights [Phys. Rev. Lett. 73 (1994) 2946]. Our formulation of the model made possible to develop an efficient Monte Carlo algorithm [Physica A 264 (1999) 107; Comp. Phys. Commun. 147 (2002) 565] where no MC step is lost.

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.

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.

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.

An upgraded version of the generator BCVEGPY2.0 for hadronic production of B meson and its excited states

NASA Astrophysics Data System (ADS)

Chang, Chao-Hsi; Wang, Jian-Xiong; Wu, Xing-Gang

2006-11-01

An upgraded version of the package BCVEGPY2.0: [C.-H. Chang, J.-X. Wang, X.-G. Wu, Comput. Phys. Commun. 174 (2006) 241] is presented, which works under LINUX system and is named as BCVEGPY2.1. With the version and a GNU C compiler additionally, users may simulate the B-events in various experimental environments very conveniently. It has been manipulated in better modularity and code reusability (less cross communication among various modules) than BCVEGPY2.0 has. Furthermore, in the upgraded version a special execution is arranged as that the GNU command make compiles a requested code with the help of a master makefile in main code directory, and then builds an executable file with the default name run. Finally, this paper may also be considered as an erratum, i.e., typo errors in BCVEGPY2.0 and corrections accordingly have been listed. New version program (BCVEGPY2.1) summaryTitle of program: BCVEGPY2.1 Catalogue identifier: ADTJ_v2_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTJ_v2_1 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Reference to original program: BCVEGPY2.0 Reference in CPC: Comput. Phys. Commun. 174 (2006) 241 Does the new version supersede the old program: No Computer: Any LINUX based on PC with FORTRAN 77 or FORTRAN 90 and GNU C compiler as well Operating systems: LINUX Programming language used: FORTRAN 77/90 Memory required to execute with typical data: About 2.0 MB No. of lines in distributed program, including test data, etc.: 31 521 No. of bytes in distributed program, including test data, etc.: 1 310 179 Distribution format: tar.gz Nature of physical problem: Hadronic production of B meson itself and its excited states Method of solution: The code with option can generate weighted and unweighted events. An interface to PYTHIA is provided to meet the needs of jets hadronization in the production. Restrictions on the complexity of the problem: The hadronic production of (cb¯)-quarkonium in S-wave and P-wave states via the mechanism of gluon-gluon fusion are given by the so-called 'complete calculation' approach. Reasons for new version: Responding to the feedback from users, we rearrange the program in a convenient way and then it can be easily adopted by the users to do the simulations according to their own experimental environment (e.g. detector acceptances and experimental cuts). We have paid many efforts to rearrange the program into several modules with less cross communication among the modules, the main program is slimmed down and all the further actions are decoupled from the main program and can be easily called for various purposes. Typical running time: The typical running time is machine and user-parameters dependent. Typically, for production of the S-wave (cb¯)-quarkonium, when IDWTUP = 1, it takes about 20 hour on a 1.8 GHz Intel P4-processor machine to generate 1000 events; however, when IDWTUP = 3, to generate 10 6 events it takes about 40 minutes only. Of the production, the time for the P-wave (cb¯)-quarkonium will take almost two times longer than that for its S-wave quarkonium. Summary of the changes (improvements): (1) The structure and organization of the program have been changed a lot. The new version package BCVEGPY2.1 has been divided into several modules with less cross communication among the modules (some old version source files are divided into several parts for the purpose). The main program is slimmed down and all the further actions are decoupled from the main program so that they can be easily called for various applications. All of the Fortran codes are organized in the main code directory named as bcvegpy2.1, which contains the main program, all of its prerequisite files and subsidiary 'folders' (subdirectory to the main code directory). The method for setting the parameter is the same as that of the previous versions [C.-H. Chang, C. Driouich, P. Eerola, X.-G. Wu, Comput. Phys. Commun. 159 (2004) 192, hep-ph/0309120. [1

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.

mr: A C++ library for the matching and running of the Standard Model parameters

NASA Astrophysics Data System (ADS)

Kniehl, Bernd A.; Pikelner, Andrey F.; Veretin, Oleg L.

2016-09-01

We present the C++ program library mr that allows us to reliably calculate the values of the running parameters in the Standard Model at high energy scales. The initial conditions are obtained by relating the running parameters in the MS bar renormalization scheme to observables at lower energies with full two-loop precision. The evolution is then performed in accordance with the renormalization group equations with full three-loop precision. Pure QCD corrections to the matching and running are included through four loops. We also provide a Mathematica interface for this program library. Catalogue identifier: AFAI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 517613 No. of bytes in distributed program, including test data, etc.: 2358729 Distribution format: tar.gz Programming language: C++. Computer: IBM PC. Operating system: Linux, Mac OS X. RAM: 1 GB Classification: 11.1. External routines: TSIL [1], OdeInt [2], boost [3] Nature of problem: The running parameters of the Standard Model renormalized in the MS bar scheme at some high renormalization scale, which is chosen by the user, are evaluated in perturbation theory as precisely as possible in two steps. First, the initial conditions at the electroweak energy scale are evaluated from the Fermi constant GF and the pole masses of the W, Z, and Higgs bosons and the bottom and top quarks including the full two-loop threshold corrections. Second, the evolution to the high energy scale is performed by numerically solving the renormalization group evolution equations through three loops. Pure QCD corrections to the matching and running are included through four loops. Solution method: Numerical integration of analytic expressions Additional comments: Available for download from URL: http://apik.github.io/mr/. The MathLink interface is tested to work with Mathematica 7-9 and, with an additional flag, also with Mathematica 10 under Linux and with Mathematica 10 under Mac OS X. Running time: less than 1 second References: [1] S. P. Martin and D. G. Robertson, Comput. Phys. Commun. 174 (2006) 133-151 [hep-ph/0501132]. [2] K. Ahnert and M. Mulansky, AIP Conf. Proc. 1389 (2011) 1586-1589 [arxiv:1110.3397 [cs.MS

Theoretical quantification of shock-timing sensitivities for direct-drive inertial confinement fusion implosions on OMEGA

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

Cao, D.; Boehly, T. R.; Gregor, M. C.

Using temporally shaped laser pulses, multiple shocks can be launched in direct-drive inertial confinement fusion implosion experiments to set the shell on a desired isentrope or adiabat. The velocity of the first shock and the times at which subsequent shocks catch up to it are measured through the VISAR diagnostic [T. R. Boehly et al., Phys. Plasmas 18, 092706 (2011)] on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. Simulations reproduce these velocity and shock-merger time measurements when using laser pulses designed for setting mid-adiabat (alpha ~ 3) implosions, but agreement degrades for lower-adiabat (alpha ~ 1)more » designs. Several possibilities for this difference are studied: (1) errors in placing the target at the center of irradiation (target offset), (2) variations in energy between the different incident beams (power imbalance), and (3) errors in modeling the laser energy coupled into the capsule. Simulation results indicate that shock timing is most sensitive to details of the density and temperature profiles in the coronal plasma, which influences the laser energy coupled into the target, and only marginally sensitive to target offset and beam power imbalance. A new technique under development to infer coronal profiles using x-ray self-emission imaging [A. K. Davis et al., Bull. Am. Phys. Soc. 61, BAPS.2016.DPP.NO8.7 (2016)] can be applied to the pulse shapes used in shock-timing experiments. This will help identify improved physics models to implement in codes and consequently enhance shock-timing predictive capability for low-adiabat pulses.« less

Critical de Broglie wavelength in superconductors

NASA Astrophysics Data System (ADS)

Talantsev, E. F.

2018-03-01

There are growing numbers of experimental evidences that the self-field critical currents, Jc(sf,T), are a new instructive tool to investigate fundamental properties of superconductors ranging from atomically thin films [M. Liao et al., Nat. Phys. 6 (2018), https://doi.org/10.1038/s41567-017-0031-6; E. F. Talantsev et al., 2D Mater. 4 (2017) 025072; A. Fete et al., Appl. Phys. Lett. 109 (2016) 192601] to millimeter-scale samples [E. F. Talantsev et al., Sci. Rep. 7 (2017) 10010]. The basic empirical equation which quantitatively accurately described experimental Jc(sf,T) was proposed by Talantsev and Tallon [Nat. Commun. 6 (2015) 7820] and it was the relevant critical field (i.e. thermodynamic field, Bc, for type-I and lower critical field, Bc1, for type-II superconductors) divided by the London penetration depth, λL. In this paper, we report new findings relating to this empirical equation. It is that the critical wavelength of the de Broglie wave, λdB,c, of the superconducting charge carrier which within a numerical pre-factor is equal to the largest of two characteristic lengths of Ginzburg-Landau theory, i.e. the coherence length, ξ, for type-I superconductors or the London penetration depth, λL, for type-II superconductors. We also formulate a microscopic criterion for the onset of dissipative transport current flow: ps ṡ 2ṡλL ln(1+2ṡ(λL ξ )) ≥ 1 2 ṡ ( h 2π), where ps is the charge carrier momentum, h is Planck’s constant and the inequality sign “ <” is reserved for the dissipation-free flow.

Constructing integrable high-pressure full-current free-boundary stellarator magnetohydrodynamic equilibrium solutions

NASA Astrophysics Data System (ADS)

Hudson, S. R.; Monticello, D. A.; Reiman, A. H.; Strickler, D. J.; Hirshman, S. P.; Ku, L.-P.; Lazarus, E.; Brooks, A.; Zarnstorff, M. C.; Boozer, A. H.; Fu, G.-Y.; Neilson, G. H.

2003-10-01

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 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-Schlüter currents, diamagnetic currents and resonant coil fields contribute to the formation of magnetic islands, and the challenge is to design 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 1986 Comput. Phys. Commun. 43 157) 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. 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 2001 Phys. Plasma 8 2083).

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.

New Nuclear Magnetic Moment of ^{209}Bi: Resolving the Bismuth Hyperfine Puzzle.

PubMed

Skripnikov, Leonid V; Schmidt, Stefan; Ullmann, Johannes; Geppert, Christopher; Kraus, Florian; Kresse, Benjamin; Nörtershäuser, Wilfried; Privalov, Alexei F; Scheibe, Benjamin; Shabaev, Vladimir M; Vogel, Michael; Volotka, Andrey V

2018-03-02

A recent measurement of the hyperfine splitting in the ground state of Li-like ^{208}Bi^{80+} has established a "hyperfine puzzle"-the experimental result exhibits a 7σ deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017)NCAOBW2041-172310.1038/ncomms15484; J. P. Karr, Nat. Phys. 13, 533 (2017)NPAHAX1745-247310.1038/nphys4159]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment (μ_{I}) of ^{209}Bi. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of μ_{I}(^{209}Bi) and combine it with nuclear magnetic resonance measurements of Bi(NO_{3})_{3} in nitric acid solutions and of the hexafluoridobismuthate(V) BiF_{6}^{-} ion in acetonitrile. The result clearly reveals that μ_{I}(^{209}Bi) is much smaller than the tabulated value used previously. Applying the new magnetic moment shifts the theoretical prediction into agreement with experiment and resolves the hyperfine puzzle.

Lifetimes and Oscillator Strengths for Ultraviolet Transitions Involving ns2nd 2D and nsnp2 2D terms in Pb II, Sn II, and Ge II

NASA Astrophysics Data System (ADS)

Federman, Steven Robert; Heidarian, Negar; Irving, Richard; Ellis, David; Ritchey, Adam M.; Cheng, Song; Curtis, Larry; Furman, Walter

2017-06-01

Radiative transitions of heavy elements are of great importance in astrophysics. Studying the transition rates and their corresponding oscillator strengths allows us to determine abundances of these heavy elements and therefore leads to better understanding of neutron capture processes. We provide the results of our studies on the transitions involving ns2nd 2D and nsnp2 2D terms to the ground term for Pb II, Sn II, and Ge II. These transitions are also of interest due to their strong mixing. Our studies involve experimental measurements performed at the Toledo Heavy Ion Accelerator and theoretical multi-configuration Dirac Hartree-Fock (MCDHF)1 calculations using the development version of the GRASP2K package2. The results are compared with Pb II lines seen in spectra acquired with the Hubble Space Telescope and with other values available in the literature. 1 P. Jönsson et al., The Computational Atomic Structure Group (2014).2 P. Jönsson et al., Comput. Phys. Commun. 184, 2197 (2013).

New Nuclear Magnetic Moment of 209Bi: Resolving the Bismuth Hyperfine Puzzle

NASA Astrophysics Data System (ADS)

Skripnikov, Leonid V.; Schmidt, Stefan; Ullmann, Johannes; Geppert, Christopher; Kraus, Florian; Kresse, Benjamin; Nörtershäuser, Wilfried; Privalov, Alexei F.; Scheibe, Benjamin; Shabaev, Vladimir M.; Vogel, Michael; Volotka, Andrey V.

2018-03-01

A recent measurement of the hyperfine splitting in the ground state of Li-like 80+208Bi has established a "hyperfine puzzle"—the experimental result exhibits a 7 σ deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017), 10.1038/ncomms15484; J. P. Karr, Nat. Phys. 13, 533 (2017), 10.1038/nphys4159]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment (μI) of 209Bi. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of μI(209ipts>) and combine it with nuclear magnetic resonance measurements of Bi (NO3 )3 in nitric acid solutions and of the hexafluoridobismuthate(V) BiF6- ion in acetonitrile. The result clearly reveals that μI(209Bi) is much smaller than the tabulated value used previously. Applying the new magnetic moment shifts the theoretical prediction into agreement with experiment and resolves the hyperfine puzzle.

High-field specific heats of A15 V3Si and Nb3Sn

NASA Astrophysics Data System (ADS)

Stewart, G. R.; Brandt, B. L.

1984-04-01

In order to further understand the anomalous behavior of the specific heat of Nb3Sn in an 18-T magnetic field discovered by Stewart, Cort, and Webb

Band Gap Distortion in Semiconductors Strongly Driven by Intense Mid-Infrared Laser Fields

NASA Astrophysics Data System (ADS)

Kono, J.; Chin, A. H.

2000-03-01

Crystalline solids non-resonantly driven by intense time-periodic electric fields are predicted to exhibit unusual band-gap distortion.(e.g., Y. Yacoby, Phys. Rev. 169, 610 (1968); L.C.M. Miranda, Solid State Commun. 45, 783 (1983); J.Z. Kaminski, Acta Physica Polonica A 83, 495(1993).) Such non-perturbative effects have not been observed to date because of the unavoidable sample damage due to the very high intensity required using conventional lasers ( 1 eV photon energy). Here, we report the first clear evidence of laser-induced bandgap shrinkage in semiconductors under intense mid-infrared (MIR) laser fields. The use of long-wavelength light reduces the required intensity and prohibits strong interband absorption, thereby avoiding the damage problem. The significant sub-bandgap absorption persists only during the existence of the MIR laser pulse, indicating the virtual nature of the effect. We show that this particular example of non-perturbative behavior, known as the dynamical Franz-Keldysh effect, occurs when the effective ponderomotive potential energy is comparable to the photon energy of the applied field. This work was supported by ONR, NSF, JST and NEDO.

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

Michel, D. T.; Maximov, A. V.; Short, R. W.

The fraction of laser energy converted into hot electrons by the two-plasmon-decay instability is found to have different overlapped intensity thresholds for various configurations on the Omega Laser Facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997); J. H. Kelly et al., J. Phys. IV 133, 75 (2006)]. A factor-of-2 difference in the overlapped intensity threshold is observed between two- and four-beam configurations. The overlapped intensity threshold increases by a factor of 2 between the 4- and 18-beam configurations and by a factor of 3 between the 4- and 60-beam configurations. This is explained by a linear common-wavemore » model where multiple laser beams drive a common electron-plasma wave in a wavevector region that bisects the laser beams (resonant common-wave region in k-space). These experimental results indicate that the hot-electron threshold depends on the hydrodynamic parameters at the quarter-critical density surface, the configuration of the laser beams, and the sum of the intensity of the beams that share the same angle with the common-wave vector.« less

Experimental implementation of phase locking in a nonlinear interferometer

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

Wang, Hailong; Jing, Jietai, E-mail: jtjing@phy.ecnu.edu.cn; Marino, A. M.

2015-09-21

Based upon two cascade four-wave mixing processes in two identical hot rubidium vapor cells, a nonlinear interferometer has been experimentally realized [Jing et al., Appl. Phys. Lett. 99, 011110 (2011); Hudelist et al., Nat. Commun. 5, 3049 (2014)]. It has a higher degree of phase sensitivity than a traditional linear interferometer and has many potential applications in quantum metrology. Phase locking of the nonlinear interferometer is needed before it can find its way into applications. In this letter, we investigate the experimental implementation of phase locking of the relative phase between the three beams at different frequencies involved in suchmore » a nonlinear interferometer. We have utilized two different methods, namely, beat note locking and coherent modulation locking. We find that coherent modulation locking can achieve much better phase stability than beat note locking in our system. Our results pave the way for real applications of a nonlinear interferometer in precision measurement and quantum manipulation, for example, phase control in phase-sensitive N-wave mixing process, N-port nonlinear interferometer and quantum-enhanced real-time phase tracking.« less

Gyrokinetic global three-dimensional simulations of linear ion-temperature-gradient modes in Wendelstein 7-X

NASA Astrophysics Data System (ADS)

Kornilov, V.; Kleiber, R.; Hatzky, R.; Villard, L.; Jost, G.

2004-06-01

Using a global approach for solving an ion gyrokinetic model in three-dimensional geometry the linear stability and structure of ion-temperature-gradient (ITG) modes in the configuration of the stellarator Wendelstein 7-X (W7-X) [G. Grieger et al., in Plasma Physics and Controlled Nuclear Fusion Research 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. 3, p. 525.] is studied. The time evolution of electrostatic perturbations is solved as an initial value problem with a particle-in-cell δf method. The vacuum magnetohydrodynamic equilibrium is calculated by the code VMEC [S. P. Hirshman and D. K. Lee, Comput. Phys. Commun. 39, 161 (1986)]. In this work the most unstable ITG mode in W7-X is presented. This mode has a pronounced ballooning-type structure; however, it is not tokamak-like. A driving mechanism analysis using the energy transfer shows that the contribution of curvature effects is non-negligible. The growth rate and the mixing-length estimate for transport are compared with those for ITG modes found in axisymmetric geometries.

Activation energies for the ν=5/2 Fractional Quantum Hall Effect at 10 Tesla

NASA Astrophysics Data System (ADS)

Zhang, Chi; Du, R. R.; Pfeiffer, L. N.; West, K. W.

2010-03-01

We reported on the low-temperature magnetotransport in a high-purity (mobility ˜ 1x10^7cm^2/Vs) modulation-doped GaAs/AlGaAs quantum well with a high electron density (6x10^11 cm-2). A quantized ν=5/2 Hall plateau is observed at B ˜ 10 T, with an activation gap δ5/2˜ 125±10 mK; the plateau can persist up to ˜ 25^o tilt-field. We determined the activation energies δ and quasi-gap energies δ^quasi for the ν=5/2, 7/3, and 8/3 fractional quantum Hall states in tilted-magnetic field (θ). The δ5/2, δ7/3 and the δ5/2^quasi , δ7/3^quasi are found to decrease in θ. We will present the systematic data and discuss their implications on the spin-polarization of ν=5/2 states observed at 10 T.[4pt] [1] R. Willett, Phys. Rev. Lett. 59, 1776 (1987).[0pt] [2] W. Pan et al, Solid State Commun. 119, 641 (2001).

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.

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.

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.

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.

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.

Spin distributions and cross sections of evaporation residues in the 28Si+176Yb reaction

NASA Astrophysics Data System (ADS)

Sudarshan, K.; Tripathi, R.; Sodaye, S.; Sharma, S. K.; Pujari, P. K.; Gehlot, J.; Madhavan, N.; Nath, S.; Mohanto, G.; Mukul, I.; Jhingan, A.; Mazumdar, I.

2017-02-01

Background: Non-compound-nucleus fission in the preactinide region has been an active area of investigation in the recent past. Based on the measurements of fission-fragment mass distributions in the fission of 202Po, populated by reactions with varying entrance channel mass asymmetry, the onset of non-compound-nucleus fission was proposed to be around ZpZt˜1000 [Phys. Rev. C 77, 024606 (2008), 10.1103/PhysRevC.77.024606], where Zp and Zt are the projectile and target proton numbers, respectively. Purpose: The present paper is aimed at the measurement of cross sections and spin distributions of evaporation residues in the 28Si+176Yb reaction (ZpZt=980 ) to investigate the fusion hindrance which, in turn, would give information about the contribution from non-compound-nucleus fission in this reaction. Method: Evaporation-residue cross sections were measured in the beam energy range of 129-166 MeV using the hybrid recoil mass analyzer (HYRA) operated in the gas-filled mode. Evaporation-residue cross sections were also measured by the recoil catcher technique followed by off-line γ -ray spectrometry at few intermediate energies. γ -ray multiplicities of evaporation residues were measured to infer about their spin distribution. The measurements were carried out using NaI(Tl) detector-based 4π-spin spectrometer from the Tata Institute of Fundamental Research, Mumbai, coupled to the HYRA. Results: Evaporation-residue cross sections were significantly lower compared to those calculated using the statistical model code pace2 [Phys. Rev. C 21, 230 (1980), 10.1103/PhysRevC.21.230] with the coupled-channel fusion model code ccfus [Comput. Phys. Commun. 46, 187 (1987), 10.1016/0010-4655(87)90045-2] at beam energies close to the entrance channel Coulomb barrier. At higher beam energies, experimental cross sections were close to those predicted by the model. Average γ -ray multiplicities or angular momentum values of evaporation residues were in agreement with the calculations of the code ccfus + pace2 within the experimental uncertainties at all the beam energies. Conclusions: Deviation of evaporation-residue cross sections from the "fusion + statistical model" predictions at beam energies close to the entrance channel Coulomb barrier indicates fusion hindrance at these beam energies which would lead to non-compound-nucleus fission. However, reasonable agreement of average angular momentum values of evaporation residues at these beam energies with those calculated using the coupled-channel fusion model with the statistical model codes ccfus + pace2 suggests that fusion suppression at beam energies close to the entrance channel Coulomb barrier where populated l waves are low is not l dependent.

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.

Integrated simulations of saturated neoclassical tearing modes in DIII-D, Joint European Torus, and ITER plasmas

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

Halpern, Federico D.; Bateman, Glenn; Kritz, Arnold H.

2006-06-15

A revised version of the ISLAND module [C. N. Nguyen et al., Phys. Plasmas 11, 3604 (2004)] is used in the BALDUR code [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1988)] to carry out integrated modeling simulations of DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)], Joint European Torus (JET) [P. H. Rebut et al., Nucl. Fusion 25, 1011 (1985)], and ITER [R. Aymar et al., Plasma Phys. Control. Fusion 44, 519 (2002)] tokamak discharges in order to investigate the adverse effects of multiple saturated magnetic islands driven by neoclassical tearing modes (NTMs). Simulations are carried outmore » with a predictive model for the temperature and density pedestal at the edge of the high confinement mode (H-mode) plasma and with core transport described using the Multi-Mode model. The ISLAND module, which is used to compute magnetic island widths, includes the effects of an arbitrary aspect ratio and plasma cross sectional shape, the effect of the neoclassical bootstrap current, and the effect of the distortion in the shape of each magnetic island caused by the radial variation of the perturbed magnetic field. Radial transport is enhanced across the width of each magnetic island within the BALDUR integrated modeling simulations in order to produce a self-consistent local flattening of the plasma profiles. It is found that the main consequence of the NTM magnetic islands is a decrease in the central plasma temperature and total energy. For the DIII-D and JET discharges, it is found that inclusion of the NTMs typically results in a decrease in total energy of the order of 15%. In simulations of ITER, it is found that the saturated magnetic island widths normalized by the plasma minor radius, for the lowest order individual tearing modes, are approximately 24% for the 2/1 mode and 12% for the 3/2 mode. As a result, the ratio of ITER fusion power to heating power (fusion Q) is reduced from Q=10.6 in simulations with no NTM islands to Q=2.6 in simulations with fully saturated NTM islands.« less

Acoustic perfect absorber based on metasurface with deep sub-wavelength thickness (Conference Presentation)

NASA Astrophysics Data System (ADS)

Assouar, Badreddine; Li, Yong

2016-04-01

The concept of the coiling up space, based on which artificial structures could exhibit extreme acoustic properties, such as high refractive index, double negativity, near-zero index, etc., have been investigated intensively recently due to the fascinating underlying physics and diverse potential applications [1-3]. One of the most important functionality is the ability to shrink bulky structures into deep sub-wavelength scale. It is therefore intuitive to prospect that the concept of coiling up space, if could be extended into the perforated system, will benefit to significantly reduce the total thickness while keeping total absorption. Conventional acoustic absorbers require a structure with a thickness comparable to the working wavelength, resulting major obstacles in real applications in low frequency range. We present a metasurface-based perfect absorber capable of achieving the total absorption of acoustic wave in extremely low frequency region. The metasurface possessing a deep sub-wavelength thickness down to a feature size of ~ lambda/223 is composed of a perforated plate and a coiled coplanar air chamber. Simulations based on fully coupled acoustic with thermodynamic equations and theoretical impedance analysis are utilized to reveal the underlying physics and the acoustic performances, showing an excellent agreement. Our realization should have high impact on amount of applications due to the extremely thin thickness, easy fabrication and high efficiency of the proposed structure. References 1. Z. Liang and J. Li, Phys. Rev. Lett. 108, 114301 (2012). 2. Y. Li, B. Liang, X. Tao, X. F. Zhu, X. Y. Zou, and J. C. Cheng, Appl. Phys. Lett. 101, 233508 (2012). 3. Y. Xie, W. Wang, H. Chen, A. Konneker, B. I. Popa, and S. A. Cummer, Nat. Commun. 5, 5553 (2014).

Beyond Born-Oppenheimer theory for ab initio constructed diabatic potential energy surfaces of singlet H3+ to study reaction dynamics using coupled 3D time-dependent wave-packet approach.

PubMed

Ghosh, Sandip; Mukherjee, Saikat; Mukherjee, Bijit; Mandal, Souvik; Sharma, Rahul; Chaudhury, Pinaki; Adhikari, Satrajit

2017-08-21

The workability of beyond Born-Oppenheimer theory to construct diabatic potential energy surfaces (PESs) of a charge transfer atom-diatom collision process has been explored by performing scattering calculations to extract accurate integral cross sections (ICSs) and rate constants for comparison with most recent experimental quantities. We calculate non-adiabatic coupling terms among the lowest three singlet states of H 3 + system (1 1 A ' , 2 1 A ' , and 3 1 A ' ) using MRCI level of calculation and solve the adiabatic-diabatic transformation equation to formulate the diabatic Hamiltonian matrix of the same process [S. Mukherjee et al., J. Chem. Phys. 141, 204306 (2014)] for the entire region of nuclear configuration space. The nonadiabatic effects in the D + + H 2 reaction has been studied by implementing the coupled 3D time-dependent wave packet formalism in hyperspherical coordinates [S. Adhikari and A. J. C. Varandas, Comput. Phys. Commun. 184, 270 (2013)] with zero and non-zero total angular momentum (J) on such newly constructed accurate (ab initio) diabatic PESs of H 3 + . We have depicted the convergence profiles of reaction probabilities for the reactive non-charge transfer, non-reactive charge transfer, and reactive charge transfer processes for different collisional energies with respect to the helicity (K) and total angular momentum (J) quantum numbers. Finally, total and state-to-state ICSs are calculated as a function of collision energy for the initial rovibrational state (v = 0, j = 0) of the H 2 molecule, and consequently, those quantities are compared with previous theoretical and experimental results.

Stabilization of electron-scale turbulence by electron density gradient in national spherical torus experiment

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

Ruiz Ruiz, J.; White, A. E.; Ren, Y.

2015-12-15

Theory and experiments have shown that electron temperature gradient (ETG) turbulence on the electron gyro-scale, k{sub ⊥}ρ{sub e} ≲ 1, can be responsible for anomalous electron thermal transport in NSTX. Electron scale (high-k) turbulence is diagnosed in NSTX with a high-k microwave scattering system [D. R. Smith et al., Rev. Sci. Instrum. 79, 123501 (2008)]. Here we report on stabilization effects of the electron density gradient on electron-scale density fluctuations in a set of neutral beam injection heated H-mode plasmas. We found that the absence of high-k density fluctuations from measurements is correlated with large equilibrium density gradient, which ismore » shown to be consistent with linear stabilization of ETG modes due to the density gradient using the analytical ETG linear threshold in F. Jenko et al. [Phys. Plasmas 8, 4096 (2001)] and linear gyrokinetic simulations with GS2 [M. Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)]. We also found that the observed power of electron-scale turbulence (when it exists) is anti-correlated with the equilibrium density gradient, suggesting density gradient as a nonlinear stabilizing mechanism. Higher density gradients give rise to lower values of the plasma frame frequency, calculated based on the Doppler shift of the measured density fluctuations. Linear gyrokinetic simulations show that higher values of the electron density gradient reduce the value of the real frequency, in agreement with experimental observation. Nonlinear electron-scale gyrokinetic simulations show that high electron density gradient reduces electron heat flux and stiffness, and increases the ETG nonlinear threshold, consistent with experimental observations.« less

Enhanced near-infrared photocatalysis of NaYF4:Yb, Tm/CdS/TiO2 composites.

PubMed

Guo, Xingyuan; Di, Weihua; Chen, Changfeng; Liu, Chunxu; Wang, Xue; Qin, Weiping

2014-01-21

The previous works by our group (Chem. Commun., 2010, 46, 2304-2306; ACS Catal., 2013, 3, 405-412; Phys. Chem. Chem. Phys., 2013, 15, 14681-14688) have reported the near-infrared-driven photocatalysis of broadband semiconductor TiO2 or ZnO that was combined with upconverting luminescence particles to form a core-shell structure. However, the photocatalytic efficiency is low for this new type of photocatalysts. In this work, NaYF4:Yb,Tm/CdS/TiO2 composites for NIR photocatalysis were prepared by linking CdS and TiO2 nanocrystals on the NaYF4:Yb,Tm microcrystal surfaces. CdS and TiO2 were well interacted to form a heterojunction structure. The energy transfer between NaYF4:Yb,Tm and the semiconductors CdS and TiO2 was investigated by steady-state and dynamic fluorescence spectroscopy. The photocatalytic activities of the as-prepared composites were evaluated by the degradation of methylene blue in aqueous solution upon NIR irradiation. Significantly, it was found that the united adhesions of CdS and TiO2 on the NaYF4:Yb,Tm particle surfaces showed much higher catalytic activities than the individual adhesion of CdS or TiO2 on the NaYF4:Yb,Tm surfaces. This was attributed mainly to the effective separation of the photogenerated electron-hole pairs due to the charge transfer across the CdS-TiO2 interface driven by the band potential difference between them. The presented composite structure of upconverting luminescence materials coupled with narrow/wide semiconductor heterojunctions provides a new model for improved NIR photocatalysis.

The Riemann Problem for the Multidimensional Isentropic System of Gas Dynamics is Ill-Posed if It Contains a Shock

NASA Astrophysics Data System (ADS)

Markfelder, Simon; Klingenberg, Christian

2018-03-01

In this paper we consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states, where one state lies in the lower and the other state in the upper half plane. The aim is to investigate whether there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. For some initial states this question has been answered by Feireisl and Kreml (J Hyperbolic Differ Equ 12(3):489-499, 2015), and also Chen and Chen (J Hyperbolic Differ Equ 4(1):105-122, 2007), where there exists a unique entropy solution. For other initial states Chiodaroli and Kreml (Arch Ration Mech Anal 214(3):1019-1049, 2014) and Chiodaroli et al. (Commun Pure Appl Math 68(7):1157-1190, 2015), showed that there are infinitely many entropy solutions. For still other initial states the question on uniqueness remained open and this will be the content of this paper. This paper can be seen as a completion of the aforementioned papers by showing that the solution is non-unique in all cases (except if the solution is smooth).

Comments on the papers recently published by M.M. Khandpekar et al.

NASA Astrophysics Data System (ADS)

Petrosyan, A. M.; Ghazaryan, V. V.; Fleck, M.

2011-09-01

It is argued that the existence of the new compounds of glycine recently reported by M.M. Khandpekar et al. (Optics Commun. 284(2011) 1583 and Optics Commun. 284(2011) 1578) is dubious. We argue that these compounds are not what the authors propose. In addition, two more similar cases are indicated.

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.

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.

Numerical algorithms for cold-relativistic plasma models in the presence of discontinuties

NASA Astrophysics Data System (ADS)

Hakim, Ammar; Cary, John; Bruhwiler, David; Geddes, Cameron; Leemans, Wim; Esarey, Eric

2006-10-01

A numerical algorithm is presented to solve cold-relativistic electron fluid equations in the presence of sharp gradients and discontinuities. The intended application is to laser wake-field accelerator simulations in which the laser induces accelerating fields thousands of times those achievable in conventional RF accelerators. The relativistic cold-fluid equations are formulated as non-classical system of hyperbolic balance laws. It is shown that the flux Jacobian for this system can not be diagonalized which causes numerical difficulties when developing shock-capturing algorithms. Further, the system is shown to admit generalized delta-shock solutions, first discovered in the context of sticky-particle dynamics (Bouchut, Ser. Adv. Math App. Sci., 22 (1994) pp. 171--190). A new approach, based on relaxation schemes proposed by Jin and Xin (Comm. Pure Appl. Math. 48 (1995) pp. 235--276) and LeVeque and Pelanti (J. Comput. Phys. 172 (2001) pp. 572--591) is developed to solve this system of equations. The method consists of finding an exact solution to a Riemann problem at each cell interface and coupling these to advance the solution in time. Applications to an intense laser propagating in an under-dense plasma are presented.

nMoldyn: a program package for a neutron scattering oriented analysis of molecular dynamics simulations.

PubMed

Róg, T; Murzyn, K; Hinsen, K; Kneller, G R

2003-04-15

We present a new implementation of the program nMoldyn, which has been developed for the computation and decomposition of neutron scattering intensities from Molecular Dynamics trajectories (Comp. Phys. Commun 1995, 91, 191-214). The new implementation extends the functionality of the original version, provides a much more convenient user interface (both graphical/interactive and batch), and can be used as a tool set for implementing new analysis modules. This was made possible by the use of a high-level language, Python, and of modern object-oriented programming techniques. The quantities that can be calculated by nMoldyn are the mean-square displacement, the velocity autocorrelation function as well as its Fourier transform (the density of states) and its memory function, the angular velocity autocorrelation function and its Fourier transform, the reorientational correlation function, and several functions specific to neutron scattering: the coherent and incoherent intermediate scattering functions with their Fourier transforms, the memory function of the coherent scattering function, and the elastic incoherent structure factor. The possibility to compute memory function is a new and powerful feature that allows to relate simulation results to theoretical studies. Copyright 2003 Wiley Periodicals, Inc. J Comput Chem 24: 657-667, 2003

TopoMS: Comprehensive topological exploration for molecular and condensed-matter systems.

PubMed

Bhatia, Harsh; Gyulassy, Attila G; Lordi, Vincenzo; Pask, John E; Pascucci, Valerio; Bremer, Peer-Timo

2018-06-15

We introduce TopoMS, a computational tool enabling detailed topological analysis of molecular and condensed-matter systems, including the computation of atomic volumes and charges through the quantum theory of atoms in molecules, as well as the complete molecular graph. With roots in techniques from computational topology, and using a shared-memory parallel approach, TopoMS provides scalable, numerically robust, and topologically consistent analysis. TopoMS can be used as a command-line tool or with a GUI (graphical user interface), where the latter also enables an interactive exploration of the molecular graph. This paper presents algorithmic details of TopoMS and compares it with state-of-the-art tools: Bader charge analysis v1.0 (Arnaldsson et al., 01/11/17) and molecular graph extraction using Critic2 (Otero-de-la-Roza et al., Comput. Phys. Commun. 2014, 185, 1007). TopoMS not only combines the functionality of these individual codes but also demonstrates up to 4× performance gain on a standard laptop, faster convergence to fine-grid solution, robustness against lattice bias, and topological consistency. TopoMS is released publicly under BSD License. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Impurity sputtering from the guard limiter of the lower hybrid wave antenna in a tokamak

NASA Astrophysics Data System (ADS)

Ou, Jing; Xiang, Nong; Men, Zongzheng

2018-01-01

The hot spots on the guard limiter of the lower hybrid wave (LHW) antenna in a tokamak were believed to be associated with the energetic electrons produced by the wave-plasma interaction, leading to a sudden increase of impurity influx and even ending with disruption. To investigate the carbon sputtering from the guard limiter of the LHW antenna, the impurity sputtering yield is calculated by coupling the module of Plasma Surface Interaction [Warrier et al., Comput. Phys. Commun. 46, 160 (2004)] with the models for the sheath of plasma containing energetic electron and for the material heat transport. It is found that the presence of a small population of energetic electrons can change significantly the impurity sputtering yield, as a result of the sheath potential modification. For the typical plasma parameters in the current tokamak, with an increase in the energetic electron component, the physical sputtering yield reaches its maximum and then decreases slowly, while the chemical sputtering yield demonstrates a very sharp increase and then decreases rapidly. In addition, effects of the ion temperature and background electron density on the impurity sputtering are also discussed.

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.

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.

GLoBES: General Long Baseline Experiment Simulator

NASA Astrophysics Data System (ADS)

Huber, Patrick; Kopp, Joachim; Lindner, Manfred; Rolinec, Mark; Winter, Walter

2007-09-01

GLoBES (General Long Baseline Experiment Simulator) is a flexible software package to simulate neutrino oscillation long baseline and reactor experiments. On the one hand, it contains a comprehensive abstract experiment definition language (AEDL), which allows to describe most classes of long baseline experiments at an abstract level. On the other hand, it provides a C-library to process the experiment information in order to obtain oscillation probabilities, rate vectors, and Δχ-values. Currently, GLoBES is available for GNU/Linux. Since the source code is included, the port to other operating systems is in principle possible. GLoBES is an open source code that has previously been described in Computer Physics Communications 167 (2005) 195 and in Ref. [7]). The source code and a comprehensive User Manual for GLoBES v3.0.8 is now available from the CPC Program Library as described in the Program Summary below. The home of GLobES is http://www.mpi-hd.mpg.de/~globes/. Program summaryProgram title: GLoBES version 3.0.8 Catalogue identifier: ADZI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADZI_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.: 145 295 No. of bytes in distributed program, including test data, etc.: 1 811 892 Distribution format: tar.gz Programming language: C Computer: GLoBES builds and installs on 32bit and 64bit Linux systems Operating system: 32bit or 64bit Linux RAM: Typically a few MBs Classification: 11.1, 11.7, 11.10 External routines: GSL—The GNU Scientific Library, www.gnu.org/software/gsl/ Nature of problem: Neutrino oscillations are now established as the leading flavor transition mechanism for neutrinos. In a long history of many experiments, see, e.g., [1], two oscillation frequencies have been identified: The fast atmospheric and the slow solar oscillations, which are driven by the respective mass squared differences. In addition, there could be interference effects between these two oscillations, provided that the coupling given by the small mixing angle θ is large enough. Such interference effects include, for example, leptonic CP violation. In order to test the unknown oscillation parameters, i.e. the mixing angle θ, the leptonic CP phase, and the neutrino mass hierarchy, new long-baseline and reactor experiments are proposed. These experiments send an artificial neutrino beam to a detector, or detect the neutrinos produced by a nuclear fission reactor. However, the presence of multiple solutions which are intrinsic to neutrino oscillation probabilities [2-5] affect these measurements. Thus optimization strategies are required which maximally exploit complementarity between experiments. Therefore, a modern, complete experiment simulation and analysis tool does not only need to have a highly accurate beam and detector simulation, but also powerful means to analyze correlations and degeneracies, especially for the combination of several experiments. The GLoBES software package is such a tool [6,7]. Solution method: GLoBES is a flexible software tool to simulate and analyze neutrino oscillation long-baseline and reactor experiments using a complete three-flavor description. On the one hand, it contains a comprehensive abstract experiment definition language (AEDL), which makes it possible to describe most classes of long baseline and reactor experiments at an abstract level. On the other hand, it provides a C-library to process the experiment information in order to obtain oscillation probabilities, rate vectors, and Δχ-values. In addition, it provides a binary program to test experiment definitions very quickly, before they are used by the application software. Restrictions: Currently restricted to discrete sets of sources and detectors. For example, the simulation of an atmospheric neutrino flux is not supported. Unusual features: Clear separation between experiment description and the simulation software. Additional comments: To find information on the latest version of the software and user manual, please check the author's web site, http://www.mpi-hd.mpg.de/~globes Running time: The examples included in the distribution take only a few minutes to complete. More sophisticated problems can take up to several days. References [1] V. Barger, D. Marfatia, K. Whisnant, Int. J. Mod. Phys. E 12 (2003) 569, hep-ph/0308123, and references therein. [2] G.L. Fogli, E. Lisi, Phys. Rev. D 54 (1996) 3667, hep-ph/9604415. [3] J. Burguet-Castell, M.B. Gavela, J.J. Gomez-Cadenas, P. Hernandez, O. Mena, Nucl. Phys. B 608 (2001) 301, hep-ph/0103258. [4] H. Minakata, H. Nunokawa, JHEP 0110 (2001) 001, hep-ph/0108085. [5] V. Barger, D. Marfatia, K. Whisnant, Phys. Rev. D 65 (2002) 073023, hep-ph/0112119. [6] P. Huber, M. Lindner, W. Winter, Comput. Phys. Commun. 167 (2005) 195. [7] P. Huber, J. Kopp, M. Lindner, M. Rolinec, W. Winter, Comput. Phys. Commun. 177 (2007) 432.

RIS3: A program for relativistic isotope shift calculations

NASA Astrophysics Data System (ADS)

Nazé, C.; Gaidamauskas, E.; Gaigalas, G.; Godefroid, M.; Jönsson, P.

2013-09-01

An atomic spectral line is characteristic of the element producing the spectrum. The line also depends on the isotope. The program RIS3 (Relativistic Isotope Shift) calculates the electron density at the origin and the normal and specific mass shift parameters. Combining these electronic quantities with available nuclear data, isotope-dependent energy level shifts are determined. Program summaryProgram title:RIS3 Catalogue identifier: ADEK_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADEK_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.: 5147 No. of bytes in distributed program, including test data, etc.: 32869 Distribution format: tar.gz Programming language: Fortran 77. Computer: HP ProLiant BL465c G7 CTO. Operating system: Centos 5.5, which is a Linux distribution compatible with Red Hat Enterprise Advanced Server. Classification: 2.1. Catalogue identifier of previous version: ADEK_v1_0 Journal reference of previous version: Comput. Phys. Comm. 100 (1997) 81 Subprograms used: Cat Id Title Reference ADZL_v1_1 GRASP2K VERSION 1_1 to be published. Does the new version supersede the previous version?: Yes Nature of problem: Prediction of level and transition isotope shifts in atoms using four-component relativistic wave functions. Solution method: The nuclear motion and volume effects are treated in first order perturbation theory. Taking the zero-order wave function in terms of a configuration state expansion |Ψ>=∑μcμ|Φ(γμPJMj)>, where P, J and MJ are, respectively, the parity and angular quantum numbers, the electron density at the nucleus and the normal and specific mass shift parameters may generally be expressed as ∑cμcν<γμPJMj|V|γνPJMj> where V is the relevant operator. The matrix elements, in turn, can be expressed as sums over radial integrals multiplied by angular coefficients. All the angular coefficients are calculated using routines from the GRASP2K version 1_1 package [1]. Reasons for new version: This new version takes the nuclear recoil corrections into account within the (m2/M approximation [2] and also allows storage of the angular coefficients for a series of calculations within a given isoelectronic sequence. Furthermore, the program JJ2LSJ, a module of the GRASP2K version 1_1 toolkit that allows a transformation of ASFs from a jj-coupled CSF basis into an LSJ-coupled CSF basis, has been especially adapted to present RIS3 results using LSJ labels of the states. This additional tool is called RIS3_LSJ. Summary of revisions: This version is compatible with the new angular approach of the GRASP2K version 1_1 package [1] and can store necessary angular coefficients. According to the formalism of the relativistic nuclear recoil, the "uncorrected" expression of the normal mass shift has been fundamentally modified compared with its expression in [3]. Restrictions: The complexity of the cases that can be handled is entirely determined by the GRASP2K package [1] used for the generation of the electronic wave functions. Unusual features: Angular data is stored on disk and can be reused. LSJ labels are used for the states. Running time: As an example, we evaluated the isotope shift parameters and the electron density at the origin using the wave functions of Be-like system. We used the MCDHF wave function built on a complete active space (CAS) with n=8 (296 626 CSFs-62 orbitals) that contains 3 non-interacting blocks of given parity and J values involving 6 different eigenvalues in total. Calculations take around 10 h on one AMD Opteron 6100 @ 2.3 GHz CPU with 8 cores (64 GB DDR3 RAM 1.333 GHz). If angular files are available the time is reduced to 20 min. The storage of the angular data takes 139 MB and 7.2 GB for the one-body and the two-body elements, respectively. References: [1] P. Jönsson, G. Gaigalas, J. Bieroń, C. Froese Fischer, I.P. Grant, New version: GRASP2K relativistic atomic structure package, Comput. Phys. Commun. 184 (9) (2013) 2197-2203. [2] E. Gaidamauskas, C. Nazé, P. Rynkun, G. Gaigalas, P. Jönsson, M. Godefroid, J. Phys. B: At. Mol. Opt. Phys. 44 (17) (2011) 175003. [3] P. Jönsson, C. Froese Fischer, Comput. Phys. Commun. 100 (1997) 81-92.

Comment on "Applications of homogenous balanced principle on investigating exact solutions to a series of time fractional nonlinear PDEs", [Commun Nonlinear Sci Numer Simulat 47 (2017) 253-266

NASA Astrophysics Data System (ADS)

Li, Xiangzheng

2018-06-01

A counterexample is given to show that the product rule of the Caputo fractional derivatives does not hold except on a special point. The function-expansion method of separation variable proposed by Rui[Commun Nonlinear Sci Numer Simulat 47 (2017) 253-266] based on the product rule must be modified.

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.

ROOT — A C++ framework for petabyte data storage, statistical analysis and visualization

NASA Astrophysics Data System (ADS)

Antcheva, I.; Ballintijn, M.; Bellenot, B.; Biskup, M.; Brun, R.; Buncic, N.; Canal, Ph.; Casadei, D.; Couet, O.; Fine, V.; Franco, L.; Ganis, G.; Gheata, A.; Maline, D. Gonzalez; Goto, M.; Iwaszkiewicz, J.; Kreshuk, A.; Segura, D. Marcos; Maunder, R.; Moneta, L.; Naumann, A.; Offermann, E.; Onuchin, V.; Panacek, S.; Rademakers, F.; Russo, P.; Tadel, M.

2011-06-01

A new stable version ("production version") v5.28.00 of ROOT [1] has been published [2]. It features several major improvements in many areas, most noteworthy data storage performance as well as statistics and graphics features. Some of these improvements have already been predicted in the original publication Antcheva et al. (2009) [3]. This version will be maintained for at least 6 months; new minor revisions ("patch releases") will be published [4] to solve problems reported with this version. New version program summaryProgram title: ROOT Catalogue identifier: AEFA_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFA_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Lesser Public License v.2.1 No. of lines in distributed program, including test data, etc.: 2 934 693 No. of bytes in distributed program, including test data, etc.: 1009 Distribution format: tar.gz Programming language: C++ Computer: Intel i386, Intel x86-64, Motorola PPC, Sun Sparc, HP PA-RISC Operating system: GNU/Linux, Windows XP/Vista/7, Mac OS X, FreeBSD, OpenBSD, Solaris, HP-UX, AIX Has the code been vectorized or parallelized?: Yes RAM: > 55 Mbytes Classification: 4, 9, 11.9, 14 Catalogue identifier of previous version: AEFA_v1_0 Journal reference of previous version: Comput. Phys. Commun. 180 (2009) 2499 Does the new version supersede the previous version?: Yes Nature of problem: Storage, analysis and visualization of scientific data Solution method: Object store, wide range of analysis algorithms and visualization methods Reasons for new version: Added features and corrections of deficiencies Summary of revisions: The release notes at http://root.cern.ch/root/v528/Version528.news.html give a module-oriented overview of the changes in v5.28.00. Highlights include File format Reading of TTrees has been improved dramatically with respect to CPU time (30%) and notably with respect to disk space. Histograms A new TEfficiency class has been provided to handle the calculation of efficiencies and their uncertainties, TH2Poly for polygon-shaped bins (e.g. maps), TKDE for kernel density estimation, and TSVDUnfold for singular value decomposition. Graphics Kerning is now supported in TLatex, PostScript and PDF; a table of contents can be added to PDF files. A new font provides italic symbols. A TPad containing GL can be stored in a binary (i.e. non-vector) image file; add support for full-scene anti-aliasing. Usability enhancements to EVE. Math New interfaces for generating random number according to a given distribution, goodness of fit tests of unbinned data, binning multidimensional data, and several advanced statistical functions were added. RooFit Introduction of HistFactory; major additions to RooStats. TMVA Updated to version 4.1.0, adding e.g. the support for simultaneous classification of multiple output classes for several multivariate methods. PROOF Many new features, adding to PROOF's usability, plus improvements and fixes. PyROOT Support of Python 3 has been added. Tutorials Several new tutorials were provided for above new features (notably RooStats). A detailed list of all the changes is available at http://root.cern.ch/root/htmldoc/examples/V5. Additional comments: For an up-to-date author list see: http://root.cern.ch/drupal/content/root-development-team and http://root.cern.ch/drupal/content/former-root-developers. The distribution file for this program is over 30 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: Depending on the data size and complexity of analysis algorithms. References: id="pr0100" view="all">http://root.cern.ch. http://root.cern.ch/drupal/content/production-version-528. I. Antcheva, M. Ballintijn, B. Bellenot, M. Biskup, R. Brun, N. Buncic, Ph. Canal, D. Casadei, O. Couet, V. Fine, L. Franco, G. Ganis, A. Gheata, D. Gonzalez Maline, M. Goto, J. Iwaszkiewicz, A. Kreshuk, D. Marcos Segura, R. Maunder, L. Moneta, A. Naumann, E. Offermann, V. Onuchin, S. Panacek, F. Rademakers, P. Russo, M. Tadel, ROOT — A C++ framework for petabyte data storage, statistical analysis and visualization, Comput. Phys. Commun. 180 (2009) 2499. http://root.cern.ch/drupal/content/root-version-v5-28-00-patch-release-notes.

An Improved Protocol for Controlled Deterministic Secure Quantum Communication Using Five-Qubit Entangled State

NASA Astrophysics Data System (ADS)

Kao, Shih-Hung; Lin, Jason; Tsai, Chia-Wei; Hwang, Tzonelih

2018-03-01

In early 2009, Xiu et al. (Opt. Commun. 282(2) 333-337 2009) presented a controlled deterministic secure quantum communication (CDSQC) protocol via a newly constructed five-qubit entangled quantum state. Later, Qin et al. (Opt. Commun. 282(13), 2656-2658 2009) pointed out two security loopholes in Xiu et al.'s protocol: (1) A correlation-elicitation (CE) attack can reveal the entire secret message; (2) A leakage of partial information for the receiver is noticed. Then, Xiu et al. (Opt. Commun. 283(2), 344-347 2010) presented a revised CDSQC protocol to remedy the CE attack problem. However, the information leakage problem still remains open. This work proposes a new CDSQC protocol using the same five-qubit entangled state which can work without the above mentioned security problems. Moreover, the Trojan Horse attacks can be automatically avoided without using detecting devices in the new CDSQC.

An Improved Protocol for Controlled Deterministic Secure Quantum Communication Using Five-Qubit Entangled State

NASA Astrophysics Data System (ADS)

Kao, Shih-Hung; Lin, Jason; Tsai, Chia-Wei; Hwang, Tzonelih

2018-06-01

In early 2009, Xiu et al. (Opt. Commun. 282(2) 333-337 2009) presented a controlled deterministic secure quantum communication (CDSQC) protocol via a newly constructed five-qubit entangled quantum state. Later, Qin et al. (Opt. Commun. 282(13), 2656-2658 2009) pointed out two security loopholes in Xiu et al.'s protocol: (1) A correlation-elicitation (CE) attack can reveal the entire secret message; (2) A leakage of partial information for the receiver is noticed. Then, Xiu et al. (Opt. Commun. 283(2), 344-347 2010) presented a revised CDSQC protocol to remedy the CE attack problem. However, the information leakage problem still remains open. This work proposes a new CDSQC protocol using the same five-qubit entangled state which can work without the above mentioned security problems. Moreover, the Trojan Horse attacks can be automatically avoided without using detecting devices in the new CDSQC.

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.].

The Vlasov-Poisson-Boltzmann System for a Disparate Mass Binary Mixture

NASA Astrophysics Data System (ADS)

Duan, Renjun; Liu, Shuangqian

2017-11-01

The Vlasov-Poisson-Boltzmann system is often used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are described by the two-component Boltzmann collision operator. The perturbation theory of the system around global Maxwellians recently has been well established in Guo (Commun Pure Appl Math 55:1104-1135, 2002). It should be more interesting to further study the existence and stability of nontrivial large time asymptotic profiles for the system even with slab symmetry in space, particularly understanding the effect of the self-consistent potential on the non-trivial long-term dynamics of the binary system. In this paper, we consider the problem in the setting of rarefaction waves. The analytical tool is based on the macro-micro decomposition introduced in Liu et al. (Physica D 188(3-4):178-192, 2004) that we have been able to develop for the case of the two-component Boltzmann equations around local bi-Maxwellians. Our focus is to explore how the disparate masses and charges of particles play a role in the analysis of the approach of the complex coupling system time-asymptotically toward a non-constant equilibrium state whose macroscopic quantities satisfy the quasineutral nonisentropic Euler system.

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. 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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

Inhomogeneities in particle composition of single, levitated aerosol particles observed by Mie resonance spectroscopy

NASA Astrophysics Data System (ADS)

Krieger, Ulrich; Lienhard, Daniel; Bastelberger, Sandra; Steimer, Sarah

2014-05-01

Recent observations have indicated that organic aerosol particles in the atmosphere may exist in an amorphous semi-solid or even solid (i.e. glassy) state, e.g. [1]. The influence of highly viscous and glassy states on the timescale of aerosol particle equilibration with respect to water vapor have been investigated for some model systems of atmospheric aerosol, e.g. [2,3]. In particular, it has been shown that the kinetics of the water absorption/desorption process is controlled entirely by liquid-phase diffusion of water molecules for a highly viscous aerosol particle. A liquid phase diffusion model based on numerically solving the non-linear diffusion equation predicts strong internal gradients in water concentration when condensed phase diffusion impedes the water uptake from the gas phase [2]. Here we observe and quantify the internal concentration gradients in single, levitated, micron size aerosol particles of aqueous shikimic acid using elastic Mie resonance spectroscopy. A single, aqueous particle is levitated in an electro-dynamic balance (for details see [2]), dried for several days at room temperature, cooled to the target temperature and exposed to a rapid change in relative humidity. In addition to measuring the elastically backscattered light of a "white light" LED source and recording the full spectrum with a spectrograph as in [2], we use a tunable diode laser (TDL) to scan high resolution TE- and TM spectra. This combination allows observing various Mie resonance mode orders simultaneously. Since we perform the experiment at low temperatures and low humidities the changes in the Mie-spectra due to water uptake are sufficiently slow to resolve the kinetics. Experimental Mie resonance spectra are inverted to concentration profiles of water within the particle by applying the numerical diffusion model [2] in conjunction with Mie calculations of multilayered spheres [4]. [1] A. Virtanen et al. (2010): An amorphous solid state of biogenic secondary organic aerosol particles, Nature 467, 824-827. [2] B. Zobrist et al. (2011): Ultra-slow water diffusion in aqueous sucrose glasses, Phys. Chem. Chem. Phys. 13, 3514-3526. [3] D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger (2012): Comparing the mechanism of water condensation and evaporation in glassy aerosol, PNAS 109, 11613-11618. [4] O. Peña and U. Pal (2009): Scattering of electromagnetic radiation by a multilayered sphere, Comput. Phys. Commun. 180, 2348-2354.

Genetic and Environmental Pathways in Type 1 Diabetes Complication

DTIC Science & Technology

2008-06-01

obese diabetic mice. Biochem Biophys Res Commun 2002. 294:592-596. 4. Beyan H, Goodier MR, Nawroly NS, Hawa MI, Bustin SA, Ogunkolade WB, Londei M...peroxidation in patients with hyperglycemic crisis . Diabetes 2004. 53:2079-2086. 14 In our second quarterly scientific progress report (09/01/07 – 11...cells induced to differentiate into insulin-positive cells. Biochem Biophys Res Commun . 2007;357(2):414-20. 44. Takahashi K, Tanabe K, Ohnuki M, Narita

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)

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.

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.

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).

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.

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

Wireless Powered Cooperative Communications: Power-Splitting Relaying With Energy Accumulation (Author’s Manuscript)

DTIC Science & Technology

2016-03-21

2016 2 i.e., wireless power transfer (WPT) and wireless information transfer (WIT), fundamental changes to the designs of green communication networks...simulta- neous wireless information and power transfer ,” IEEE Commun. Mag., vol. 53, no. 4, pp. 86–93, Apr. 2015. [6] H. Tabassum, E. Hossain, A...broadcasting for simultaneous wire- less information and power transfer ,” IEEE Trans. Wireless Commun., vol. 12, no. 5, pp. 1989–2001, May 2013. [9] K. Huang

Error suppression and correction for quantum annealing

NASA Astrophysics Data System (ADS)

Lidar, Daniel

While adiabatic quantum computing and quantum annealing enjoy a certain degree of inherent robustness against excitations and control errors, there is no escaping the need for error correction or suppression. In this talk I will give an overview of our work on the development of such error correction and suppression methods. We have experimentally tested one such method combining encoding, energy penalties and decoding, on a D-Wave Two processor, with encouraging results. Mean field theory shows that this can be explained in terms of a softening of the closing of the gap due to the energy penalty, resulting in protection against excitations that occur near the quantum critical point. Decoding recovers population from excited states and enhances the success probability of quantum annealing. Moreover, we have demonstrated that using repetition codes with increasing code distance can lower the effective temperature of the annealer. References: K.L. Pudenz, T. Albash, D.A. Lidar, ``Error corrected quantum annealing with hundreds of qubits'', Nature Commun. 5, 3243 (2014). K.L. Pudenz, T. Albash, D.A. Lidar, ``Quantum annealing correction for random Ising problems'', Phys. Rev. A. 91, 042302 (2015). S. Matsuura, H. Nishimori, T. Albash, D.A. Lidar, ``Mean Field Analysis of Quantum Annealing Correction''. arXiv:1510.07709. W. Vinci et al., in preparation.

Analysis of scattering by spheres having a negative acoustical refractive index

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2005-04-01

Electromagnetic waves having oppositely directed phase and group velocities propagate in metamaterials having a negative permeability and negative permittivity [J. B. Pendry and D. R. Smith, Phys. Today 57(6), 37-44 (2004)]. Such materials are predicted to have unusual electromagnetic scattering properties [R. Ruppin, Solid State Commun. 116, 411-415 (2000)]. If it is possible to fabricate acoustical materials having a simultaneously negative effective elastic modulus and density (in a dynamical sense), the mechanical energy flux will have the opposite direction as the wave-vector associated with phase evolution. Rays descriptive of the energy flux refracted by such hypothetical materials at interfaces with ordinary fluids would be characterized by a negative acoustical refractive index. Partial-wave-series calculations of high frequency scattering by fluid spheres having an acoustical refractive index at (or close to) 1 reveal backscattering enhancements associated with glory rays which, unlike ordinary spheres [P. L. Marston and D. S. Langley, J. Acoust. Soc. Am. 73, 1464-1475 (1983)], require only a single internal chord. Generalized Lamb waves on elastic shells having opposite phase and group velocities also cause enhanced backscattering associated with unusual rays [G. Kaduchak, D. H. Hughes, and P. L. Marston, J. Acoust. Soc. Am. 96, 3704-3714 (1994)].

Towards an accurate representation of electrostatics in classical force fields: Efficient implementation of multipolar interactions in biomolecular simulations

NASA Astrophysics Data System (ADS)

Sagui, Celeste; Pedersen, Lee G.; Darden, Thomas A.

2004-01-01

The accurate simulation of biologically active macromolecules faces serious limitations that originate in the treatment of electrostatics in the empirical force fields. The current use of "partial charges" is a significant source of errors, since these vary widely with different conformations. By contrast, the molecular electrostatic potential (MEP) obtained through the use of a distributed multipole moment description, has been shown to converge to the quantum MEP outside the van der Waals surface, when higher order multipoles are used. However, in spite of the considerable improvement to the representation of the electronic cloud, higher order multipoles are not part of current classical biomolecular force fields due to the excessive computational cost. In this paper we present an efficient formalism for the treatment of higher order multipoles in Cartesian tensor formalism. The Ewald "direct sum" is evaluated through a McMurchie-Davidson formalism [L. McMurchie and E. Davidson, J. Comput. Phys. 26, 218 (1978)]. The "reciprocal sum" has been implemented in three different ways: using an Ewald scheme, a particle mesh Ewald (PME) method, and a multigrid-based approach. We find that even though the use of the McMurchie-Davidson formalism considerably reduces the cost of the calculation with respect to the standard matrix implementation of multipole interactions, the calculation in direct space remains expensive. When most of the calculation is moved to reciprocal space via the PME method, the cost of a calculation where all multipolar interactions (up to hexadecapole-hexadecapole) are included is only about 8.5 times more expensive than a regular AMBER 7 [D. A. Pearlman et al., Comput. Phys. Commun. 91, 1 (1995)] implementation with only charge-charge interactions. The multigrid implementation is slower but shows very promising results for parallelization. It provides a natural way to interface with continuous, Gaussian-based electrostatics in the future. It is hoped that this new formalism will facilitate the systematic implementation of higher order multipoles in classical biomolecular force fields.

Flood of January 1997 in the Carson River Basin, California and Nevada

USGS Publications Warehouse

Thomas, Karen A.; Williams, Rhea P.

1997-01-01

In late December 1996, storms built up a large snowpack (more than 180 percent of normal) in the higher altitudes of the Sierra Nevada (Daniel Greenlee, Natural Resource Conservation Service, oral commun., 1997) and also covered the valleys along the eastern Sierra Nevada. Then, a subtropical storm system originating in the central Pacific Ocean near the Hawaiian Islands brought heavy, unseasonably warm rain to the Sierra Nevada from December 30, 1996, through January 2, 1997. During this period, the Natural Resource Conservation Service recorded 16.4 inches (provisional data; Daniel Greenlee, oral commun., 1997) of precipitation at Ebbetts Pass, Calif. (8,700 feet above sea level), and the National Weather Service recorded 3.5 inches (National Oceanic and Atmospheric Administration, National Climate Data Center, written commun., 1997) at Minden (4,710 feet above sea level). Rain falling below about 10,000 feet depleted about 20 percent of the high-altitude snowpack and melted about 80 percent of the snowpack below about 7,000 feet.

Digital data sets that describe aquifer characteristics of the Rush Springs Aquifer in western Oklahoma

USGS Publications Warehouse

Runkle, D.L.; Becker, M.F.; Rea, Alan

1997-01-01

This diskette contains digitized aquifer boundaries and maps of hydraulic conductivity, recharge, and ground-water level elevation contours for the Rush Spring aquifer in western Oklahoma. This area encompasses all or part of Blaine, Caddo, Canadian, Comanche, Custer, Dewey, Grady, Stephens, and Washita Counties. These digital data sets were developed by Mark F. Becker to use as input into a computer model that simulated ground-water flow in the Rush Springs aquifer (Mark F. Becker, U.S. Geological Survey, written commun., 1997). For the purposes of modeling the ground-water flow in the Rush Springs aquifer, Mark F. Becker (written commun., 1997) defined the Rush Springs aquifer to include the Rush Springs Formation, alluvial and terrace deposits along major streams, and parts of the Marlow Formations, particularly in the eastern part of the aquifer boundary area. The Permian-age Rush Springs Formation consists of highly cross-bedded sandstone with some interbedded dolomite and gypsum. The Rush Springs Formation is overlain by Quaternary-age alluvial and terrace deposits that consist of unconsolidated clay, silt, sand, and gravel. The Rush Springs Formation is underlain by the Permian-age Marlow Formation that consists of interbedded sandstones, siltstones, mudstones, gypsum-anhydrite, and dolomite beds (Mark F. Becker, written commun., 1997). The parts of the Marlow Formation that have high permeability and porosity are where the Marlow Formation is included as part of the Rush Springs aquifer. The Rush Springs aquifer underlies about 2,400 square miles of western Oklahoma and is an important source of water for irrigation, livestock, industrial, municipal, and domestic use. Irrigation wells are reported to have well yields greater than 1,000 gallons per minute (Mark F. Becker, written commun., 1997). Mark F. Becker created some of the aquifer boundaries, hydraulic conductivity, and recharge data sets by digitizing parts of previously published surficial geology maps. The hydraulic conductivity and recharge values are the input data to the ground-water flow model (Mark F. Becker, written commun., 1997). The water-level elevation data set was prepared at a scale of 1:250,000 by Mark F. Becker (written commun., 1997) from water levels measured in wells prior to the year 1950. Ground-water flow models are numerical representations that simplify and aggregate natural systems. Models are not unique; different combinations of aquifer characteristics may produce similar results. Therefore, values of hydraulic conductivity and recharge used in the model and presented in this data set are not precise, but are within a reasonable range when compared to independently collected data.

Erratum to "10 Gbit/s mode-multiplexed QPSK transmission using MDM-to-MFDM based single coherent receiver for intra- and inter data center networking" [Opt. Commun. 391 (2017) 106-110

NASA Astrophysics Data System (ADS)

Asif, Rameez; Haithem, Mustafa

2018-03-01

We revisited our previous work "10 Gbit/s mode-multiplexed QPSK transmission using MDM-to-MFDM based single coherent receiver for intraand inter data center networking" [Opt. Commun. 391 (2017) 106-110] and discover a mistake in the Appendix 'A', i.e. mode-selective coherent detection technique. In this section, the direct referencing of the previous work at appropriate points is not adequate (page no. 109).

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.

Eavesdropping on the improved three-party quantum secret sharing protocol

NASA Astrophysics Data System (ADS)

Gao, Gan

2011-02-01

Lin et al. [Song Lin, Fei Gao, Qiao-yan Wen, Fu-chen Zhu, Opt. Commun. 281 (2008) 4553] pointed out that the multiparty quantum secret sharing protocol [Zhan-jun Zhang, Gan Gao, Xin Wang, Lian-fang Han, Shou-hua Shi, Opt. Commun. 269 (2007) 418] is not secure and proposed an improved three-party quantum secret sharing protocol. In this paper, we study the security of the improved three-party quantum secret sharing protocol and find that it is still not secure. Finally, a further improved three-party quantum secret sharing protocol is proposed.

Radial inhomogeneities in particle composition of single, levitated aerosol particles observed by Mie resonance spectroscopy (Invited)

NASA Astrophysics Data System (ADS)

Krieger, U. K.; Steimer, S.; Lienhard, D.; Bastelberger, S.

2013-12-01

Recent observations have indicated that organic aerosol particles in the atmosphere may exist in an amorphous semi-solid or even solid (i.e. glassy) state, e.g. [1]. The influence of highly viscous and glassy states on the timescale of aerosol particle equilibration with respect to water vapor have been investigated for some model systems of atmospheric aerosol, e.g. [2,3]. In particular, it has been shown that the kinetics of the water absorption/desorption process is controlled entirely by liquid-phase diffusion of water molecules for a highly viscous aerosol particle. A liquid phase diffusion model based on numerically solving the non-linear diffusion equation predicts strong internal gradients in water concentration when condensed phase diffusion impedes the water uptake from the gas phase [2]. Here we observe and quantify the internal concentration gradients in single, levitated, micron size aerosol particles of aqueous MBTCA (3-methyl-1,2,3-Butanetricarboxylic acid) and shikimic acid using elastic Mie resonance spectroscopy. A single, aqueous particle is levitated in an electro-dynamic balance (for details see [2]), dried for several days at room temperature, cooled to the target temperature and exposed to a rapid change in relative humidity. In addition to measuring the elastically backscattered light of a 'white light ' LED source and recording the full spectrum with a spectrograph as in [2], we use a tunable diode laser (TDL) to scan high resolution TE- and TM spectra. This combination allows observing various Mie resonance mode orders simultaneously. Since we perform the experiment at low temperatures and low humidities the changes in the Mie-spectra due to water uptake are sufficiently slow to resolve the kinetics. Experimental Mie resonance spectra are inverted to concentration profiles of water within the particle by applying the numerical diffusion model [2] in conjunction with Mie calculations of multilayered spheres [4]. Potential implications for gas to particle partitioning and heterogeneous chemistry are discussed. [1] A. Virtanen et al. (2010): An amorphous solid state of biogenic secondary organic aerosol particles, Nature 467, 824-827. [2] B. Zobrist et al. (2011): Ultra-slow water diffusion in aqueous sucrose glasses, Phys. Chem. Chem. Phys. 13, 3514-3526. [3] D. L. Bones, J. P. Reid, D. M. Lienhard, and U. K. Krieger (2012): Comparing the mechanism of water condensation and evaporation in glassy aerosol, PNAS 109, 11613-11618. [4] O. Peña and U. Pal (2009): Scattering of electromagnetic radiation by a multilayered sphere, Comput. Phys. Commun. 180, 2348-2354.

Effective collision strengths for fine-structure forbidden transitions among the 3s^23p^3 levels of K V

NASA Astrophysics Data System (ADS)

Bell, Kenneth; Wilson, Nigel

2001-05-01

Electron temperatures and densities are difficult to determine in many astrophysical plasmas. However, it is well known that diagnostics on forbidden line intensity ratios for ions in the phosphorous isoelectronic sequence are of great importance in astrophysics, particularly for nebulae. A key element in the analysis is highly accurate atomic data. In this work we extend the earlier calculations of Butler, Zeippen and Le Bourlot (Astron. Astrophys. 203 189 (1988)) on electron scattering by K v. We have obtained effective collision strengths for a wide range of electron temperatures using the R-matrix method. Twenty-two LS target eigenstates are included in the expansion of the total wavefunction, consisting of the seven n=3 states with configuration 3s^23p^3 and 3s3p^4, twelve n=3 states with configuration 3s^23p^23d, and three n=4 states with configuration 3s^23p^24s. The fine-structure collision strengths have been obtained by transforming to a jj-coupling scheme using the JAJOM program of Saraph (Comp. Phys. Commun. 15 247 (1978)) and have been determined at a sufficiently fine energy mesh to delineate properly the resonance structure. Results for both collision strengths and for effective collision strengths will be presented at the conference and comparison will be made with the earlier work.

Increasing the magnetic-field capability of the magneto-inertial fusion electrical discharge system using an inductively coupled coil

NASA Astrophysics Data System (ADS)

Barnak, D. H.; Davies, J. R.; Fiksel, G.; Chang, P.-Y.; Zabir, E.; Betti, R.

2018-03-01

Magnetized high energy density physics (HEDP) is a very active and relatively unexplored field that has applications in inertial confinement fusion, astrophysical plasma science, and basic plasma physics. A self-contained device, the Magneto-Inertial Fusion Electrical Discharge System, MIFEDS [G. Fiksel et al., Rev. Sci. Instrum. 86, 016105 (2015)], was developed at the Laboratory for Laser Energetics to conduct magnetized HEDP experiments on both the OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495-506 (1997)] and OMEGA EP [J. H. Kelly et al., J. Phys. IV France 133, 75 (2006) and L. J. Waxer et al., Opt. Photonics News 16, 30 (2005)] laser systems. Extremely high magnetic fields are a necessity for magnetized HEDP, and the need for stronger magnetic fields continues to drive the redevelopment of the MIFEDS device. It is proposed in this paper that a magnetic coil that is inductively coupled rather than directly connecting to the MIFEDS device can increase the overall strength of the magnetic field for HEDP experiments by increasing the efficiency of energy transfer while decreasing the effective magnetized volume. A brief explanation of the energy delivery of the MIFEDS device illustrates the benefit of inductive coupling and is compared to that of direct connection for varying coil size and geometry. A prototype was then constructed to demonstrate a 7-fold increase in energy delivery using inductive coupling.

Understanding Reflectance Anisotropy: Surface-structure signatures and bulk-related features

NASA Astrophysics Data System (ADS)

Gero Schmidt, W.

2000-03-01

Reflectance anisotropy spectroscopy (RAS) is becoming an increasingly important tool for in situ control of semiconductor processing with real-time feedback. The understanding and interpretation of the measured spectra, however, has been hampered by relatively slow theoretical progress. Using a massively parallel real-space multigrid technique [1] and ab initio pseudopotentials we calculated the optical spectra of a variety of III-V(001) growth structures and stepped Si(111):H surfaces. Our results agree well with experiment, notably with respect to the stoichiometric changes induced by different surface preparations. We identify two distinct sources for the optical anisotropy: (i) highly structure-dependent features are caused by transitions involving electronic surface states, and (ii) derivative-like oscillations or peaks at the bulk critical point energies arise from transitions between surface-modified bulk wave functions. The latter are nearly independent from the actual surface structure. The agreement between the calculated and measured spectra is further improved by applying quasi-particle corrections obtained from numerically efficient, simplified GW calculations [2]. The combination of converged first-principles calculations with an approximate treatment of many-particle effects allows the reliable identification of ``surface-structure fingerprints'' in the optical spectra, paving the way for the exploitation of their rich technological potential. [1ex] [1] EL Briggs, DJ Sullivan, J Bernholc, Phys. Rev. B 54, 14362 (1996). [2] F Bechstedt, R Del Sole, G Cappellini, L Reining, Solid State Commun. 84, 765 (1992).

Rayleigh--Taylor spike evaporation

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

Schappert, G. T.; Batha, S. H.; Klare, K. A.

2001-09-01

Laser-based experiments have shown that Rayleigh--Taylor (RT) growth in thin, perturbed copper foils leads to a phase dominated by narrow spikes between thin bubbles. These experiments were well modeled and diagnosed until this '' spike'' phase, but not into this spike phase. Experiments were designed, modeled, and performed on the OMEGA laser [T. R. Boehly, D. L. Brown, R. S. Craxton , Opt. Commun. 133, 495 (1997)] to study the late-time spike phase. To simulate the conditions and evolution of late time RT, a copper target was fabricated consisting of a series of thin ridges (spikes in cross section) 150more » {mu}m apart on a thin flat copper backing. The target was placed on the side of a scale-1.2 hohlraum with the ridges pointing into the hohlraum, which was heated to 190 eV. Side-on radiography imaged the evolution of the ridges and flat copper backing into the typical RT bubble and spike structure including the '' mushroom-like feet'' on the tips of the spikes. RAGE computer models [R. M. Baltrusaitis, M. L. Gittings, R. P. Weaver, R. F. Benjamin, and J. M. Budzinski, Phys. Fluids 8, 2471 (1996)] show the formation of the '' mushrooms,'' as well as how the backing material converges to lengthen the spike. The computer predictions of evolving spike and bubble lengths match measurements fairly well for the thicker backing targets but not for the thinner backings.« less

Nonequilibrium ferroelectric-ferroelastic 10 nm nanodomains: wrinkles, period-doubling, and power-law relaxation

NASA Astrophysics Data System (ADS)

Scott, James F.; Evans, Donald M.; Katiyar, Ram S.; McQuaid, Raymond G. P.; Gregg, J. Marty

2017-08-01

Since the 1935 work of Landau-Lifshitz and of Kittel in 1946 all ferromagnetic, ferroelectric, and ferroelastic domains have been thought to be straight-sided with domain widths proportional to the square root of the sample thickness. We show in the present work that this is not true. We also discover period doubling domains predicted by Metaxas et al (2008 Phys. Rev. Lett. 99 217208) and modeled by Wang and Zhao (2015 Sci. Rep. 5 8887). We examine non-equilibrium ferroic domain structures in perovskite oxides with respect to folding, wrinkling, and relaxation and suggest that structures are kinetically limited and in the viscous flow regime predicted by Metaxas et al in 2008 but never observed experimentally. Comparisons are made with liquid crystals and hydrodynamic instabilities, including chevrons, and fractional power-law relaxation. As Shin et al (2016 Soft Matter 12 3502) recently emphasized: ‘An understanding of how these folds initiate, propagate, and interact with each other is still lacking’. Inside each ferroelastic domain are ferroelectric 90° nano-domains with 10 nm widths and periodicity in agreement with the 10 nm theoretical minima predicted by Feigl et al (2014 Nat. Commun. 5 4677). Evidence is presented for domain-width period doubling, which is common in polymer films but unknown in ferroic domains. A discussion of the folding-to-period doubling phase transition model of Wang and Zhao is included.

RF current distribution and topology of RF sheath potentials in front of ICRF antennae

NASA Astrophysics Data System (ADS)

Colas, L.; Heuraux, S.; Brémond, S.; Bosia, G.

2005-08-01

The 2D (radial/poloidal) spatial topology of RF-induced convective cells developing radially in front of ion cyclotron range of frequency (ICRF) antennae is investigated, in relation to the spatial distribution of RF currents over the metallic structure of the antenna. This is done via a Green's function, determined from the ICRF wave coupling equations, and well-suited to open field lines extending toroidally far away on both sides of the antenna. Using such formalism, combined with a full-wave calculation using the 3D antenna code ICANT (Pécoul S. et al 2000 Comput. Phys. Commun. 146 166-87), two classes of convective cells are analysed. The first one appears in front of phased arrays of straps, and depending on the strap phasing, its topology is interpreted using the poloidal profiles of either the RF current or the RF voltage of the strip line theory. The other class of convective cells is specific to antenna box corners and is evidenced for the first time. Based on such analysis, general design rules are worked out in order to reduce the RF-sheath potentials, which generalize those proposed in the earlier literature, and concrete antenna design options are tested numerically. The merits of aligning all strap centres on the same (tilted) flux tube, and of reducing the antenna box toroidal conductivity in its lower and upper parts, are discussed.

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

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

Liu, Yueqiang, E-mail: yueqiang.liu@ccfe.ac.uk; Chapman, I. T.; Graves, J. P.

2014-05-15

A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does notmore » contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects.« less

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.

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.

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

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.

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.

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.

Modular reweighting software for statistical mechanical analysis of biased equilibrium data

NASA Astrophysics Data System (ADS)

Sindhikara, Daniel J.

2012-07-01

Here a simple, useful, modular approach and software suite designed for statistical reweighting and analysis of equilibrium ensembles is presented. Statistical reweighting is useful and sometimes necessary for analysis of equilibrium enhanced sampling methods, such as umbrella sampling or replica exchange, and also in experimental cases where biasing factors are explicitly known. Essentially, statistical reweighting allows extrapolation of data from one or more equilibrium ensembles to another. Here, the fundamental separable steps of statistical reweighting are broken up into modules - allowing for application to the general case and avoiding the black-box nature of some “all-inclusive” reweighting programs. Additionally, the programs included are, by-design, written with little dependencies. The compilers required are either pre-installed on most systems, or freely available for download with minimal trouble. Examples of the use of this suite applied to umbrella sampling and replica exchange molecular dynamics simulations will be shown along with advice on how to apply it in the general case. New version program summaryProgram title: Modular reweighting version 2 Catalogue identifier: AEJH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 179 118 No. of bytes in distributed program, including test data, etc.: 8 518 178 Distribution format: tar.gz Programming language: C++, Python 2.6+, Perl 5+ Computer: Any Operating system: Any RAM: 50-500 MB Supplementary material: An updated version of the original manuscript (Comput. Phys. Commun. 182 (2011) 2227) is available Classification: 4.13 Catalogue identifier of previous version: AEJH_v1_0 Journal reference of previous version: Comput. Phys. Commun. 182 (2011) 2227 Does the new version supersede the previous version?: Yes Nature of problem: While equilibrium reweighting is ubiquitous, there are no public programs available to perform the reweighting in the general case. Further, specific programs often suffer from many library dependencies and numerical instability. Solution method: This package is written in a modular format that allows for easy applicability of reweighting in the general case. Modules are small, numerically stable, and require minimal libraries. Reasons for new version: Some minor bugs, some upgrades needed, error analysis added. analyzeweight.py/analyzeweight.py2 has been replaced by “multihist.py”. This new program performs all the functions of its predecessor while being versatile enough to handle other types of histograms and probability analysis. “bootstrap.py” was added. This script performs basic bootstrap resampling allowing for error analysis of data. “avg_dev_distribution.py” was added. This program computes the averages and standard deviations of multiple distributions, making error analysis (e.g. from bootstrap resampling) easier to visualize. WRE.cpp was slightly modified purely for cosmetic reasons. The manual was updated for clarity and to reflect version updates. Examples were removed from the manual in favor of online tutorials (packaged examples remain). Examples were updated to reflect the new format. An additional example is included to demonstrate error analysis. Running time: Preprocessing scripts 1-5 minutes, WHAM engine <1 minute, postprocess script ∼1-5 minutes.

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.

Analysis of metallic impurity density profiles in low collisionality Joint European Torus H-mode and L-mode plasmas

NASA Astrophysics Data System (ADS)

Puiatti, M. E.; Valisa, M.; Angioni, C.; Garzotti, L.; Mantica, P.; Mattioli, M.; Carraro, L.; Coffey, I.; Sozzi, C.

2006-04-01

This paper describes the behavior of nickel in low confinement (L-mode) and high confinement (H-mode) Joint European Torus (JET) discharges [P. J. Lomas, Plasma Phys. Control. Fusion 31, 1481 (1989)] characterized by the application of radio-frequency (rf) power heating and featuring ITER (International Thermonuclear Experimental Reactor) relevant collisionality. The impurity transport is analyzed on the basis of perturbative experiments (laser blow off injection) and is compared with electron heat and deuterium transport. In the JET plasmas analyzed here, ion cyclotron resonance heating (ICRH) is applied either in mode conversion (MC) to heat the electrons or in minority heating (MH) to heat the ions. The two heating schemes have systematically different effects on nickel transport, yielding flat or slightly hollow nickel density profiles in the case of ICRH in MC and peaked nickel density profiles in the case of rf applied in MH. Accordingly, both diffusion coefficients and pinch velocities of nickel are found to be systematically different. Linear gyrokinetic calculations by means of the code GS2 [M. Kotschenreuther, G. Rewoldt, and W.M. Tang, Comput. Phys. Commun. 88, 128 (1995)] provide a possible explanation of such different behavior by exploring the effects produced by the different microinstabilities present in these plasmas. In particular, trapped electron modes driven by the stronger electron temperature gradients measured in the MC cases, although subdominant, produce a contribution to the impurity pinch directed outwards that is qualitatively in agreement with the pinch reversal found in the experiment. Particle and heat diffusivities appear to be decoupled in MH shots, with χe and DD≫DNi, and are instead quite similar in the MC ones. In the latter case, nickel transport appears to be driven by the same turbulence that drives the electron heat transport and is sensitive to the value of the electron temperature gradient length. These findings give ground to the idea that in ITER it should be possible to find conditions in which the risk of accumulation of metals such as nickel can be contained.