Formal scattering theory by an algebraic approach
NASA Astrophysics Data System (ADS)
Alhassid, Y.; Levine, R. D.
1985-02-01
Formal scattering theory is recast in a Lie-algebraic form. The central result is an algebraic Lippmann-Schwinger equation for the wave operator from which an algebraic form of the Born series (containing only linked terms) is obtained. When a finite Lie algebra is sufficient, The Mo/ller wave operator, on the energy shell, can be solved for explicitly as an element of the corresponding group. The method is illustrated for the separable potential whose relevant algebra is found to be U(1,1).
C*-algebraic scattering theory and explicitly solvable quantum field theories
NASA Astrophysics Data System (ADS)
Warchall, Henry A.
1985-06-01
A general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable, but require the use of C*-algebraic techniques because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory, in a setting free of other complications commonly associated with the specification of dynamics. One of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations (CCR). The automorphism groups considered are induced by one-parameter groups of symplectic transformations on the classical phase space over which the Weyl algebra of the CCR is built; each symplectic group is conjugate by a fixed symplectic transformation to a one-parameter unitary group. The second result, an analog to the Birman-Belopol'skii theorem in two-Hilbert-space scattering theory, gives sufficient conditions for the existence of Mo/ller wave morphisms in theories with time-development automorphism groups of the above type. In a paper which follows, this framework is used to analyze a particular model system for which wave operators fail to exist in any natural representation of the observable algebra, but for which wave morphisms and an associated S matrix are easily constructed.
Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
NASA Technical Reports Server (NTRS)
Sun, Yan; Kouri, Donald J.; Truhlar, Donald G.; Schwenke, David W.
1990-01-01
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
Second-Order Algebraic Theories
NASA Astrophysics Data System (ADS)
Fiore, Marcelo; Mahmoud, Ola
Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the viewpoint of categorical algebra. Specifically, the paper introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semantic level, that of second-order algebras and second-order functorial models. Our development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.
NASA Technical Reports Server (NTRS)
Iachello, Franco
1995-01-01
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.
Computer algebra and transport theory.
Warsa, J. S.
2004-01-01
Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.
Imperfect Cloning Operations in Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Kitajima, Yuichiro
2015-01-01
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal -imperfect cloning operation which tolerates a finite loss of fidelity in the cloned state, and show that an individual system's algebra of observables is abelian if and only if there is a universal -imperfect cloning operation in the case where the loss of fidelity is less than . Therefore in this case no universal -imperfect cloning operation is possible in algebraic quantum theory.
Algebraic methods in system theory
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Willems, J. C.; Willsky, A. S.
1975-01-01
Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.
Electromagnetic scattering theory
NASA Technical Reports Server (NTRS)
Bird, J. F.; Farrell, R. A.
1986-01-01
Electromagnetic scattering theory is discussed with emphasis on the general stochastic variational principle (SVP) and its applications. The stochastic version of the Schwinger-type variational principle is presented, and explicit expressions for its integrals are considered. Results are summarized for scalar wave scattering from a classic rough-surface model and for vector wave scattering from a random dielectric-body model. Also considered are the selection of trial functions and the variational improvement of the Kirchhoff short-wave approximation appropriate to large size-parameters. Other applications of vector field theory discussed include a general vision theory and the analysis of hydromagnetism induced by ocean motion across the geomagnetic field. Levitational force-torque in the magnetic suspension of the disturbance compensation system (DISCOS), now deployed in NOVA satellites, is also analyzed using the developed theory.
Recent advances in Multi-Channel Algebraic Scattering
Karataglidis, S.; Fraser, P. R.; Amos, K.; Canton, L.; Pisent, G.; Svenne, J. P.; Knijff, D. van der
2011-10-28
For coupled-channel descriptions of low-energy nucleon-induced interactions involving nuclei with particle-unstable exited states, it is necessary to include the widths of the target states. How those widths may affect the elastic scattering cross sections is examined within the framework of the Multi-Channel Algebraic Scattering (MCAS) method.
Decomposition Theory in the Teaching of Elementary Linear Algebra.
ERIC Educational Resources Information Center
London, R. R.; Rogosinski, H. P.
1990-01-01
Described is a decomposition theory from which the Cayley-Hamilton theorem, the diagonalizability of complex square matrices, and functional calculus can be developed. The theory and its applications are based on elementary polynomial algebra. (KR)
L∞-algebra models and higher Chern-Simons theories
NASA Astrophysics Data System (ADS)
Ritter, Patricia; Sämann, Christian
2016-10-01
We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of L∞-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie p-algebra extensions of 𝔰𝔬(p + 2). Finally, we study a number of L∞-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.
Metric Lie 3-algebras in Bagger-Lambert theory
NASA Astrophysics Data System (ADS)
de Medeiros, Paul; Figueroa-O'Farrill, José; Méndez-Escobar, Elena
2008-08-01
We recast physical properties of the Bagger-Lambert theory, such as shift-symmetry and decoupling of ghosts, the absence of scale and parity invariance, in Lie 3-algebraic terms, thus motivating the study of metric Lie 3-algebras and their Lie algebras of derivations. We prove a structure theorem for metric Lie 3-algebras in arbitrary signature showing that they can be constructed out of the simple and one-dimensional Lie 3-algebras iterating two constructions: orthogonal direct sum and a new construction called a double extension, by analogy with the similar construction for Lie algebras. We classify metric Lie 3-algebras of signature (2, p) and study their Lie algebras of derivations, including those which preserve the conformal class of the inner product. We revisit the 3-algebraic criteria spelt out at the start of the paper and select those algebras with signature (2, p) which satisfy them, as well as indicate the construction of more general metric Lie 3-algebras satisfying the ghost-decoupling criterion.
Scattering theory for arbitrary potentials
Kadyrov, A.S.; Bray, I.; Stelbovics, A.T.; Mukhamedzhanov, A.M.
2005-09-15
The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. Definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.
An Algebraic Construction of Boundary Quantum Field Theory
NASA Astrophysics Data System (ADS)
Longo, Roberto; Witten, Edward
2011-04-01
We build up local, time translation covariant Boundary Quantum Field Theory nets of von Neumann algebras {mathcal A_V} on the Minkowski half-plane M + starting with a local conformal net {mathcal A} of von Neumann algebras on {mathbb R} and an element V of a unitary semigroup {mathcal E(mathcal A)} associated with {mathcal A}. The case V = 1 reduces to the net {mathcal A_+} considered by Rehren and one of the authors; if the vacuum character of {mathcal A} is summable, {mathcal A_V} is locally isomorphic to {mathcal A_+}. We discuss the structure of the semigroup {mathcal E(mathcal A)}. By using a one-particle version of Borchers theorem and standard subspace analysis, we provide an abstract analog of the Beurling-Lax theorem that allows us to describe, in particular, all unitaries on the one-particle Hilbert space whose second quantization promotion belongs to {mathcal E(mathcal A^{(0)})} with {mathcal A^{(0)}} the U(1)-current net. Each such unitary is attached to a scattering function or, more generally, to a symmetric inner function. We then obtain families of models via any Buchholz-Mack-Todorov extension of {mathcal A^{(0)}}. A further family of models comes from the Ising model.
Topological insulators and C∗-algebras: Theory and numerical practice
NASA Astrophysics Data System (ADS)
Hastings, Matthew B.; Loring, Terry A.
2011-07-01
We apply ideas from C∗-algebra to the study of disordered topological insulators. We extract certain almost commuting matrices from the free Fermi Hamiltonian, describing band projected coordinate matrices. By considering topological obstructions to approximating these matrices by exactly commuting matrices, we are able to compute invariants quantifying different topological phases. We generalize previous two dimensional results to higher dimensions; we give a general expression for the topological invariants for arbitrary dimension and several symmetry classes, including chiral symmetry classes, and we present a detailed K-theory treatment of this expression for time reversal invariant three dimensional systems. We can use these results to show non-existence of localized Wannier functions for these systems. We use this approach to calculate the index for time-reversal invariant systems with spin-orbit scattering in three dimensions, on sizes up to 12 3, averaging over a large number of samples. The results show an interesting separation between the localization transition and the point at which the average index (which can be viewed as an "order parameter" for the topological insulator) begins to fluctuate from sample to sample, implying the existence of an unsuspected quantum phase transition separating two different delocalized phases in this system. One of the particular advantages of the C∗-algebraic technique that we present is that it is significantly faster in practice than other methods of computing the index, allowing the study of larger systems. In this paper, we present a detailed discussion of numerical implementation of our method.
Fourier theory and C∗-algebras
NASA Astrophysics Data System (ADS)
Bédos, Erik; Conti, Roberto
2016-07-01
We discuss a number of results concerning the Fourier series of elements in reduced twisted group C∗-algebras of discrete groups, and, more generally, in reduced crossed products associated to twisted actions of discrete groups on unital C∗-algebras. A major part of the article gives a review of our previous work on this topic, but some new results are also included.
Symmetric linear systems - An application of algebraic systems theory
NASA Technical Reports Server (NTRS)
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
From string theory to algebraic geometry and back
Brinzanescu, Vasile
2011-02-10
We describe some facts in physics which go up to the modern string theory and the related concepts in algebraic geometry. Then we present some recent results on moduli-spaces of vector bundles on non-Kaehler Calabi-Yau 3-folds and their consequences for heterotic string theory.
Algebraic isomorphism in two-dimensional anomalous gauge theories
Carvalhaes, C.G.; Natividade, C.P.
1997-08-01
The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the {Theta}-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra. {copyright} 1997 Academic Press, Inc.
Full potential multiple scattering theory
MacLaren, J.M.
1994-10-20
A practical method for performing self-consistent electronic structure calculations based upon full-potential multiple-scattering theory is presented. Solutions to the single site Schroedinger equation are obtained by solving coupled channel integral equations for a potential which is analytically continued out to the circumscribing sphere. This potential coincides with the full cell potential inside each atomic cell. Scattering matrices and wavefunctions for the full cell potential are obtained from surface Wronskian relations. The charge density is obtained from the single particle Green`s function. This Green`s function is computed using the cell scattering matrices and wavefunctions using the layer multiple scattering theory. Self consistent solutions require a solution at each iteration to the Poisson equation. The Poisson equation is solved using a variational cellular method. In the approach a local solution to each cell is augmented by adding a series of regular harmonics (solutions to Laplace`s equation). Minimizing the coulomb energy, subject to continuity of the potential across all cell boundary provides an expression for the coefficients of the regular harmonics. This method is applied to BCC Nb. Calculated properties converge well in angular momentum and show comparable accuracy to full potential linearized muffin-tin orbital calculations.
Algebraic formulation of quantum theory, particle identity and entanglement
NASA Astrophysics Data System (ADS)
Govindarajan, T. R.
2016-08-01
Quantum theory as formulated in conventional framework using statevectors in Hilbert spaces misses the statistical nature of the underlying quantum physics. Formulation using operators 𝒞∗ algebra and density matrices appropriately captures this feature in addition leading to the correct formulation of particle identity. In this framework, Hilbert space is an emergent concept. Problems related to anomalies and quantum epistemology are discussed.
Partial Fractions in Calculus, Number Theory, and Algebra
ERIC Educational Resources Information Center
Yackel, C. A.; Denny, J. K.
2007-01-01
This paper explores the development of the method of partial fraction decomposition from elementary number theory through calculus to its abstraction in modern algebra. This unusual perspective makes the topic accessible and relevant to readers from high school through seasoned calculus instructors.
Category of trees in representation theory of quantum algebras
Moskaliuk, N. M.; Moskaliuk, S. S.
2013-10-15
New applications of categorical methods are connected with new additional structures on categories. One of such structures in representation theory of quantum algebras, the category of Kuznetsov-Smorodinsky-Vilenkin-Smirnov (KSVS) trees, is constructed, whose objects are finite rooted KSVS trees and morphisms generated by the transition from a KSVS tree to another one.
Vortex lattice theory: A linear algebra approach
NASA Astrophysics Data System (ADS)
Chamoun, George C.
Vortex lattices are prevalent in a large class of physical settings that are characterized by different mathematical models. We present a coherent and generalized Hamiltonian fluid mechanics-based formulation that reduces all vortex lattices into a classic problem in linear algebra for a non-normal matrix A. Via Singular Value Decomposition (SVD), the solution lies in the null space of the matrix (i.e., we require nullity( A) > 0) as well as the distribution of its singular values. We demonstrate that this approach provides a good model for various types of vortex lattices, and makes it possible to extract a rich amount of information on them. The contributions of this thesis can be classified into four main points. The first is asymmetric equilibria. A 'Brownian ratchet' construct was used which converged to asymmetric equilibria via a random walk scheme that utilized the smallest singular value of A. Distances between configurations and equilibria were measured using the Frobenius norm ||·||F and 2-norm ||·||2, and conclusions were made on the density of equilibria within the general configuration space. The second contribution used Shannon Entropy, which we interpret as a scalar measure of the robustness, or likelihood of lattices to occur in a physical setting. Third, an analytic model was produced for vortex street patterns on the sphere by using SVD in conjunction with expressions for the center of vorticity vector and angular velocity. Equilibrium curves within the configuration space were presented as a function of the geometry, and pole vortices were shown to have a critical role in the formation and destruction of vortex streets. The fourth contribution entailed a more complete perspective of the streamline topology of vortex streets, linking the bifurcations to critical points on the equilibrium curves.
Huang, Yu-tin; Johansson, Henrik
2013-04-26
We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.
Do malaria parasites follow the algebra of sex ratio theory?
Schall, Jos J
2009-03-01
The ratio of male to female gametocytes seen in infections of Plasmodium and related haemosporidian parasites varies substantially, both within and among parasite species. Sex ratio theory, a mainstay of evolutionary biology, accounts for this variation. The theory provides an algebraic solution for the optimal sex ratio that will maximize parasite fitness. A crucial term in this solution is the probability of selfing by clone-mates within the vector (based on the clone number and their relative abundance). Definitive tests of the theory have proven elusive because of technical challenges in measuring clonal diversity within infections. Newly developed molecular methods now provide opportunities to test the theory with an exquisite precision. PMID:19201653
"Phonon" scattering beyond perturbation theory
NASA Astrophysics Data System (ADS)
Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing
2016-02-01
Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.
Bagger-Lambert theory for general Lie algebras
NASA Astrophysics Data System (ADS)
Gomis, Jaume; Milanesi, Giuseppe; Russo, Jorge G.
2008-06-01
We construct the totally antisymmetric structure constants fABCD of a 3-algebra with a Lorentzian bi-invariant metric starting from an arbitrary semi-simple Lie algebra. The structure constants fABCD can be used to write down a maximally superconformal 3d theory that incorporates the expected degrees of freedom of multiple M2 branes, including the ``center-of-mass" mode described by free scalar and fermion fields. The gauge field sector reduces to a three dimensional BF term, which underlies the gauge symmetry of the theory. We comment on the issue of unitarity of the quantum theory, which is problematic, despite the fact that the specific form of the interactions prevent the ghost fields from running in the internal lines of any Feynman diagram. Giving an expectation value to one of the scalar fields leads to the maximally supersymmetric 3d Yang-Mills Lagrangian with the addition of two U(1) multiplets, one of them ghost-like, which is decoupled at large gYM.
Experimental confirmation of neoclassical Compton scattering theory
Aristov, V. V.; Yakunin, S. N.; Despotuli, A. A.
2013-12-15
Incoherent X-ray scattering spectra of diamond and silicon crystals recorded on the BESSY-2 electron storage ring have been analyzed. All spectral features are described well in terms of the neoclassical scattering theory without consideration for the hypotheses accepted in quantum electrodynamics. It is noted that the accepted tabular data on the intensity ratio between the Compton and Rayleigh spectral components may significantly differ from the experimental values. It is concluded that the development of the general theory (considering coherent scattering, incoherent scattering, and Bragg diffraction) must be continued.
Scattering theory of stochastic electromagnetic light waves.
Wang, Tao; Zhao, Daomu
2010-07-15
We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3 x 3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.
Noncommutative Common Cause Principles in algebraic quantum field theory
Hofer-Szabo, Gabor; Vecsernyes, Peter
2013-04-15
States in algebraic quantum field theory 'typically' establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V{sub A} and V{sub B}, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V{sub A} and V{sub B} and the set {l_brace}C, C{sup Up-Tack }{r_brace} screens off the correlation between A and B.
Scattering theory with path integrals
Rosenfelder, R.
2014-03-15
Starting from well-known expressions for the T-matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.
Calculation of exchange energies using algebraic perturbation theory
Burrows, B. L.; Dalgarno, A.; Cohen, M.
2010-04-15
An algebraic perturbation theory is presented for efficient calculations of localized states and hence of exchange energies, which are the differences between low-lying states of the valence electron of a molecule, formed by the collision of an ion Y{sup +} with an atom X. For the case of a homonuclear molecule these are the gerade and ungerade states and the exchange energy is an exponentially decreasing function of the internuclear distance. For such homonuclear systems the theory is used in conjunction with the Herring-Holstein technique to give accurate exchange energies for a range of intermolecular separations R. Since the perturbation parameter is essentially 1/R, this method is suitable for large R. In particular, exchange energies are calculated for X{sub 2}{sup +} systems, where X is H, Li, Na, K, Rb, or Cs.
Introducing Scattering Theory with a Computer
ERIC Educational Resources Information Center
Merrill, John R.
1973-01-01
Discusses a new method of presenting the scattering theory, including classical explanation of cross sections, quantum mechanical expressions for phase shifts, and use of a computer to solve problems. (CC)
Theory of waves incoherently scattered
NASA Technical Reports Server (NTRS)
Bauer, P.
1974-01-01
Electromagnetic waves impinging upon a plasma at frequencies larger than the plasma frequency, suffer weak scattering. The scattering arises from the existence of electron density fluctuations. The received signal corresponds to a particular spatial Fourier component of the fluctuations, the wave vector of which is a function of the wavelength of the radiowave. Wavelengths short with respect to the Debye length of the medium relate to fluctuations due to non-interacting Maxwellian electrons, while larger wavelengths relate to fluctuations due to collective Coulomb interactions. In the latter case, the scattered signal exhibits a spectral distribution which is characteristic of the main properties of the electron and ion gases and, therefore, provides a powerful diagnosis of the state of the ionosphere.
Theory of Light Scattering in Axion Electrodynamics
NASA Astrophysics Data System (ADS)
Ochiai, Tetsuyuki
2012-09-01
Taking account of the axion term in the Maxwell Lagrangian, we present a rigorous theory of light scattering in piecewise-constant axion fields. In particular, we focus on axionic substances with confined and/or curved geometries, and the scattering matrices of an axionic slab, cylinder, and sphere are derived analytically. The axion term generates a surface current with off-diagonal optical conductivity, giving rise to a new type of photospin--orbit interaction. As a result, various novel light-scattering phenomena can take place. We demonstrate enhanced Faraday rotation, parity-violating light scattering, and strong perturbation of dipole radiation.
K-theory of the chair tiling via AF-algebras
NASA Astrophysics Data System (ADS)
Julien, Antoine; Savinien, Jean
2016-08-01
We compute the K-theory groups of the groupoid C∗-algebra of the chair tiling, using a new method. We use exact sequences of Putnam to compute these groups from the K-theory groups of the AF-algebras of the substitution and the induced lower dimensional substitutions on edges and vertices.
Scattering Theory for Lindblad Master Equations
NASA Astrophysics Data System (ADS)
Falconi, Marco; Faupin, Jérémy; Fröhlich, Jürg; Schubnel, Baptiste
2016-08-01
We study scattering theory for a quantum-mechanical system consisting of a particle scattered off a dynamical target that occupies a compact region in position space. After taking a trace over the degrees of freedom of the target, the dynamics of the particle is generated by a Lindbladian acting on the space of trace-class operators. We study scattering theory for a general class of Lindbladians with bounded interaction terms. First, we consider models where a particle approaching the target is always re-emitted by the target. Then we study models where the particle may be captured by the target. An important ingredient of our analysis is a scattering theory for dissipative operators on Hilbert space.
Spatial Stochastic Systems Theory and Multiple Scattering of Waves.
NASA Astrophysics Data System (ADS)
Liu, Keh-Chung
In this thesis, two methods are established for deriving the expressions of the space-time correlation function of the multiply scattered fields caused by discontinuous random media, including randomly distributed discrete scatterers and irregular interfaces. These two methods are: (1) method of spatial stochastic systems, (2) method of discontinuous stochastic field. For the first method, the basic concept and theory about the spatial stochastic system and the generalized convolution estab- lished in the author's earlier papers are developed, and the problem of determining the multiply scattered field in complex media is reduced to a simple algebraic operation of generalized convolutions that is obtained from a system decomposition diagram and the corresponding operator equations (Chapter II). By means of this method, the general formulas for the mean value, mean square value and space correlation function of the multiply scattered field are established. These formulas consist of only a single summation and a single integration, and the integrands can be obtained from a recurrence formula (Chapters III -V). For the second method, a discontinuous stochastic field (beta)((')r,(omega)), which represents the properties of the random medium (randomly distributed discrete scatterers), is defined. Because of the intro- duction of (beta)((')r,(omega)) the whole process of solving the stochastic wave equation by means of the stochastic integral equation and the Neumann series expansion is greatly simplified. The result shows that the space correlation function of the multiply scattered field can be exactly expressed as the form of a series, each term of which is an integral of the statistical moment of (beta)((')r,(omega)) of corresponding order. The convergence speed of this series mainly depends on the contrast in speed between the scatterer material and the surrounding medium, i.e., the fluctuation of the random medium. Thus, the task is reduced to the calculation of
The Clifford algebra of physical space and Dirac theory
NASA Astrophysics Data System (ADS)
Vaz, Jayme, Jr.
2016-09-01
The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term β \\psi in the usual Dirac factorization of the Klein–Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible expression for the Dirac equation. We show that, behind this other possible factorization is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss several different aspects of Dirac theory using this formalism. In particular, we show that there are four different possible sets of definitions for the parity, time reversal, and charge conjugation operations for the Dirac equation.
The Clifford algebra of physical space and Dirac theory
NASA Astrophysics Data System (ADS)
Vaz, Jayme, Jr.
2016-09-01
The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term β \\psi in the usual Dirac factorization of the Klein-Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible expression for the Dirac equation. We show that, behind this other possible factorization is the formalism of the Clifford algebra of physical space. We exploit this fact, and discuss several different aspects of Dirac theory using this formalism. In particular, we show that there are four different possible sets of definitions for the parity, time reversal, and charge conjugation operations for the Dirac equation.
Scattering theory, multiparticle detection, and time
NASA Astrophysics Data System (ADS)
Briggs, John S.; Feagin, James M.
2014-11-01
We consider the theory of multiple-particle fragmentation processes in the light of modern multihit position-sensitive detection. First, we give a formulation of time-independent many-body scattering theory as a direct generalization of standard textbook two-body potential scattering but in such a way as to emphasize position rather than momentum detection. Noteworthy is that classical asymptotic motion of fragments is shown to emerge from this quantum-mechanical time-independent theory and enables the definition of a classical time parameter. This in turn allows a transition to be made to a time-dependent scattering theory, even in the case where all Hamiltonians are time independent. Such a time-dependent description is the basis of the imaging theorem, which connects position detection to momentum detection.
Minimal unitary (covariant) scattering theory
Lindesay, J.V.; Markevich, A.
1983-06-01
In the minimal three particle equations developed by Lindesay the two body input amplitude was an on shell relativistic generalization of the non-relativistic scattering model characterized by a single mass parameter ..mu.. which in the two body (m + m) system looks like an s-channel bound state (..mu.. < 2m) or virtual state (..mu.. > 2m). Using this driving term in covariant Faddeev equations generates a rich covariant and unitary three particle dynamics. However, the simplest way of writing the relativisitic generalization of the Faddeev equations can take the on shell Mandelstam parameter s = 4(q/sup 2/ + m/sup 2/), in terms of which the two particle input is expressed, to negative values in the range of integration required by the dynamics. This problem was met in the original treatment by multiplying the two particle input amplitude by THETA(s). This paper provides what we hope to be a more direct way of meeting the problem.
Noyes, H.P.
1990-01-29
We construct discrete space-time coordinates separated by the Lorentz-invariant intervals h/mc in space and h/mc{sup 2} in time using discrimination (XOR) between pairs of independently generated bit-strings; we prove that if this space is homogeneous and isotropic, it can have only 1, 2 or 3 spacial dimensions once we have related time to a global ordering operator. On this space we construct exact combinatorial expressions for free particle wave functions taking proper account of the interference between indistinguishable alternative paths created by the construction. Because the end-points of the paths are fixed, they specify completed processes; our wave functions are born collapsed''. A convenient way to represent this model is in terms of complex amplitudes whose squares give the probability for a particular set of observable processes to be completed. For distances much greater than h/mc and times much greater than h/mc{sup 2} our wave functions can be approximated by solutions of the free particle Dirac and Klein-Gordon equations. Using a eight-counter paradigm we relate this construction to scattering experiments involving four distinguishable particles, and indicate how this can be used to calculate electromagnetic and weak scattering processes. We derive a non-perturbative formula relating relativistic bound and resonant state energies to mass ratios and coupling constants, equivalent to our earlier derivation of the Bohr relativistic formula for hydrogen. Using the Fermi-Yang model of the pion as a relativistic bound state containing a nucleon-antinucleon pair, we find that (G{sub {pi}N}{sup 2}){sup 2} = (2m{sub N}/m{sub {pi}}){sup 2} {minus} 1. 21 refs., 1 fig.
New Method for One-Loop Scattering Amplitudes in Field Theory
Ossola, Giovanni
2009-12-17
We review the main features of the OPP method for the evaluation of one-loop amplitudes of arbitrary scattering processes. In this approach, the coefficients of the scalar integrals are extracted by means of simple algebraic equations constructed by numerically evaluating the numerator of the integrand for specific choices of the integration momentum. No analytical information on the structure of the amplitude is needed, allowing for a purely numerical, but still algebraic, implementation of the algorithm. The method works for any set of internal and/or external masses, without being limited to massless theories.
K-theory of locally finite graph C∗-algebras
NASA Astrophysics Data System (ADS)
Iyudu, Natalia
2013-09-01
We calculate the K-theory of the Cuntz-Krieger algebra OE associated with an infinite, locally finite graph, via the Bass-Hashimoto operator. The formulae we get express the Grothendieck group and the Whitehead group in purely graph theoretic terms. We consider the category of finite (black-and-white, bi-directed) subgraphs with certain graph homomorphisms and construct a continuous functor to abelian groups. In this category K0 is an inductive limit of K-groups of finite graphs, which were calculated in Cornelissen et al. (2008) [3]. In the case of an infinite graph with the finite Betti number we obtain the formula for the Grothendieck group K0(OE)=Z, where β(E) is the first Betti number and γ(E) is the valency number of the graph E. We note that in the infinite case the torsion part of K0, which is present in the case of a finite graph, vanishes. The Whitehead group depends only on the first Betti number: K1(OE)=Z. These allow us to provide a counterexample to the fact, which holds for finite graphs, that K1(OE) is the torsion free part of K0(OE).
Surface-integral formulation of scattering theory
Kadyrov, A.S. Bray, I.; Mukhamedzhanov, A.M.; Stelbovics, A.T.
2009-07-15
We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surface-integrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.
NASA Technical Reports Server (NTRS)
Byrnes, C. I.
1980-01-01
It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.
Theory of Multiple Coulomb Scattering from Extended Nuclei
DOE R&D Accomplishments Database
Cooper, L. N.; Rainwater, J.
1954-08-01
Two independent methods are described for calculating the multiple scattering distribution for projected angle scattering resulting when very high energy charged particles traverse a thick scatterer. The results are compared with the theories of Moliere and Olbert.
Quantum Algorithms for Problems in Number Theory, Algebraic Geometry, and Group Theory
NASA Astrophysics Data System (ADS)
van Dam, Wim; Sasaki, Yoshitaka
2013-09-01
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same problem appears to be intractable on classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article will review the current state of quantum algorithms, focusing on algorithms for problems with an algebraic flavor that achieve an apparent superpolynomial speedup over classical computation.
Numerical algebraic geometry: a new perspective on gauge and string theories
NASA Astrophysics Data System (ADS)
Mehta, Dhagash; He, Yang-Hui; Hauensteine, Jonathan D.
2012-07-01
There is a rich interplay between algebraic geometry and string and gauge theories which has been recently aided immensely by advances in computational algebra. However, symbolic (Gröbner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these shortcomings. The so-called `embarrassing parallelizability' allows us to solve many problems and extract physical information which elude symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.
Theory of scattering by complex potentials
Thylwe, K.; Froeman, N.
1983-10-15
The scattering problem for a non-relativistic spinless particle under the influence of a complex effective potential, which is spherically symmetric and tends to zero faster than 1/r at infinity, is considered. Certain general relations, which illuminate the influence of the imaginary part of the potential on the scattering process, are derived with the use of the expression for the probability current density. The rigorous phase-integral method developed by N. Froeman and P. O. Froeman is used for obtaining an exact, general formula for the scattering matrix, or equivalently, for the phase shift. The formula is expressed in terms of phase-integral approximations of an arbitrary order and certain quantities defined by convergent series. Estimating the latter quantities and omitting small corrections, an approximate formula is derived for the phase shift, valid for the case that only one complex turning point contributes essentially to the phase shift. Criteria for classifying a scattering problem as such a one-turning-point problem are given. The treatment is made general enough to also cover situations of interest in Regge-pole or complex angular momentum theory.
NASA Astrophysics Data System (ADS)
Taormina, Anne
1993-05-01
The representation theory of the doubly extended N=4 superconformal algebra is reviewed. The modular properties of the corresponding characters can be derived, using characters sumrules for coset realizations of these N=4 algebras. Some particular combinations of massless characters are shown to transform as affine SU(2) characters under S and T, a fact used to completely classify the massless sector of the partition function.
Analysis of Computer Algebra System Tutorials Using Cognitive Load Theory
ERIC Educational Resources Information Center
May, Patricia
2004-01-01
Most research in the area of Computer Algebra Systems (CAS) has been designed to compare the effectiveness of instructional technology to traditional lecture-based formats. While results are promising, research also indicates evidence of the steep learning curve imposed by the technology. Yet no studies have been conducted to investigate this…
Higher gauge theories from Lie n-algebras and off-shell covariantization
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Heller, Marc Andre; Ikeda, Noriaki; Kaneko, Yukio; Watamura, Satoshi
2016-07-01
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1].
Structure of 23Al from a multi-channel algebraic scattering model based on mirror symmetry
NASA Astrophysics Data System (ADS)
Fraser, P. R.; Kadyrov, A. S.; Massen-Hane, K.; Amos, K.; Canton, L.; Karataglidis, S.; van der Knijff, D.; Bray, I.
2016-09-01
The proton-rich nucleus 23Al has a ground state just 123 keV below the one-proton emission threshold, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering method to describe states as resonances of a valence proton coupled to a 22Mg rotor core. Six states with low-excitation energies and defined {J}π are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.
Multiple scattering theory for space filling potentials
Butler, W.H. ); Brown, R.G. . Dept. of Physics); Nesbet, R.K. . Almaden Research Center)
1990-01-01
Multiple scattering theory (MST) provides an efficient technique for solving the wave equation for the special case of muffin-tin potentials. Here MST is extended to treat space filling non-muffin tin potentials and its validity, accuracy and efficiency are tested by application of the two dimensional empty lattice test. For this test it is found that the traditional formulation of MST does not coverage as the number of partial waves is increased. A simple modification of MST, however, allows this problem to be solved exactly and efficiently. 15 refs., 3 tabs.
Effective theories for dark matter nucleon scattering
NASA Astrophysics Data System (ADS)
Hisano, Junji; Nagai, Ryo; Nagata, Natsumi
2015-05-01
We reformulate the calculation of the dark matter-nucleon scattering cross sections based on the method of effective field theories. We assume that the scatterings are induced by the exchange of colored mediators, and construct the effective theories by integrating out the colored particles. All of the leading order matching conditions as well as the renormalization group equations are presented. We consider a Majorana fermion, and real scalar and vector bosons for the dark matter and show the results for each case. The treatment for the twist-2 operators is discussed in detail, and it is shown that the scale of evaluating their nucleon matrix elements does not have to be the hadronic scale. The effects of the QCD corrections are evaluated on the assumption that the masses of the colored mediators are much heavier than the electroweak scale. Our formulation is systematic and model-independent, and thus suitable to be implemented in numerical packages, such as micrOMEGAs and DarkSUSY.
Real forms of very extended Kac-Moody algebras and theories with eight supersymmetries
NASA Astrophysics Data System (ADS)
Riccioni, Fabio; West, Peter; Van Proeyen, Antoine
2008-05-01
We consider all theories with eight supersymmetries whose reduction to three dimensions gives rise to scalars that parametrise symmetric manifolds. We conjecture that these theories are non-linear realisations of very-extended Kac-Moody algebras for suitable choices of real forms. We show for the most interesting cases that the bosonic sector of the supersymmetric theory is precisely reproduced by the corresponding non-linear realisation.
Chen Famin; Wu Yongshi
2010-11-15
We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys. 09 (2008) 101.]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.
NASA Astrophysics Data System (ADS)
Chen, Fa-Min; Wu, Yong-Shi
2010-11-01
We present a superspace formulation of the D=3, N=4, 5 superconformal Chern-Simons Matter theories, with matter supermultiplets valued in a symplectic 3-algebra. We first construct an N=1 superconformal action and then generalize a method used by Gaitto and Witten to enhance the supersymmetry from N=1 to N=5. By decomposing the N=5 supermultiplets and the symplectic 3-algebra properly and proposing a new superpotential term, we construct the N=4 superconformal Chern-Simons matter theories in terms of two sets of generators of a (quaternion) symplectic 3-algebra. The N=4 theories can also be derived by requiring that the supersymmetry transformations are closed on-shell. The relationship between the 3-algebras, Lie superalgebras, Lie algebras, and embedding tensors (proposed in [E. A. Bergshoeff, O. Hohm, D. Roest, H. Samtleben, and E. Sezgin, J. High Energy Phys.JHEPFG1029-8479 09 (2008) 101.10.1088/1126-6708/2008/09/101]) is also clarified. The general N=4, 5 superconformal Chern-Simons matter theories in terms of ordinary Lie algebras can be re-derived in our 3-algebra approach. All known N=4, 5 superconformal Chern-Simons matter theories can be recovered in the present superspace formulation for super-Lie algebra realization of symplectic 3-algebras.
NASA Astrophysics Data System (ADS)
Orantin, N.
2007-09-01
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that fine tuning the parameters ensure that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct.
Supersymmetry and the discrete light-cone quantization limit of the Lie 3-algebra model of M theory
NASA Astrophysics Data System (ADS)
Sato, Matsuo
2012-02-01
In M. Sato, J. High Energy Phys.JHEPFG1029-8479 07 (2010) 02610.1007/JHEP07(2010)026, we proposed two models of M theory, the Hermitian 3-algebra model and Lie 3-algebra model. In this paper, we study the Lie 3-algebra model with a Lorentzian Lie 3-algebra. This model is ghost-free despite the Lorentzian 3-algebra. We show that our model satisfies two criteria as a model of M theory. First, we show that the model possesses N=1 supersymmetry in 11 dimensions. Second, we show the model reduces to Banks-Fischler-Shenker-Susskind matrix theory with finite size matrices in a discrete light-cone quantization limit.
The Casimir Effect from the Point of View of Algebraic Quantum Field Theory
NASA Astrophysics Data System (ADS)
Dappiaggi, Claudio; Nosari, Gabriele; Pinamonti, Nicola
2016-06-01
We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital ∗-algebra of observables whose generating functionals are characterized by a labelling space which is at the same time optimal and separating and fulfils the F-locality property. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincaré vacuum and KMS states. Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the extended algebras, built in globally hyperbolic subregions can be collected in a global counterpart only after a suitable deformation which is expressed locally in terms of a *-isomorphism. As a last step, we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.
Scale-adaptive tensor algebra for local many-body methods of electronic structure theory
Liakh, Dmitry I
2014-01-01
While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).
ERIC Educational Resources Information Center
Cohen, Simon; Sherman, Gary J.
These two modules cover aspects of the coding process and algebraic coding theory. The first unit defines coding as a branch of information and communication science, which draws extensively upon many diverse mathematical fields, primarily abstract and linear algebra, number theory, probability and statistics, and combinatorial theory. Aspects of…
The theory of Enceladus and Dione: An application of computerized algebra in dynamical astronomy
NASA Technical Reports Server (NTRS)
Jefferys, W. H.; Ries, L. M.
1974-01-01
A theory of Saturn's satellites Enceladus and Dione is discussed which is literal (all constants of integration appear explicitly), canonically invariant (the Hori-Lie method is used), and which correctly handles the eccentricity-type resonance between the two satellites. Algebraic manipulations are designed to be performed using the TRIGMAN formula manipulation language, and computer programs were developed so that, with minor modifications, they can be used on the Mimas-Tethys and Titan-Hyperion systems.
NASA Astrophysics Data System (ADS)
Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
2011-11-01
This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field, even if our continually evolving understanding of the subject might soon render this compilation incomplete. Why the fascination with scattering amplitudes, which have attracted the imagination and dedicated effort of so many physicists? Part of it stems from the belief, supported now by numerous examples, that unexpected simplifications of otherwise apparently complicated calculations do not happen by accident. Instead they provide a strong motivation to seek out an underlying explanation. The insight thereby gained can subsequently be used to make the next class of seemingly impossible calculations not only possible, but in some cases even trivial. This two-pronged strategy of exploring and exploiting the structure of gauge theory amplitudes appeals to a wide audience from formal theorists interested in mathematical structure for the sake of its own beauty to more phenomenologically-minded physicists eager to speed up the next generation of analysis software. Understandably it is the maximally supersymmetric 𝒩 = 4 Yang-Mills theory (SYM) which has the simplest structure and has correspondingly received the most attention. Rarely in theoretical physics are we fortunate enough to encounter a toy model which is simple enough to be solved completely yet rich enough to possess interesting non-trivial structure while simultaneously, and most importantly, being applicable (even if only as a good approximation) to a wide range of 'real' systems. The canonical example in quantum mechanics is of course the harmonic
On the similarity of theories of anelastic and scattering attenuation
Wennerberg, L.; Frankel, A.
1989-01-01
We point out basic parallels between theories of anelastic and scattering attenuation. We consider approximations to scattering effects presented by O'Doherty and Anstey (1971), Sato (1982), and Wu (1982). We use the linear theory of anelasticity. We note that the frequency dependence of Q can be related to a distribution of scales of physical properties of the medium. The frequency dependence of anelastic Q is related to the distribution of relaxation times in exactly the same manner as the frequency dependence of scattering Q is related to the distribution of scatterer sizes. Thus, the well-known difficulty of separating scattering from intrinsic attenuation is seen from this point of view as a consequence of the fact that certain observables can be interpreted by identical equations resulting from either of two credible physical theories describing fundamentally different processes. -from Authors
Novel limiting circle theory in acoustic wave scattering and absorption
NASA Astrophysics Data System (ADS)
Huang, Changzheng
Wave scattering theory is the basis for many key technologies that have important military and commercial applications. The familiar examples are radar, sonar, and various ultrasound instruments commonly used in remote sensing, target identification, non-destructive evaluation, medical diagnosis, and many other areas. Their mathematical model involves the solution of the so- called inverse scattering problem where an incident wave is used to probe a remote or inaccessible object. From the scattered field measurement, the shape and/or the material composition of the object can be determined. A new wave scattering theory, termed limiting circle theory (LCT), has been developed in this dissertation based on a novel approach of decomposing the wave scattering matrix. LCT has rigorously proved that the scattered wave field from any penetrable object (of cylinder and sphere geometries) is composed of three contributions: a rigid background, a soft background, and a pure resonance. This is a significant modification to the existing resonance scattering theory (RST) which states that the scattered field is made up of only two components: a proper background (either rigid or soft), and a pure resonance. LCT formalism led to the discovery of the limiting circle patterns associated with all normal modes or partial waves. These patterns provide a clear understanding of the resonance behavior such as the resonance period and the resonance intensity. The analytical LCT approach could also be the key to solving the background problems for shell structures that have remained unsolved for many years in acoustics.
Theory of Thomson scattering in inhomogeneous media
NASA Astrophysics Data System (ADS)
Kozlowski, P. M.; Crowley, B. J. B.; Gericke, D. O.; Regan, S. P.; Gregori, G.
2016-04-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems.
Theory of Thomson scattering in inhomogeneous media.
Kozlowski, P M; Crowley, B J B; Gericke, D O; Regan, S P; Gregori, G
2016-01-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems. PMID:27068215
Theory of Thomson scattering in inhomogeneous media
Kozlowski, P. M.; Crowley, B. J. B.; Gericke, D. O.; Regan, S. P.; Gregori, G.
2016-01-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems. PMID:27068215
Representations of Conformal Nets, Universal C*-Algebras and K-Theory
NASA Astrophysics Data System (ADS)
Carpi, Sebastiano; Conti, Roberto; Hillier, Robin; Weiner, Mihály
2013-05-01
We study the representation theory of a conformal net {{A}} on S 1 from a K-theoretical point of view using its universal C*-algebra {C^*({A})}. We prove that if {{A}} satisfies the split property then, for every representation π of {{A}} with finite statistical dimension, {π(C^*({A}))} is weakly closed and hence a finite direct sum of type I∞ factors. We define the more manageable locally normal universal C*-algebra {C_ln^*({A})} as the quotient of {C^*({A})} by its largest ideal vanishing in all locally normal representations and we investigate its structure. In particular, if {{A}} is completely rational with n sectors, then {C_ln^*({A})} is a direct sum of n type I∞ factors. Its ideal {{K}_{A}} of compact operators has nontrivial K-theory, and we prove that the DHR endomorphisms of {C^*({A})} with finite statistical dimension act on {{K}_{A}}, giving rise to an action of the fusion semiring of DHR sectors on {K_0({K}_{A})}. Moreover, we show that this action corresponds to the regular representation of the associated fusion algebra.
An invariance theorem in acoustic scattering theory
NASA Astrophysics Data System (ADS)
Ha-Duong, T.
1996-10-01
Karp's theorem states that if the far-field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle is invariant under the group of orthogonal transformations in 0266-5611/12/5/007/img1 (rotations in 0266-5611/12/5/007/img2), then the scatterer is a sphere (circle). The theorem is generalized to the case where the invariant group of the far field pattern is only a subgroup of the orthogonal group, and for a class of mixed boundary conditions.
Scattering theory with localized non-Hermiticities
Znojil, Miloslav
2008-07-15
In the context of the recent interest in solvable models of scattering mediated by non-Hermitian Hamiltonians (cf. H. F. Jones, Phys. Rev. D 76, 125003 (2007)) we show that the well-known variability of the ad hoc choice of the metric {theta} which defines the physical Hilbert space of states can help us to clarify several apparent paradoxes. We argue that with a suitable {theta}, a fully plausible physical picture of the scattering can be recovered. Quantitatively, our new recipe is illustrated on an exactly solvable toy model.
Molecular graphene under the eye of scattering theory
NASA Astrophysics Data System (ADS)
Hammar, H.; Berggren, P.; Fransson, J.
2013-12-01
The recent experimental observations of designer Dirac fermions and topological phases in molecular graphene are addressed theoretically. Using scattering theory, we calculate the electronic structure of finite lattices of scattering centers dual to the honeycomb lattice. In good agreement with experimental observations, we obtain a V-shaped electron density of states around the Fermi energy. By varying the lattice parameter we simulate electron and hole doping of the structure, and by adding and removing scattering centers we simulate, respectively, vacancy and impurity defects. Specifically, for the vacancy defect we verify the emergence of a sharp resonance near the Fermi energy for increasing strength of the scattering potential.
NASA Astrophysics Data System (ADS)
Méliot, Pierre-Loïc
2010-12-01
In this thesis, we investigate the asymptotics of random partitions chosen according to probability measures coming from the representation theory of the symmetric groups S_n and of the finite Chevalley groups GL(n,F_q) and Sp(2n,F_q). More precisely, we prove laws of large numbers and central limit theorems for the q-Plancherel measures of type A and B, the Schur-Weyl measures and the Gelfand measures. Using the RSK algorithm, it also gives results on longest increasing subsequences in random words. We develop a technique of moments (and cumulants) for random partitions, thereby using the polynomial functions on Young diagrams in the sense of Kerov and Olshanski. The algebra of polynomial functions, or observables of Young diagrams is isomorphic to the algebra of partial permutations; in the last part of the thesis, we try to generalize this beautiful construction.
A modified Lax-Phillips scattering theory for quantum mechanics
NASA Astrophysics Data System (ADS)
Strauss, Y.
2015-07-01
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
A modified Lax-Phillips scattering theory for quantum mechanics
Strauss, Y.
2015-07-15
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
S-duality and the prepotential in N={2}^{star } theories (I): the ADE algebras
NASA Astrophysics Data System (ADS)
Billó, M.; Frau, M.; Fucito, F.; Lerda, A.; Morales, J. F.
2015-11-01
The prepotential of N={2}^{star } supersymmetric theories with unitary gauge groups in an Ω background satisfies a modular anomaly equation that can be recursively solved order by order in an expansion for small mass. By requiring that S-duality acts on the prepotential as a Fourier transform we generalise this result to N={2}^{star } theories with gauge algebras of the D and E type and show that their prepotentials can be written in terms of quasi-modular forms of SL(2, {Z}) . The results are checked against microscopic multi-instanton calculus based on localization for the A and D series and reproduce the known 1-instanton prepotential of the pure N=2 theories for any gauge group of ADE type. Our results can also be used to obtain the multi-instanton terms in the exceptional theories for which the microscopic instanton calculus and the ADHM construction are not available.
Comments on polaron-phonon scattering theory
NASA Astrophysics Data System (ADS)
Tulub, A. V.
2015-10-01
We use the polaron state function described in terms of coupled classical and quantum fields to calculate the cross section of phonon scattering on a polaron. The value of the resonance momentum is determined by asymptotic values of several integrals. Calculating them with crystal parameters taken into account leads to bounds on the maximum value of the coupling constant. We confirm that the applicability domain of the strong-coupling approximation is near zero.
Multiple scattering of polarized light: comparison of Maxwell theory and radiative transfer theory.
Voit, Florian; Hohmann, Ansgar; Schäfer, Jan; Kienle, Alwin
2012-04-01
For many research areas in biomedical optics, information about scattering of polarized light in turbid media is of increasing importance. Scattering simulations within this field are mainly performed on the basis of radiative transfer theory. In this study a polarization sensitive Monte Carlo solution of radiative transfer theory is compared to exact Maxwell solutions for all elements of the scattering Müller matrix. Different scatterer volume concentrations are modeled as a multitude of monodisperse nonabsorbing spheres randomly positioned in a cubic simulation volume which is irradiated with monochromatic incident light. For all Müller matrix elements effects due to dependent scattering and multiple scattering are analysed. The results are in overall good agreement between the two methods with deviations related to dependent scattering being prominent for high volume concentrations and high scattering angles.
On Algebraic Singularities, Finite Graphs and D-Brane Gauge Theories: A String Theoretic Perspective
NASA Astrophysics Data System (ADS)
He, Yang-Hui
2002-09-01
In this writing we shall address certain beautiful inter-relations between the construction of 4-dimensional supersymmetric gauge theories and resolution of algebraic singularities, from the perspective of String Theory. We review in some detail the requisite background in both the mathematics, such as orbifolds, symplectic quotients and quiver representations, as well as the physics, such as gauged linear sigma models, geometrical engineering, Hanany-Witten setups and D-brane probes. We investigate aspects of world-volume gauge dynamics using D-brane resolutions of various Calabi-Yau singularities, notably Gorenstein quotients and toric singularities. Attention will be paid to the general methodology of constructing gauge theories for these singular backgrounds, with and without the presence of the NS-NS B-field, as well as the T-duals to brane setups and branes wrapping cycles in the mirror geometry. Applications of such diverse and elegant mathematics as crepant resolution of algebraic singularities, representation of finite groups and finite graphs, modular invariants of affine Lie algebras, etc. will naturally arise. Various viewpoints and generalisations of McKay's Correspondence will also be considered. The present work is a transcription of excerpts from the first three volumes of the author's PhD thesis which was written under the direction of Prof. A. Hanany - to whom he is much indebted - at the Centre for Theoretical Physics of MIT, and which, at the suggestion of friends, he posts to the ArXiv pro hac vice; it is his sincerest wish that the ensuing pages might be of some small use to the beginning student.
Scattering theory of nonlinear thermoelectric transport.
Sánchez, David; López, Rosa
2013-01-11
We investigate nonlinear transport properties of quantum conductors in response to both electrical and thermal driving forces. Within the scattering approach, we determine the nonequilibrium screening potential of a generic mesoscopic system and find that its response is dictated by particle and entropic injectivities which describe the charge and entropy transfer during transport. We illustrate our model analyzing the voltage and thermal rectification of a resonant tunneling barrier. Importantly, we discuss interaction induced contributions to the thermopower in the presence of large temperature differences.
The theory of Enceladus and Dione - An application of computerized algebra in dynamical astronomy
NASA Technical Reports Server (NTRS)
Jefferys, W. H.; Ries, L. M.
1975-01-01
The orbits of the satellites of the outer planets are poorly known, due to lack of attention over the past half century. We have been developing a new theory of Saturn's satellites Enceladus and Dione which is literal (all constants of integration appear explicitly), canonically invariant (the Hori-Lie method is used), and which correctly handles the eccentricity-type resonance between the two satellites. The algebraic manipulations are being performed using the TRIGMAN formula manipulation language, and the programs have been developed so that with minor modifications they can be used on the Mimas-Tethys and Titan-Hyperion systems.
A Theory of Radar Scattering by the Moon
NASA Technical Reports Server (NTRS)
Senior, T. B. A.; Siegel, K. M.
1959-01-01
A theory is described in which the moon is regarded as a "quasi-smooth" scatterer at radar frequencies. A scattered pulse is then composed of a number of individual returns each of which is provided by a single scattering area. In this manner it is possible to account for all the major features of the pulse, and the evidence in favor of the theory is presented. From a study of the measured power received at different frequencies, it is shown that the scattering area nearest to the earth is the source of a specular return, and it is then possible to obtain information about the material of which the area is composed. The electromagnetic constants are derived and their significance discussed.
ERIC Educational Resources Information Center
Store, Jessie Chitsanzo
2012-01-01
There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research…
Inverse-scattering theory and the density perturbations from inflation.
Habib, Salman; Heitmann, Katrin; Jungman, Gerard
2005-02-18
We show how to use inverse-scattering theory as the basis for the inflationary reconstruction program, the goal of which is to gain information about the physics which drives inflation. Inverse-scattering theory provides an effective and well-motivated procedure, having a sound mathematical basis and being of sufficient generality that it can be considered the foundation for a nonparametric reconstruction program. We show how simple properties of the power spectrum translate directly into statements about the evolution of the background geometry during inflation. PMID:15783718
NASA Astrophysics Data System (ADS)
Nazarov, Anton
2012-11-01
In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces
NASA Astrophysics Data System (ADS)
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-01
A quantum scattering theory is developed for Fock states scattered by two-level systems in the free space. Compared to existing scattering theories that treat incident light semi-classically, the theory fully quantizes the incident light as Fock states. This non-perturbative method provides exact scattering matrix.
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix. PMID:27628348
Theory of direct scattering of neutral and charged atoms
NASA Technical Reports Server (NTRS)
Franco, V.
1979-01-01
The theory for direct elastic and inelastic collisions between composite atomic systems formulated within the framework of the Glauber approximation is presented. It is shown that the phase-shift function is the sum of a point Coulomb contribution and of an expression in terms of the known electron-hydrogen-atom and proton-hydrogen-atom phase shift function. The scattering amplitude is reexpressed, the pure Coulomb scattering in the case of elastic collisions between ions is isolated, and the exact optical profile function is approximated by a first-order expansion in Glauber theory which takes into account some multiple collisions. The approximate optical profile function terms corresponding to interactions involving one and two electrons are obtained in forms of Meijer G functions and as a one-dimensional integral, and for collisions involving one or two neutral atoms, the scattering amplitude is further reduced to a simple closed-form expression.
Topics in electromagnetic, acoustic, and potential scattering theory
NASA Astrophysics Data System (ADS)
Nuntaplook, Umaporn
With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves --- is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering in radially symmetric media is sufficient to gain insight into scattering in more complex media. Meeting the challenge of variable refractive indices and possibly complicated boundary conditions therefore requires accurate and efficient numerical methods, and where possible, analytic solutions to the radial equations from the governing scalar and vector wave equations (in acoustics and electromagnetic theory, respectively). Until relatively recently, researchers assumed a constant refractive index throughout the medium of interest. However, the most interesting and increasingly useful cases are those with non-constant refractive index profiles. In the majority of this dissertation the focus is on media with piecewise constant refractive indices in radially symmetric media. The method discussed is based on the solution of Maxwell's equations for scattering of plane electromagnetic waves from a dielectric (or "transparent") sphere in terms of the related Helmholtz equation. The main body of the dissertation (Chapters 2 and 3) is concerned with scattering from (i) a uniform spherical inhomogeneity embedded in an external medium with different properties, and (ii) a piecewise-uniform central inhomogeneity in the external medium. The latter results contain a natural generalization of
Classification of two-dimensional conformal supergravity theories with finite-dimensional algebras
McCabe, J.; Velikson, B.
1989-07-15
We present a list of all the finite supersymmetric extensions of thetwo-dimensional (2D) conformal algebra SO(2,2), which could lead to 2D superconformal gravity theories. The on-shell matter multiplets of the algebrasallowing canonical spin-0 and -1/2 matter are constructed. Usingthese multiplets the Weyl and Yang-Mills anomalies are calculated. There aremany new models. One new model is free of both Yang-Mills and Weyl anomalies,SU(1,1)/times/SU(2/vert bar/1,1), but only the algebrasSU(1,1)/sup 2/, OSP(1/vert bar/2)/sup 2/,OSP(2/vert bar/2)/sup 2/, SU(1,1)/times/OSP(1/vert bar/2),OSP(1/vert bar/2)/times/OSP(2/vert bar/2), andSU(1,1)/times/OSP(2/vert bar/2) lead to models free of all anomalies. Thesemodels correspond to the known string models.
Scattering-theory analysis of waveguide-resonator coupling
Xu; Li; Lee; Yariv
2000-11-01
Using a formalism similar to the quantum scattering theory, we analyze the problem of coupling between optical waveguides and high Q resonators. We give the optical transmission and reflection coefficients as functions of the waveguide-resonator coupling, cavity loss (gain), and cavity resonant frequency. Based on these results, the recently proposed concept of "critical coupling" is discussed. Using a matrix formalism based on the scattering analysis, we find the dispersion relation of indirectly coupled resonator optical waveguides. The coupling between waveguides and multiple cavities is investigated and the reflection and transmission coefficients are derived.
Random scattering matrices and the circuit theory of Andreev conductances
NASA Astrophysics Data System (ADS)
Argaman, N.
1997-04-01
The conductance of a normal-metal mesoscopic system in proximity to superconducting electrode(s) is calculated. The normal-metal part may have a general geometry, and is described as a "circuit" with "leads" and "junctions". The junctions are each ascribed a scattering matrix which is averaged over the circular orthogonal ensemble, using recently developed techniques. The results for the electrical conductance reproduce and extend Nazarov's circuit theory, thus bridging between the scattering and the bulk approaches. The method is also applied to the heat conductance.
NASA Astrophysics Data System (ADS)
Hofer-Szabó, Gábor; Vecsernyés, Péter
2012-02-01
In the paper it will be shown that Reichenbach's Weak Common Cause Principle is not valid in algebraic quantum field theory with locally finite degrees of freedom in general. Namely, for any pair of projections A, B supported in spacelike separated double cones {mathcal{O}}a and {mathcal{O}}b, respectively, a correlating state can be given for which there is no nontrivial common cause (system) located in the union of the backward light cones of {mathcal{O}}a and {mathcal{O}}b and commuting with the both A and B. Since noncommuting common cause solutions are presented in these states the abandonment of commutativity can modulate this result: noncommutative Common Cause Principles might survive in these models.
Four loop scattering in the Nambu-Goto theory
NASA Astrophysics Data System (ADS)
Conkey, Peter; Dubovsky, Sergei
2016-05-01
We initiate the study of multiloop scattering amplitudes in the Nambu-Goto theory on the worldsheet of a non-critical string. We start with a brute force calculation of two loop four particle scattering. Somewhat surprisingly, even though non-trivial UV counterterms are present at this order, on-shell amplitudes remain polynomial in the momenta of colliding particles. We show that this can be understood as a consequence of existence of certain close by (semi)integrable models. Furthermore, these arguments can be extended to obtain the answer for three and four loop scattering, bypassing the brute force calculation. The resulting amplitudes develop non-polynomial (logarithmic) dependence on the momenta starting at three loops.
A microscopic, coupled-channel theory of pion scattering
Kagarlis, M.A.; Johnson, M.B.; Fortune, H.T.
1995-05-15
The authors develop a new and comprehensive coordinate-space theory of pion-nucleus scattering to facilitate disentangling the conventional aspects of pion scattering from the non-conventional ones relevant to issues of hadron dynamics. They work in coordinate space in order to both unify and extend the relatively extensive and successful analyses of exclusive pion-nucleus reactions previously made within a similar framework. They construct the optical potential microscopically in shell-model framework by summing particle-hole pair configurations, leading naturally to a coupled-channel formulation. The theory includes a complete treatment of all spin-isospin components of the pion-nucleon scattering amplitude, and Fermi averaging is done explicitly. The authors present numerical results showing the significance of Fermi motion and spin dependence on charge-exchange angular distributions: Single and double spin flip are shown to play dominant and generally unappreciated roles in charge-exchange reactions, and corrections for Fermi motion are shown to be needed in order to quantitatively separate medium effects from conventional multiple scattering. 72 refs., 11 figs.
Scattering theory of spin-orbit active adatoms on graphene
NASA Astrophysics Data System (ADS)
Pachoud, Alexandre; Ferreira, Aires; Ã-zyilmaz, B.; Castro Neto, A. H.
2014-07-01
The scattering of two-dimensional massless Dirac fermions from local spin-orbit interactions with an origin in dilute concentrations of physisorbed atomic species on graphene is theoretically investigated. The hybridization between graphene and the adatoms' orbitals lifts spin and valley degeneracies of the pristine host material, giving rise to rich spin-orbit coupling mechanisms with features determined by the exact adsorption position on the honeycomb lattice—bridge, hollow, or top position—and the adatoms' outer-shell orbital type. Effective graphene-only Hamiltonians are derived from symmetry considerations, while a microscopic tight-binding approach connects effective low-energy couplings and graphene-adatom hybridization parameters. Within the T-matrix formalism, a theory for (spin-dependent) scattering events involving graphene's charge carriers, and the spin-orbit active adatoms is developed. Spin currents associated with intravalley and intervalley scattering are found to tend to oppose each other. We establish that under certain conditions, hollow-position adatoms give rise to the spin Hall effect, through skew scattering, while top-position adatoms induce transverse charge currents via trigonal potential scattering. We also identify the critical Fermi energy range where the spin Hall effect is dramatically enhanced, and the associated transverse spin currents can be reversed.
NASA Technical Reports Server (NTRS)
Schwenke, David W.; Mladenovic, Mirjana; Zhao, Meishan; Truhlar, Donald G.; Sun, Yan
1988-01-01
The computational steps in calculating quantum mechanical reactive scattering amplitudes by the L2 generalized Newton variational principle are discussed with emphasis on computational strategies and recent improvements that make the calculations more efficient. Special emphasis is placed on quadrature techniques, storage management strategies, use of symmetry, and boundary conditions. It is concluded that an efficient implementation of these procedures provides a powerful algorithm for the accurate solution of the Schroedinger equation for rearrangements.
Benchmark calculations of thermal reaction rates. I - Quantal scattering theory
NASA Technical Reports Server (NTRS)
Chatfield, David C.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
The thermal rate coefficient for the prototype reaction H + H2 yields H2 + H with zero total angular momentum is calculated by summing, averaging, and numerically integrating state-to-state reaction probabilities calculated by time-independent quantum-mechanical scattering theory. The results are very carefully converged with respect to all numerical parameters in order to provide high-precision benchmark results for confirming the accuracy of new methods and testing their efficiency.
Theory and phenomenology of coherent neutrino-nucleus scattering
McLaughlin, Gail
2015-07-15
We review the theory and phenomenology of coherent elastic neutrino-nucleus scattering (CEνNS). After a brief introduction, we summarize the places where CEνNS is already in use and then turn to future physics opportunities from CEνNS. CEνNS has been proposed as a way to limit or discover beyond the standard model physics, measure the nuclear-neutron radius and constrain the Weinberg angle.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax = (l,m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l,m)tr where phase shifts δl>ltr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δl>ltr set to zero [Zhang andmore » Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N(ltr + 1)2] and includes higher-L contributions via linear algebra [R2 process with rank N(lmax +1)2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.« less
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L_{max} = (l,m)_{max}, while scattering matrices, which determine spectral properties, are truncated at L_{tr} = (l,m)_{tr} where phase shifts δl>l_{tr} are negligible. Historically, L_{max} is set equal to L_{tr}, which is correct for large enough L_{max} but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L_{max} > L_{tr} with δl>l_{tr} set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R^{3} process with rank N(l_{tr} + 1)^{2}] and includes higher-L contributions via linear algebra [R^{2} process with rank N(l_{max} +1)^{2}]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1_{0} CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L_{max} for a given L_{tr}.
Hybrid theory and calculation of e-N2 scattering
NASA Technical Reports Server (NTRS)
Chandra, N.; Temkin, A.
1976-01-01
A theory of electron-molecule scattering is developed which is a synthesis of close-coupling and adiabatic-nuclei theories. Specifically, the theory is close-coupling with respect to vibrational degrees of freedom and adiabatic-nuclei with respect to rotation. It can be applied to any number of partial waves required; the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations is given which indicates those partial waves and energy domains requiring the various approximations. The theory allows all cross sections (pure rotational, vibrational, simultaneous vibration-rotation, differential, and total) to be calculated, and explicit formulas for all these cross sections are given. The theory is applied to low-energy e-N2 scattering. The fixed-nuclei results are such that the criterion shows clearly that vibrational close coupling is necessary, but only for the Pi sub g partial wave. It is found that the close-coupling calculation for this wave gives rise to the substructure as well as the gross structure of the 2.4-eV resonance and that vibrational excitation cross sections are about twice as large as previously inferred.
An effective field theory for forward scattering and factorization violation
NASA Astrophysics Data System (ADS)
Rothstein, Ira Z.; Stewart, Iain W.
2016-08-01
Starting with QCD, we derive an effective field theory description for forward scattering and factorization violation as part of the soft-collinear effective field theory (SCET) for high energy scattering. These phenomena are mediated by long distance Glauber gluon exchanges, which are static in time, localized in the longitudinal distance, and act as a kernel for forward scattering where | t| ≪ s. In hard scattering, Glauber gluons can induce corrections which invalidate factorization. With SCET, Glauber exchange graphs can be calculated explicitly, and are distinct from graphs involving soft, collinear, or ultrasoft gluons. We derive a complete basis of operators which describe the leading power effects of Glauber exchange. Key ingredients include regulating light-cone rapidity singularities and subtractions which prevent double counting. Our results include a novel all orders gauge invariant pure glue soft operator which appears between two collinear rapidity sectors. The 1-gluon Feynman rule for the soft operator coincides with the Lipatov vertex, but it also contributes to emissions with ≥ 2 soft gluons. Our Glauber operator basis is derived using tree level and one-loop matching calculations from full QCD to both SCETII and SCETI. The one-loop amplitude's rapidity renormalization involves mixing of color octet operators and yields gluon Reggeization at the amplitude level. The rapidity renormalization group equation for the leading soft and collinear functions in the forward scattering cross section are each given by the BFKL equation. Various properties of Glauber gluon exchange in the context of both forward scattering and hard scattering factorization are described. For example, we derive an explicit rule for when eikonalization is valid, and provide a direct connection to the picture of multiple Wilson lines crossing a shockwave. In hard scattering operators Glauber subtractions for soft and collinear loop diagrams ensure that we are not sensitive to
The potential of effective field theory in NN scattering
NASA Astrophysics Data System (ADS)
Beane, S. R.; Cohen, T. D.; Phillips, D. R.
1998-03-01
We study an effective field theory of interacting nucleons at distances much greater than the pion's Compton wavelength. In this regime the NN potential is conjectured to be the sum of a delta function and its derivatives. The question we address is whether this sum can be consistently truncated at a given order in the derivative expansion, and systematically improved by going to higher orders. Regularizing the Lippmann-Schwinger equation using a cutoff we find that the cutoff can be taken to infinity only if the effective range is negative. A positive effective range — which occurs in nature — requires that the cutoff be kept finite and below the scale of the physics which has been integrated out, i.e. O( mπ). Comparison of cutoff schemes and dimensional regularization reveals that the physical scattering amplitude is sensitive to the choice of regulator. Moreover, we show that the presence of some regulator scale, a feature absent in dimensional regularization, is essential if the effective field theory of NN scattering is to be useful. We also show that one can define a procedure where finite cutoff dependence in the scattering amplitude is removed order by order in the effective potential. However, the characteristic momentum in the problem is given by the cutoff, and not by the external momentum. It follows that in the presence of a finite cutoff there is no small parameter in the effective potential, and consequently no systematic truncation of the derivative expansion can be made. We conclude that there is no effective field theory of NN scattering with nucleons alone.
ERIC Educational Resources Information Center
Senarat, Somprasong; Tayraukham, Sombat; Piyapimonsit, Chatsiri; Tongkhambanjong, Sakesan
2013-01-01
The purpose of this research is to develop a multidimensional computerized adaptive test for diagnosing the cognitive process of grade 7 students in learning algebra by applying multidimensional item response theory. The research is divided into 4 steps: 1) the development of item bank of algebra, 2) the development of the multidimensional…
Three-dimensional theory of weakly nonlinear Compton scattering
NASA Astrophysics Data System (ADS)
Albert, F.; Anderson, S. G.; Gibson, D. J.; Marsh, R. A.; Siders, C. W.; Barty, C. P. J.; Hartemann, F. V.
2011-01-01
Nonlinear effects are known to occur in light sources when the wiggler parameter, or normalized 4-potential, A =e√-AμAμ /m0c, approaches unity. In this paper, it is shown that nonlinear spectral features can appear at arbitrarily low values of A if the fractional bandwidth of the undulator, Δϕ-1, is sufficiently small and satisfies the condition A2Δϕ ˜1. Consequences for the spectral brightness of Compton scattering light sources are outlined. Compton and Thomson scattering theories are compared with the Klein-Nishina cross-section formula to highlight differences in the case of narrow band gamma-ray operation. A weakly nonlinear Compton scattering theory is developed in one (plane wave) and three (local plane wave approximation) dimensions. Analytical models are presented and benchmarked against numerical calculations solving the Lorentz force equation with a fourth-order Runge-Kutta algorithm. Finally, narrow band gamma-ray spectra are calculated for realistic laser and electron beams.
Theory of high-energy electron scattering by composite targets
Coester, F.
1988-01-01
The emphasis of these expository lectures is on the role of relativistic invariance and the unity of the theory for medium and high energies. Sec. 2 introduces the kinematic notation and provides an elementary derivation of the general cross section. The relevant properties of the Poincare group and the transformation properties of current operators and target states are described in Sec 3. In Sec. 4 representations of target states with kinematic light-front symmetry are briefly discussed. The focus is on two applications. An impulse approximation of inclusive electron nucleus scattering at both medium and high energies. A parton model of the proton applied to deep inelastic scattering of polarized electrons by polarized protons. 19 refs.
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
WLWL scattering in Higgsless models: Identifying better effective theories
NASA Astrophysics Data System (ADS)
Belyaev, Alexander S.; Chivukula, R. Sekhar; Christensen, Neil D.; He, Hong-Jian; Kurachi, Masafumi; Simmons, Elizabeth H.; Tanabashi, Masaharu
2009-09-01
The three-site model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this paper we analyze how well the three-site model performs as a general exemplar of Higgsless models in describing WLWL scattering, and which modifications can make it more representative. We employ general sum rules relating the masses and couplings of the Kaluza-Klein modes of the gauge fields in continuum and deconstructed Higgsless models as a way to compare the different theories. We show that the size of the four-point vertex for the (unphysical) Nambu-Goldstone modes and the degree to which the sum rules are saturated by contributions from the lowest-lying Kaluza-Klein resonances both provide good measures of the extent to which a highly deconstructed theory can accurately describe the low-energy physics of a continuum 5D Higgsless model. After comparing the three-site model to flat and warped continuum models, we analyze extensions of the three-site model to a longer open linear moose with an additional U(1) group and to a ring (“breaking electroweak symmetry strongly” or “hidden local symmetry”) model with three sites and three links. Both cases may be readily analyzed in the framework of the general sum rules. We demonstrate that WLWL scattering in the ring model can very closely approximate scattering in the continuum models, provided that the hidden local symmetry parameter a is chosen to mimic ρ-meson dominance of ππ scattering in QCD. The hadron and lepton collider phenomenology of both extended models is briefly discussed, with a focus on the complementary information to be gained from precision measurements of the Z' line shape and ZWW coupling at a high-energy lepton collider.
Applications of effective field theory to electron scattering
NASA Astrophysics Data System (ADS)
Diaconescu, Luca Radu
In this work two calculations are presented. In the first, we compute the vector analyzing power (VAP) for the elastic scattering of transversely polarized electrons from protons at low energies, using an effective theory of electrons, protons, and photons. We study all contributions through second order in E/M, where E and M are the electron energy and nucleon mass, respectively. The leading order VAP arises from the imaginary part of the interference of one- and two-photon exchange amplitudes. Sub-leading contributions are generated by the nucleon magnetic moment and charge radius, as well as recoil corrections to the leading-order amplitude. Working to second order in E/M), we obtain a prediction for A_n that is free of unknown parameters and that agrees with the recent measurement of the VAP in backward angle electron proton scattering. In the second part of this thesis the longitudinal asymmetry due to Z exchange is calculated in quasi-elastic electron-deuteron scattering at momentum transfers |Q^2| of about 0.1 GeV^2 relevant for the SAMPLE experiment. The deuteron and pn scattering-state wave functions are obtained from solutions of a Schrodinger equation with the Argonne v18 potential. Electromagnetic and weak neutral one- and two-nucleon currents are included in the calculation. The two-nucleon currents of pion range are shown to be identical to those derived in Effective Field Theory. The results indicate that two-body contributions to the asymmetry are small (about 0.2%) around the quasi-elastic peak, but become relatively more significant (about 3%) in the high-energy wing of the quasi-elastic peak.
Terahertz scattering by granular composite materials: An effective medium theory
NASA Astrophysics Data System (ADS)
Kaushik, Mayank; Ng, Brian W.-H.; Fischer, Bernd M.; Abbott, Derek
2012-01-01
Terahertz (THz) spectroscopy and imaging have emerged as important tools for identification and classification of various substances, which exhibit absorption characteristics at distinct frequencies in the THz range. The spectral fingerprints can potentially be distorted or obscured by electromagnetic scattering caused by the granular nature of some substances. In this paper, we present THz time domain transmission measurements of granular polyethylene powders in order to investigate an effective medium theory that yields a parameterized model, which can be used to estimate the empirical measurements to good accuracy.
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
Classical theory of rotational rainbow scattering from uncorrugated surfaces.
Khodorkovsky, Yuri; Averbukh, Ilya Sh; Pollak, Eli
2010-08-01
A classical perturbation theory is developed to study rotational rainbow scattering of molecules from uncorrugated frozen surfaces. Considering the interaction of the rigid rotor with the translational motion towards the surface to be weak allows for a perturbative treatment, in which the known zeroth order motion is that of a freely rotating molecule hitting a surface. Using perturbation theory leads to explicit expressions for the angular momentum deflection function with respect to the initial orientational angle of the rotor that are valid for any magnitude of the initial angular momentum. The rotational rainbows appear as peaks both in the final angular momentum and rotational energy distributions, as well as peaks in the angular distribution, although the surface is assumed to be uncorrugated. The derived analytic expressions are compared with numerical simulation data. Even when the rotational motion is significantly coupled to the translational motion, the predictions of the perturbative treatment remain qualitatively correct. PMID:21399336
Bcs-Bec Crossover Without Appeal to Scattering Length Theory
NASA Astrophysics Data System (ADS)
Malik, G. P.
2014-01-01
BCS-BEC (an acronym formed from Bardeen, Cooper, Schrieffer and Bose-Einstein condensation) crossover physics has customarily been addressed in the framework of the scattering length theory (SLT), which requires regularization/renormalization of equations involving infinities. This paper gives a frame by frame picture, as it were, of the crossover scenario without appealing to SLT. While we believe that the intuitive approach followed here will make the subject accessible to a wider readership, we also show that it sheds light on a feature that has not been under the purview of the customary approach: the role of the hole-hole scatterings vis-à-vis the electron-electron scatterings as one goes from the BCS to the BEC end. More importantly, we show that there are critical values of the concentration (n)and the interaction parameter (λ) at which the condensation of Cooper pairs takes place; this is a finding in contrast with the view that such pairs are automatically condensed.
NASA Technical Reports Server (NTRS)
Weatherford, Charles A.
1993-01-01
One version of the multichannel theory for electron-target scattering based on the Schwinger variational principle, the SMC method, requires the introduction of a projection parameter. The role of the projection parameter a is investigated and it is shown that the principal-value operator in the SMC equation is Hermitian regardless of the value of a as long as it is real and nonzero. In a basis that is properly orthonormalizable, the matrix representation of this operator is also Hermitian. The use of such basis is consistent with the Schwinger variational principle because the Lippmann-Schwinger equation automatically builds in the correct boundary conditions. Otherwise, an auxiliary condition needs to be introduced, and Takatsuka and McKoy's original value of a is one of the three possible ways to achieve Hermiticity. In all cases but one, a can be uncoupled from the Hermiticity condition and becomes a free parameter. An equation for a based on the variational stability of the scattering amplitude is derived; its solution has an interesting property that the scattering amplitude from a converged SMC calculation is independent of the choice of a even though the SMC operator itself is a-dependent. This property provides a sensitive test of the convergence of the calculation. For a static-exchange calculation, the convergence requirement only depends on the completeness of the one-electron basis, but for a general multichannel case, the a-invariance in the scattering amplitude requires both the one-electron basis and the N plus 1-electron basis to be complete. The role of a in the SMC equation and the convergence property are illustrated using two examples: e-CO elastic scattering in the static-exchange approximation, and a two-state treatment of the e-H2 Chi(sup 1)Sigma(sub g)(+) yields b(sup 3)Sigma(sub u)(+) excitation.
Open-Closed Homotopy Algebras and Strong Homotopy Leibniz Pairs Through Koszul Operad Theory
NASA Astrophysics Data System (ADS)
Hoefel, Eduardo; Livernet, Muriel
2012-08-01
Open-closed homotopy algebras (OCHA) and strong homotopy Leibniz pairs (SHLP) were introduced by Kajiura and Stasheff in 2004. In an appendix to their paper, Markl observed that an SHLP is equivalent to an algebra over the minimal model of a certain operad, without showing that the operad is Koszul. In the present paper, we show that both OCHA and SHLP are algebras over the minimal model of the zeroth homology of two versions of the Swiss-cheese operad and prove that these two operads are Koszul. As an application, we show that the OCHA operad is non-formal as a 2-colored operad but is formal as an algebra in the category of 2-collections.
NASA Astrophysics Data System (ADS)
D'Yakonov, A. G.
2011-03-01
Characteristic matrices and metrics of equivalence systems are studied that help give an efficient description of conjunctions of equivalence systems. Using these results, families of correct polynomials in the algebraic approach to classification are described.
NASA Astrophysics Data System (ADS)
Ding, Chizhu; Yang, Kecheng; Li, Wei; Guo, Wenping; Zhang, Xiaohui; Xia, Min
2014-10-01
Discerning the geometry of spheroidal scatterers of micron order is an important topic in identifying marine microbes. Optical diffraction tomography theory indicates that under the first-order Born approximation for weak scattering, scattering amplitude in the far zone and scattering potential of the scatterer have a Fourier relationship. In this paper, we describe a method based on diffraction tomography theory and determine the size and the shape of spheroidal scatterers by reconstructing the distribution of scattering potential from angular resolved scattered field. As a demonstration of this method, the scattering from spheroidal particles with equal-volume-sphere radii of 0.5429, 1.00, and 2.00 μm and an aspect ratio that varies from 0.4 to 1.5 was modeled by using T-matrix theory and used as test data. Simulation results show that in the case of low contrast, size and shape determination can be achieved with sub-wavelength precision.
Guenaydin, M.; Sierra, G.; Townsend, P.K.
1985-01-01
In this talk we give a review of our work on the construction and classification of N = 2 Maxwell-Einstein Supergravity theories (MESGT), study of the underlying algebraical and geometrical structure of these theories, and their compact and non-compact gaugings. We begin by summarizing our construction of the N = 2 MESGT's in five dimensions and give a geometrical interpretation to various scalar dependent quantities in the Lagrangian, based on the constraiants implied by supersymmetry. This is followed by a complete classification of the N = 2 MESGT's whose target manifolds parametrized by the scalar fields are symmetric spaces. 39 refs.
Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.
Meair, Jonathan; Jacquod, Philippe
2013-02-27
We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance. PMID:23343784
Siegert pseudostate formulation of scattering theory: General three-dimensional case
NASA Astrophysics Data System (ADS)
Krainov, Lev O.; Batishchev, Pavel A.; Tolstikhin, Oleg I.
2016-04-01
This paper generalizes the Siegert pseudostate (SPS) formulation of scattering theory to arbitrary finite-range potentials without any symmetry in the three-dimensional (3D) case. The orthogonality and completeness properties of 3D SPSs are established. The SPS expansions for scattering states, outgoing-wave Green's function, scattering matrix, and scattering amplitude, that is, all major objects of scattering theory, are derived. The theory is illustrated by calculations for several model potentials. The results enable one to apply 3D SPSs as a purely discrete basis capable of representing both discrete and continuous spectra in solving various stationary and time-dependent quantum-mechanical problems.
Covariant Spectator Theory of np scattering: Isoscalar interaction currents
Gross, Franz L.
2014-06-01
Using the Covariant Spectator Theory (CST), one boson exchange (OBE) models have been found that give precision fits to low energy $np$ scattering and the deuteron binding energy. The boson-nucleon vertices used in these models contain a momentum dependence that requires a new class of interaction currents for use with electromagnetic interactions. Current conservation requires that these new interaction currents satisfy a two-body Ward-Takahashi (WT), and using principals of {\\it simplicity\\/} and {\\it picture independence\\/}, these currents can be uniquely determined. The results lead to general formulae for a two-body current that can be expressed in terms of relativistic $np$ wave functions, ${\\it \\Psi}$, and two convenient truncated wave functions, ${\\it \\Psi}^{(2)}$ and $\\widehat {\\it \\Psi}$, which contain all of the information needed for the explicit evaluation of the contributions from the interaction current. These three wave functions can be calculated from the CST bound or scattering state equations (and their off-shell extrapolations). A companion paper uses this formalism to evaluate the deuteron magnetic moment.
Virtual Compton scattering off the nucleon in chiral perturbation theory
Hemmert, T.R.; Holstein, B.R.; Knoechlein, G.; Scherer, S.
1997-03-01
We investigate the spin-independent part of the virtual Compton scattering (VCS) amplitude off the nucleon within the framework of chiral perturbation theory. We perform a consistent calculation to third order in external momenta according to Weinberg`s power counting. With this calculation we can determine the second- and fourth-order structure-dependent coefficients of the general low-energy expansion of the spin-averaged VCS amplitude based on gauge invariance, crossing symmetry, and the discrete symmetries. We discuss the kinematical regime to which our calculation can be applied and compare our expansion with the multipole expansion by Guichon, Liu, and Thomas. We establish the connection of our calculation with the generalized polarizabilities of the nucleon where it is possible. {copyright} {ital 1997} {ital The American Physical Society}
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.
2015-05-01
We examine the consequences of the effective field theory (EFT) of dark matter–nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.
2015-05-01
We examine the consequences of the effective field theory (EFT) of dark matter–nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implicationsmore » of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.« less
Three-dimensional theory of stimulated Raman scattering
NASA Astrophysics Data System (ADS)
Sørensen, Martin W.; Sørensen, Anders S.
2009-09-01
We present a three-dimensional theory of stimulated Raman scattering (SRS) or super-radiance. In particular we address how the spatial and temporal properties of the generated SRS beam or Stokes beam of radiation depends on the spatial properties of the gain medium. Maxwell equations for the Stokes field operators and of the atomic operators are solved analytically and a correlation function for the Stokes field is derived. In the analysis we identify a super-radiating part of the Stokes radiation that exhibit beam characteristics. We show how the intensity in this beam builds up in time and at some point largely dominates the total Stokes radiation of the gain medium. We show how the SRS depends on the Fresnel number and the optical depth and that in fact these two factors are the only factors describing the coherent radiation.
Dark matter effective field theory scattering in direct detection experiments
NASA Astrophysics Data System (ADS)
Schneck, K.; Cabrera, B.; Cerdeño, D. G.; Mandic, V.; Rogers, H. E.; Agnese, R.; Anderson, A. J.; Asai, M.; Balakishiyeva, D.; Barker, D.; Basu Thakur, R.; Bauer, D. A.; Billard, J.; Borgland, A.; Brandt, D.; Brink, P. L.; Bunker, R.; Caldwell, D. O.; Calkins, R.; Chagani, H.; Chen, Y.; Cooley, J.; Cornell, B.; Crewdson, C. H.; Cushman, P.; Daal, M.; Di Stefano, P. C. F.; Doughty, T.; Esteban, L.; Fallows, S.; Figueroa-Feliciano, E.; Godfrey, G. L.; Golwala, S. R.; Hall, J.; Harris, H. R.; Hofer, T.; Holmgren, D.; Hsu, L.; Huber, M. E.; Jardin, D. M.; Jastram, A.; Kamaev, O.; Kara, B.; Kelsey, M. H.; Kennedy, A.; Leder, A.; Loer, B.; Lopez Asamar, E.; Lukens, P.; Mahapatra, R.; McCarthy, K. A.; Mirabolfathi, N.; Moffatt, R. A.; Morales Mendoza, J. D.; Oser, S. M.; Page, K.; Page, W. A.; Partridge, R.; Pepin, M.; Phipps, A.; Prasad, K.; Pyle, M.; Qiu, H.; Rau, W.; Redl, P.; Reisetter, A.; Ricci, Y.; Roberts, A.; Saab, T.; Sadoulet, B.; Sander, J.; Schnee, R. W.; Scorza, S.; Serfass, B.; Shank, B.; Speller, D.; Toback, D.; Upadhyayula, S.; Villano, A. N.; Welliver, B.; Wilson, J. S.; Wright, D. H.; Yang, X.; Yellin, S.; Yen, J. J.; Young, B. A.; Zhang, J.; SuperCDMS Collaboration
2015-05-01
We examine the consequences of the effective field theory (EFT) of dark matter-nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.; Cabrera, B.; Cerdeno, D. G.; Mandic, V.; Rogers, H. E.; Agnese, R.; Anderson, A. J.; Asai, M.; Balakishiyeva, D.; Barker, D.; Basu Thakur, R.; Bauer, D. A.; Billard, J.; Borgland, A.; Brandt, D.; Brink, P. L.; Bunker, R.; Caldwell, D. O.; Calkins, R.; Chagani, H.; Chen, Y.; Cooley, J.; Cornell, B.; Crewdson, C. H.; Cushman, Priscilla B.; Daal, M.; Di Stefano, P. C.; Doughty, T.; Esteban, L.; Fallows, S.; Figueroa-Feliciano, E.; Godfrey, G. L.; Golwala, S. R.; Hall, Jeter C.; Harris, H. R.; Hofer, T.; Holmgren, D.; Hsu, L.; Huber, M. E.; Jardin, D. M.; Jastram, A.; Kamaev, O.; Kara, B.; Kelsey, M. H.; Kennedy, A.; Leder, A.; Loer, B.; Lopez Asamar, E.; Lukens, W.; Mahapatra, R.; McCarthy, K. A.; Mirabolfathi, N.; Moffatt, R. A.; Morales Mendoza, J. D.; Oser, S. M.; Page, K.; Page, W. A.; Partridge, R.; Pepin, M.; Phipps, A.; Prasad, K.; Pyle, M.; Qiu, H.; Rau, W.; Redl, P.; Reisetter, A.; Ricci, Y.; Roberts, A.; Saab, T.; Sadoulet, B.; Sander, J.; Schnee, R. W.; Scorza, S.; Serfass, B.; Shank, B.; Speller, D.; Toback, D.; Upadhyayula, S.; Villano, A. N.; Welliver, B.; Wilson, J. S.; Wright, D. H.; Yang, X.; Yellin, S.; Yen, J. J.; Young, B. A.; Zhang, J.
2015-05-01
We examine the consequences of the effective eld theory (EFT) of dark matter-nucleon scattering or current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. We demonstrate that spectral di*erences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. We also discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.
Dark matter effective field theory scattering in direct detection experiments
Schneck, K.; Cabrera, B.; Cerdeño, D. G.; Mandic, V.; Rogers, H. E.; Agnese, R.; Anderson, A. J.; Asai, M.; Balakishiyeva, D.; Barker, D.; Basu Thakur, R.; Bauer, D. A.; Billard, J.; Borgland, A.; Brandt, D.; Brink, P. L.; Bunker, R.; Caldwell, D. O.; Calkins, R.; Chagani, H.; Chen, Y.; Cooley, J.; Cornell, B.; Crewdson, C. H.; Cushman, P.; Daal, M.; Di Stefano, P. C. F.; Doughty, T.; Esteban, L.; Fallows, S.; Figueroa-Feliciano, E.; Godfrey, G. L.; Golwala, S. R.; Hall, J.; Harris, H. R.; Hofer, T.; Holmgren, D.; Hsu, L.; Huber, M. E.; Jardin, D. M.; Jastram, A.; Kamaev, O.; Kara, B.; Kelsey, M. H.; Kennedy, A.; Leder, A.; Loer, B.; Lopez Asamar, E.; Lukens, P.; Mahapatra, R.; McCarthy, K. A.; Mirabolfathi, N.; Moffatt, R. A.; Morales Mendoza, J. D.; Oser, S. M.; Page, K.; Page, W. A.; Partridge, R.; Pepin, M.; Phipps, A.; Prasad, K.; Pyle, M.; Qiu, H.; Rau, W.; Redl, P.; Reisetter, A.; Ricci, Y.; Roberts, A.; Saab, T.; Sadoulet, B.; Sander, J.; Schnee, R. W.; Scorza, S.; Serfass, B.; Shank, B.; Speller, D.; Toback, D.; Upadhyayula, S.; Villano, A. N.; Welliver, B.; Wilson, J. S.; Wright, D. H.; Yang, X.; Yellin, S.; Yen, J. J.; Young, B. A.; Zhang, J.
2015-05-18
We examine the consequences of the effective field theory (EFT) of dark matter-nucleon scattering for current and proposed direct detection experiments. Exclusion limits on EFT coupling constants computed using the optimum interval method are presented for SuperCDMS Soudan, CDMS II, and LUX, and the necessity of combining results from multiple experiments in order to determine dark matter parameters is discussed. Here. we demonstrate that spectral differences between the standard dark matter model and a general EFT interaction can produce a bias when calculating exclusion limits and when developing signal models for likelihood and machine learning techniques. In conclusion, we discuss the implications of the EFT for the next-generation (G2) direct detection experiments and point out regions of complementarity in the EFT parameter space.
Generalizations of Karp's theorem to elastic scattering theory
NASA Astrophysics Data System (ADS)
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
Unified connected theory of few-body reaction mechanisms in N-body scattering theory
NASA Technical Reports Server (NTRS)
Polyzou, W. N.; Redish, E. F.
1978-01-01
A unified treatment of different reaction mechanisms in nonrelativistic N-body scattering is presented. The theory is based on connected kernel integral equations that are expected to become compact for reasonable constraints on the potentials. The operators T/sub +-//sup ab/(A) are approximate transition operators that describe the scattering proceeding through an arbitrary reaction mechanism A. These operators are uniquely determined by a connected kernel equation and satisfy an optical theorem consistent with the choice of reaction mechanism. Connected kernel equations relating T/sub +-//sup ab/(A) to the full T/sub +-//sup ab/ allow correction of the approximate solutions for any ignored process to any order. This theory gives a unified treatment of all few-body reaction mechanisms with the same dynamic simplicity of a model calculation, but can include complicated reaction mechanisms involving overlapping configurations where it is difficult to formulate models.
Theory and Measurement of Partially Correlated Persistent Scatterers
NASA Astrophysics Data System (ADS)
Lien, J.; Zebker, H. A.
2011-12-01
Interferometric synthetic aperture radar (InSAR) time-series methods can effectively estimate temporal surface changes induced by geophysical phenomena. However, such methods are susceptible to decorrelation due to spatial and temporal baselines (radar pass separation), changes in orbital geometries, atmosphere, and noise. These effects limit the number of interferograms that can be used for differential analysis and obscure the deformation signal. InSAR decorrelation effects may be ameliorated by exploiting pixels that exhibit phase stability across the stack of interferograms. These so-called persistent scatterer (PS) pixels are dominated by a single point-like scatterer that remains phase-stable over the spatial and temporal baseline. By identifying a network of PS pixels for use in phase unwrapping, reliable deformation measurements may be obtained even in areas of low correlation, where traditional InSAR techniques fail to produce useful observations. PS identification is challenging in natural terrain, due to low reflectivity and few corner reflectors. Shanker and Zebker [1] proposed a PS pixel selection technique based on maximum-likelihood estimation of the associated signal-to-clutter ratio (SCR). In this study, we further develop the underlying theory for their technique, starting from statistical backscatter characteristics of PS pixels. We derive closed-form expressions for the spatial, rotational, and temporal decorrelation of PS pixels as a function of baseline and signal-to-clutter ratio. We show that previous decorrelation and critical baseline expressions [2] are limiting cases of our result. We then describe a series of radar scattering simulations and show that the simulated decorrelation matches well with our analytic results. Finally, we use our decorrelation expressions with maximum-likelihood SCR estimation to analyze an area of the Hayward Fault Zone in the San Francisco Bay Area. A series of 38 images of the area were obtained from C
Plethystic algebras and vector symmetric functions.
Rota, G C; Stein, J A
1994-01-01
An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]). PMID:11607504
Matrix operator theory of radiative transfer. 1: rayleigh scattering.
Plass, G N; Kattawar, G W; Catchings, F E
1973-02-01
An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles including the polar angle theta = 0 degrees ; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions. Both the general theory and its history together with the method of calculation are discussed. As a first example of the method numerous curves are given for both the reflected and transmitted radiance for Rayleigh scattering from a homogeneous layer for a range of optical thicknesses from 0.0019 to 4096, surface albedo A = 0, 0.2, and 1, and cosine of solar zenith angle micro = 1, 0.5397, and 0.1882. It is shown that the matrix operator approach contains the doubling method as a special case.
Field-theoretical description of deep inelastic scattering
Geyer, B.; Robaschik, D.; Wieczorek, E.
1980-01-01
The most important theoretical notions concerning deep inelastic scattering are reviewed. Topics discussed are the model-independent approach, which is based on the general principles of quantum field theory, the application of quantum chromodynamics to deep inelastic scattering, approaches based on the quark--parton model, the light cone algebra, and conformal invariance, and also investigations in the framework of perturbation theory.
NASA Astrophysics Data System (ADS)
Hamhalter, Jan; Turilova, Ekaterina
2014-10-01
It is shown that any order isomorphism between the structures of unital associative JB subalgebras of JB algebras is given naturally by a partially linear Jordan isomorphism. The same holds for nonunital subalgebras and order isomorphisms preserving the unital subalgebra. Finally, we recover usual action of time evolution group on a von Neumann factor from group of automorphisms of the structure of Abelian subalgebras.
Combinatorics of n-point functions via Hopf algebra in quantum field theory
Mestre, Angela; Oeckl, Robert
2006-05-15
We use a coproduct on the time-ordered algebra of field operators to derive simple relations between complete, connected and 1-particle irreducible n-point functions. Compared to traditional functional methods our approach is much more intrinsic and leads to efficient algorithms suitable for concrete computations. It may also be used to efficiently perform tree level computations.
ERIC Educational Resources Information Center
Bair, Sherry L.; Rich, Beverly S.
2011-01-01
This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…
Student Reactions to Learning Theory Based Curriculum Materials in Linear Algebra--A Survey Analysis
ERIC Educational Resources Information Center
Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff
2016-01-01
In this report we examine students' perceptions of the implementation of carefully designed curriculum materials (called modules) in linear algebra courses at three different universities. The curricular materials were produced collaboratively by STEM and mathematics education faculty as members of a professional learning community (PLC) over…
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
High-energy scatterings in infinite-derivative field theory and ghost-free gravity
NASA Astrophysics Data System (ADS)
Talaganis, Spyridon; Mazumdar, Anupam
2016-07-01
In this paper, we will consider scattering diagrams in the context of infinite-derivative theories. First, we examine a finite-order, higher-derivative scalar field theory and find that we cannot eliminate the growth of scattering diagrams for large external momenta. Then, we employ an infinite-derivative scalar toy model and obtain that the external momentum dependence of scattering diagrams is convergent as the external momenta become very large. In order to eliminate the external momentum growth, one has to dress the bare vertices of the scattering diagrams by considering renormalised propagator and vertex loop corrections to the bare vertices. Finally, we investigate scattering diagrams in the context of a scalar toy model which is inspired by a ghost-free and singularity-free infinite-derivative theory of gravity, where we conclude that infinite derivatives can eliminate the external momentum growth of scattering diagrams and make the scattering diagrams convergent in the ultraviolet.
Yoshida, Ken-ichi; Itoh, Tamitake; Biju, Vasudevanpillai; Ishikawa, Mitsuru; Ozaki, Yukihiro
2009-02-15
We examined an electromagnetic (EM) theory of surface-enhanced resonance Raman scattering (SERRS) using single Ag nanoaggregates. The SERRS-EM theory is characterized by twofold EM enhancement induced by the coupling of plasmon resonance with both excitation and emission of Raman scattering plus fluorescence. The total emission cross-section spectra of enhanced Raman scattering and enhanced fluorescence were calculated using the following parameters: the spectrum of enhancement factor induced by plasmon resonance, resonance Raman scattering overlapped with fluorescence, and excitation wavelengths. The calculations well agreed with experimental total emission cross-section spectra, thus providing strong indications that the SERRS-EM theory is quantitatively correct.
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media
Tong Zhisong; Korotkova, Olga
2010-09-15
The theory of scattering of scalar stochastic fields from deterministic and random media is generalized to the electromagnetic domain under the first-order Born approximation. The analysis allows for determining the changes in spectrum, coherence, and polarization of electromagnetic fields produced on their propagation from the source to the scattering volume, interaction with the scatterer, and propagation from the scatterer to the far field. An example of scattering of a field produced by a {delta}-correlated partially polarized source and scattered from a {delta}-correlated medium is provided.
Modern integral equation techniques for quantum reactive scattering theory
Auerbach, S.M.
1993-11-01
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H{sub 2} {yields} H{sub 2}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H+H{sub 2} state resolved integral cross sections {sigma}{sub v{prime}j{prime},vj}(E) for the transitions (v = 0,j = 0) to (v{prime} = 1,j{prime} = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.
Path integral formulation of scattering theory with application to scattering by black holes
Zhang, T.R.
1985-01-01
The computational power of Feynman path integrals was exploited. Path-integration formalism for the quantum mechanics scattering and classical wave scattering was generalized. Firstly, the standard WKB approximation was generalized to the cases where the critical points of the action functional are degenerate. Three typical semiclassical scattering features served as examples for a classification of degenerate critical points: conservation laws, rainbows, glories. Secondly, the method developed for non-relativistic quantum mechanics scattering was used in the case of classical wave scattering. Scattering by Schwarzschild black holes was chosen as an example, and WKB cross sections for scalar, vector, and tensor fields were worked out. Finally, 2s-th Bessel function behavior of WKB cross section for helicity-s polarized glory scattering in curved space time was proved.
NASA Technical Reports Server (NTRS)
Ruge, J. W.; Stueben, K.
1987-01-01
The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.
NASA Astrophysics Data System (ADS)
Hong, Sang-Hoon; Wdowinski, Shimon
2012-01-01
Common vegetation scattering theories indicate that short wavelength Synthetic Aperture Radar (SAR) observations (X- and C-band) measure mainly vegetation canopies as the short-wavelength radar signal interacts mostly with upper sections of the vegetation. Furthermore, these theories also suggest that SAR cross- polarization (cross-pol) observations reflect only volume scattering. Consequently most SAR decomposition techniques assume that the cross-pol signal represents solely volume scattering. However, short-wavelength and cross-pol observations from the Everglades wetlands, south Florida, suggest that a significant portion of the SAR signal scatters from the surface and not only from the upper sections of the vegetation. The indication for surface scattering in wetland environment is derived from phase observable processed using interferometric techniques. The interferometric SAR (InSAR) observations reveal coherent phase signal in all polarizations and all wavelengths, reflecting water level changes beneath the vegetation. This coherent phase signal cannot be explained by neither volume scattering nor radar signal interaction with the upper sections of the vegetations, because canopies and branches are frequently move by wind. The only way that such coherent signal can be maintained and represents surface water level changes is when a multiple bounce from the vegetation and surface occurs. The simplest multi-bounce scattering mechanism that generate cross-pol signal occurs by rotated dihedrals. Thus, we use the rotated dihedral mechanism to explain the InSAR wetland observations and to revise the current vegetation scattering theories to accounts also for double bounce component in cross-pol observations.
Average wavefunction method for multiple scattering theory and applications
Singh, H.
1985-01-01
A general approximation scheme, the average wavefunction approximation (AWM), applicable to scattering of atoms and molecules off multi-center targets, is proposed. The total potential is replaced by a sum of nonlocal, separable interactions. Each term in the sum projects the wave function onto a weighted average in the vicinity of a given scattering center. The resultant solution is an infinite order approximation to the true solution, and choosing the weighting function as the zeroth order solution guarantees agreement with the Born approximation to second order. In addition, the approximation also becomes increasingly more accurate in the low energy long wave length limit. A nonlinear, nonperturbative literature scheme for the wave function is proposed. An extension of the scheme to multichannel scattering suitable for treating inelastic scattering is also presented. The method is applied to elastic scattering of a gas off a solid surface. The formalism is developed for both periodic as well as disordered surfaces. Numerical results are presented for atomic clusters on a flat hard wall with a Gaussian like potential at each atomic scattering site. The effect of relative lateral displacement of two clusters upon the scattering pattern is shown. The ability of AWM to accommodate disorder through statistical averaging over cluster configuration is illustrated. Enhanced uniform back scattering is observed with increasing roughness on the surface. Finally, the AWM is applied to atom-molecule scattering.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Scattering from elastic sea beds: first-order theory.
Jackson, D R; Ivakin, A N
1998-01-01
A perturbation model for high-frequency sound scattering from an irregular elastic sea bed is considered. The sea bed is assumed homogeneous on the average and two kinds of irregularities are assumed to cause scattering: roughness of the water-sea bed interface and volume inhomogeneities of the sediment mass density and the speeds of compressional and shear waves. The first-order small perturbation approximation is used to obtain expressions for the scattering amplitude and bistatic scattering strength. The angular dependence of the scattering strength is calculated for sedimentary rock and the influence of shear elasticity is examined by comparison with the case of a fluid bottom. Shear effects are shown to be strong and complicated.
Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering
DOE R&D Accomplishments Database
Tang, K. T.; Karplus, M.
1970-10-01
A quantum mechanical study is made of reactive scattering in the (H, H{sub 2}) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g. reaction configuration), are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and semi-empirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, H{sub 2}) reaction, a much simpler approximation method, the “linear model” is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational state of dependence and other properties of the total and differential reactions cross sections are determined. These results of the quantum mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shifts in the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.
Scattering theory for the quantum envelope of a classical system
Sudarshan, E.C.G.
1993-12-31
Classical dynamics, reformulated in terms of its quantum envelope is studied for the stationary states of the interacting system. The dynamical variable of ``elapsed time`` plays a crucial role in this study. It is shown that the perturbation series for the elapsed time can be summed in various simple cases even when standard perturbation series diverge. For the special class of systems where the interactions fall off sufficiently fast at infinity one could define ``in`` and ``out`` states; and consequently the wave matrices and scattering matrices. The scattering phase shifts bear a simple relation to the time delay in scattering.
Nakatsuka, Takao; Nishimura, Jun
2008-08-01
The Molière theory of multiple Coulomb scattering is improved to take account of ionization loss by applying a differential formulation of the theory. Distributions for the deflection angle theta over, as well as for any linear combination between theta over and the lateral displacement r over, under the ionization process are derived by a series expansion with the same universal functions f(n)(theta) of Molière, except that the values for both the expansion parameter B and the scale angle thetaM are corrected from those under the fixed-energy process. We find that Goudsmit-Saunderson angular distribution with ionization is also expressed by the same characteristic parameters B and thetaM derived above by the Molière theory. The transport mechanism of Molière process of multiple Coulomb scattering and the stochastic property of Molière series expansion are also investigated and discussed.
Path-integral formulation of scattering theory: Central potentials
Gerry, C.C.; Singh, V.A.
1980-05-15
We consider central-potential scattering and determine a path-integral representation for the S matrix in polar coordinates. This is obtained by transforming to polar coordinates a Cartesian form of the nonrelativistic S matrix given by Campbell et al., and implementing an idea of Faddeev to obtain the appropriate asymptotic conditions. Our results are applied to scattering in an inverse-square potential to determine the correct phase shifts as well as the S matrix.
NASA Astrophysics Data System (ADS)
McLenaghan, Raymond G.; Smirnov, Roman G.; The, Dennis
2004-03-01
We develop a new approach to the study of Killing tensors defined in pseudo-Riemannian spaces of constant curvature that is ideologically close to the classical theory of invariants. The main idea, which provides the foundation of the new approach, is to treat a Killing tensor as an algebraic object determined by a set of parameters of the corresponding vector space of Killing tensors under the action of the isometry group. The spaces of group invariants and conformal group invariants of valence two Killing tensors defined in the Minkowski plane are described. The group invariants, which are the generators of the space of invariants, are applied to the problem of classification of orthogonally separable Hamiltonian systems defined in the Minkowski plane. Transformation formulas to separable coordinates expressed in terms of the parameters of the corresponding space of Killing tensors are presented. The results are applied to the problem of orthogonal separability of the Drach superintegrable potentials.
Singularity in the Laboratory Frame Angular Distribution Derived in Two-Body Scattering Theory
ERIC Educational Resources Information Center
Dick, Frank; Norbury, John W.
2009-01-01
The laboratory (lab) frame angular distribution derived in two-body scattering theory exhibits a singularity at the maximum lab scattering angle. The singularity appears in the kinematic factor that transforms the centre of momentum (cm) angular distribution to the lab angular distribution. We show that it is caused in the transformation by the…
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Linear algebraic calculation of the Green's function for large-scale electronic structure theory
NASA Astrophysics Data System (ADS)
Takayama, R.; Hoshi, T.; Sogabe, T.; Zhang, S.-L.; Fujiwara, T.
2006-04-01
A linear algebraic method named the shifted conjugate-orthogonal conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green’s function and the density matrix without calculating eigenstates. The problem is reduced to independent linear equations at many energy points and the calculation is actually carried out only for a single energy point. The method is robust against the round-off error and the calculation can reach the machine accuracy. With the observation of residual vectors, the accuracy can be controlled, microscopically, independently for each element of the Green’s function, and dynamically, at each step in dynamical simulations. The method is applied to both a semiconductor and a metal.
The Aharonov–Bohm effect in scattering theory
Sitenko, Yu.A.; Vlasii, N.D.
2013-12-15
The Aharonov–Bohm effect is considered as a scattering event with nonrelativistic charged particles of the wavelength which is less than the transverse size of an impenetrable magnetic vortex. The quasiclassical WKB method is shown to be efficient in solving this scattering problem. We find that the scattering cross section consists of two terms, one describing the classical phenomenon of elastic reflection and another one describing the quantum phenomenon of diffraction; the Aharonov–Bohm effect is manifested as a fringe shift in the diffraction pattern. Both the classical and the quantum phenomena are independent of the choice of a boundary condition at the vortex edge, providing that probability is conserved. We show that a propagation of charged particles can be controlled by altering the flux of a magnetic vortex placed on their way. -- Highlights: •Aharonov–Bohm effect as a scattering event. •Impenetrable magnetic vortex of nonzero transverse size. •Scattering cross section is independent of a self-adjoint extension employed. •Classical phenomenon of elastic reflection and quantum phenomenon of diffraction. •Aharonov–Bohm effect as a fringe shift in the diffraction pattern.
The Retrieval of Ozone Profiles from Limb Scatter Measurements: Theory
NASA Technical Reports Server (NTRS)
Flittner, D. E.; Herman, B. M.; Bhartia, P. K.; McPeters, R. D.; Hilsenrath, E.
1999-01-01
An algorithm is presented for retrieving vertical profiles of O3 concentration using measurements of UV and visible light scattered from the limb of the atmosphere. The UV measurements provide information about the O3 profile in the upper and middle stratosphere, while only visible wavelengths are capable of probing the lower stratospheric O3 profile. Sensitivity to the underlying scene reflectance is greatly reduced by normalizing measurements at a tangent height high in the atmosphere (approximately 55 km), and relating measurements taken at lower altitudes to this normalization point. To decrease the effect of scattering by thin aerosols/clouds that may be present in the field of view, these normalized measurements are then combined by pairing wavelengths with strong and weak O3 absorption. We conclude that limb scatter can be used to measure O3 between 15 km and 50 km with 2-3 km vertical resolution and better than 10% accuracy.
Hybrid Theory of Electron-Hydrogenic Systems Elastic Scattering
NASA Technical Reports Server (NTRS)
Bhatia, A. K.
2007-01-01
Accurate electron-hydrogen and electron-hydrogenic cross sections are required to interpret fusion experiments, laboratory plasma physics and properties of the solar and astrophysical plasmas. We have developed a method in which the short-range and long-range correlations can be included at the same time in the scattering equations. The phase shifts have rigorous lower bounds and the scattering lengths have rigorous upper bounds. The phase shifts in the resonance region can be used to calculate very accurately the resonance parameters.
Scattering by ensembles of small particles experiment, theory and application
NASA Technical Reports Server (NTRS)
Gustafson, B. A. S.
1980-01-01
A hypothetical self consistent picture of evolution of prestellar intertellar dust through a comet phase leads to predictions about the composition of the circum-solar dust cloud. Scattering properties of thus resulting conglomerates with a bird's-nest type of structure are investigated using a micro-wave analogue technique. Approximate theoretical methods of general interest are developed which compared favorably with the experimental results. The principal features of scattering of visible radiation by zodiacal light particles are reasonably reproduced. A component which is suggestive of (ALPHA)-meteoroids is also predicted.
Theory of resonant multiphonon Raman scattering in graphene monolayers
NASA Astrophysics Data System (ADS)
Basko, Denis; Aleiner, Igor
2007-03-01
The Raman spectrum of graphene consists of distinct narrow peaks corresponding to different optical phonon branches as well as their overtones [1]. We show how the relative intensities of the overtone peaks encode information about relative strengths of different inelastic scattering processes electrons are subject to. In particular, assuming that the most important processes are electron-phonon and electron-electron scattering, it is shown that one can deduce their relative interaction strengths from the Raman spectra. [1] A. C. Ferrari et al., Phys. Rev. Lett. 97, 187401 (2006); A. Gupta et al., cond-mat/0606593; D. Graf et al., cond-mat/0607562.
Batishchev, Pavel A.; Tolstikhin, Oleg I.
2007-06-15
The Siegert pseudostate (SPS) formulation of scattering theory, originally developed by Tolstikhin, Ostrovsky, and Nakamura [Phys. Rev. A, 58, 2077 (1998)] for s-wave scattering in a spherically symmetric finite-range potential, is generalized to nonzero angular momenta. The orthogonality and completeness properties of SPSs are established and SPS expansions for the outgoing-wave Green's function, physical states, and scattering matrix are obtained. The present formulation completes the theory of SPSs in the one-channel case, making its application to three-dimensional problems possible. The results are illustrated by calculations for several model potentials.
NASA Astrophysics Data System (ADS)
Daon, Shauli; Pollak, Eli; Miret-Artés, S.
2012-11-01
Inspired by the semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984), 10.1063/1.446609], we derive explicit expressions for the angular distribution of particles scattered from thermal surfaces. At very low surface temperature, the observed experimental background scattering is proportional to the spectral density of the phonons. The angular distribution is a sum of diffraction peaks and a broad background reflecting the spectral density. The theory is applied to measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface.
Application of Mie theory to assess structure of spheroidal scattering in backscattering geometries
Chalut, Kevin J.; Giacomelli, Michael G.; Wax, Adam
2010-01-01
Inverse light scattering analysis seeks to associate measured scattering properties with the most probable theoretical scattering distribution. Although Mie theory is a spherical scattering model, it has been used successfully for discerning the geometry of spheroidal scatterers. The goal of this study was an in-depth evaluation of the consequences of analyzing the structure of spheroidal geometries, which are relevant to cell and tissue studies in biology, by employing Mie-theory-based inverse light scattering analysis. As a basis for this study, the scattering from spheroidal geometries was modeled using T-matrix theory and used as test data. In a previous study, we used this technique to investigate the case of spheroidal scatterers aligned with the optical axis. In the present study, we look at a broader scope which includes the effects of aspect ratio, orientation, refractive index, and incident light polarization. Over this wide range of parameters, our results indicate that this method provides a good estimate of spheroidal structure. PMID:18677348
A dynamical formulation of one-dimensional scattering theory and its applications in optics
Mostafazadeh, Ali
2014-02-15
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrödinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, antilasing, and unidirectional invisibility. -- Highlights: • Proposes a dynamical theory of scattering in one dimension. • Derives and solves dynamical equations for scattering data. • Gives a new inverse scattering prescription. • Constructs optical potentials with desired scattering properties.
Generalized Yang-Mills theory and gravity
NASA Astrophysics Data System (ADS)
Ho, Pei-Ming
2016-02-01
We propose a generalization of Yang-Mills theory for which the symmetry algebra does not have to be factorized as mutually commuting algebras of a finite-dimensional Lie algebra and the algebra of functions on base space. The algebra of diffeomorphism can be constructed as an example, and a class of gravity theories can be interpreted as generalized Yang-Mills theories. These theories, in general, include a graviton, a dilaton and a rank-two antisymmetric field, although Einstein gravity is also included as a special case. We present calculations suggesting that the connection in scattering amplitudes between Yang-Mills theory and gravity via Bern-Carrasco-Johansson duality can be made more manifest in this formulation.
NASA Astrophysics Data System (ADS)
Connes, Alain; Kreimer, Dirk
This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann-Hilbert problem. We shall first show that for any quantum field theory, the combinatorics of Feynman graphs gives rise to a Hopf algebra which is commutative as an algebra. It is the dual Hopf algebra of the enveloping algebra of a Lie algebra whose basis is labelled by the one particle irreducible Feynman graphs. The Lie bracket of two such graphs is computed from insertions of one graph in the other and vice versa. The corresponding Lie group G is the group of characters of . We shall then show that, using dimensional regularization, the bare (unrenormalized) theory gives rise to a loop
Symmetries of tree-level scattering amplitudes in N=6 superconformal Chern-Simons theory
Bargheer, Till; Loebbert, Florian; Meneghelli, Carlo
2010-08-15
Constraints of the osp(6|4) symmetry on tree-level scattering amplitudes in N=6 superconformal Chern-Simons theory are derived. Supplemented by Feynman diagram calculations, solutions to these constraints, namely, the four- and six-point superamplitudes, are presented and shown to be invariant under Yangian symmetry. This introduces integrability into the amplitude sector of the theory.
NASA Astrophysics Data System (ADS)
Lyakh, Dmitry I.; Bartlett, Rodney J.
2014-01-01
The fundamentality of the exponential representation of a second-quantised correlated wave function is emphasised with an accent on the physical sense of cluster amplitudes as cumulants of the correlated ansatz. Three main wave function formalisms, namely, the configuration-interaction theory, the coupled-cluster approach, and the many-body perturbation theory (as well as their extensions, e.g. the equation-of-motion coupled-cluster method, multireference schemes, etc.), are represented in an exponential form, leading to a formulation of the working equations in terms of cluster amplitudes. By expressing the corresponding many-body tensor equations in terms of cluster amplitudes, we could unambiguously check connectivity types and the asymptotic behaviour of all tensors/scalars involved (in the formal limit of an infinite number of correlated particles). In particular, the appearance of disconnected cluster amplitudes corresponds to unphysical correlations. Besides, we demonstrate that the equation-of-motion coupled-cluster approach, as well as certain excited-state configuration-interaction methods, can be recast in a fully connected (exponential) form, thus breaking the common belief that all truncated configuration-interaction methods violate connectivity. Our work is based on the recently developed algebraic framework which can be viewed as a complement to the classical diagrammatic analysis.
Numerical validation of the generalized Harvey-Shack surface scatter theory
NASA Astrophysics Data System (ADS)
Choi, Narak; Harvey, James E.
2013-11-01
The generalized Harvey-Shack (GHS) surface scatter theory is numerically compared to the classical small perturbation method, the Kirchhoff approximation method, and the rigorous method of moments for one-dimensional ideally conducting surfaces whose surface power spectral density function is Gaussian or exhibits an inverse power law (fractal) behavior. In spite of its simple analytic form, our numerical comparison shows that the new GHS theory is valid (with reasonable accuracy) over a broader range of surface parameter space than either of the two classical surface scatter theories.
Zhou, Yun Pollak, Eli; Miret-Artés, Salvador
2014-01-14
A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to “soft” corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.
Theory for Neutron Scattering from Polymers in Tubes: Lozenges, Dangling Ends and Retraction
NASA Astrophysics Data System (ADS)
Read, D. J.; McLeish, T. C. B.
1997-03-01
We present a consistent explanation for the 'lozenge' shapes in contour plots of the two-dimensional neutron scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We also present a complete theory for the calculation of neutron scattering functions in the following experimental situation: a melt of partially deuterated block copolymers is stretched and sufficient time allowed for the polymers to retract along their tubes but for no further relaxation processes to occur before quenching below the glass transition temperature. The theory is necessary for the modelling of neutron scattering experiments which test the retraction theory for strongly stretched melts. We expect to be able to comment on the success of the theory for one such experiment.
NASA Astrophysics Data System (ADS)
Werneth, Charles; Maung Maung, Khin; Norbury, John
2012-10-01
Non-relativistic multiple scattering theories (NRMST) are formulated by separating the unperturbed Hamiltonian from the interaction and writing the Lippmann-Schwinger equation as an infinite series in the multiple sums of pseudo two-body operators, known as the Watson tau-operators. The advantage of using the multiple scattering theory (MST) is that the pseudo two-body operators are often well approximated by free two-body nucleon-nucleon operators, which are obtained from parameterizations of experimental data. Relativistic theories are needed to properly describe the production of new particles, such as pions, from nucleus-nucleus collisions. Relativistic multiple scattering theories (RMST) have been developed for nucleon-nucleus scattering; however, no RMST for nucleus-nucleus scattering has yet been derived.footnotetextMaung K M, Norbury J W, and Coleman T 2007 J. Phys. G 34 1861. The purpose of this research is to derive an RMST for nucleus-nucleus scattering and to include delta degrees of freedom in the interaction, the minimum requirement for pion production.
ERIC Educational Resources Information Center
Pavelle, Richard; And Others
1981-01-01
Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)
Elastic Proton Scattering of Medium Mass Nuclei from Coupled-Cluster Theory
Hagen, G.; MichelN.,
2012-01-01
Using coupled-cluster theory and interactions from chiral effective field theory, we compute overlap functions for transfer and scattering of low-energy protons on the target nucleus 40Ca. Effects of three-nucleon forces are included phenomenologically as in-medium two-nucleon interactions. Using known asymptotic forms for one-nucleon overlap functions we derive a simple and intuitive way of computing scattering observables such as elastic scattering phase shifts and cross sections. As a first application and proof of principle, we compute phase shifts and differential interaction cross sections at energies of 9.6 and 12.44 MeV and compare with experimental data. Our computed diffraction minima are in fair agreement with experimental results, while we tend to overestimate the cross sections at large scattering angles.
NASA Astrophysics Data System (ADS)
Masoero, Davide; Raimondo, Andrea; Valeri, Daniele
2016-09-01
We assess the ODE/IM correspondence for the quantum g -KdV model, for a non-simply laced Lie algebra g. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra g^{(1)} , and constructing the relevant {Ψ} -system among subdominant solutions. We then use the {Ψ} -system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum g -KdV model. We also consider generalized Airy functions for twisted Kac-Moody algebras and we construct new explicit solutions to the Bethe Ansatz equations. The paper is a continuation of our previous work on the ODE/IM correspondence for simply-laced Lie algebras.
On the theory and simulation of multiple Coulomb scattering of heavy-charged particles.
Striganov, S I
2005-01-01
The Moliere theory of multiple Coulomb scattering is modified to take into account the difference between processes of scattering off atomic nuclei and electrons. A simple analytical expression for angular distribution of charged particles passing through a thick absorber is found. It does not assume any special form for a differential scattering cross section and has a wider range of applicability than a gaussian approximation. A well-known method to simulate multiple Coulomb scatterings is based on treating 'soft' and 'hard' collisions differently. An angular deflection in a large number of 'soft' collisions is sampled using the proposed distribution function, a small number of 'hard' collision are simulated directly. A boundary between 'hard' and 'soft' collisions is defined, providing a precise sampling of a scattering angle (1% level) and a small number of 'hard' collisions. A corresponding simulating module takes into account projectile and nucleus charged distributions and exact kinematics of a projectile-electron interaction.
A theory for scattering by density fluctuations based on three-wave interaction
NASA Technical Reports Server (NTRS)
Harker, K. J.; Crawford, F. W.
1973-01-01
The theory of scattering by charged particle fluctuations of a plasma is developed for the case of zero magnetic field. The source current is derived on the basis of: (1) a three wave interaction between the incident and scattered electromagnetic waves and one electrostatic plasma wave (either Langmuir or ion acoustic), and (2) a synchronous interaction between the same two electromagnetic waves and the discrete components of the charged particle fluctuations. Previous work is generalized by no longer making the assumption that the frequency of the electromagnetic waves in large compared to the plasma frequency. The general result is then applied to incoherent scatter, and to scatter by strongly driven plasma waves. An expansion is carried out for each of those cases to determine the lower order corrections to the usual high frequency scattering formulas.
NASA Technical Reports Server (NTRS)
Jin, Y.-Q.; Kong, J. A.
1985-01-01
The strong fluctuation theory is applied to the study of the atmospheric snowfall which is modeled as a layer of random discrete-scatterers medium. As functions of size distribution, fractional volume, and radius of scatterers, the relationship is illustrated between the reflectivity factor and precipitation rate, the attenuation of the centimeter and millimeter waves, and the line-of-sight transmission of coherent and incoherent wave components. The theoretical results are shown to match favorably with experimental data.
Sahoo, Tapas; Pollak, Eli
2015-08-14
A second order classical perturbation theory is developed to calculate the sticking probability of a particle scattered from an uncorrugated thermal surface. An analytic expression for the temperature dependent energy loss of the particle to the surface is derived by employing a one-dimensional generalized Langevin equation. The surface temperature reduces the energy loss, since the thermal surface transfers energy to the particle. Using a Gaussian energy loss kernel and the multiple collision theory of Fan and Manson [J. Chem. Phys. 130, 064703 (2009)], enables the determination of the fraction of particles trapped on the surface after subsequent momentum reversals of the colliding particle. This then leads to an estimate of the trapping probability. The theory is tested for the model scattering of Ar on a LiF(100) surface. Comparison with numerical simulations shows excellent agreement of the analytical theory with simulations, provided that the energy loss is determined by the second order perturbation theory.
Covariant spectator theory of np scattering: Deuteron quadrupole moment
Gross, Franz
2015-01-26
The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to np scattering data. Included in the calculation are a new class of isoscalar np interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experiential result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better than 1%, similar to the results obtained recently from _{X}EFT predictions to order N^{3}LO.
Covariant spectator theory of np scattering: Deuteron quadrupole moment
Gross, Franz
2015-01-26
The deuteron quadrupole moment is calculated using two CST model wave functions obtained from the 2007 high precision fits to np scattering data. Included in the calculation are a new class of isoscalar np interaction currents automatically generated by the nuclear force model used in these fits. The prediction for model WJC-1, with larger relativistic P-state components, is 2.5% smaller that the experiential result, in common with the inability of models prior to 2014 to predict this important quantity. However, model WJC-2, with very small P-state components, gives agreement to better than 1%, similar to the results obtained recently frommore » XEFT predictions to order N3LO.« less
Example of a quantum field theory based on a nonlinear Lie algebra
Schoutens, K. . Inst. for Theoretical Physics); Sevrin, A. ); van Nieuwenhuizen, P. . Theory Div.)
1991-11-01
In this contribution to Tini Veltman's Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields ( the metric') are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates.
Example of a quantum field theory based on a nonlinear Lie algebra
Schoutens, K.; Sevrin, A.; van Nieuwenhuizen, P.
1991-11-01
In this contribution to Tini Veltman`s Festschrift we shall give a paedagogical account of our work on a new class of gauge theories called W gravities. They contain higher spin gauge fields, but the usual no-go theorems for interacting field theories with spins exceeding two do not apply since these theories are in two dimensions. It is, of course, well known that ghost-free interacting massless spin 2 fields (`the metric`) are gauge fields, and correspond to the geometrical notion of general coordinate transformations in general relativity, but it is yet unknown what extension of these ideas is introduced by the presence of massless higher spin gauge fields. A parallel with supergravity may be drawn: there the presence of massless spin 3/2 fields (gravitinos) corresponds to local fermi-bose symmetries of which these gravitinos are the gauge fields. Their geometrical meaning becomes only clear if one introduces superspace (with bosonic and fermionic coordinates): they correspond to local transformations of the fermionic coordinates. For W gravity one might speculate on a kind of W-superspace with extra bosonic coordinates.
Low frequency sound scattering from spherical assemblages of bubbles using effective medium theory.
Hahn, Thomas R
2007-12-01
The determination of the acoustic field scattered by an underwater assembly of gas bubbles or similar resonant monopole scatterers is of considerable theoretical and practical interest. This problem is addressed from a theoretical point of view within the framework of the effective medium theory for the case of spherically shaped assemblages. Although being valid more generally, the effective medium theory is an ideal instrument to study multiple scattering effects such as low frequency collective resonances, acoustically coupled breathing modes of the entire assembly. Explicit expressions for the scattering amplitude and cross sections are derived, as well as closed form expressions for the resonance frequency and spectral shape of the fundamental collective mode utilizing analytical S-matrix methods. This approach allows, in principle, a simultaneous inversion for the assembly radius and void fraction directly from the scattering cross sections. To demonstrate the validity of the approach, the theory is applied to the example of idealized, spherically shaped schools of swim bladder bearing fish. The analytic results of the theory are compared to numerical first-principle benchmark computations and excellent agreement is found, even for densely packed schools and frequencies across the bladder resonance.
Normal forms of an abstract Dirac operator and applications to scattering theory
NASA Astrophysics Data System (ADS)
Thaller, Bernd
1988-01-01
The unitary transformations which convert an abstract Dirac operator into an ``even'' (resp. ``odd'') operator are determined. The problem is formulated and solved completely within the general setup of supersymmetric quantum mechanics. This leads to some apparently new applications in relativistic quantum mechanics, where the transformations are known as the Foldy-Wouthuysen (resp. Cini-Touschek) transformations. The scattering theory for abstract Dirac operators is discussed and the utility of the general theory is illustrated by proving existence of relativistic Mo/ller operators for scattering from long-range magnetic fields.
Dahlqvist, P
1999-12-01
We apply periodic orbit theory to study the asymptotic distribution of escape times from an intermittent map. The dynamical zeta function exhibits a branch point which is associated with an asymptotic power law escape. By an analytic continuation technique we compute a pair of complex conjugate zeroes beyond the branch point, associated with a preasymptotic exponential decay. The crossover time from an exponential to a power law is also predicted. The theoretical predictions are confirmed by numerical simulation. Applications to conductance fluctuations in quantum dots are discussed.
NASA Astrophysics Data System (ADS)
Ruan, Zhichao; Fan, Shanhui
2012-04-01
We develop a temporal coupled-mode theory to describe the interaction of plane wave with an individual scatterer having an arbitrary shape. The theory involves the expansion of the fields on cylindrical or spherical wave basis for the two-dimensional and three-dimensional cases, respectively, and describes the scattering process in terms of a background scattering matrix and the resonant radiation coefficients into different cylindrical or spherical wave channels. This theory provides a general formula for the scattering and absorption cross sections. We show that for a subwavelength asymmetric scatterer with a single resonance, the scattering and absorption cross sections can exceed the single-resonance limit for some specific incident angles of illumination, but the sum of these cross sections over all angles has an upper limit. We validate the theory with numerical simulations of a metallic scatterer that does not have any rotation symmetry.
Twining characters and orbit Lie algebras
Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph
1996-12-05
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.
NASA Astrophysics Data System (ADS)
Blanchard, Philippe; Hellmich, Mario; Ługiewicz, Piotr; Olkiewicz, Robert
Quantum mechanics is the greatest revision of our conception of the character of the physical world since Newton. Consequently, David Hilbert was very interested in quantum mechanics. He and John von Neumann discussed it frequently during von Neumann's residence in Göttingen. He published in 1932 his book Mathematical Foundations of Quantum Mechanics. In Hilbert's opinion it was the first exposition of quantum mechanics in a mathematically rigorous way. The pioneers of quantum mechanics, Heisenberg and Dirac, neither had use for rigorous mathematics nor much interest in it. Conceptually, quantum theory as developed by Bohr and Heisenberg is based on the positivism of Mach as it describes only observable quantities. It first emerged as a result of experimental data in the form of statistical observations of quantum noise, the basic concept of quantum probability.
Scattering of an electromagnetic plane wave by a Luneburg lens. I. Ray theory.
Lock, James A
2008-12-01
For a plane wave incident on either a Luneburg lens or a modified Luneburg lens, the magnitude and phase of the transmitted electric field are calculated as a function of the scattering angle in the context of ray theory. It is found that the ray trajectory and the scattered intensity are not uniformly convergent in the vicinity of edge ray incidence on a Luneburg lens, which corresponds to the semiclassical phenomenon of orbiting. In addition, it is found that rays transmitted through a large-focal-length modified Luneburg lens participate in a far-zone rainbow, the details of which are exactly analytically soluble in ray theory. Using these results, the Airy theory of the modified Luneburg lens is derived and compared with the Airy theory of the rainbows of a homogeneous sphere. PMID:19037388
NASA Astrophysics Data System (ADS)
Suzumura, Yukio
2003-08-01
Convex tilted rear walls in a stage enclosure, an array of circular columns installed in front of walls, and triangular reflectors above the stage were newly adopted as scattering obstacles in an acoustic design of Tsuyama Music Cultural Hall, called ``Bell Fole‸t Tsuyama.'' The fundamental shape of the hall was designed using the theory of subjective preference. To calculate the effects of scattered reflections on a sound field in a real concert hall is extremely laborious. For this reason, the evaluation of effects of scattered reflections on the sound field in the hall was made experimentally by use of a
Elements of QED-NRQED effective field theory: NLO scattering at leading power
NASA Astrophysics Data System (ADS)
Dye, Steven P.; Gonderinger, Matthew; Paz, Gil
2016-07-01
The proton radius puzzle, i.e. the large discrepancy in the extraction of the proton charge radius between regular and muonic hydrogen, challenges our understanding of the structure of the proton. It can also be an indication of a new force that couples to muons, but not to electrons. An effective field theory analysis using nonrelativistic quantum electrodynamics (NRQED) indicates that the muonic hydrogen result can be interpreted as a large, compared to some model estimates, muon-proton spin-independent contact interaction. The muonic hydrogen result can be tested by a muon-proton scattering experiment, MUSE, that is planned at the Paul Scherrer Institute in Switzerland. The typical momenta of the muons in this experiment are of the order of the muon mass. In this energy regime the muons are relativistic but the protons are still nonrelativistic. The interaction between the muons and protons can be described by a hybrid QED-NRQED effective field theory. We present some elements of this effective field theory. In particular we consider O (Z α ) scattering up to power m2/M2 , where m (M ) is the muon (proton) mass and Z =1 for a proton, and O (Z2α2) scattering at leading power. We show how the former reproduces Rosenbluth scattering up to power m2/M2 and the latter the relativistic scattering off a static potential. Proton structure corrections at O (Z2α2) will be considered in a subsequent paper.
Matrix operator theory of radiative transfer. I - Rayleigh scattering.
NASA Technical Reports Server (NTRS)
Plass, G. N.; Kattawar, G. W.; Catchings, F. E.
1973-01-01
An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.
Topics in Nonsupersymmetric Scattering Amplitudes in Gauge and Gravity Theories
NASA Astrophysics Data System (ADS)
Nohle, Joshua David
In Chapters 1 and 2, we introduce and review the duality between color and kinematics in Yang-Mills theory uncovered by Bern, Carrasco and Johansson (BCJ). In Chapter 3, we provide evidence in favor of the conjectured duality between color and kinematics for the case of nonsupersymmetric pure Yang-Mills amplitudes by constructing a form of the one-loop four-point amplitude of this theory that makes the duality manifest. Our construction is valid in any dimension. We also describe a duality-satisfying representation for the two-loop four-point amplitude with identical four-dimensional external helicities. We use these results to obtain corresponding gravity integrands for a theory containing a graviton, dilaton, and antisymmetric tensor, simply by replacing color factors with specified diagram numerators. Using this, we give explicit forms of ultraviolet divergences at one loop in four, six, and eight dimensions, and at two loops in four dimensions. In Chapter 4, we extend the four-point one-loop nonsupersymmetric pure Yang-Mills discussion of Chapter 3 to include fermions and scalars circulating in the loop with all external gluons. This gives another nontrivial loop-level example showing that the duality between color and kinematics holds in nonsupersymmetric gauge theory. The construction is valid in any spacetime dimension and written in terms of formal polarization vectors. We also convert these expressions into a four-dimensional form with explicit external helicity states. Using this, we compare our results to one-loop duality-satisfying amplitudes that are already present in literature. In Chapter 5, we switch from the topic of color-kinematics duality to discuss the recently renewed interest in the soft behavior of gravitons and gluons. Specifically, we discuss the subleading low-energy behavior. Cachazo and Strominger recently proposed an extension of the soft-graviton theorem found by Weinberg. In addition, they proved the validity of their extension at
Shaped beam scattering by an aggregate of particles using generalized Lorenz-Mie theory
NASA Astrophysics Data System (ADS)
Briard, Paul; Wang, Jia jie; Han, Yi Ping
2016-04-01
In this paper, the light scattering by an aggregate of particles illuminated by an arbitrary shaped beam is analyzed within the framework of generalized Lorenz-Mie theory (GLMT). The theoretical derivations of aggregated particles illuminated by an arbitrary shaped beam are revisited, with special attention paid to the computation of beam shape coefficients of a shaped beam for aggregated particles. The theoretical treatments as well as a home-made code are then verified by making comparisons between our numerical results and those calculated using a public available T-Matrix code MSTM. Good agreements are achieved which partially indicate the correctness of both codes. Additionally, more numerical results are presented to study the scattered fields of aggregated particles illuminated by a focused Gaussian beam. Several large enhancements in the scattered intensity distributions are found which are believed to be due to the Bragg's scattering by a linear chain of spheres.
NASA Astrophysics Data System (ADS)
Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.
2010-12-01
In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for Ca40,42,44,48 with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+Ca40,42,44,48 systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.
Bhuyan, M.; Panda, R. N.; Routray, T. R.; Patra, S. K.
2010-12-15
In the framework of relativistic mean field (RMF) theory, we have calculated the density distribution of protons and neutrons for {sup 40,42,44,48}Ca with NL3 and G2 parameter sets. The microscopic proton-nucleus optical potentials for p+{sup 40,42,44,48}Ca systems are evaluated from the Dirac nucleon-nucleon scattering amplitude and the density of the target nucleus using relativistic-Love-Franey and McNeil-Ray-Wallace parametrizations. We have estimated the scattering observables, such as the elastic differential scattering cross section, analyzing power and the spin observables with the relativistic impulse approximation (RIA). The results have been compared with the experimental data for a few selective cases and we find that the use of density as well as the scattering matrix parametrizations are crucial for the theoretical prediction.
Semiclassical multi-phonon theory for atom-surface scattering: Application to the Cu(111) system
Daon, Shauli; Pollak, Eli
2015-05-07
The semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984)] is further developed to include the full multi-phonon transitions in atom-surface scattering. A practically applicable expression is developed for the angular scattering distribution by utilising a discretized bath of oscillators, instead of the continuum limit. At sufficiently low surface temperature good agreement is found between the present multi-phonon theory and the previous one-, and two-phonon theory derived in the continuum limit in our previous study [Daon, Pollak, and Miret-Artés, J. Chem. Phys. 137, 201103 (2012)]. The theory is applied to the measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface. We find that the present multi-phonon theory substantially improves the agreement between experiment and theory, especially at the higher surface temperatures. This provides evidence for the importance of multi-phonon transitions in determining the angular distribution as the surface temperature is increased.
Harmonic oscillator representation in the theory of scattering and nuclear reactions
NASA Technical Reports Server (NTRS)
Smirnov, Yuri F.; Shirokov, A. M.; Lurie, Yuri, A.; Zaitsev, S. A.
1995-01-01
The following questions, concerning the application of the harmonic oscillator representation (HOR) in the theory of scattering and reactions, are discussed: the formulation of the scattering theory in HOR; exact solutions of the free motion Schroedinger equation in HOR; separable expansion of the short range potentials and the calculation of the phase shifts; 'isolated states' as generalization of the Wigner-von Neumann bound states embedded in continuum; a nuclear coupled channel problem in HOR; and the description of true three body scattering in HOR. As an illustration the soft dipole mode in the (11)Li nucleus is considered in a frame of the (9)Li+n+n cluster model taking into account of three body continuum effects.
Scattering theory for the Klein-Gordon equation with nondecreasing potentials
Cruz, Maximino; Arredondo R, Juan H.
2008-11-15
The Klein-Gordon equation is considered in the case of nondecreasing potentials. The energy inner product is nonpositive on a subspace of infinite dimension, not consisting entirely of eigenvectors of the associated operator. A scattering theory for this case is developed and asymptotic completeness for generalized Moeller operators is proven.
NASA Astrophysics Data System (ADS)
Setare, M. R.; Adami, H.
2016-08-01
The Chern-Simons-like theories of gravity (CSLTG) are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz-Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.
Array algebra estimation in signal processing
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.
Hybrid theory and calculation of e-N2 scattering. [quantum mechanics - nuclei (nuclear physics)
NASA Technical Reports Server (NTRS)
Chandra, N.; Temkin, A.
1975-01-01
A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.
Parity violation in neutron deuteron scattering in pionless effective field theory
NASA Astrophysics Data System (ADS)
Vanasse, Jared J.
In this dissertation the parity violating neutron deuteron scattering amplitudes are calculated using pionless effective field theory to leading order. The five low energy parity violating constants present in pionless effective field theory are estimated by matching onto the ``best" values for the parameters of the model by Desplanques, Donoghue, and Holstein (DDH). Using these estimates and the calculated amplitudes, predictions for the spin rotation of a neutron through a deuteron target are given with a value of 1.8 × 10-8 rad cm-1. Also given are the longitudinal analyzing power in neutron deuteron scattering with a polarized neutron yielding 2.2 × 10-8, and a polarized deuteron giving 4.0 × 10-8. These observables are discussed in the broader context of hadronic parity violation and as possible future experiments to determine the values of the five low energy parity violating constant present in pionless effective theory.
West, R.; Tsang, Leung; Winebrenner, D.P. )
1993-03-01
Dense medium radiative transfer theory is applied to a three-layer model consisting of two scattering layers overlying a homogeneous half space with a size distribution of particles in each layer. A model with a distribution of sizes gives quite different results than those obtained from a model with a single size. The size distribution is especially important in the low frequency limit when scattering is strongly dependent on particle size. The size distribution and absorption characteristics also affect the extinction behavior as a function of fractional volume. Theoretical results are also compared with experimental data. The sizes, permittivities, and densities used in the numerical illustrations are typical values for snow.
Mie light-scattering granulometer with adaptive numerical filtering. I. Theory.
Hespel, L; Delfour, A
2000-12-20
A search procedure based on a least-squares method including a regularization scheme constructed from numerical filtering is presented. This method, with the addition of a nephelometer, can be used to determine the particle-size distributions of various scattering media (aerosols, fogs, rocket exhausts, motor plumes) from angular static light-scattering measurements. For retrieval of the distribution function, the experimental data are matched with theoretical patterns derived from Mie theory. The method is numerically investigated with simulated data, and the performance of the inverse procedure is evaluated. The results show that the retrieved distribution function is quite reliable, even for strong levels of noise.
Splines and the Galerkin method for solving the integral equations of scattering theory
NASA Astrophysics Data System (ADS)
Brannigan, M.; Eyre, D.
1983-06-01
This paper investigates the Galerkin method with cubic B-spline approximants to solve singular integral equations that arise in scattering theory. We stress the relationship between the Galerkin and collocation methods.The error bound for cubic spline approximates has a convergence rate of O(h4), where h is the mesh spacing. We test the utility of the Galerkin method by solving both two- and three-body problems. We demonstrate, by solving the Amado-Lovelace equation for a system of three identical bosons, that our numerical treatment of the scattering problem is both efficient and accurate for small linear systems.
ERIC Educational Resources Information Center
Schaufele, Christopher; Zumoff, Nancy
Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
Rayleigh theory of ultrasound scattering applied to liquid-filled contrast nanoparticles
NASA Astrophysics Data System (ADS)
Flegg, M. B.; Poole, C. M.; Whittaker, A. K.; Keen, I.; Langton, C. M.
2010-06-01
We present a novel modified theory based upon Rayleigh scattering of ultrasound from composite nanoparticles with a liquid core and solid shell. We derive closed form solutions to the scattering cross-section and have applied this model to an ultrasound contrast agent consisting of a liquid-filled core (perfluorooctyl bromide, PFOB) encapsulated by a polymer shell (poly-caprolactone, PCL). Sensitivity analysis was performed to predict the dependence of the scattering cross-section upon material and dimensional parameters. A rapid increase in the scattering cross-section was achieved by increasing the compressibility of the core, validating the incorporation of high compressibility PFOB; the compressibility of the shell had little impact on the overall scattering cross-section although a more compressible shell is desirable. Changes in the density of the shell and the core result in predicted local minima in the scattering cross-section, approximately corresponding to the PFOB-PCL contrast agent considered; hence, incorporation of a lower shell density could potentially significantly improve the scattering cross-section. A 50% reduction in shell thickness relative to external radius increased the predicted scattering cross-section by 50%. Although it has often been considered that the shell has a negative effect on the echogeneity due to its low compressibility, we have shown that it can potentially play an important role in the echogeneity of the contrast agent. The challenge for the future is to identify suitable shell and core materials that meet the predicted characteristics in order to achieve optimal echogenity.
New family of Maxwell like algebras
NASA Astrophysics Data System (ADS)
Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.
2016-08-01
We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.
Li, Jing; Hong, Wenxue
2014-12-01
The feature extraction and feature selection are the important issues in pattern recognition. Based on the geometric algebra representation of vector, a new feature extraction method using blade coefficient of geometric algebra was proposed in this study. At the same time, an improved differential evolution (DE) feature selection method was proposed to solve the elevated high dimension issue. The simple linear discriminant analysis was used as the classifier. The result of the 10-fold cross-validation (10 CV) classification of public breast cancer biomedical dataset was more than 96% and proved superior to that of the original features and traditional feature extraction method. PMID:25868233
Li, Jing; Hong, Wenxue
2014-12-01
The feature extraction and feature selection are the important issues in pattern recognition. Based on the geometric algebra representation of vector, a new feature extraction method using blade coefficient of geometric algebra was proposed in this study. At the same time, an improved differential evolution (DE) feature selection method was proposed to solve the elevated high dimension issue. The simple linear discriminant analysis was used as the classifier. The result of the 10-fold cross-validation (10 CV) classification of public breast cancer biomedical dataset was more than 96% and proved superior to that of the original features and traditional feature extraction method.
A multiple scattering theory for EM wave propagation in a dense random medium
NASA Technical Reports Server (NTRS)
Karam, M. A.; Fung, A. K.; Wong, K. W.
1985-01-01
For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.
Chiral symmetry and π-π scattering in the Covariant Spectator Theory
Biernat, Elmar P.; Peña, M. T.; Ribeiro, J. E.; Stadler, Alfred; Gross, Franz
2014-11-14
The π-π scattering amplitude calculated with a model for the quark-antiquark interaction in the framework of the Covariant Spectator Theory (CST) is shown to satisfy the Adler zero constraint imposed by chiral symmetry. The CST formalism is established in Minkowski space and our calculations are performed in momentum space. We prove that the axial-vector Ward-Takahashi identity is satisfied by our model. Then we show that, similarly to what happens within the Bethe-Salpeter formalism, application of the axial-vector Ward Takahashi identity to the CST π-π scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. Thus, the Adlermore » self-consistency zero for π-π scattering in the chiral limit emerges as the result for this sum.« less
Applicability of modified effective-range theory to positron-atom and positron-molecule scattering
Idziaszek, Zbigniew; Karwasz, Grzegorz
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 the effective range for e{sup +}-Ar and e{sup +}-N{sub 2} collisions.
Realization of low-scattering metamaterial shell based on cylindrical wave expanding theory.
Wu, Xiaoyu; Hu, Chenggang; Wang, Min; Pu, Mingbo; Luo, Xiangang
2015-04-20
In this paper, we demonstrate the design of a low-scattering metamaterial shell with strong backward scattering reduction and a wide bandwidth at microwave frequencies. Low echo is achieved through cylindrical wave expanding theory, and such shell only contains one metamaterial layer with simultaneous low permittivity and permeability. Cut-wire structure is selected to realize the low electromagnetic (EM) parameters and low loss on the resonance brim region. The full-model simulations show good agreement with theoretical calculations, and illustrate that near -20dB reduction is achieved and the -10 dB bandwidth can reach up to 0.6 GHz. Compared with the cloak based on transformation electromagnetics, the design possesses advantage of simpler requirement of EM parameters and is much easier to be implemented when only backward scattering field is cared. PMID:25969080
Semenov, Alexander; Babikov, Dmitri
2014-01-16
For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.
Matrix operator theory of radiative transfer. II - Scattering from maritime haze.
NASA Technical Reports Server (NTRS)
Kattawar, G. W.; Plass, G. N.; Catchings, F. E.
1973-01-01
Matrix operator theory is used to calculate the reflected and transmitted radiance of photons that have interacted with plane-parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo are tabulated. The forward peak and other features in the single-scattered phase function cause the radiance in many cases to be very different from that for Rayleigh scattering. In particular, the variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked and the relative limb darkening under very thick layers is greater for haze M than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = 0 is always greater and the cloud albedo is always less for haze M than for Rayleigh layers.
Discrete ordinate theory of radiative transfer. 2: Scattering from maritime haze
NASA Technical Reports Server (NTRS)
Kattawar, G. W.; Plass, G. N.; Catchings, F. E.
1971-01-01
Discrete ordinate theory was used to calculate the reflected and transmitted radiance of photons which have interacted with plane parallel maritime haze layers. The results are presented for three solar zenith angles, three values of the surface albedo, and a range of optical thicknesses from very thin to very thick. The diffuse flux at the lower boundary and the cloud albedo were tabulated. The forward peak and other features in the single scattered phase function caused the radiance in many cases to be very different from that for Rayleigh scattering. The variation of the radiance with both the zenith or nadir angle and the azimuthal angle is more marked, and the relative limb darkening under very thick layers is greater, for haze than for Rayleigh scattering. The downward diffuse flux at the lower boundary for A = O is always greater and the cloud albedo is always less for haze than for Rayleigh layers.
Discrimination in a General Algebraic Setting.
Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.
Discrimination in a General Algebraic Setting
Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras. PMID:26171421
ERIC Educational Resources Information Center
Hagerty, Gary; Smith, Stanley; Goodwin, Danielle
2010-01-01
In 2001, Black Hills State University (BHSU) redesigned college algebra to use the computer-based mastery learning program, Assessment and Learning in Knowledge Spaces [1], historical development of concepts modules, whole class discussions, cooperative activities, relevant applications problems, and many fewer lectures. This resulted in a 21%…
Coupled wave equations theory of surface-enhanced femtosecond stimulated Raman scattering.
McAnally, Michael O; McMahon, Jeffrey M; Van Duyne, Richard P; Schatz, George C
2016-09-01
We present a coupled wave semiclassical theory to describe plasmonic enhancement effects in surface-enhanced femtosecond stimulated Raman scattering (SE-FSRS). A key result is that the plasmon enhanced fields which drive the vibrational equation of motion for each normal mode results in dispersive lineshapes in the SE-FSRS spectrum. This result, which reproduces experimental lineshapes, demonstrates that plasmon-enhanced stimulated Raman methods provide unique sensitivity to a plasmonic response. Our derived SE-FSRS theory shows a plasmonic enhancement of |gpu|(2)ImχR(ω)gst (2)/ImχR(ω), where |gpu|(2) is the absolute square of the plasmonic enhancement from the Raman pump, χR(ω) is the Raman susceptibility, and gst is the plasmonic enhancement of the Stokes field in SE-FSRS. We conclude with a discussion on potential future experimental and theoretical directions for the field of plasmonically enhanced coherent Raman scattering. PMID:27608988
Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel
2013-07-19
We investigate the transport properties of a correlated metal within dynamical mean-field theory. Canonical Fermi liquid behavior emerges only below a very low temperature scale T(FL). Surprisingly the quasiparticle scattering rate follows a quadratic temperature dependence up to much higher temperatures and crosses over to saturated behavior around a temperature scale T(sat). We identify these quasiparticles as constituents of the hidden Fermi liquid. The non-Fermi-liquid transport above T(FL), in particular the linear-in-T resistivity, is shown to be a result of a strongly temperature dependent band dispersion. We derive simple expressions for the resistivity, Hall angle, thermoelectric power and Nernst coefficient in terms of a temperature dependent renormalized band structure and the quasiparticle scattering rate. We discuss possible tests of the dynamical mean-field theory picture of transport using ac measurements. PMID:23909344
Ab initio theory of the scattering-independent anomalous Hall effect.
Weischenberg, Jürgen; Freimuth, Frank; Sinova, Jairo; Blügel, Stefan; Mokrousov, Yuriy
2011-09-01
We report on first-principles calculations of the side-jump contribution to the anomalous Hall conductivity (AHC) directly from the electronic structure of a perfect crystal. We implemented our approach for a short-range scattering disorder model within the density functional theory and computed the full scattering-independent AHC in elemental bcc Fe, hcp Co, fcc Ni, and L1(0) FePd and FePt alloys. The full AHC thus calculated agrees systematically with experiment to a degree unattainable so far, correctly capturing the previously missing elements of side-jump contributions, hence paving the way to a truly predictive theory of the anomalous Hall effect and turning it from a characterization tool to a probing tool of multiband complex electronic band structures.
Xu, Wenhu; Haule, Kristjan; Kotliar, Gabriel
2013-07-19
We investigate the transport properties of a correlated metal within dynamical mean-field theory. Canonical Fermi liquid behavior emerges only below a very low temperature scale T(FL). Surprisingly the quasiparticle scattering rate follows a quadratic temperature dependence up to much higher temperatures and crosses over to saturated behavior around a temperature scale T(sat). We identify these quasiparticles as constituents of the hidden Fermi liquid. The non-Fermi-liquid transport above T(FL), in particular the linear-in-T resistivity, is shown to be a result of a strongly temperature dependent band dispersion. We derive simple expressions for the resistivity, Hall angle, thermoelectric power and Nernst coefficient in terms of a temperature dependent renormalized band structure and the quasiparticle scattering rate. We discuss possible tests of the dynamical mean-field theory picture of transport using ac measurements.
The application of contraction theory to an iterative formulation of electromagnetic scattering
NASA Technical Reports Server (NTRS)
Brand, J. C.; Kauffman, J. F.
1985-01-01
Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.
Deep inelastic scattering near the endpoint in soft-collinear effective theory
Chay, Junegone; Kim, Chul
2007-01-01
We apply the soft-collinear effective theory to deep inelastic scattering near the endpoint region. The forward scattering amplitude and the structure functions are shown to factorize as a convolution of the Wilson coefficients, the jet functions, and the parton distribution functions. The behavior of the parton distribution functions near the endpoint region is considered. It turns out that it evolves with the Altarelli-Parisi kernel even in the endpoint region, and the parton distribution function can be factorized further into a collinear part and the soft Wilson line. The factorized form for the structure functions is obtained by the two-step matching, and the radiative corrections or the evolution for each factorized part can be computed in perturbation theory. We present the radiative corrections of each factorized part to leading order in {alpha}{sub s}, including the zero-bin subtraction for the collinear part.
Coupled wave equations theory of surface-enhanced femtosecond stimulated Raman scattering
NASA Astrophysics Data System (ADS)
McAnally, Michael O.; McMahon, Jeffrey M.; Van Duyne, Richard P.; Schatz, George C.
2016-09-01
We present a coupled wave semiclassical theory to describe plasmonic enhancement effects in surface-enhanced femtosecond stimulated Raman scattering (SE-FSRS). A key result is that the plasmon enhanced fields which drive the vibrational equation of motion for each normal mode results in dispersive lineshapes in the SE-FSRS spectrum. This result, which reproduces experimental lineshapes, demonstrates that plasmon-enhanced stimulated Raman methods provide unique sensitivity to a plasmonic response. Our derived SE-FSRS theory shows a plasmonic enhancement of |gp u|2I m {" separators="χR(ω ) gst 2 }/I m {" separators="χR(ω ) }, where |gpu|2 is the absolute square of the plasmonic enhancement from the Raman pump, χR(ω) is the Raman susceptibility, and gst is the plasmonic enhancement of the Stokes field in SE-FSRS. We conclude with a discussion on potential future experimental and theoretical directions for the field of plasmonically enhanced coherent Raman scattering.
Nukala, Madhuri; Mendrok, Jana
2014-12-10
Lateral light scattering simulations of printed dots are analyzed using general radiative transfer theory. We investigated the appearance of a printed paper in relation to the medium parameters like thickness of the paper sample, its optical properties, and the asymmetry factor. It was found that the appearance of a print greatly depends on these factors making it either brighter or darker. A thicker substrate with higher single scattering albedo backed with an absorbing surface makes the dots brighter due to increased number of scattering events. Additionally, it is shown that the optical effects of print also depend on illuminating and viewing angles along with the depth of ink penetration. A larger single scattering angle implies less intensity and the dots appear much blurred due to the shadowing effect prominent when viewed from sides. A fully penetrated dot of the same extinction coefficient as a partial penetrated one is darker due to increased absorption. These results can be used in applications dealing with lateral light scattering.
Multiple-scattering effects in nucleus-nucleus reactions with Glauber theory
NASA Astrophysics Data System (ADS)
Hatakeyama, Shinya; Ebata, Shuichiro; Horiuchi, Wataru; Kimura, Masaaki
2014-09-01
A study of new unstable nuclei has become possible in new radioactive beam facilities. In order to understand the relationship between reaction observables and nuclear structure, we need reaction theory which exactly reflects the nuclear structure. The Glauber theory is a powerful tool of analyzing high energy nuclear reactions. The theory describes the multiple scattering processes, whereas the optical limit approximation (OLA), which is widely used, ignores those processes. Those effects are expected to play an important role in the nuclear collision involving unstable nuclei (see for example Phys. Rev. C 54, 1843 (1996)). Here we apply the Glauber theory to nucleus-nucleus reactions. The wave functions are generated by the Skyrme-Hartree-Fock method and are expressed in a Slater determinant that allows us to evaluate the complete Glauber amplitude easily. We calculate total reaction cross sections, elastic cross sections and differential elastic cross sections for 16~24O, 40~70Ca, 56,58Ni, 100~140Sn, 190~214Pb on proton, 4He, 12C targets and compare with experimental data. The Glauber theory gives much better description than the OLA, especially at larger scattering angles.
Chang, J; Graber, H L; Barbour, R L; Aronson, R
1996-07-10
We present a useful strategy for imaging perturbations of the macroscopic absorption cross section of dense-scattering media using steady-state light sources. A perturbation model based on transport theory is derived, and the inverse problem is simplified to a system of linear equations, WΔμ = ΔR, where W is the weight matrix, Δμ is a vector of the unknown perturbations, and ΔR is the vector of detector readings. Monte Carlo simulations compute the photon flux across the surfaces of phantoms containing simple or complex inhomogeneities. Calculation of the weight matrix is also based on the results of Monte Carlo simulations. Three reconstruction algorithms-conjugate gradient descent, projection onto convex sets, and the simultaneous algebraic reconstruction technique, with or without imposed positivity constraints-are used for image reconstruction. A rescaling technique that improves the conditioning of the weight matrix is also developed. Results show that the analysis of time-independent data by a perturbation model is capable of resolving the internal structure of a dense-scattering medium. Imposition of positivity constraints improves image quality at the cost of a reduced convergence rate. Use of the rescaling technique increases the initial rate of convergence, resulting in accurate images in a smaller number of iterations.
Bremmer, Rolf H; van Gemert, Martin J C; Faber, Dirk J; van Leeuwen, Ton G; Aalders, Maurice C G
2013-08-01
Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 mm-1 at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys.19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt.38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime
NASA Astrophysics Data System (ADS)
Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.
2013-08-01
Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt.
Jucys-Murphy elements for Birman-Murakami-Wenzl algebras
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.
2011-05-01
The Burman-Wenzl-Murakami algebra, considered as the quotient of the braid group algebra, possesses the commutative set of Jucys-Murphy elements. We show that the set of Jucys-Murphy elements is maximal commutative for the generic Birman-Wenzl-Murakami algebra and reconstruct the representation theory of the tower of Birman-Wenzl-Murakami algebras.
Low-energy electron scattering from CO. 2: Ab-initio study using the frame-transformation theory
NASA Technical Reports Server (NTRS)
Chandra, N.
1976-01-01
The Wigner-Eisenbud R matrix method has been combined with the frame transformation theory to study electron scattering from molecular systems. The R matrix, calculated at the boundary point of the molecular core radius, has been transformed to the space frame in order to continue the solution of the scattering equations in the outer region where rotational motion of the nuclei is taken into account. This procedure has been applied to a model calculation of thermal energy electron scattering from CO.
Correlated R-matrix theory of electron scattering: A coupled-cluster approach
NASA Astrophysics Data System (ADS)
Sur, Chiranjib; Pradhan, Anil; Sadayappan, P.
2007-06-01
Study of electron scattering from heavy atoms/ions not only demands high speed computing machines but also improved theoretical descriptions of the relativistic and correlation effects for the target atoms/ions as well. We will give an outline of the coupled-cluster R-matrix (CCRM) theory to incorporate the effect of electron correlation through coupled-cluster theory (CCT), the size extensive and one of the most accurate many body theories which is equivalant to an all-order many-body perturbation theory (MBPT). General theoretical formulation of CCRM and the computational implementation using the high level Mathematica style language compiler known as Tensor Contraction Engine (TCE) will be presented. Electronic structure calculations using CCT involve large collections of tensor contractions (generalized matrix multiplications). TCE searches for an optimal implementation of these tensor contraction expressions and generates high performance FORTRAN code for CCT. We will also comment on the interfacing of TCE generated code with the Breit-Pauli R-matrix code to make a next generation CCRM software package. This theoretical formulation and the new sets of codes can be used to study electron scattering / photoionization in heavy atomic systems where relativistic and electron correlation effects are very important.
NASA Astrophysics Data System (ADS)
Hoshi, Takeo; Yamazaki, Keita; Akiyama, Yohei
A novel linear-algebraic algorithm, multiple Arnoldi method, was developed in an interdisciplinary study between physics and applied mathematics and realized one-hundred-million-atom (100-nm-scale) electronic state calculations on the K computer. The algorithms are Krylov-subspace solvers for generalized shifted linear equations and were implemented in our order-N calculation code ELSES (http://www.elses.jp/). Moreover, a method for calculating eigen states is presented as a theoretical extension.
NASA Astrophysics Data System (ADS)
Masoero, Davide; Raimondo, Andrea; Valeri, Daniele
2016-06-01
We study the ODE/IM correspondence for ODE associated to {widehat{mathfrak{g}}}-valued connections, for a simply-laced Lie algebra {mathfrak{g}}. We prove that subdominant solutions to the ODE defined in different fundamental representations satisfy a set of quadratic equations called {Ψ}-system. This allows us to show that the generalized spectral determinants satisfy the Bethe Ansatz equations.
NASA Astrophysics Data System (ADS)
Shi, F.; Lowe, M. J. S.; Xi, X.; Craster, R. V.
2016-07-01
We develop an elastodynamic theory to predict the diffuse scattered field of elastic waves by randomly rough surfaces, for the first time, with the aid of the Kirchhoff approximation (KA). Analytical expressions are derived incorporating surface statistics, to represent the expectation of the angular distribution of the diffuse intensity for different modes. The analytical solutions are successfully verified with numerical Monte Carlo simulations, and also validated by comparison with experiments. We then apply the theory to quantitatively investigate the effects of the roughness and the shear-to-compressional wave speed ratio on the mode conversion and the scattering intensity, from low to high roughness within the valid region of KA. Both the direct and the mode converted intensities are significantly affected by the roughness, which leads to distinct scattering patterns for different wave modes. The mode conversion effect is very strong around the specular angle and it is found to increase as the surface appears to be more rough. In addition, the 3D roughness induced coupling between the out-of-plane shear horizontal (SH) mode and the in-plane modes is studied. The intensity of the SH mode is shown to be very sensitive to the out-of-plane correlation length, being influenced more by this than by the RMS value of the roughness. However, it is found that the depolarization pattern for the diffuse field is independent of the actual value of the roughness.
Scattering theory for finitely many sphere interactions supported by concentric spheres
Hounkonnou, M.N.; Hounkpe, M.; Shabani, J.
1997-06-01
We study stationary scattering theory for finitely many sphere interactions formally given by the Hamiltonian H={minus}{Delta}+{summation}{sub j=1}{sup N}{alpha}{sub j}{delta}({vert_bar}x{vert_bar}{minus}R{sub j}) and its generalizations to the case of interactions of the second type and interactions with nonseparated boundary conditions. In a previous publication [J. Math. Phys. {bold 29}, 660{endash}664 (1988)], it was shown that the self-adjoint Hamiltonian H{sub {l_brace}{alpha}{sub l}{r_brace},{l_brace}R{r_brace}} corresponding to H may be defined as a limit in norm resolvent convergence of a family H{sub {var_epsilon}} of local scaled short-range Hamiltonians. In this paper we also study scattering theory corresponding to H{sub {var_epsilon}} and show that the scattering quantities associated with H{sub {var_epsilon}} converge to those of H{sub {l_brace}{alpha}{sub l}{r_brace},{l_brace}R{r_brace}} as {var_epsilon}{r_arrow}0. {copyright} {ital 1997 American Institute of Physics.}
Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look
NASA Astrophysics Data System (ADS)
Siemens, D.; Bernard, V.; Epelbaum, E.; Gasparyan, A.; Krebs, H.; Meißner, Ulf-G.
2016-07-01
Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant β functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the Δ resonance. The explicit inclusion of the leading contributions of the Δ isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the predictions from the recent Roy-Steiner-equation analysis of pion-nucleon scattering.
NASA Astrophysics Data System (ADS)
Prager, Stefan; Zech, Alexander; Aquilante, Francesco; Dreuw, Andreas; Wesolowski, Tomasz A.
2016-05-01
The combination of Frozen Density Embedding Theory (FDET) and the Algebraic Diagrammatic Construction (ADC) scheme for the polarization propagator for describing environmental effects on electronically excited states is presented. Two different ways of interfacing and expressing the so-called embedding operator are introduced. The resulting excited states are compared with supermolecular calculations of the total system at the ADC(2) level of theory. Molecular test systems were chosen to investigate molecule-environment interactions of varying strength from dispersion interaction up to multiple hydrogen bonds. The overall difference between the supermolecular and the FDE-ADC calculations in excitation energies is lower than 0.09 eV (max) and 0.032 eV in average, which is well below the intrinsic error of the ADC(2) method itself.
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-15
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.
Coverings of topological semi-abelian algebras
NASA Astrophysics Data System (ADS)
Mucuk, Osman; Demir, Serap
2016-08-01
In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.
Born Hartree Bethe approximation in the theory of inelastic electron molecule scattering
NASA Astrophysics Data System (ADS)
Kretinin, I. Yu; Krisilov, A. V.; Zon, B. A.
2008-11-01
We propose a new approximation in the theory of inelastic electron atom and electron molecule scattering. Taking into account the completeness property of atomic and molecular wavefunctions, considered in the Hartree approximation, and using Bethe's parametrization for electronic excitations during inelastic collisions via the mean excitation energy, we show that the calculation of the inelastic total integral cross-sections (TICS), in the framework of the first Born approximation, involves only the ground-state wavefunction. The final analytical formula obtained for the TICS, i.e. for the sum of elastic and inelastic ones, contains no adjusting parameters. Calculated TICS for electron scattering by light atoms and molecules (He, Ne, and H2) are in good agreement within the experimental data; results show asymptotic coincidence for heavier ones (Ar, Kr, Xe and N2).
A predictive theory for elastic scattering and recoil of protons from ^{4}He
Hupin, Guillaume; Quaglioni, Sofia; Navratil, Petr
2014-12-08
Low-energy cross sections for elastic scattering and recoil of protons from ^{4}He nuclei (also known as α particles) are calculated directly by solving the Schrodinger equation for five nucleons interacting through accurate two- and three-nucleon forces derived within the framework of chiral effective field theory. Precise knowledge of these processes at various proton backscattering/recoil angles and energies is needed for the ion-beam analysis of numerous materials, from the surface layers of solids, to thin films, to fusion-reactor materials. Indeed, the same elastic scattering process, in two different kinematic configurations, can be used to probe the concentrations and depth profiles of either hydrogen or helium. Furthermore, we compare our results to available experimental data and show that direct calculations with modern nuclear potentials can help to resolve remaining inconsistencies among data sets and can be used to predict these cross sections when measurements are not available.
NASA Astrophysics Data System (ADS)
Odedina, M. O.; Afullo, T. J.
2010-02-01
The forward scattering amplitudes for the spherical raindrops are determined for all raindrop sizes at different frequencies by using the Mie scattering theory. The real parts of the extinction cross sections are used to generate power law models at different frequencies. These are integrated over different established raindrop-size distribution models to formulate rain attenuation models. Using the developed rain attenuation models with 5 year rain rate statistics at R0.01 determined in previous work, the specific rain attenuation is computed. The experimental results obtained from the horizontally polarized signal level measurements recorded in Durban for different rain attenuation bounds are compared with the theoretical results. Finally, the best theoretical model is used to estimate the seasonal cumulative distribution of rain attenuation for Durban, South Africa.
From scattering theory to complex wave dynamics in non-Hermitian PT-symmetric resonators.
Schomerus, Henning
2013-04-28
I review how methods from mesoscopic physics can be applied to describe the multiple wave scattering and complex wave dynamics in non-Hermitian PT-symmetric resonators, where an absorbing region is coupled symmetrically to an amplifying region. Scattering theory serves as a convenient tool to classify the symmetries beyond the single-channel case and leads to effective descriptions that can be formulated in the energy domain (via Hamiltonians) and in the time domain (via time evolution operators). These models can then be used to identify the mesoscopic time and energy scales that govern the spectral transition from real to complex eigenvalues. The possible presence of magneto-optical effects (a finite vector potential) in multi-channel systems leads to a variant (termed PTT' symmetry) that imposes the same spectral constraints as PT symmetry. I also provide multi-channel versions of generalized flux-conservation laws.
A predictive theory for elastic scattering and recoil of protons from 4He
Hupin, Guillaume; Quaglioni, Sofia; Navratil, Petr
2014-12-08
Low-energy cross sections for elastic scattering and recoil of protons from 4He nuclei (also known as α particles) are calculated directly by solving the Schrodinger equation for five nucleons interacting through accurate two- and three-nucleon forces derived within the framework of chiral effective field theory. Precise knowledge of these processes at various proton backscattering/recoil angles and energies is needed for the ion-beam analysis of numerous materials, from the surface layers of solids, to thin films, to fusion-reactor materials. Indeed, the same elastic scattering process, in two different kinematic configurations, can be used to probe the concentrations and depth profiles ofmore » either hydrogen or helium. Furthermore, we compare our results to available experimental data and show that direct calculations with modern nuclear potentials can help to resolve remaining inconsistencies among data sets and can be used to predict these cross sections when measurements are not available.« less
Giebink, D.R.
1980-10-01
A relativistic, phenomenological scattering theory for particles with arbitrary spin is presented, and the relation between off-mass-shell and off-energy-shell theories is discussed. The theory is formulated from the Hilbert-space representation of particles with spin in relativistic quantum mechanics. This topic is reviewed in a basis-independent manner by appealing to the properties of the rotation and Lorentz groups and their representations. Spin is discussed and a set of basis state vectors for the single-particle Hilbert space is derived from this perspective. Two- and three-particle Hilbert-space bases are then constructed, and angular momentum is discussed. The z-circumflex and helicity bases are presented as examples of the general procedure. These foundations allow the on-shell scattering amplitude to be defined. The space-inversion and time-reversal properties of this amplitude suggest that a new scattering function be defined such that a continuation of that function to negative energies can be considered. Antiparticle scattering events are associated with the continued function, and the CPT theorem arises as a natural consequence of this association. Moreover, these considerations lead to the definition of an off-mass-shell scattering function. The resulting off-mass-shell scattering theory has a number of very appealing properties. The off-energy-shell theory is dependent on fewer variables than the off-mass-shell theory, and is more susceptible to a phenomenological treatment.
W{sub L}W{sub L} scattering in Higgsless models: Identifying better effective theories
Belyaev, Alexander S.; Chivukula, R. Sekhar; Christensen, Neil D.; Simmons, Elizabeth H.; He Hongjian; Kurachi, Masafumi; Tanabashi, Masaharu
2009-09-01
The three-site model has been offered as a benchmark for studying the collider phenomenology of Higgsless models. In this paper we analyze how well the three-site model performs as a general exemplar of Higgsless models in describing W{sub L}W{sub L} scattering, and which modifications can make it more representative. We employ general sum rules relating the masses and couplings of the Kaluza-Klein modes of the gauge fields in continuum and deconstructed Higgsless models as a way to compare the different theories. We show that the size of the four-point vertex for the (unphysical) Nambu-Goldstone modes and the degree to which the sum rules are saturated by contributions from the lowest-lying Kaluza-Klein resonances both provide good measures of the extent to which a highly deconstructed theory can accurately describe the low-energy physics of a continuum 5D Higgsless model. After comparing the three-site model to flat and warped continuum models, we analyze extensions of the three-site model to a longer open linear moose with an additional U(1) group and to a ring ('breaking electroweak symmetry strongly' or 'hidden local symmetry') model with three sites and three links. Both cases may be readily analyzed in the framework of the general sum rules. We demonstrate that W{sub L}W{sub L} scattering in the ring model can very closely approximate scattering in the continuum models, provided that the hidden local symmetry parameter a is chosen to mimic {rho}-meson dominance of {pi}{pi} scattering in QCD. The hadron and lepton collider phenomenology of both extended models is briefly discussed, with a focus on the complementary information to be gained from precision measurements of the Z{sup '} line shape and ZWW coupling at a high-energy lepton collider.
Reprint of : Scattering theory approach to bosonization of non-equilibrium mesoscopic systems
NASA Astrophysics Data System (ADS)
Sukhorukov, Eugene V.
2016-08-01
Between many prominent contributions of Markus Büttiker to mesoscopic physics, the scattering theory approach to the electron transport and noise stands out for its elegance, simplicity, universality, and popularity between theorists working in this field. It offers an efficient way to theoretically investigate open electron systems far from equilibrium. However, this method is limited to situations where interactions between electrons can be ignored, or considered perturbatively. Fortunately, this is the case in a broad class of metallic systems, which are commonly described by the Fermi liquid theory. Yet, there exist another broad class of electron systems of reduced dimensionality, the so-called Tomonaga-Luttinger liquids, where interactions are effectively strong and cannot be neglected even at low energies. Nevertheless, strong interactions can be accounted exactly using the bosonization technique, which utilizes the free-bosonic character of collective excitations in these systems. In the present work, we use this fact in order to develop the scattering theory approach to the bosonization of open quasi-one dimensional electron systems far from equilibrium.
NASA Astrophysics Data System (ADS)
Kolokolova, L.; Gustafson, B. A. S.
2001-08-01
It is common practice to use effective medium theories (EMT) to estimate average, "effective" optical constants of inhomogeneous materials. A variety of EMTs were developed for different internal structures of the medium and for a variety of shapes, size distributions and physical properties of the inhomogeneities. The most popular EMTs (Maxwell Garnett, Bruggeman, Looyenga, etc.) consider inhomogeneities that are much smaller than the wavelength. The so-called extended EMTs were developed to find effective optical constants in the case of inhomogeneities comparable and slightly larger than the wavelength. This paper compares angular distribution and wavelength dependence of intensity and polarization of scattered light obtained from calculations using the most popular EMTs and extended EMTs with the results of microwave analog measurements at the microwave facilities of the University of Florida. We simulated the light scattering by organic grains with silicate inclusions of size parameter View the MathML source, View the MathML source, and 1.24 View the MathML source). The conclusion is that for inclusions of a small size and for a small volume fraction of them in the mixture all EMTs yield similar results and show reasonable agreement with experimental results. The accuracy is better for the angular dependencies of the intensity and of the polarization of the scattered light than for their wavelength dependencies. For inhomogeneities comparable and larger than the wavelength extended EMTs work better but for smaller inclusions non-extended EMTs show more accurate results. Large volume fractions of the inclusions in the mixture (>10%) essentially reduce the accuracy of the results obtained with EMTs. Based on our study we do not recommend to use EMTs in the back-scattering domain and at the scattering angles 30°<θ<70°.
NASA Astrophysics Data System (ADS)
Ohkawa, E.; Mikada, H.; Goto, T.; Takekawa, J.; Onishi, K.; Taniguchi, K.; Ashida, Y.
2009-12-01
The temperature of external materials of buildings rises when they are exposed to sunlight, and the room temperature rises too if the buildings’ external wall is in the sunlight. Therefore the crisis of electric power supply is frequently caused by air conditioning in midsummer. Recently, it has been experimentally confirmed that such temperature rising of such building materials may be suppressed when they are coated with paint including fine silicic spheres whose diameters are in micron to submicron scale. So we are able to reduce the energy consumption if room temperature is controlled not with any air conditioning but with these paints, and the heat island effects would be lowered. However, the mechanism of this temperature suppression has not been investigated. Experimental consideration of this paint has been done, but the mechanism how the paint controls the temperature rise has hardly been clarified theoretically. Since the best composition of the spheres and their best size are not understood well, it is necessary to theoretically clarify the controlling mechanism for the temperature rise to develop efficient paint. In this study, we aimed to find out the mechanism of the temperature suppression. When the electromagnetic wave at a frequency near eigenfrequencies of atoms, molecules or bindings enters the atoms or the molecules, they resonate and move intensely, and finally rise the temperature. Therefore, we presume that the temperature rise could be controlled if the electromagnetic waves around the eigenfrequencies could be removed. Here, we consider electromagnetic wave of light. Then we assumed that the electromagnetic waves in a certain range of frequencies were scattered to shield the radiated heat energy in the insolation and that the transmitted light through the paint layer is weakened. For verifying the hypotheses and finding the range of effective size, we used the Mie theory of a light scattering theory to calculate the intensity of scattered
NASA Technical Reports Server (NTRS)
Richmond, J. H.
1974-01-01
Piecewise-sinusoidal expansion functions and Galerkin's method are employed to formulate a solution for an arbitrary thin-wire configuration in a homogeneous conducting medium. The analysis is performed in the real or complex frequency domain. In antenna problems, the solution determines the current distribution, impedance, radiation efficiency, gain and far-field patterns. In scattering problems, the solution determines the absorption cross section, scattering cross section and the polarization scattering matrix. The electromagnetic theory is presented for thin wires and the forward-scattering theorem is developed for an arbitrary target in a homogeneous conducting medium.
Recurrence relations of Kummer functions and Regge string scattering amplitudes
NASA Astrophysics Data System (ADS)
Lee, Jen-Chi; Mitsuka, Yoshihiro
2013-04-01
We discover an infinite number of recurrence relations among Regge string scattering amplitudes [11, 30] of different string states at arbitrary mass levels in the open bosonic string theory. As a result, all Regge string scattering amplitudes can be algebraically solved up to multiplicative factors. Instead of decoupling zero-norm states in the fixed angle regime, the calculation is based on recurrence relations and addition theorem of Kummer functions of the second kind. These recurrence relations among Regge string scattering amplitudes are dual to linear relations or symmetries among high-energy fixed angle string scattering amplitudes discovered previously.
Interpreting Ulysses data using inverse scattering theory: Oblique Alfvén waves
NASA Astrophysics Data System (ADS)
Wheeler, Harry R.; Reynolds, M. A.; Hamilton, R. L.
2015-03-01
Solitary wave structures observed by the Ulysses spacecraft in the solar wind were analyzed using both inverse scattering theory and direct numerical integration of the derivative nonlinear Schrödinger (DNLS) equation. Several of these structures were found to be consistent with soliton solutions of the DNLS equation. Such solitary structures have been commonly observed in the space plasma environment and may, in fact, be long-lived solitons. While the generation of these solitons may be due to an instability mechanism, e.g., the mirror instability, they may be observable far from the source region due to their coherent nature.
Unified theory of bound and scattering molecular Rydberg states as quantum maps
NASA Astrophysics Data System (ADS)
Dietz, Barbara; Lombardi, Maurice; Seligman, Thomas H.
2004-08-01
Using a representation of multichannel quantum defect theory in terms of a quantum Poincaré map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show that this representation not only simplifies the understanding of the method, but moreover produces considerable numerical advantages. Finally we show under what circumstances the usual semi-classical approximations yield satisfactory results. In particular we see that singularities that cause problems in semi-classics are irrelevant to the quantum map.
Strangeness S =-1 hyperon-nucleon scattering in covariant chiral effective field theory
NASA Astrophysics Data System (ADS)
Li, Kai-Wen; Ren, Xiu-Lei; Geng, Li-Sheng; Long, Bingwei
2016-07-01
Motivated by the successes of covariant baryon chiral perturbation theory in one-baryon systems and in heavy-light systems, we study relevance of relativistic effects in hyperon-nucleon interactions with strangeness S =-1 . In this exploratory work, we follow the covariant framework developed by Epelbaum and Gegelia to calculate the Y N scattering amplitude at leading order. By fitting the five low-energy constants to the experimental data, we find that the cutoff dependence is mitigated, compared with the heavy-baryon approach. Nevertheless, the description of the experimental data remains quantitatively similar at leading order.
Fermion-fermion scattering in quantum field theory with superconducting circuits.
García-Álvarez, L; Casanova, J; Mezzacapo, A; Egusquiza, I L; Lamata, L; Romero, G; Solano, E
2015-02-20
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations. PMID:25763944
Derivation of the chemical-equilibrium rate coefficient using scattering theory
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1977-01-01
Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.
Fermion-fermion scattering in quantum field theory with superconducting circuits.
García-Álvarez, L; Casanova, J; Mezzacapo, A; Egusquiza, I L; Lamata, L; Romero, G; Solano, E
2015-02-20
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations.
Raman Scattering from 1,3-Propanedithiol at a Hot Spot: Theory Meets Experiment
El-Khoury, Patrick Z.; Hess, Wayne P.
2013-08-21
We compute the Raman spectra of 1,3-propanedithiol (PDT) in the gas phase, in methanol, linked either to the face or vertex of a finite tetrahedral Ag20 cluster, and linking two Ag20 clusters using tools of density functional theory. The calculated normal mode-dependent molecular polarizability derivative tensors are employed to simulate single molecule surface-enhanced Raman (SERS) spectra. This is achieved by rotating the polarizability tensors of an individual molecule with respect to explicitly defined vector components of the incident and scattered radiation. Our results provide a basis for understanding commonly observed phenomena in single molecule SERS spectroscopy.
Gluon scattering in N=4 super-Yang-Mills theory fromweak to strong coupling
Dixon, Lance J.; /SLAC
2008-03-25
I describe some recent developments in the understanding of gluon scattering amplitudes in N = 4 super-Yang-Mills theory in the large-N{sub c} limit. These amplitudes can be computed to high orders in the weak coupling expansion, and also now at strong coupling using the AdS/CFT correspondence. They hold the promise of being solvable to all orders in the gauge coupling, with the help of techniques based on integrability. They are intimately related to expectation values for polygonal Wilson loops composed of light-like segments.
Novaes, Marcel
2015-06-15
We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.
Amann, Christian P; Denisov, Dmitry; Dang, Minh Triet; Struth, Bernd; Schall, Peter; Fuchs, Matthias
2015-07-21
We employ x-ray scattering on sheared colloidal suspensions and mode coupling theory to study structure factor distortions of glass-forming systems under shear. We find a transition from quadrupolar elastic distortion at small strains to quadrupolar and hexadecupolar modes in the stationary state. The latter are interpreted as signatures of plastic rearrangements in homogeneous, thermalized systems. From their transient evolution with strain, we identify characteristic strain and length-scale values where these plastic rearrangements dominate. This characteristic strain coincides with the maximum of the shear stress versus strain curve, indicating the proliferation of plastic flow. The hexadecupolar modes dominate at the wavevector of the principal peak of the equilibrium structure factor that is related to the cage-effect in mode coupling theory. We hence identify the structural signature of plastic flow of glasses. PMID:26203034
Amann, Christian P. Fuchs, Matthias; Denisov, Dmitry; Dang, Minh Triet; Schall, Peter; Struth, Bernd
2015-07-21
We employ x-ray scattering on sheared colloidal suspensions and mode coupling theory to study structure factor distortions of glass-forming systems under shear. We find a transition from quadrupolar elastic distortion at small strains to quadrupolar and hexadecupolar modes in the stationary state. The latter are interpreted as signatures of plastic rearrangements in homogeneous, thermalized systems. From their transient evolution with strain, we identify characteristic strain and length-scale values where these plastic rearrangements dominate. This characteristic strain coincides with the maximum of the shear stress versus strain curve, indicating the proliferation of plastic flow. The hexadecupolar modes dominate at the wavevector of the principal peak of the equilibrium structure factor that is related to the cage-effect in mode coupling theory. We hence identify the structural signature of plastic flow of glasses.
Complex time solutions with nontrivial topology and multiparticle scattering in Yang-Mills theory
NASA Astrophysics Data System (ADS)
Gould, Thomas M.; R. Poppitz, Erich
1993-08-01
A classical solution in Yang-Mills thoery is given a new semiclassical interpretation in terms of particle scattering. It solves the complex time boundary value problem which arises in the semiclassical approximation to a multiparticle transition probability in the one-instanton sector at fixed energy. The imaginary part of the action of the solution on the complex time contour and its topological charge obey the same relation as the self-dual Euclidean configurations. Hence the solution is relevant for the problem of tunneling with fermion number violation in the electroweak theory. It describes transitions from an initial state with a smaller number of particles to a final state with a larger umber of particles. The implications of these results for multiparticle production in the electroweak theory are also discussed.
Noncommutative correction to Aharonov-Bohm scattering: A field theory approach
Anacleto, M.A.; Gomes, M.; Silva, A.J. da; Spehler, D.
2004-10-15
We study a noncommutative nonrelativistic theory in 2+1 dimensions of a scalar field coupled to the Chern-Simons field. In the commutative situation this model has been used to simulate the Aharonov-Bohm effect in the field theory context. We verified that, contrary to the commutative result, the inclusion of a quartic self-interaction of the scalar field is not necessary to secure the ultraviolet renormalizability of the model. However, to obtain a smooth commutative limit the presence of a quartic gauge invariant self-interaction is required. For small noncommutativity we fix the corrections to the Aharonov-Bohm scattering and prove that up to one loop the model is free from dangerous infrared/ultraviolet divergences.
Dynamic neutron scattering from conformational dynamics. I. Theory and Markov models
NASA Astrophysics Data System (ADS)
Lindner, Benjamin; Yi, Zheng; Prinz, Jan-Hendrik; Smith, Jeremy C.; Noé, Frank
2013-11-01
The dynamics of complex molecules can be directly probed by inelastic neutron scattering experiments. However, many of the underlying dynamical processes may exist on similar timescales, which makes it difficult to assign processes seen experimentally to specific structural rearrangements. Here, we show how Markov models can be used to connect structural changes observed in molecular dynamics simulation directly to the relaxation processes probed by scattering experiments. For this, a conformational dynamics theory of dynamical neutron and X-ray scattering is developed, following our previous approach for computing dynamical fingerprints of time-correlation functions [F. Noé, S. Doose, I. Daidone, M. Löllmann, J. Chodera, M. Sauer, and J. Smith, Proc. Natl. Acad. Sci. U.S.A. 108, 4822 (2011)]. Markov modeling is used to approximate the relaxation processes and timescales of the molecule via the eigenvectors and eigenvalues of a transition matrix between conformational substates. This procedure allows the establishment of a complete set of exponential decay functions and a full decomposition into the individual contributions, i.e., the contribution of every atom and dynamical process to each experimental relaxation process.
Jensen, Lasse; Schatz, George C.
2006-03-27
The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. In this work, we present the first calculation of the resonance Raman scattering (RRS) spectrum of rhodamine 6G (R6G) which is a prototype molecule in surface-enhanced Raman scattering (SERS). The calculation is done using a recently developed time-dependent density functional theory (TDDFT) method, which uses a short-time approximation to evaluate the Raman scattering cross section. The normal Raman spectrum calculated with this method is in good agreement with experimental results. The calculated RRS spectrum shows qualitative agreement with SERS results at a wavelength that corresponds to excitation of the S1 state, but there are significant differences with the measured RRS spectrum at wavelengths that correspond to excitation of the vibronic sideband of S1. Although the agreement with the experiments is not perfect, the results provide insight into the RRS spectrum of R6G at wavelengths close to the absorption maximum where experiments are hindered due to strong fluorescence. The calculated resonance enhancements are found to be on the order of 105. This indicates that a surface enhancement factor of about 1010 would be required in SERS in order to achieve single-molecule detection of R6G.
Hopf algebras and topological recursion
NASA Astrophysics Data System (ADS)
Esteves, João N.
2015-11-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).
The algebras of large N matrix mechanics
Halpern, M.B.; Schwartz, C.
1999-09-16
Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.
Spectra and scattering of light lattice nuclei from effective field theory
NASA Astrophysics Data System (ADS)
Kirscher, J.; Barnea, N.; Gazit, D.; Pederiva, F.; van Kolck, U.
2015-11-01
An effective field theory is used to describe light nuclei, calculated from quantum chromodynamics on a lattice at unphysically large pion masses. The theory is calibrated at leading order to two available data sets on two- and three-body nuclei for two pion masses. At those pion masses we predict the quartet and doublet neutron-deuteron scattering lengths, and the α -particle binding energy. For mπ=510 MeV we obtain, respectively, 4anD=2.3 ±1.3 fm, 2anD=2.2 ±2.1 fm, and Bα=35 ±22 MeV, while for mπ=805 MeV 4anD=1.6 ±1.3 fm, 2anD=0.62 ±1.0 fm, and Bα=94 ±45 MeV are found. Phillips- and Tjon-like correlations to the triton binding energy are established. We find the theoretical uncertainty in the respective correlation bands to be independent of the pion mass. As a benchmark, we present results for the physical pion mass, using experimental two-body scattering lengths and the triton binding energy as input. Hints of subtle changes in the structure of the triton and α particle are discussed.
Regeta, Khrystyna; Allan, Michael; Winstead, Carl; McKoy, Vincent; Mašín, Zdeněk; Gorfinkiel, Jimena D
2016-01-14
We measured differential cross sections for elastic (rotationally integrated) electron scattering on pyrimidine, both as a function of angle up to 180(∘) at electron energies of 1, 5, 10, and 20 eV and as a function of electron energy in the range 0.1-14 eV. The experimental results are compared to the results of the fixed-nuclei Schwinger variational and R-matrix theoretical methods, which reproduce satisfactorily the magnitudes and shapes of the experimental cross sections. The emphasis of the present work is on recording detailed excitation functions revealing resonances in the excitation process. Resonant structures are observed at 0.2, 0.7, and 4.35 eV and calculations for different symmetries confirm their assignment as the X̃(2)A2, Ã(2)B1, and B̃(2)B1 shape resonances. As a consequence of superposition of coherent resonant amplitudes with background scattering the B̃(2)B1 shape resonance appears as a peak, a dip, or a step function in the cross sections recorded as a function of energy at different scattering angles and this effect is satisfactorily reproduced by theory. The dip and peak contributions at different scattering angles partially compensate, making the resonance nearly invisible in the integral cross section. Vibrationally integrated cross sections were also measured at 1, 5, 10 and 20 eV and the question of whether the fixed-nuclei cross sections should be compared to vibrationally elastic or vibrationally integrated cross section is discussed.
NASA Astrophysics Data System (ADS)
Nagasaka, Y.; Hatakeyama, T.; Okuda, M.; Nagashima, A.
1988-07-01
This article is devoted to the theory and experiment of the forced Rayleigh scattering method for measurement of thermal diffusivity of liquids which can be employed in the form of an instrument operated optically in a contact-free manner. The theoretical considerations included are: (1) effect of cell wall, (2) effect of dye, (3) effect of Gaussian beam intensity distribution, (4) effect of heating duration time, and (5) effect of coupled dye and wall for a heavily absorbing sample. The errors caused by inadequate setting of optical conditions are also analyzed: (1) effects of grating thickness and (2) effects of initial temperature amplitude. Experimental verifications of the theory have been carried out through the measurements on toluene and water as standard reference substances. As a result of these experiments and theory, the criteria for optimum measuring conditions became available. To demonstrate the applicability of the present theory and the apparatus, the thermal diffusivities of toluene and methanol have been measured near room temperature under atmospheric pressure. The accuracy of the present measurement is estimated to be ±3%.
Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras
NASA Astrophysics Data System (ADS)
Zhang, Tianjie; Gao, Xing; Guo, Li
2016-10-01
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.
A note on derivations of Murray–von Neumann algebras
Kadison, Richard V.; Liu, Zhe
2014-01-01
A Murray–von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray–von Neumann algebras. We show that the “extended derivations” of a Murray–von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray–von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer’s seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements. PMID:24469831
N-body quantum scattering theory in two Hilbert spaces. VI. Compactness conditions
NASA Astrophysics Data System (ADS)
Chandler, Colston; Gibson, Archie G.
1992-10-01
It is shown how to implement in a practical way the approximation theory previously developed [J. Funct. Anal. 52, 80 (1983)] for nonrelativistic N-body quantum systems of particles interacting via pair potentials belonging to a certain general class. This is done by constructing the projection operators Π which generate the approximations, and by proving that certain operators Π(J*J-I)Π are Hilbert-Schmidt and that certain other operators VΠE(Δ) are trace class for all finite real intervals Δ. Two types of projections Π are considered. The results for the first type generalize previous results of Combes and Simon for asymptotic channels with only two clusters. The results for the second type provide an alternative approach to N-body scattering and spectral problems which is both practical and theoretically correct. The compactness results are used to prove that the approximate theories are exact theories for approximate Hamiltonians, that the approximate wave operators are asymptotically complete and satisfy the invariance principle, that the kernels of certain N-body equations are compact, and that the Hunziker-van Winter-Zhislin (HVZ) theorem holds for the approximate systems. Furthermore, the approximate Hamiltonians and wave operators converge to the corresponding exact operators in an appropriate limit as the order of the approximation increases.
NASA Astrophysics Data System (ADS)
Yao, De-Liang; Siemens, D.; Bernard, V.; Epelbaum, E.; Gasparyan, A. M.; Gegelia, J.; Krebs, H.; Meißner, Ulf-G.
2016-05-01
We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S- and P -partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.
Off-axis multiple scattering of a laser beam in turbid media Comparison of theory and experiment
NASA Astrophysics Data System (ADS)
Gerstl, Siegfried A. W.; Zardecki, Andrew; Unruh, Wesley P.; Stupin, David M.; Stokes, Grant H.
1987-03-01
The off-axis forward-scattered radiation from a low energy He-Ne laser, scattered by high density hydrosols, is studied experimentally and theoretically. The validity range of theoretical calculations is determined using four measurements with two optical depths and two detector fields of view. For narrow field of view detectors, experimental and theoretical agreement is good close to the beam axis and decreases with transverse distance; agreement is good at greater distances from the beam axis using an open detector. The small-angle approximation adequately describes multiple scattering close to the beam; calculations are significantly improved by combining the small-angle approximation with diffusion theory.
Off-axis multiple scattering of a laser beam in turbid media: comparison of theory and experiment.
Gersti, S A; Zardecki, A; Unruh, W P; Stupin, D M; Stokes, G H; Elliott, N E
1987-03-01
The off-axis forward-scattered radiation from a low energy He-Ne laser, scattered by high density hydrosols, is studied experimentally and theoretically. The validity range of theoretical calculations is determined using four measurements with two optical depths and two detector fields of view. For narrow field of view detectors, experimental and theoretical agreement is good close to the beam axis and decreases with transverse distance; agreement is good at greater distances from the beam axis using an open detector. The small-angle approximation adequately describes multiple scattering close to the beam; calculations are significantly improved by combining the small-angle approximation with diffusion theory.
Scattering theory for the defocusing fourth-order Schrödinger equation
NASA Astrophysics Data System (ADS)
Miao, Changxing; Zheng, Jiqiang
2016-02-01
In this paper, we study the global well-posedness and scattering theory for the defocusing fourth-order nonlinear Schrödinger equation (FNLS) \\text{i}{{u}t}+{{Δ }2}u +\\mid u{{\\mid}p}u=0 in dimensions d≥slant 8 . We prove that if the solution u is apriorily bounded in the critical Sobolev space, that is, u\\in Lt∞≤ft(I;\\overset{\\centerdot}{\\mathop{H}} x{{sc}}≤ft({{{R}}d}\\right)\\right) with all {{s}c}:=\\frac{d}{2}-\\frac{4}{p}≥slant 1 if p is an even integer or {{s}c}\\in ≤ft[1,2+p\\right) otherwise, then u is global and scatters. We will give a uniform way to treat the energy-subcritical, energy-critical and energy-supercritical FNLS by making use of the strategy derived from concentration compactness ideas, and we are able to overcome the logarithmic blowup in the double Duhamel trick in dimension eight by exploiting the refined dispersive estimate which is in sharp contrast to the Schrödinger equation.
Coherent Raman scattering with incoherent light for a multiply resonant mixture: Theory
NASA Astrophysics Data System (ADS)
Kirkwood, Jason C.; Ulness, Darin J.; Stimson, Michael J.; Albrecht, A. C.
1998-02-01
The theory for coherent Raman scattering (CRS) with broadband incoherent light is presented for a multiply resonant, multicomponent mixture of molecules that exhibits simultaneous multiple resonances with the frequencies of the driving fields. All possible pairwise hyperpolarizability contributions to the signal intensity are included in the theoretical treatment-(resonant-resonant, resonant-nonresonant, and nonresonant-nonresonant correlations between chromophores) and it is shown how the different types of correlations manifest themselves as differently behaved components of the signal intensity. The Raman resonances are modeled as Lorentzians in the frequency domain, as is the spectral density of the incoherent light. The analytic results for this multiply resonant mixture are presented and applied to a specific binary mixture. These analytic results will be used to recover frequencies and dephasing times in a series of experiments on multiply resonant mixtures.
Self-interaction correction in multiple scattering theory: application to transition metal oxides
Daene, Markus W; Lueders, Martin; Ernst, Arthur; Diemo, Koedderitzsch; Temmerman, Walter M; Szotek, Zdzislawa; Wolfam, Hergert
2009-01-01
We apply to transition metal monoxides the self-interaction corrected (SIC) local spin density (LSD) approximation, implemented locally in the multiple scattering theory within the Korringa-Kohn-Rostoker (KKR) band structure method. The calculated electronic structure and in particular magnetic moments and energy gaps are discussed in reference to the earlier SIC results obtained within the LMTO-ASA band structure method, involving transformations between Bloch and Wannier representations to solve the eigenvalue problem and calculate the SIC charge and potential. Since the KKR can be easily extended to treat disordered alloys, by invoking the coherent potential approximation (CPA), in this paper we compare the CPA approach and supercell calculations to study the electronic structure of NiO with cation vacancies.
NASA Technical Reports Server (NTRS)
Anderson, D. E., Jr.; Meier, R. R.; Hodges, R. R., Jr.; Tinsley, B. A.
1987-01-01
The H Balmer alpha nightglow is investigated by using Monte Carlo models of asymmetric geocoronal atomic hydrogen distributions as input to a radiative transfer model of solar Lyman-beta radiation in the thermosphere and atmosphere. It is shown that it is essential to include multiple scattering of Lyman-beta radiation in the interpretation of Balmer alpha airglow data. Observations of diurnal variation in the Balmer alpha airglow showing slightly greater intensities in the morning relative to evening are consistent with theory. No evidence is found for anything other than a single sinusoidal diurnal variation of exobase density. Dramatic changes in effective temperature derived from the observed Balmer alpha line profiles are expected on the basis of changing illumination conditions in the thermosphere and exosphere as different regions of the sky are scanned.
Applications of Quantum Theory of Atomic and Molecular Scattering to Problems in Hypersonic Flow
NASA Technical Reports Server (NTRS)
Malik, F. Bary
1995-01-01
The general status of a grant to investigate the applications of quantum theory in atomic and molecular scattering problems in hypersonic flow is summarized. Abstracts of five articles and eleven full-length articles published or submitted for publication are included as attachments. The following topics are addressed in these articles: fragmentation of heavy ions (HZE particles); parameterization of absorption cross sections; light ion transport; emission of light fragments as an indicator of equilibrated populations; quantum mechanical, optical model methods for calculating cross sections for particle fragmentation by hydrogen; evaluation of NUCFRG2, the semi-empirical nuclear fragmentation database; investigation of the single- and double-ionization of He by proton and anti-proton collisions; Bose-Einstein condensation of nuclei; and a liquid drop model in HZE particle fragmentation by hydrogen.
NASA Astrophysics Data System (ADS)
Jensen, L.; Zhao, L. L.; Autschbach, J.; Schatz, G. C.
2005-11-01
We present a method to calculate both normal Raman-scattering (NRS) and resonance Raman-scattering (RRS) spectra from the geometrical derivatives of the frequency-dependent polarizability. In the RRS case, the polarizability derivatives are calculated from resonance polarizabilities by including a finite lifetime of the electronic excited states using time-dependent density-functional theory. The method is a short-time approximation to the Kramers, Heisenberg, and Dirac formalism. It is similar to the simple excited-state gradient approximation method if only one electronic excited state is important, however, it is not restricted to only one electronic excited state. Since the method can be applied to both NRS and RRS, it can be used to obtain complete Raman excitation profiles. To test the method we present the results for the S2 state of uracil and the S4,S3, and S2 states of pyrene. As expected, the results are almost identical to the results obtained from the excited-state gradient approximation method. Comparing with the experimental results, we find in general quite good agreement which enables an assignment of the experimental bands to bands in the calculated spectrum. For uracil the inclusion of explicit waters in the calculations was found to be necessary to match the solution spectra. The calculated resonance enhancements are on the order of 104-106, which is in agreement with experimental findings. For pyrene the method is also able to distinguish between the three different electronic states for which experimental data are available. The neglect of anharmonicity and solvent effects in the calculations leads to some discrepancy between theory and experiment.
ERIC Educational Resources Information Center
Alexander, John W., Jr.; Rosenberg, Nancy S.
This document consists of two modules. The first of these views applications of algebra and elementary calculus to curve fitting. The user is provided with information on how to: 1) construct scatter diagrams; 2) choose an appropriate function to fit specific data; 3) understand the underlying theory of least squares; 4) use a computer program to…
The operator algebra approach to quantum groups
Kustermans, Johan; Vaes, Stefaan
2000-01-01
A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116
Classical and quantum Kummer shape algebras
NASA Astrophysics Data System (ADS)
Odzijewicz, A.; Wawreniuk, E.
2016-07-01
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.
Some Applications of Algebraic System Solving
ERIC Educational Resources Information Center
Roanes-Lozano, Eugenio
2011-01-01
Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve"…
Berginc, G
2013-11-30
We have developed a general formalism based on Green's functions to calculate the coherent electromagnetic field scattered by a random medium with rough boundaries. The approximate expression derived makes it possible to determine the effective permittivity, which is generalised for a layer of an inhomogeneous random medium with different types of particles and bounded with randomly rough interfaces. This effective permittivity describes the coherent propagation of an electromagnetic wave in a random medium with randomly rough boundaries. We have obtained an expression, which contains the Maxwell – Garnett formula at the low-frequency limit, and the Keller formula; the latter has been proved to be in good agreement with experiments for particles whose dimensions are larger than a wavelength. (coherent light scattering)
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2011-04-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.
Classification of central extensions of Lax operator algebras
Schlichenmaier, Martin
2008-11-18
Lax operator algebras were introduced by Krichever and Sheinman as further developments of Krichever's theory of Lax operators on algebraic curves. They are infinite dimensional Lie algebras of current type with meromorphic objects on compact Riemann surfaces (resp. algebraic curves) as elements. Here we report on joint work with Oleg Sheinman on the classification of their almost-graded central extensions. It turns out that in case that the finite-dimensional Lie algebra on which the Lax operator algebra is based on is simple there is a unique almost-graded central extension up to equivalence and rescaling of the central element.
NASA Astrophysics Data System (ADS)
McGovern, J. A.; Phillips, D. R.; Grießhammer, H. W.
2013-01-01
We analyse the proton Compton-scattering differential cross section for photon energies up to 325 MeV using Chiral Effective Field Theory (χEFT) and extract new values for the electric and magnetic polarisabilities of the proton. Our approach builds in the key physics in two different regimes: photon energies ω ≲ m π ("low energy"), and the higher energies where the Δ(1232) resonance plays a key role. The Compton amplitude is complete at N4LO, {O}( {e^2 δ ^4 } ), in the low-energy region, and at NLO, {O}( {e^2 δ ^0 } ), in the resonance region. Throughout, the Delta-pole graphs are dressed with π N loops and γN Δ vertex corrections. A statistically consistent database of proton Compton experiments is used to constrain the free parameters in our amplitude: the M1 γN Δ transition strength b 1 (which is fixed in the resonance region) and the polarisabilities α E1 and β M1 (which are fixed from data below 170 MeV). In order to obtain a reasonable fit, we find it necessary to add the spin polarisability γ M1 M1 as a free parameter, even though it is, strictly speaking, predicted in χEFT at the order to which we work. We show that the fit is consistent with the Baldin sum rule, and then use that sum rule to constrain α E1 + β M1. In this way we obtain α E1 = [10.65 ± 0.35(stat) ± 0.2(Baldin) ± 0.3(theory)] × 10-4 fm3 and β M1 = [3.15 ∓ 0.35(state) ± 0.2(Baldin) ∓ 0.3()theory] × 10-4 fm3, with χ2 = 113.2 for 135 degrees of freedom. A detailed rationale for the theoretical uncertainties assigned to this result is provided.
NASA Technical Reports Server (NTRS)
Moore, R. K.; Fung, A. K.; Dome, G. J.; Birrer, I. J.
1978-01-01
The wind direction properties of radar backscatter from the sea were empirically modelled using a cosine Fourier series through the 4th harmonic in wind direction (referenced to upwind). A comparison with 1975 JONSWAP (Joint North Sea Wave Project) scatterometer data, at incidence angles of 40 and 65, indicates that effects to third and fourth harmonics are negligible. Another important result is that the Fourier coefficients through the second harmonic are related to wind speed by a power law expression. A technique is also proposed to estimate the wind speed and direction over the ocean from two orthogonal scattering measurements. A comparison between two different types of sea scatter theories, one type presented by the work of Wright and the other by that of Chan and Fung, was made with recent scatterometer measurements. It demonstrates that a complete scattering model must include some provisions for the anisotropic characteristics of the sea scatter, and use a sea spectrum which depends upon wind speed.
Algebraic Systems and Pushdown Automata
NASA Astrophysics Data System (ADS)
Petre, Ion; Salomaa, Arto
We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.
Jagannathan, Srinivasan; Küsel, Elizabeth T; Ratilal, Purnima; Makris, Nicholas C
2012-08-01
Bistatic, long-range measurements of acoustic scattered returns from vertically extended, air-filled tubular targets were made during three distinct field experiments in fluctuating continental shelf waveguides. It is shown that Sonar Equation estimates of mean target-scattered intensity lead to large errors, differing by an order of magnitude from both the measurements and waveguide scattering theory. The use of the Ingenito scattering model is also shown to lead to significant errors in estimating mean target-scattered intensity in the field experiments because they were conducted in range-dependent ocean environments with large variations in sound speed structure over the depth of the targets, scenarios that violate basic assumptions of the Ingenito model. Green's theorem based full-field modeling that describes scattering from vertically extended tubular targets in range-dependent ocean waveguides by taking into account nonuniform sound speed structure over the target's depth extent is shown to accurately describe the statistics of the targets' scattered field in all three field experiments. Returns from the man-made targets are also shown to have a very different spectral dependence from the natural target-like clutter of the dominant fish schools observed, suggesting that judicious multi-frequency sensing may often provide a useful means of distinguishing fish from man-made targets.
Srivastava, V; Jarzembski, M A
1991-02-01
Comparison of Mie theory calculations of the internal electromagnetic source function for a 120-microm-diameter water droplet with geometrical optics suggests that the field enhancement located at the critical ring region encircling the axis in the forward direction of the droplet can support stimulated Raman scattering as found experimentally.
A Metric Conceptual Space Algebra
NASA Astrophysics Data System (ADS)
Adams, Benjamin; Raubal, Martin
The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
ERIC Educational Resources Information Center
Deakin, Michael A. B.
1974-01-01
Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)
Representations of filtered solvable Lie algebras
Panov, Alexander N
2012-01-31
The representation theory of filtered solvable Lie algebras is constructed. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found. Bibliography: 9 titles.
NASA Astrophysics Data System (ADS)
Raouafi, N.-E.
2002-05-01
The aim of the present work is to present theoretical results on the Stokes parameters of a resonance spectral line, scattered by moving atoms (or ions) in the presence of a local magnetic field. We assume that the scattered line is sensitive to the Hanle effect due to the magnetic field and also to Doppler redistribution due to the atomic motions. The present theory is developed for a two-level atom, in the framework of the density matrix formalism Blum (1981). Analogous results given in Sahal-Bréchot et al. (1986) for the magnetic-field effect alone, and in Sahal-Bréchot et al. (\\cite{Sahal98}) for the velocity-field effect alone, can be obtained from our theory by cancelling in the equations, respectively, the velocity field or the magnetic field. The results of our theory are general and can be used for astrophysical studies concerning the Hanle effect and the Doppler redistribution effect on the linear polarization parameters of the scattered radiation. They can be used particularly to interpret linear polarization of coronal spectral lines to get a complete determination of vectorial quantities such as the coronal magnetic field and the solar wind velocity field vectors. As an application, the atomic velocity field distribution is supposed to be Maxwellian with a drift velocity field vector. This latter describes the macroscopic motion of the scattering atoms. In the solar corona, it can be assimilated into the solar wind velocity field vector.
Rayleigh Scattering Density Measurements, Cluster Theory, and Nucleation Calculations at Mach 10
NASA Technical Reports Server (NTRS)
Balla, R. Jeffrey; Everhart, Joel L.
2012-01-01
In an exploratory investigation, quantitative unclustered laser Rayleigh scattering measurements of density were performed in the air in the NASA Langley Research Center's 31 in. Mach 10 wind tunnel. A review of 20 previous years of data in supersonic and Mach 6 hypersonic flows is presented where clustered signals typically overwhelmed molecular signals. A review of nucleation theory and accompanying nucleation calculations are also provided to interpret the current observed lack of clustering. Data were acquired at a fixed stagnation temperature near 990Kat five stagnation pressures spanning 2.41 to 10.0 MPa (350 to 1454 psi) using a pulsed argon fluoride excimer laser and double-intensified charge-coupled device camera. Data averaged over 371 images and 210 pixels along a 36.7mmline measured freestream densities that agree with computed isentropic-expansion densities to less than 2% and less than 6% at the highest and lowest densities, respectively. Cluster-free Mach 10 results are compared with previous clustered Mach 6 and condensation-free Mach 14 results. Evidence is presented indicating vibrationally excited oxygen and nitrogen molecules are absorbed as the clusters form, release their excess energy, and inhibit or possibly reverse the clustering process. Implications for delaying clustering and condensation onset in hypersonic and hypervelocity facilities are discussed.
Theory of neutron scattering from thermally excited quasiparticles in superfluid 4He
NASA Astrophysics Data System (ADS)
Griffin, A.; Talbot, E.
1981-11-01
We present the first detailed theoretical study of the inelastic neutron scattering contribution Sth(Q-->,ω) from thermally excited quasiparticles in superfluid 4He, with emphasis on the low-Q collisionless limit. In the temperature region where rotons are the dominant excitation, our results for Sth(Q-->,ω) scale with Landau's normal fluid density. We argue that Sth(Q-->,ω) is the origin of the broad temperature-dependent continuum which Woods and Svensson (1978) have observed at temperatures above about 1.7 K. Our specific model calculations of Sth(Q-->,ω) are based on evaluating the regular part of the longitudinal momentum current-current correlation function within the Bogoliubov approximation, but the experimental quasiparticle (roton) spectrum is used in our numerical calculations. Our expression satisfies the normal fluid f-sum rule in the long-wavelength collisionless limit and is in essential agreement with the general picture suggested by Pines and Nozières in 1964. Our present theory involves several approximations which probably limit its validity to Q<~0.5 Å-1. Some generalizations to deal with the larger values of Q studied by Woods and Svensson are briefly discussed.
Molecular cavity optomechanics as a theory of plasmon-enhanced Raman scattering.
Roelli, Philippe; Galland, Christophe; Piro, Nicolas; Kippenberg, Tobias J
2016-02-01
The exceptional enhancement of Raman scattering by localized plasmonic resonances in the near field of metallic nanoparticles, surfaces or tips (SERS, TERS) has enabled spectroscopic fingerprinting down to the single molecule level. The conventional explanation attributes the enhancement to the subwavelength confinement of the electromagnetic field near nanoantennas. Here, we introduce a new model that also accounts for the dynamical nature of the plasmon-molecule interaction. We thereby reveal an enhancement mechanism not considered before: dynamical backaction amplification of molecular vibrations. We first map the system onto the canonical Hamiltonian of cavity optomechanics, in which the molecular vibration and the plasmon are parametrically coupled. We express the vacuum optomechanical coupling rate for individual molecules in plasmonic 'hot-spots' in terms of the vibrational mode's Raman activity and find it to be orders of magnitude larger than for microfabricated optomechanical systems. Remarkably, the frequency of commonly studied molecular vibrations can be comparable to or larger than the plasmon's decay rate. Together, these considerations predict that an excitation laser blue-detuned from the plasmon resonance can parametrically amplify the molecular vibration, leading to a nonlinear enhancement of Raman emission that is not predicted by the conventional theory. Our optomechanical approach recovers known results, provides a quantitative framework for the calculation of cross-sections, and enables the design of novel systems that leverage dynamical backaction to achieve additional, mode-selective enhancements. It also provides a quantum mechanical framework to analyse plasmon-vibrational interactions in terms of molecular quantum optomechanics. PMID:26595330
Scattering parameters for cold Li-Rb and Na-Rb collisions derived from variable phase theory
Ouerdane, H.; Jamieson, M.J.
2004-08-01
We show how the scattering phase shift, the s-wave scattering length, and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds for the scattering length and the scattering volume. We show how, in the framework of the variable phase method, Levinson's theorem yields the number of bound states supported by a potential. We report results from a study of the heteronuclear alkali-metal dimers NaRb and LiRb. We consider ab initio molecular potentials for the X {sup 1}{sigma}{sup +} and a {sup 3}{sigma}{sup +} states of both dimers and compare and discuss results obtained from experimentally based X {sup 1}{sigma}{sup +} and a {sup 3}{sigma}{sup +} potentials of NaRb. We explore the mass dependence of the scattering data by considering all isotopomers and we calculate the numbers of bound states supported by the molecular potentials for each isotopomer.
NASA Astrophysics Data System (ADS)
Melnikov, N. B.; Reser, B. I.; Paradezhenko, G. V.
2016-08-01
To study the spin-density correlations in the ferromagnetic metals above the Curie temperature, we relate the spin correlator and neutron scattering cross-section. In the dynamic spin-fluctuation theory, we obtain explicit expressions for the effective and local magnetic moments and spatial spin-density correlator. Our theoretical results are demonstrated by the example of bcc Fe. The effective and local moments are found in good agreement with results of polarized neutron scattering experiment over a wide temperature range. The calculated short-range order is small (up to 4 Å) and slowly decreases with temperature.
Tureanu, Anca
2006-09-15
In the framework of quantum field theory on noncommutative space-time with the symmetry group O(1,1)xSO(2), we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with this symmetry, leads to the mere impossibility of drawing any conclusion on the analyticity of the 2{yields}2-scattering amplitude in cos {theta}, {theta} being the scattering angle. Discussions on the possible ways of obtaining high-energy bounds analogous to the Froissart-Martin bound on the total cross section are also presented.
NASA Technical Reports Server (NTRS)
Srivastava, Vandana; Jarzembski, Maurice A.
1991-01-01
This paper uses Mie theory to treat electromagnetic scattering and to evaluate field enhancement in the forward direction of a small droplet irradiated by a high-energy beam and compares the results of calculations with the field-enhancement evaluation obtained via geometrical optics treatment. Results of this comparison suggest that the field enhancement located at the critical ring region encircling the axis in the forward direction of the droplet can support laser-induced Raman scattering. The results are supported by experimental observations of the interaction of a 120-micron-diam water droplet with a high-energy Nd:YAG laser beam.
An Algebraic Model for the mathfrak{su}(2|2) Light-Cone String Field Theory
NASA Astrophysics Data System (ADS)
Moriyama, S.
We first revisit the light-cone string field theory on the flat andpp-wave background. By our systematic analysis, we find that some unsatisfactions in the previous construction can be overcome. After that, we head for the construction of the LCSFT on the bubbling geometry with an isometry [mathfrak{psu}(2|2)]^2 ltimes {mathbb R}. We clarify the structure of expansion and propose toy models for it. This proceeding is based on the collaboration with Kishimoto [I. Kishimoto and S. Moriyama, J. High Energy Phys. textbf{08} (2010), 013, arXiv:1005.4719 (Ref. 1)].
Sound extinction by fish schools: forward scattering theory and data analysis.
Raveau, M; Feuillade, C
2015-02-01
A model used previously to study collective back scattering from fish schools [Feuillade et al., J. Acoust. Soc. Am. 99(1), 196-208 (1996)], is used to analyze the forward scattering properties of these objects. There is an essential physical difference between back and forward scattering from fish schools. Strong frequency dependent interference effects, which affect the back scattered field amplitude, are absent in the forward scattering case. This is critically important for data analysis. There is interest in using back scattering and transmission data from fish schools to study their size, the species and abundance of fish, and fish behavior. Transmission data can be processed to determine the extinction of the field by a school. The extinction of sound depends on the forward scattering characteristics of the school, and data inversion to provide information about the fish should be based upon a forward scattering paradigm. Results are presented of an analysis of transmission data obtained in September 1995 during an experiment performed in the Gulf of Lion in the Mediterranean Sea [Diachok, J. Acoust. Soc. Am. 105(4), 2107-2128 (1999)]. The analysis shows that using forward scattering leads to significantly larger estimates of fish abundance than previous analysis based upon back scattering approaches.
Sound extinction by fish schools: forward scattering theory and data analysis.
Raveau, M; Feuillade, C
2015-02-01
A model used previously to study collective back scattering from fish schools [Feuillade et al., J. Acoust. Soc. Am. 99(1), 196-208 (1996)], is used to analyze the forward scattering properties of these objects. There is an essential physical difference between back and forward scattering from fish schools. Strong frequency dependent interference effects, which affect the back scattered field amplitude, are absent in the forward scattering case. This is critically important for data analysis. There is interest in using back scattering and transmission data from fish schools to study their size, the species and abundance of fish, and fish behavior. Transmission data can be processed to determine the extinction of the field by a school. The extinction of sound depends on the forward scattering characteristics of the school, and data inversion to provide information about the fish should be based upon a forward scattering paradigm. Results are presented of an analysis of transmission data obtained in September 1995 during an experiment performed in the Gulf of Lion in the Mediterranean Sea [Diachok, J. Acoust. Soc. Am. 105(4), 2107-2128 (1999)]. The analysis shows that using forward scattering leads to significantly larger estimates of fish abundance than previous analysis based upon back scattering approaches. PMID:25697989
NASA Astrophysics Data System (ADS)
Barmparis, Georgios D.; Puzyrev, Yevgeniy S.; Zhang, X.-G.; Pantelides, Sokrates T.
2015-12-01
Inelastic scattering and carrier capture by defects in semiconductors are the primary causes of hot-electron-mediated degradation of power devices, which holds up their commercial development. At the same time, carrier capture is a major issue in the performance of solar cells and light-emitting diodes. A theory of nonradiative (multiphonon) inelastic scattering by defects, however, is nonexistent, while the theory for carrier capture by defects has had a long and arduous history. Here we report the construction of a comprehensive theory of inelastic scattering by defects, with carrier capture being a special case. We distinguish between capture under thermal equilibrium conditions and capture under nonequilibrium conditions, e.g., in the presence of an electrical current or hot carriers where carriers undergo scattering by defects and are described by a mean free path. In the thermal-equilibrium case, capture is mediated by a nonadiabatic perturbation Hamiltonian, originally identified by Huang and Rhys and by Kubo, which is equal to linear electron-phonon coupling to first order. In the nonequilibrium case, we demonstrate that the primary capture mechanism is within the Born-Oppenheimer approximation (adiabatic transitions), with coupling to the defect potential inducing Franck-Condon electronic transitions, followed by multiphonon dissipation of the transition energy, while the nonadiabatic terms are of secondary importance (they scale with the inverse of the mass of typical atoms in the defect complex). We report first-principles density-functional-theory calculations of the capture cross section for a prototype defect using the projector-augmented wave, which allows us to employ all-electron wave functions. We adopt a Monte Carlo scheme to sample multiphonon configurations and obtain converged results. The theory and the results represent a foundation upon which to build engineering-level models for hot-electron degradation of power devices and the performance
Theory and Simulations of Refractive Substructure in Resolved Scatter-broadened Images
NASA Astrophysics Data System (ADS)
Johnson, Michael D.; Gwinn, Carl R.
2015-06-01
At radio wavelengths, scattering in the interstellar medium distorts the appearance of astronomical sources. Averaged over a scattering ensemble, the result is a blurred image of the source. However, Narayan & Goodman and Goodman & Narayan showed that for an incomplete average, scattering introduces refractive substructure in the image of a point source that is both persistent and wideband. We show that this substructure is quenched but not smoothed by an extended source. As a result, when the scatter-broadening is comparable to or exceeds the unscattered source size, the scattering can introduce spurious compact features into images. In addition, we derive efficient strategies to numerically compute realistic scattered images, and we present characteristic examples from simulations. Our results show that refractive substructure is an important consideration for ongoing missions at the highest angular resolutions, and we discuss specific implications for RadioAstron and the Event Horizon Telescope.
NASA Technical Reports Server (NTRS)
Kobayashi, Satoru; Tanelli, Simone; Im, Eastwood
2005-01-01
Effects of multiple scattering on reflectivity are studied for millimeter wavelength weather radars. A time-independent vector theory, including up to second-order scattering, is derived for a single layer of hydrometeors of a uniform density and a uniform diameter. In this theory, spherical waves with a Gaussian antenna pattern are used to calculate ladder and cross terms in the analytical scattering theory. The former terms represent the conventional multiple scattering, while the latter terms cause backscattering enhancement in both the copolarized and cross-polarized components. As the optical thickness of the hydrometeor layer increases, the differences from the conventional plane wave theory become more significant, and essentially, the reflectivity of multiple scattering depends on the ratio of mean free path to radar footprint radius. These results must be taken into account when analyzing radar reflectivity for use in remote sensing.
Takano, Yoshihide; Liou, Kuo-Nan
2010-07-10
We have developed a hit-and-miss Monte Carlo geometric ray-tracing program to compute the scattering phase matrix for concentrically stratified spheres. Using typical refractive indices for water and aerosols in the calculations, numerous rainbow features appear in the phase matrix that deviate from the results calculated from homogeneous spheres. In the context of geometric ray tracing, rainbows and glory are identified by means of their ray paths, which provide physical explanation for the features produced by the "exact" Lorenz-Mie theory. The computed results for the phase matrix, the single-scattering albedo, and the asymmetry factor for a size parameter of approximately 600 compared closely with those evaluated from the "exact" theory. PMID:20648178
Constraint algebra in bigravity
Soloviev, V. O.
2015-07-15
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
Constraint algebra in bigravity
NASA Astrophysics Data System (ADS)
Soloviev, V. O.
2015-07-01
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
Scattering coefficients of an inductive strip in a finline Theory and experiment
NASA Astrophysics Data System (ADS)
Knorr, J. B.; Deal, J. C.
1985-10-01
This paper describes the application of the spectral-domain method to the computation of the scattering coefficients of an inductive strip in a millimeter-wave finline. Measured scattering data are compared with numerical data to establish the accuracy of the results. The predicted and measured responses of several finline resonators are also compared.
NASA Astrophysics Data System (ADS)
Schempp, Walter J.
2013-09-01
Based on projective geometry, a quantum holographic approach to the orbiton / spinon dynamics of quantum blackholography and clinical magnetic resonance tomography is mathematically described. Crucial applications of the conformal steady-state free-precession modality and automorphic scattering theory are the evidence for a supermassive central black hole in the Milky Way galaxy and the modalities of clinical cardiovascular magnetic resonance tomography and diffusion weighted magnetic resonance tomography of non-invasive radiological diagnostics.
NASA Astrophysics Data System (ADS)
Ceolato, Romain; Riviere, Nicolas
2016-07-01
Spectral polarimetric light-scattering by particulate media has recently attracted growing interests for various applications due to the production of directional broadband light sources. Here the spectral polarimetric light-scattering signatures of particulate media are simulated using a numerical model based on the spectral Vector Radiative Transfer Equation (VRTE). A microphysical analysis is conducted to understand the dependence of the light-scattering signatures upon the microphysical parameters of particles. We reveal that depolarization from multiple scattering results in remarkable spectral and directional features, which are simulated by our model over a wide spectral range from visible to near-infrared. We propose to use these features to improve the inversion of the scattering problem in the fields of remote sensing, astrophysics, material science, or biomedical.
Scattering theory and the Aharonov-Bohm effect in quasiclassical physics
Sitenko, Yurii A.; Vlasii, Nadiia D.
2011-06-15
Research Highlights: > Scattering Aharonov-Bohm effect. > Short-wavelength limit of scattered nonrelativistic particles. > Fraunhofer diffraction in the forward direction. > Fresnel diffraction in the forward region in conical space. > Enclosed magnetic flux is a gate for the propagation of quasiclassical particles. - Abstract: Scattering of a nonrelativistic quantum-mechanical particle by an impenetrable magnetic vortex is considered. The nonvanishing transverse size of the vortex is taken into account, and the limit of short, as compared to this size, wavelengths of the scattered particle is analyzed. We show that the scattering Aharonov-Bohm effect persists in the quasiclassical limit owing to the diffraction persisting in the short-wavelength limit. As a result, the vortex flux serves as a gate for the propagation of short-wavelength, almost classical, particles. This quasiclassical effect is more feasible to experimental detection in the case when space outside the vortex is conical.
Numerical algebraic geometry and algebraic kinematics
NASA Astrophysics Data System (ADS)
Wampler, Charles W.; Sommese, Andrew J.
In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.
Private quantum subsystems and quasiorthogonal operator algebras
NASA Astrophysics Data System (ADS)
Levick, Jeremy; Jochym-O'Connor, Tomas; Kribs, David W.; Laflamme, Raymond; Pereira, Rajesh
2016-03-01
We generalize a recently discovered example of a private quantum subsystem to find private subsystems for Abelian subgroups of the n-qubit Pauli group, which exist in the absence of private subspaces. In doing so, we also connect these quantum privacy investigations with the theory of quasiorthogonal operator algebras through the use of tools from group theory and operator theory.
NASA Astrophysics Data System (ADS)
Arola, E.; Strange, P.; Kulikov, N. I.; Woods, M. J.; Gyorffy, B. L.
1998-01-01
We apply our recent formalism of magnetic scattering of X-rays to ferromagnetic iron and Cr 47Fe 53 alloy. The theory has been constructed in the framework of the fully relativistic spin-polarized KKR-type multiple-scattering theory. We discuss how to adapt our theory for substitutionally random alloys in context of the coherent potential approximation (CPA) and apply it to anomalous magnetic scattering of X-rays at the LII,III absorption edges of iron and chromium in Cr 47Fe 53.
Efficient method for scattering problems in open billiards: Theory and applications
NASA Astrophysics Data System (ADS)
Akguc, Gursoy B.; Seligman, Thomas H.
2006-12-01
We present an efficient method to solve scattering problems in two-dimensional open billiards with two leads and a complicated scattering region. The basic idea is to transform the scattering region to a rectangle, which will lead to complicated dynamics in the interior, but simple boundary conditions. The method can be specialized to closed billiards, and it allows the treatment of interacting particles in the billiard. We apply this method to quantum echoes measured recently in a microwave cavity, and indicate how it can be used for interacting particles.
Alarcón, J.M.; Martin Camalich, J.; Oller, J.A.
2013-09-15
We present a novel analysis of the πN scattering amplitude in covariant baryon chiral perturbation theory up to O(p{sup 3}) within the extended-on-mass-shell renormalization scheme and including the Δ(1232) explicitly in the δ-counting. We take the hadronic phase shifts provided by partial wave analyses as basic experimental information to fix the low-energy constants. Subsequently, we study in detail the various observables and low-energy theorems related to the πN scattering amplitude. In particular, we discuss the results and chiral expansion of the phase shifts, the threshold coefficients, the Goldberger–Treiman relation, the pion–nucleon sigma term and the extrapolation onto the subthreshold region. The chiral representation of the amplitude in the theory with the Δ presents a good convergence from very low energies in the subthreshold region up to energies above threshold and below the Δ(1232) peak, leading also to a phenomenological description perfectly consistent with the one reported by the respective partial wave analyses and independent determinations. We conclude that a model-independent and systematic framework to analyze πN-scattering observables using directly experimental data shall be possible in covariant baryon chiral perturbation theory. -- Highlights: •The chiral series shows a better convergence than previous analyses. •Improved prediction of the πN scattering phenomenology. •This analysis connects reliably the subthreshold and physical regions for the first time using ChPT. •Extraction of an accurate value of σ{sub πN} from experimental data. •σ{sub πN} extracted is compatible with related phenomenology.
Resonant Raman scattering theory for Kitaev models and their Majorana fermion boundary modes
NASA Astrophysics Data System (ADS)
Perreault, Brent; Knolle, Johannes; Perkins, Natalia B.; Burnell, F. J.
2016-09-01
We study the inelastic light scattering response in two- (2D) and three-dimensional (3D) Kitaev spin-liquid models with Majorana spinon band structures in the symmetry classes BDI and D leading to protected gapless surface modes. We present a detailed calculation of the resonant Raman/Brillouin scattering vertex relevant to iridate and ruthenate compounds whose low-energy physics is believed to be proximate to these spin-liquid phases. In the symmetry class BDI, we find that while the resonant scattering on thin films can detect the gapless boundary modes of spin liquids, the nonresonant processes do not couple to them. For the symmetry class D, however, we find that the coupling between both types of light-scattering processes and the low-energy surface states is strongly suppressed. Additionally, we describe the effect of weak time-reversal symmetry breaking perturbations on the bulk Raman response of these systems.
Extension of Glauber theory to account for intratarget diffraction in multicenter scattering
NASA Astrophysics Data System (ADS)
Miller, B. R.; Bartell, L. S.
1980-01-01
A 1975 treatment of single-double multiple scattering of electrons by randomly oriented vapor-phase molecules is put on a firmer footing and extended to higher order. It is shown how to include effects of intramolecular Fresnel diffraction, as an electron scattered by one atom propagates to the next, without ever explicitly evaluating the scattered wave function in the target. Theoretically derived estimates are made of the limitations of the approach at various levels of approximation. Numerical calculations are compared as a function of energy and scattering angle with newly available high quality calculations by Kohl and Arvedson (KA). In the expected range of applicability — roughly, 10 keV and higher - the present approach yields results that are satisfactory and (unlike those of KA) inexpensive enough for use in routine electron diffraction analyses.
Theory of scattering of electromagnetic waves of the microwave range in a turbid medium
NASA Astrophysics Data System (ADS)
Konstantinov, O. V.; Matveentsev, A. V.
2013-02-01
The coefficient of extinction of electromagnetic waves of the microwave range due to their scattering from clusters suspended in an amorphous medium and responsible for turbidity is calculated. Turbidity resembles the case when butter clusters transform water into milk. In the case under investigation, the clusters are conductors (metallic or semiconducting). The extinction coefficient is connected in a familiar way with the cross section of light scattering from an individual cluster. A new formula is derived for the light scattering cross section in the case when damping of oscillations of an electron is due only to spontaneous emission of light quanta. In this case, the resonant scattering cross section for light can be very large. It is shown that this can be observed only in a whisker nanocluster. In addition, the phonon energy on a whisker segment must be higher than the photon energy, which is close to the spacing between the electron energy levels in the cluster.
Dzakpasu, Rhonda; Axelrod, Daniel
2004-01-01
The theoretical basis of an optical microscope technique to image dynamically scattered light fluctuation decay rates (dynamic light scattering microscopy) is developed. It is shown that relative motions between scattering centers even smaller than the optical resolution of the microscope are sufficient to produce significant phase variations resulting in interference intensity fluctuations in the image plane. The timescale and time dependence for the temporal autocorrelation function of these intensity fluctuations is derived. The spatial correlation distance, which reports the average distance between constructive and destructive interference in the image plane, is calculated and compared with the pixel size, and the distance dependence of the spatial correlation function is derived. The accompanying article in this issue describes an experimental implementation of dynamic light scattering microscopy. PMID:15298930
A semiclassical method in the theory of light scattering by semiconductor quantum dots
Lang, I. G.; Korovin, L. I. Pavlov, S. T.
2008-06-15
A semiclassical method is proposed for the theoretical description of elastic light scattering by arbitrary semiconductor quantum dots under conditions of size quantization. This method involves retarded potentials and allows one to dispense with boundary conditions for electric and magnetic fields. Exact results for the Umov-Poynting vector at large distances from quantum dots in the case of monochromatic and pulsed irradiation and formulas for differential scattering cross sections are obtained.
Quantization of Algebraic Reduction
Sniatycki, Jeodrzej
2007-11-14
For a Poisson algebra obtained by algebraic reduction of symmetries of a quantizable system we develop an analogue of geometric quantization based on the quantization structure of the original system.
Learning Algebra in a Computer Algebra Environment
ERIC Educational Resources Information Center
Drijvers, Paul
2004-01-01
This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…
Bottcher, C.; Strayer, M.R.; Werby, M.F.
1993-10-01
The Helmholtz-Poincare Wave Equation (H-PWE) arises in many areas of classical wave scattering theory. In particular it can be found for the cases of acoustical scattering from submerged bounded objects and electromagnetic scattering from objects. The extended boundary integral equations (EBIE) method is derived from considering both the exterior and interior solutions of the H-PWE`s. This coupled set of expressions has the advantage of not only offering a prescription for obtaining a solution for the exterior scattering problem, but it also obviates the problem of irregular values corresponding to fictitious interior eigenvalues. Once the coupled equations are derived, they can by obtained in matrix form be expanding all relevant terms in partial wave expansions, including a biorthogonal expansion of the Green function. However some freedom of choice in the choice of the surface expansion is available since the unknown surface quantities may be expanded in a variety of ways to long as closure is obtained. Out of many possible choices, we develop an optimal method to obtain such expansions which is based on the optimum eigenfunctions related to the surface of the object. In effect, we convert part of the problem (that associated with the Fredholms integral equation of the first kind) an eigenvalue problem of a related Hermition operator. The methodology will be explained in detail and examples will be presented.
NASA Astrophysics Data System (ADS)
Rado, G. T.; Hicken, R. J.
1988-04-01
A new theory of the Brillouin shift in the inelastic scattering of light by magnetostatic spin waves is presented. Contrary to previous work, the present calculations do include exchange effects and treat the magnetic surface anisotropy constants Ks and Kss directly rather than via the stratagem of effective volume anisotropies. The experimental data for {110} Fe on W are explained about as well by the present theory as by previous work. A detailed analysis reveals the previously unnoticed fact that the signs of Ks and Kss for (1¯10) Fe on W are opposite to those for (1¯10) Fe on GaAs. Some new spin-wave modes arising from exchange are predicted and shown to occur outside the frequency range which has been investigated experimentally. A quantitative explanation is proposed for the occasional applicability of a theory based on effective volume anisotropies and zero exchange.
Profiles of Algebraic Competence
ERIC Educational Resources Information Center
Humberstone, J.; Reeve, R.A.
2008-01-01
The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…
Developing Thinking in Algebra
ERIC Educational Resources Information Center
Mason, John; Graham, Alan; Johnson-Wilder, Sue
2005-01-01
This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Vague Congruences and Quotient Lattice Implication Algebras
Qin, Xiaoyan; Xu, Yang
2014-01-01
The aim of this paper is to further develop the congruence theory on lattice implication algebras. Firstly, we introduce the notions of vague similarity relations based on vague relations and vague congruence relations. Secondly, the equivalent characterizations of vague congruence relations are investigated. Thirdly, the relation between the set of vague filters and the set of vague congruences is studied. Finally, we construct a new lattice implication algebra induced by a vague congruence, and the homomorphism theorem is given. PMID:25133207
NASA Astrophysics Data System (ADS)
Ancora, Daniele; Zacharopoulos, Athanasios; Ripoll, Jorge; Zacharakis, Giannis
2015-07-01
One of the major challenges within Optical Imaging, photon propagation through clear layers embedded between scattering tissues, can be now efficiently modelled in real-time thanks to the Monte Carlo approach based on GPU. Because of its nature, the photon propagation problem can be very easily parallelized and ran on low cost hardware, avoiding the need for expensive Super Computers. A comparison between Diffusion and MC photon propagation theory is presented in this work with application to neuroimaging, investigating low scattering regions in a mouse-like phantom. Regions such as the Cerebral Spinal Fluid, are currently not taken into account in the classical computational models because of the impossibility to accurately simulate light propagation using fast Diffusive Equation approaches, leading to inaccuracies during the reconstruction process. The goal of the study presented here, is to reduce and further improve the computation accuracy of the reconstructed solution in a highly realistic scenario in the case of neuroimaging in preclinical mouse models.
A Bond-order Theory on the Phonon Scattering by Vacancies in Two-dimensional Materials
Xie, Guofeng; Shen, Yulu; Wei, Xiaolin; Yang, Liwen; Xiao, Huaping; Zhong, Jianxin; Zhang, Gang
2014-01-01
We theoretically investigate the phonon scattering by vacancies, including the impacts of missing mass and linkages () and the variation of the force constant of bonds associated with vacancies () by the bond-order-length-strength correlation mechanism. We find that in bulk crystals, the phonon scattering rate due to change of force constant is about three orders of magnitude lower than that due to missing mass and linkages . In contrast to the negligible in bulk materials, in two-dimensional materials can be 3–10 folds larger than . Incorporating this phonon scattering mechanism to the Boltzmann transport equation derives that the thermal conductivity of vacancy defective graphene is severely reduced even for very low vacancy density. High-frequency phonon contribution to thermal conductivity reduces substantially. Our findings are helpful not only to understand the severe suppression of thermal conductivity by vacancies, but also to manipulate thermal conductivity in two-dimensional materials by phononic engineering. PMID:24866858
FAST TRACK COMMUNICATION: Kac Moody algebras and controlled chaos
NASA Astrophysics Data System (ADS)
Wesley, Daniel H.
2007-02-01
Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi Yau, or M theory on a manifold of G2 holonomy.
NASA Astrophysics Data System (ADS)
Rosen, David L.; Pendleton, J. David
1995-09-01
Light scattered from optically active spheres was theoretically analyzed for biodetection. The circularly polarized signal of near-forward scattering from circularly dichroic spheres was calculated. Both remote and point biodetection were considered. The analysis included the effect of a circular aperture and beam block at the detector. If the incident light is linearly polarized, a false signal would limit the sensitivity of the biodetector. If the incident light is randomly polarized, shot noise would limit the sensitivity. Suggested improvements to current techniques include a beam block, precise angular measurements, randomly polarized light, index-matching fluid, and larger apertures for large particles.
Theory of Two-Magnon Raman Scattering in Iron Pnictides and Chalcogenides
Chen, C. C.
2011-08-15
Although the parent iron-based pnictides and chalcogenides are itinerant antiferromagnets, the use of local moment picture to understand their magnetic properties is still widespread. We study magnetic Raman scattering from a local moment perspective for various quantum spin models proposed for this new class of superconductors. These models vary greatly in the level of magnetic frustration and show a vastly different two-magnon Raman response. Light scattering by two-magnon excitations thus provides a robust and independent measure of the underlying spin interactions. In accord with other recent experiments, our results indicate that the amount of magnetic frustration in these systems may be small.
NASA Astrophysics Data System (ADS)
Gaebler, Peter J.; Eulenfeld, Tom; Wegler, Ulrich
2015-12-01
In this study, frequency-dependent seismic scattering and intrinsic attenuation parameters for the crustal structure beneath the W-Bohemia/Vogtland swarm earthquake region close to the border of Czech Republic and Germany are estimated. Synthetic seismogram envelopes are modelled using elastic and acoustic radiative transfer theory. Scattering and absorption parameters are determined by fitting these synthetic envelopes to observed seismogram envelopes from 14 shallow local events from the October 2008 W-Bohemia/Vogtland earthquake swarm. The two different simulation approaches yield similar results for the estimated crustal parameters and show a comparable frequency dependence of both transport mean free path and intrinsic absorption path length. Both methods suggest that intrinsic attenuation is dominant over scattering attenuation in the W-Bohemia/Vogtland region for the investigated epicentral distance range and frequency bands from 3 to 24 Hz. Elastic simulations of seismogram envelopes suggest that forward scattering is required to explain the data, however, the degree of forward scattering is not resolvable. Errors in the parameter estimation are smaller in the elastic case compared to results from the acoustic simulations. The frequency decay of the transport mean free path suggests a random medium described by a nearly exponential autocorrelation function. The fluctuation strength and correlation length of the random medium cannot be estimated independently, but only a combination of the parameters related to the transport mean free path of the medium can be computed. Furthermore, our elastic simulations show, that using our numerical method, it is not possible to resolve the value of the mean free path of the random medium.
Computer algebra and operators
NASA Technical Reports Server (NTRS)
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
Automated Angular Momentum Recoupling Algebra
NASA Astrophysics Data System (ADS)
Williams, H. T.; Silbar, Richard R.
1992-04-01
We present a set of heuristic rules for algebraic solution of angular momentum recoupling problems. The general problem reduces to that of finding an optimal path from one binary tree (representing the angular momentum coupling scheme for the reduced matrix element) to another (representing the sub-integrals and spin sums to be done). The method lends itself to implementation on a microcomputer, and we have developed such an implementation using a dialect of LISP. We describe both how our code, called RACAH, works and how it appears to the user. We illustrate the use of RACAH for several transition and scattering amplitude matrix elements occurring in atomic, nuclear, and particle physics.
TWO-PHOTON EXCHANGE IN ELECTRON-PROTON ELASTIC SCATTERING: THEORY UPDATE
Andrei Afanasev
2007-05-21
Recent theoretical developments in the studies of two-photon exchange effects in elastic electron-proton scattering are reviewed. Two-photon exchange mechanism is considered a likely source of discrepancy between polarized and unpolarized experimental measurements of the proton electric form factor at momentum transfers of several GeV$^2$. This mechanism predicts measurable effects that are currently studied experimentally.
Modules as Learning Tools in Linear Algebra
ERIC Educational Resources Information Center
Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff; Loch, Sergio
2014-01-01
This paper reports on the experience of STEM and mathematics faculty at four different institutions working collaboratively to integrate learning theory with curriculum development in a core undergraduate linear algebra context. The faculty formed a Professional Learning Community (PLC) with a focus on learning theories in mathematics and…
Lie algebras and linear differential equations.
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Rahimi, A.
1972-01-01
Certain symmetry properties possessed by the solutions of linear differential equations are examined. For this purpose, some basic ideas from the theory of finite dimensional linear systems are used together with the work of Wei and Norman on the use of Lie algebraic methods in differential equation theory.
Superconformal algebras on the boundary of AdS3
NASA Astrophysics Data System (ADS)
Rasmussen, Jørgen
1999-07-01
Motivated by recent progress on the correspondence between string theory on nti-de Sitter space and conformal field theory, we provide an explicit construction of an infinite dimensional class of superconformal algebras on the boundary of AdS3. These space-time algebras are N extended superconformal algebras of the kind obtainable by hamiltonian reduction of affine SL(2|N/2) current superalgebras for N even, and are induced by the same current superalgebras residing on the world sheet. Thus, such an extended superconformal algebra is generated by N supercurrents and an SL(N/2) current algebra in addition to a U(1) current algebra. The results are obtained within the framework of free field realizations.
Algebraic independence properties related to certain infinite products
NASA Astrophysics Data System (ADS)
Tanaka, Taka-aki
2011-09-01
In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables.
Radiative transfer theory for inhomogeneous media with random extinction and scattering coefficients
NASA Technical Reports Server (NTRS)
Manning, Robert M.
1989-01-01
The small-angle scattering approximation of the scalar radiative transfer equation (RTE) is examined for the case where the extinction and scattering coefficients have a component that is a deterministic function of position along the propagation path and a component that is a random function of position transverse to the propagation direction. It is found that the resulting stochastic RTE can be reduced to a system of two stochastic integrodifferential equations for the average and fluctuating components of the radiant intensity. Two transfer equations are obtained describing the average radiant intensity and the spatial correlation function of the intensity fluctuations. The average intensity equation is then solved and applied to a simple propagation scenario. An approximate solution is also derived for the equation giving the correlation function. The developed equations can be applied to problems involving short wavelength electromagnetic wave propagation through media possessing the variable characteristics of turbulence and turbidity, such as plasmas, the atmosphere, and the ocean.
NASA Astrophysics Data System (ADS)
Onvlee, Jolijn; Vogels, Sjoerd N.; van der Avoird, Ad; Groenenboom, Gerrit C.; van de Meerakker, Sebastiaan Y. T.
2015-05-01
A Stark decelerator is used in combination with velocity map imaging to study collisions of NO radicals with rare gas atoms in a counterpropagating crossed beam geometry. This powerful combination of techniques results in scattering images with extremely high resolution, in which rotational and L-type rainbows with superimposed quantum mechanical diffraction oscillations are visible. The experimental data are in excellent agreement with quantum mechanical scattering calculations. Furthermore, hard-shell models and a partial wave analysis are used to clarify the origin of the various structures that are visible. A specific feature is found for NO molecules colliding with Ar atoms that is extremely sensitive to the precise shape of the potential energy surface. Its origin is explained in terms of interfering partial waves with very high angular momentum, corresponding to trajectories with large impact parameters.
NASA Technical Reports Server (NTRS)
Mitchell, D. G.; Roelof, E. C.
1976-01-01
A simplified analytical technique is presented for modeling the interplanetary scintillation of radio sources of finite angular size with a power-law electron-density-fluctuation power spectrum. The simplification results from the representation of the scintillation spectrum in confluent hypergeometric functions. The approximations presented allow fast numerical evaluation of a spectrum for a weakly scattering but extended medium with less than 10% error over the entire spectrum. Parameters describing anisotropic electron irregularities as well as anisotropic source structure are included, and the dependence of the spectrum normalization on the scales of the medium is derived explicitly. The parametric description of the domains of convergence of the approximate expansions also provides a simple conceptualization of the relative contributions of the scattered radiation along the line of sight to the observed spectrum. This is particularly useful for sources of finite angular size. This technique is applied to previously published observations.
Scattering theory for the radial H˙1/2-critical wave equation with a cubic convolution
NASA Astrophysics Data System (ADS)
Miao, Changxing; Zhang, Junyong; Zheng, Jiqiang
2015-12-01
In this paper, we study the global well-posedness and scattering for the wave equation with a cubic convolution ∂t2 u - Δu = ± (| x | - 3 *| u | 2) u in dimensions d ≥ 4. We prove that if the radial solution u with life-span I obeys (u, ut) ∈ Lt∞ (I ; H˙x 1 / 2 (Rd) × H˙x - 1 / 2 (Rd)), then u is global and scatters. By the strategy derived from concentration compactness, we show that the proof of the global well-posedness and scattering is reduced to disprove the existence of two scenarios: soliton-like solution and high to low frequency cascade. Making use of the No-waste Duhamel formula and double Duhamel trick, we deduce that these two scenarios enjoy the additional regularity by the bootstrap argument of [7]. This together with virial analysis implies the energy of such two scenarios is zero and so we get a contradiction.
A bond-order theory on the phonon scattering by vacancies in two-dimensional materials.
Xie, Guofeng; Shen, Yulu; Wei, Xiaolin; Yang, Liwen; Xiao, Huaping; Zhong, Jianxin; Zhang, Gang
2014-01-01
We theoretically investigate the phonon scattering by vacancies, including the impacts of missing mass and linkages (τ(V)(-1)) and the variation of the force constant of bonds associated with vacancies (τ(A)(-1)) by the bond-order-length-strength correlation mechanism. We find that in bulk crystals, the phonon scattering rate due to change of force constant τ(A)(-1) is about three orders of magnitude lower than that due to missing mass and linkages τ(V)(-1). In contrast to the negligible τ(A)(-1) in bulk materials, τ(A)(-1) in two-dimensional materials can be 3-10 folds larger than τ(V)(-1). Incorporating this phonon scattering mechanism to the Boltzmann transport equation derives that the thermal conductivity of vacancy defective graphene is severely reduced even for very low vacancy density. High-frequency phonon contribution to thermal conductivity reduces substantially. Our findings are helpful not only to understand the severe suppression of thermal conductivity by vacancies, but also to manipulate thermal conductivity in two-dimensional materials by phononic engineering.
Inverse scattering solutions by a sinc basis, multiple source, moment method--Part I: Theory.
Johnson, S A; Tracy, M L
1983-10-01
A new method for solving the inverse scattering problem for the scalar, inhomogeneous, exact, Helmholtz wave equation is presented. No perturbation approximations are used and the method is applicable even for many cases where weak to moderate attenuation and moderate to strong refraction of incident fields occur. The ill-posed nature of the inverse scattering problem for a single monochromatic source is known. However, the use of multiple sources, the collection of redundant (i.e., overdetermined) data, and the constraining of the fields and complex refractive index to be spatially band limited constitutes a new problem. The cases we have tested by computer simulation indicate that the new problem is well posed, a unique solution, and is stable with noisy data. The method is an application of the well-known method of moments with sinc basis and delta testing functions to discretize the problem. The inverse scattering solution may be obtained by solving the resulting set of simultaneous, quadratic, multivariate equations. Several algorithms for solving these equations are given. PMID:6686901
Supersymmetric extension of Galilean conformal algebras
Bagchi, Arjun; Mandal, Ipsita
2009-10-15
The Galilean conformal algebra has recently been realized in the study of the nonrelativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field theory. In this paper, we extend the analysis to include supersymmetry. We work at the level of the coordinates in superspace to construct the N=1 super-Galilean conformal algebra. One of the interesting outcomes of the analysis is that one is able to naturally extend the finite algebra to an infinite one. This looks structurally similar to the N=1 superconformal algebra in two dimensions, but is different. We also comment on the extension of our construction to cases of higher N.
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
NASA Astrophysics Data System (ADS)
Min, Wei
Chapters 2-7 focus on physical enzymology. Despite its long history, recent single-molecule spectroscopy, among many others techniques, has generated new quantitative data that reveal unobserved features of protein dynamics and enzyme catalysis at unprecedented levels. Much of these are beyond the classic framework of transition state theory and Michalis-Menten (MM) enzyme kinetics. Due to the complexity of the problem, theoretical developments in this area have much lagged behind experiments. After an initial experimental characterization on single-molecule protein conformational fluctuations, we then develop a dynamical rate theory for enzyme catalyzed chemical reactions, from a statistical mechanics approach. Towards this goal, we formulate a two-dimensional (2D) multi-surface free energy description of the entire catalytic process that explicitly combines the concept of "fluctuating enzymes" with the MM enzyme kinetics. The outcome of this framework has two folds. On the rate theory side, going much beyond transition state theory, it connects conformational fluctuations to catalysis, allows for the interplay between energetics (e.g. Haldane's stain energy) and dynamics (e.g. Koshland's induced fit), and predicts the time dependence of single-enzyme catalysis. On the enzyme kinetics side, it gives mechanistic and unified understanding of MM and non-MM (both positive and negative cooperativity) kinetics of monomeric enzymes, in term of non-equilibrium steady state cycle on the 2D free energy surface. Chapters 8-11 present the principle and application of a new ultra-sensitive nonlinear optical microspectroscopy, femtosecond (fs) triple-resonant coherent anti-Stokes Raman scattering (CARS), in which the amplitude and phase of input fs laser pulses are optimally shaped to be in triple resonant with the molecular electronic and vibrational transitions to generate a coherent nonlinear signal beam at a new color with a highest possible efficiency. This technique
EXPERIMENTAL STUDIES OF IBS (INTRA-BEAM SCATTERING) IN RHIC AND COMPARISON WITH THEORY.
FEDOTOV, A.V.; FISCHER, W.; TEPIKIAN, S.; WEI, J.
2006-05-29
A high-energy electron cooling system is presently being developed to overcome emittance growth due to Intra-beam Scattering (IBS) in RHIC. A critical item for choosing appropriate parameters of the cooler is an accurate description of the IBS. The analytic models were verified vs dedicated IBS measurements. Analysis of the 2004 data with the Au ions showed very good agreement for the longitudinal growth rates but significant disagreement with exact IBS models for the transverse growth rates. Experimental measurements were improved for the 2005 run with the Cu ions. Here, we present comparison of the 2005 data with theoretical models.
Franz Gross, Alfred Stadler
2010-09-01
We present the effective range expansions for the 1S0 and 3S1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with \\chi^2/N{data} \\simeq 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.
Connecting Algebra and Chemistry.
ERIC Educational Resources Information Center
O'Connor, Sean
2003-01-01
Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)
The kinematic algebra from the self-dual sector
NASA Astrophysics Data System (ADS)
Monteiro, Ricardo; O'Connell, Donal
2011-07-01
We identify a diffeomorphism Lie algebra in the self-dual sector of Yang-Mills theory, and show that it determines the kinematic numerators of tree-level MHV amplitudes in the full theory. These amplitudes can be computed off-shell from Feynman diagrams with only cubic vertices, which are dressed with the structure constants of both the Yang-Mills colour algebra and the diffeomorphism algebra. Therefore, the latter algebra is the dual of the colour algebra, in the sense suggested by the work of Bern, Carrasco and Johansson. We further study perturbative gravity, both in the self-dual and in the MHV sectors, finding that the kinematic numerators of the theory are the BCJ squares of the Yang-Mills numerators.
Edwards, D M
2016-03-01
Damping of magnetization dynamics in a ferromagnetic metal, arising from spin-orbit coupling, is usually characterised by the Gilbert parameter α. Recent calculations of this quantity, using a formula due to Kambersky, find that it is infinite for a perfect crystal owing to an intraband scattering term which is of third order in the spin-orbit parameter ξ. This surprising result conflicts with recent work by Costa and Muniz who study damping numerically by direct calculation of the dynamical transverse susceptibility in the presence of spin-orbit coupling. We resolve this inconsistency by following the approach of Costa and Muniz for a slightly simplified model where it is possible to calculate α analytically. We show that to second order in ξ one retrieves the Kambersky result for α, but to higher order one does not obtain any divergent intraband terms. The present work goes beyond that of Costa and Muniz by pointing out the necessity of including the effect of long-range Coulomb interaction in calculating damping for large ξ. A direct derivation of the Kambersky formula is given which shows clearly the restriction of its validity to second order in ξ so that no intraband scattering terms appear. This restriction has an important effect on the damping over a substantial range of impurity content and temperature. The experimental situation is discussed. PMID:26837050
Babikov, Dmitri; Semenov, Alexander
2016-01-28
A mixed quantum/classical approach to inelastic scattering (MQCT) is developed in which the relative motion of two collision partners is treated classically, and the rotational and vibrational motion of each molecule is treated quantum mechanically. The cases of molecule + atom and molecule + molecule are considered including diatomics, symmetric-top rotors, and asymmetric-top rotor molecules. Phase information is taken into consideration, permitting calculations of elastic and inelastic, total and differential cross sections for excitation and quenching. The method is numerically efficient and intrinsically parallel. The scaling law of MQCT is favorable, which enables calculations at high collision energies and for complicated molecules. Benchmark studies are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates that MQCT is a viable approach to inelastic scattering. At higher collision energies it can confidently replace the computationally expensive full-quantum calculations. At low collision energies and for low-mass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with full-quantum calculations at low energies. PMID:26618533
NASA Astrophysics Data System (ADS)
Edwards, D. M.
2016-03-01
Damping of magnetization dynamics in a ferromagnetic metal, arising from spin-orbit coupling, is usually characterised by the Gilbert parameter α. Recent calculations of this quantity, using a formula due to Kambersky, find that it is infinite for a perfect crystal owing to an intraband scattering term which is of third order in the spin-orbit parameter ξ. This surprising result conflicts with recent work by Costa and Muniz who study damping numerically by direct calculation of the dynamical transverse susceptibility in the presence of spin-orbit coupling. We resolve this inconsistency by following the approach of Costa and Muniz for a slightly simplified model where it is possible to calculate α analytically. We show that to second order in ξ one retrieves the Kambersky result for α, but to higher order one does not obtain any divergent intraband terms. The present work goes beyond that of Costa and Muniz by pointing out the necessity of including the effect of long-range Coulomb interaction in calculating damping for large ξ. A direct derivation of the Kambersky formula is given which shows clearly the restriction of its validity to second order in ξ so that no intraband scattering terms appear. This restriction has an important effect on the damping over a substantial range of impurity content and temperature. The experimental situation is discussed.
Babikov, Dmitri; Semenov, Alexander
2016-01-28
A mixed quantum/classical approach to inelastic scattering (MQCT) is developed in which the relative motion of two collision partners is treated classically, and the rotational and vibrational motion of each molecule is treated quantum mechanically. The cases of molecule + atom and molecule + molecule are considered including diatomics, symmetric-top rotors, and asymmetric-top rotor molecules. Phase information is taken into consideration, permitting calculations of elastic and inelastic, total and differential cross sections for excitation and quenching. The method is numerically efficient and intrinsically parallel. The scaling law of MQCT is favorable, which enables calculations at high collision energies and for complicated molecules. Benchmark studies are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates that MQCT is a viable approach to inelastic scattering. At higher collision energies it can confidently replace the computationally expensive full-quantum calculations. At low collision energies and for low-mass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with full-quantum calculations at low energies.
Linear Algebra Revisited: An Attempt to Understand Students' Conceptual Difficulties
ERIC Educational Resources Information Center
Britton, Sandra; Henderson, Jenny
2009-01-01
This article looks at some of the conceptual difficulties that students have in a linear algebra course. An overview of previous research in this area is given, and the various theories that have been espoused regarding the reasons that students find linear algebra so difficult are discussed. Student responses to two questions testing the ability…
Keyl, Michael; Schlingemann, Dirk-M.
2010-02-15
We present an approach to a noncommutativelike phase space which allows to analyze quasifree states on the algebra of canonical anti-commutation relations (CAR) in analogy to quasifree states on the algebra of canonical commutation relations (CCR). The used mathematical tools are based on a new algebraic structure the 'Grassmann algebra of canonical anticommutation relations' (GAR algebra) which is given by the twisted tensor product of a Grassmann and a CAR algebra. As a new application, the corresponding theory provides an elegant tool for calculating the fidelity of two quasifree fermionic states which is needed for the study of entanglement distillation within fermionic systems.
Theory of neutron scattering from superfluid 4He at finite temperatures
NASA Astrophysics Data System (ADS)
Talbot, E.; Griffin, A.
1984-03-01
The dynamic structure factor S(Q-->,ω) for a Bose-condensed system is calculated microscopically at temperatures where there are a significant number of thermally excited quasiparticles present. Our work is based on the one-loop diagrammatic approximation, which has been used by Wong and Gould to discuss the low-temperature limit. In our numerical calculations (for Q=0.35 and 0.8 Å-1) of proper, irreducible quantities, we use the Bogoliubov approximation for the coherence factors in conjunction with the experimentally determined quasiparticle spectrum. We find that at high temperatures, the collisionless phonon resonance exhibited by S(Q-->,ω) has a width which increases with the number of thermally excited rotons, in rough agreement with the neutron scattering data of Cowley and Woods as well as those of Woods and Svensson. Our results are compared with those based on a phenomenological treatment of the phonon-roton coupling.
Gross, Franz; Stadler, Alfred
2010-09-15
We present the effective range expansions for the {sup 1}S{sub 0} and {sup 3}S{sub 1} scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with {chi}{sup 2}/N{sub data{approx_equal}}1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.
NASA Astrophysics Data System (ADS)
Ferrando, A.; García-March, M. A.
2016-06-01
We present a novel procedure for solving the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use scattering modes, which are solutions to the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore allow the problem to be solved. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role to Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations needed to determine these polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in it. We show that the solution permits one to obtain analytical expressions. These can used to obtain mathematical expressions for meaningful quantities, such as the distance at which the positive and negative singularities merge, closing the loop of a vortex line. Furthermore, we present an example of the calculation of an specific discrete-Gauss state, which is the solution of the diffraction of a Laguerre-Gauss state showing definite angular momentum (that is, a highly charged vortex) by a thin diffractive element showing certain discrete symmetry. We show that this problem is therefore solved in a much simpler way than by using the previous procedure based on the integral Fresnel diffraction method.
KRETZER,S.VOGELSANG,W.
2003-09-15
In the past two runs of RHIC, the first measurements with polarized proton beams have been performed. For many years to come, the RHIC spin program will offer exciting physics, exploring QCD and the nucleon in new ways. The aim of this small workshop was to attract several spin theorists to the center for about two weeks, in order to collaborate with both experimentalists and theorists at RBRC, and to initiate and/or complete studies of relevance to RHIC spin. A major focus of polarized-pp measurements at RHIC is on measuring the spin-dependent gluon density, {Delta}g. A channel for accessing {Delta}g is high-p{sub T} pion production. The unpolarized cross section for this reaction has been measured by PHENIX and was found in good agreement with a perturbative-QCD based (NLO) calculation. It was a remarkable and exciting coincidence that PHENIX presented also the first results for the spin asymmetry for {rvec p}{rvec p} {yields} {pi}{sup 0}X during this workshop. This sparked a lot of additional activity and discussion. First steps toward the interpretation of the data were taken. Marco Stratmann and Barbara Jager (Regensburg University) presented recent work on the NLO calculation of the polarized cross section and the spin asymmetry, setting the stage for future full analysis of the data in terms of {Delta}g. Applications to {rvec e}{rvec p} scattering, very relevant to eRHIC, were also worked out and published during this workshop. Stratmann also discussed the procedure of NLO calculations for the case of transverse polarization in pp scattering.
Operator product expansion algebra
Holland, Jan; Hollands, Stefan
2013-07-15
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE,
An algebra of discrete event processes
NASA Technical Reports Server (NTRS)
Heymann, Michael; Meyer, George
1991-01-01
This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.
Chen, Ye; Liu, Jonathan T C
2013-06-01
Dual-axis confocal (DAC) microscopy has been found to exhibit superior rejection of out-of-focus and multiply scattered background light compared to conventional single-axis confocal microscopy. DAC microscopes rely on the use of separated illumination and collection beam paths that focus and intersect at a single focal volume (voxel) within tissue. While it is generally recognized that the resolution and contrast of a DAC microscope depends on both the crossing angle of the DAC beams, 2θ, and the focusing numerical aperture of the individual beams, α, a detailed study to investigate these dependencies has not been performed. Contrast and resolution are considered as two main criteria to assess the performance of a point-scanned DAC microscope (DAC-PS) and a line-scanned DAC microscope (DAC-LS) as a function of θ and α. The contrast and resolution of these designs are evaluated by Monte-Carlo scattering simulations and diffraction theory calculations, respectively. These results can be used for guiding the optimal designs of DAC-PS and DAC-LS microscopes.
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
ERIC Educational Resources Information Center
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…
Algebraic Reasoning through Patterns
ERIC Educational Resources Information Center
Rivera, F. D.; Becker, Joanne Rossi
2009-01-01
This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…
ERIC Educational Resources Information Center
Merlin, Ethan M.
2013-01-01
This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…
NASA Astrophysics Data System (ADS)
Baireuther, P.; Hutasoit, J. A.; Tworzydło, J.; Beenakker, C. W. J.
2016-04-01
We formulate a linear response theory of the chiral magnetic effect in a finite Weyl semimetal, expressing the electrical current density j induced by a slowly oscillating magnetic field B or chiral chemical potential μ in terms of the scattering matrix of Weyl fermions at the Fermi level. Surface conduction can be neglected in the infinite-system limit for δ j/δ μ , but not for δ j/δ B: the chirally circulating surface Fermi arcs give a comparable contribution to the bulk Weyl cones no matter how large the system is, because their smaller number is compensated by an increased flux sensitivity. The Fermi arc contribution to {μ }-1δ j/δ B has the universal value {(e/h)}2, protected by chirality against impurity scattering—unlike the bulk contribution of opposite sign.
Zhang, X.-G.; Rous, P.J.; Van Hove, M.A. ); MacLaren, J.M. ); Gonis, A. ); Somorjai, G.A. California Univ., Berkeley, CA . Dept. of Chemistry)
1990-07-25
We use a newly developed real-space multiple scattering theory (RS-MST) to calculate low-energy electron diffraction (LEED) intensities from stepped surfaces. In this calculation the electron wavefunctions are expanded in terms of an angular momentum basis, utilizing the property of removal invariance of systems with semi-infinite periodicity. This strongly reduces the dependence of the calculation on the interlayer spacing and thus opens up the possibility of treating more open surfaces. This includes in particular stepped surfaces, to which conventional methods cannot be applied. Applications of the formalism to various stepped surfaces are presented. In particular, the results for Cu(311) and (331) surfaces obtained from both the layer doubling and RS-MST methods are compared. In addition, numerical techniques which can improve the convergence as well as the speed of the RS-MST approach are discussed. 6 refs., 3 figs.
NASA Astrophysics Data System (ADS)
Hagelberg, Frank
2004-03-01
In this contribution, we address the problem how to determine accurately the nonadiabatic content of any given dynamic process involving molecular motion. More specifically, we generate a dynamic electronic wave function using Electron Nuclear Dynamics (END) theory^2 and cast this wave function into the language of electronic excitations. This is achieved by adiabatic transport of an electronic basis along the classical nuclear trajectories of the studied molecular system. This basis is chosen as the static UHF molecular ground state determinant of the system in conjunction with all determinants that arise from the ground state by single, double and triple substitutions. Projecting the dynamic wave function into this basis, we arrive at a natural distinction between adiabatic and nonadiabatic components of the motion considered. We will discuss this concept by the examples of various scattering problems, among them the interaction of proton projectiles with methylene targets. ^2E. Deumens et al., Rev. Mod. Phys. 1994, 66, 917.
Extended conformal field theories
NASA Astrophysics Data System (ADS)
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
Special issue on cluster algebras in mathematical physics
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2013-11-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March
Special issue on cluster algebras in mathematical physics
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2014-02-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March
Special issue on cluster algebras in mathematical physics
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2013-10-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March
Special issue on cluster algebras in mathematical physics
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2013-12-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March
Hybrid Theory of P-Wave Electron-Hydrogen Elastic Scattering
NASA Technical Reports Server (NTRS)
Bhatia, Anand
2012-01-01
We report on a study of electron-hydrogen scattering, using a combination of a modified method of polarized orbitals and the optical potential formalism. The calculation is restricted to P waves in the elastic region, where the correlation functions are of Hylleraas type. It is found that the phase shifts are not significantly affected by the modification of the target function by a method similar to the method of polarized orbitals and they are close to the phase shifts calculated earlier by Bhatia. This indicates that the correlation function is general enough to include the target distortion (polarization) in the presence of the incident electron. The important fact is that in the present calculation, to obtain similar results only 35-term correlation function is needed in the wave function compared to the 220-term wave function required in the above-mentioned previous calculation. Results for the phase shifts, obtained in the present hybrid formalism, are rigorous lower bounds to the exact phase shifts.
Rotationally inelastic scattering of OH by molecular hydrogen: Theory and experiment
Schewe, H. Christian Meijer, Gerard; Ma, Qianli; Dagdigian, Paul J.; Vanhaecke, Nicolas; Wang, Xingan; Kłos, Jacek; Alexander, Millard H.; Meerakker, Sebastiaan Y. T. van de; Avoird, Ad van der
2015-05-28
We present an experimental and theoretical investigation of rotationally inelastic transitions of OH, prepared in the X{sup 2}Π, v = 0, j = 3/2 F{sub 1}f level, in collisions with molecular hydrogen (H{sub 2} and D{sub 2}). In a crossed beam experiment, the OH radicals were state selected and velocity tuned over the collision energy range 75–155 cm{sup −1} using a Stark decelerator. Relative parity-resolved state-to-state integral cross sections were determined for collisions with normal and para converted H{sub 2}. These cross sections, as well as previous OH–H{sub 2} measurements at 595 cm{sup −1} collision energy by Schreel and ter Meulen [J. Chem. Phys. 105, 4522 (1996)], and OH–D{sub 2} measurements for collision energies 100–500 cm{sup −1} by Kirste et al. [Phys. Rev. A 82, 042717 (2010)], were compared with the results of quantum scattering calculations using recently determined ab initio potential energy surfaces [Ma et al., J. Chem. Phys. 141, 174309 (2014)]. Good agreement between the experimental and computed relative cross sections was found, although some structure seen in the OH(j = 3/2 F{sub 1}f → j = 5/2 F{sub 1}e) + H{sub 2}(j = 0) cross section is not understood.
Rotationally inelastic scattering of OH by molecular hydrogen: Theory and experiment
NASA Astrophysics Data System (ADS)
Schewe, H. Christian; Ma, Qianli; Vanhaecke, Nicolas; Wang, Xingan; Kłos, Jacek; Alexander, Millard H.; van de Meerakker, Sebastiaan Y. T.; Meijer, Gerard; van der Avoird, Ad; Dagdigian, Paul J.
2015-05-01
We present an experimental and theoretical investigation of rotationally inelastic transitions of OH, prepared in the X2Π, v = 0, j = 3/2 F1f level, in collisions with molecular hydrogen (H2 and D2). In a crossed beam experiment, the OH radicals were state selected and velocity tuned over the collision energy range 75-155 cm-1 using a Stark decelerator. Relative parity-resolved state-to-state integral cross sections were determined for collisions with normal and para converted H2. These cross sections, as well as previous OH-H2 measurements at 595 cm-1 collision energy by Schreel and ter Meulen [J. Chem. Phys. 105, 4522 (1996)], and OH-D2 measurements for collision energies 100-500 cm-1 by Kirste et al. [Phys. Rev. A 82, 042717 (2010)], were compared with the results of quantum scattering calculations using recently determined ab initio potential energy surfaces [Ma et al., J. Chem. Phys. 141, 174309 (2014)]. Good agreement between the experimental and computed relative cross sections was found, although some structure seen in the OH(j = 3/2 F1f → j = 5/2 F1e) + H2(j = 0) cross section is not understood.
Rotationally inelastic scattering of OH by molecular hydrogen: Theory and experiment.
Schewe, H Christian; Ma, Qianli; Vanhaecke, Nicolas; Wang, Xingan; Kłos, Jacek; Alexander, Millard H; van de Meerakker, Sebastiaan Y T; Meijer, Gerard; van der Avoird, Ad; Dagdigian, Paul J
2015-05-28
We present an experimental and theoretical investigation of rotationally inelastic transitions of OH, prepared in the X(2)Π, v = 0, j = 3/2 F1f level, in collisions with molecular hydrogen (H2 and D2). In a crossed beam experiment, the OH radicals were state selected and velocity tuned over the collision energy range 75-155 cm(-1) using a Stark decelerator. Relative parity-resolved state-to-state integral cross sections were determined for collisions with normal and para converted H2. These cross sections, as well as previous OH-H2 measurements at 595 cm(-1) collision energy by Schreel and ter Meulen [J. Chem. Phys. 105, 4522 (1996)], and OH-D2 measurements for collision energies 100-500 cm(-1) by Kirste et al. [Phys. Rev. A 82, 042717 (2010)], were compared with the results of quantum scattering calculations using recently determined ab initio potential energy surfaces [Ma et al., J. Chem. Phys. 141, 174309 (2014)]. Good agreement between the experimental and computed relative cross sections was found, although some structure seen in the OH(j = 3/2 F1f → j = 5/2 F1e) + H2(j = 0) cross section is not understood. PMID:26026450
Covariant Spectator Theory of np scattering: Deuteron magnetic moment and form factors
Gross, Franz L.
2014-06-01
The deuteron magnetic moment is calculated using two model wave functions obtained from 2007 high precision fits to $np$ scattering data. Included in the calculation are a new class of isoscalar $np$ interaction currents which are automatically generated by the nuclear force model used in these fits. After normalizing the wave functions, nearly identical predictions are obtained: model WJC-1, with larger relativistic P-state components, gives 0.863(2), while model WJC-2 with very small $P$-state components gives 0.864(2) These are about 1\\% larger than the measured value of the moment, 0.857 n.m., giving a new prediction for the size of the $\\rho\\pi\\gamma$ exchange, and other purely transverse interaction currents that are largely unconstrained by the nuclear dynamics. The physical significance of these results is discussed, and general formulae for the deuteron form factors, expressed in terms of deuteron wave functions and a new class of interaction current wave functions, are given.
Theory of light scattering at nanoparticles and optical forces between small particles
NASA Astrophysics Data System (ADS)
Saenz, Juan Jose
Appropriate combinations of laser beams can be used to trap and manipulate small particles with ``optical tweezers'' as well as to induce significant ``optical binding'' forces between particles. Here we review some basic concepts related to the optical forces on small (subwavelength) particles, focusing on the interplay between scattering asymmetry and momentum transfer. These forces are, in general, non-conservative (curl forces) which lead to a number of intriguing predictions regarding the dynamics of nanoparticles. Optical forces between small particles are usually strongly anisotropic depending on the interference landscape of the external fields. This is in contrast with the familiar isotropic van der Waals and, in general, Casimir-Lifshitz interactions between neutral bodies arising from random electromagnetic waves generated by equilibrium quantum and thermal fluctuations. As we will see, artificially created random fluctuating light fields can be used to induce and control dispersion forces between small colloidal particles. Interestingly, for relatively high refractive index semiconductor nanoparticles, the interactions can be tuned from attractive to strongly repulsive when the frequency of the external fluctuating field is tuned near the first magnetic Mie-resonance. Interactions induced by randomly fluctuating light fields open a path towards the control of translational invariant interactions with tuneable strength and range in colloidal systems.
Rotational-vibrational coupling in the theory of electron-molecule scattering
NASA Technical Reports Server (NTRS)
Temkin, A.; Sullivan, E. C.
1974-01-01
The adiabatic-nuclei approximation of vibrational-rotational excitation of homonuclear diatomic molecules can be simply augmented to describe the vibrational-rotational coupling by including the dependence of the vibrational wave function on j. Appropriate formulas are given, and the theory, is applied to e-H2 excitation, whereby it is shown that deviations from the simple Born-Oppenheimer approximation measured by Wong and Schultz can be explained. More important, it can be seen that the inclusion of the j-dependent centrifugal term is essential for transitions involving high-rotational quantum numbers.
Basic and heavy ion scattering in time dependent Hartree-Fock Theory
Weiss, M.S.
1984-05-17
Time Dependent Hartree-Fock theory, TDHF, is the most sophisticated, microscopic approach to nuclear dynamics yet practiced. Although it is far from a description of nature it does allow us to examine multiply interactive many-body systems semi quantum mechanically and to visualize otherwise covert processes. Some of the properties of the TDHF equations are stated leaving the interested reader to one of several excellent review articles for the derivations. Some of the applications to the collision of heavy ions are briefly described. (WHK)
A Linear Algebra Measure of Cluster Quality.
ERIC Educational Resources Information Center
Mather, Laura A.
2000-01-01
Discussion of models for information retrieval focuses on an application of linear algebra to text clustering, namely, a metric for measuring cluster quality based on the theory that cluster quality is proportional to the number of terms that are disjoint across the clusters. Explains term-document matrices and clustering algorithms. (Author/LRW)
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-01
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Using Group Explorer in Teaching Abstract Algebra
ERIC Educational Resources Information Center
Schubert, Claus; Gfeller, Mary; Donohue, Christopher
2013-01-01
This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in…
Leibniz algebras associated with representations of filiform Lie algebras
NASA Astrophysics Data System (ADS)
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
NASA Astrophysics Data System (ADS)
Fujii, Masafumi
2014-03-01
It is shown that Mie's solution to Maxwell's equations no longer holds for the analysis of resonance of a plasmonic metal nanosphere. The conventional Mie's solution is based on the spherical Bessel and the spherical Hankel functions of an outgoing wave, whereas the permittivity of metals of a negative real part leads to a phase velocity that directs inward to the sphere, which is opposite from the direction of the energy flow as often discussed for negative-index metamaterials. This is a fundamental problem overlooked for a long time; a correction can be found from the viewpoint of a time-reversal problem involving negative permittivity media. The continuity of the field solution at the sphere surface is shown to be corrected by replacing the spherical Hankel function of an outgoing wave with that of an incoming wave, i.e., by adopting the complex conjugate of the conventional solutions. The corrected theory has been verified by the analyses of various metal nanospheres. In addition, the derivation of the scattering cross sections based on the corrected theory has elucidated that the conservation law of energy holds and that, more importantly, the conventional Mie's solution gives the same amplitude of the cross sections when they are obtained for real, not complex, frequency.
Valier-Brasier, Tony; Conoir, Jean-Marc; Coulouvrat, François; Thomas, Jean-Louis
2015-10-01
Sound propagation in dilute suspensions of small spheres is studied using two models: a hydrodynamic model based on the coupled phase equations and an acoustic model based on the ECAH (ECAH: Epstein-Carhart-Allegra-Hawley) multiple scattering theory. The aim is to compare both models through the study of three fundamental kinds of particles: rigid particles, elastic spheres, and viscous droplets. The hydrodynamic model is based on a Rayleigh-Plesset-like equation generalized to elastic spheres and viscous droplets. The hydrodynamic forces for elastic spheres are introduced by analogy with those of droplets. The ECAH theory is also modified in order to take into account the velocity of rigid particles. Analytical calculations performed for long wavelength, low dilution, and weak absorption in the ambient fluid show that both models are strictly equivalent for the three kinds of particles studied. The analytical calculations show that dilatational and translational mechanisms are modeled in the same way by both models. The effective parameters of dilute suspensions are also calculated. PMID:26520342
NASA Technical Reports Server (NTRS)
Tsang, L.; Newton, R. W.; Kong, J. A.
1982-01-01
The strong fluctuation random medium theory is applied to calculate scattering from a half-space of dielectric mixture. The first and second moments of the fields are calculated, respectively, by using the bilocal and the distorted Born approximations, and the low frequency limit is taken. The singularity of the dyadic Green's function is taken into account. Expressions for the effective permittivity for the full space case are derived. It is shown that the derived result of the effect permittivity is identical to that of the Polder and van Santern mixing formula. The correlation function of the random medium is obtained by using simple physical arguments and is expressed in terms of the fractional volumes and particle sizes of the constituents of the mixture. Backscattering coefficients of a half-space dielectric mixture are also calculated. Numerical results of the effective permittivity and backscattering coefficients are illustrated using typical parameters encountered in microwave remote sensing of dry and wet snow. It is also shown that experimental data can be matched with the theory by using physical parameters of the medium as obtained from ground truth measurements.
NASA Astrophysics Data System (ADS)
Mondescu, Radu Paul
1999-08-01
In this dissertation we report new theoretical results-both analytical and numerical-concerning a variety of polymeric systems. Applying path-integral and differentiable manifolds techniques, we have obtained original results concerning the statistics of a Gaussian polymer embedded on a sphere, a cylinder, a cone and a torus. Generally, we found that the curvature of the surfaces induces a geometrical localization area. Next we employ field theoretical (instanton calculus) and differential equations techniques (Darboux method) to obtain approximate and exact new results regarding the average size and the Green function of a Gaussian, one- dimensional polymer chain subjected to a multi-stable potential (the tunnel effect in polymer physics). Extending the multiple scattering formalism, we have investigated the steady-state dynamics of suspensions of spheres and Gaussian polymer chains without excluded volume interactions. We have calculated the self- diffusion and friction coefficients for probe objects (sphere and polymer chain) and the shear viscosity of the suspensions. At certain values of the concentration of the ambient medium, motion of probe objects freezes. Deviation from the Stokes-Einstein behavior is observed and interpreted. Next, we have calculated the diffusion coefficient and the change in the viscosity of a dilute solution of freely translating and rotating diblock, Gaussian copolymers. Regimes that lead to increasing the efficiency of separation processes have been identified. The parallel between Navier-Stokes and Lamé equations was exploited to extend the effective medium formalism to the computation of the effective shear and Young moduli and the Poisson ratio of a composite material containing rigid, monodispersed, penetrable spheres. Our approach deals efficiently with the high concentration regime of inclusions.
The algebra of diffeomorphisms from the world sheet
NASA Astrophysics Data System (ADS)
Schulgin, Waldemar; Troost, Jan
2014-09-01
The quantum theory of a massless spin two particle is strongly constrained by diffeomorphism invariance, which is in turn implied by unitarity. We explicitly exhibit the space-time diffeomorphism algebra of string theory, realizing it in terms of world sheet vertex operators. Viewing diffeomorphisms as field redefinitions in the two-dimensional conformal field theory renders the calculation of their algebra straightforward. Next, we generalize the analysis to combinations of space-time anti-symmetric tensor gauge transformations and diffeomorphisms. We also point out a left-right split of the algebra combined with a twist that reproduces the C-bracket of double field theory. We further compare our derivation to an analysis in terms of marginal deformations as well as vertex operator algebras.
Confluences of the Painlevé equations, Cherednik algebras and q-Askey scheme
NASA Astrophysics Data System (ADS)
Mazzocco, Marta
2016-09-01
In this paper we produce seven new algebras as confluences of the Cherednik algebra of type \\check {{{{C}1}}} {{C}1} and we characterise their spherical-sub-algebras. The limit of the spherical sub-algebra of the Cherednik algebra of type \\check {{{{C}1}}} {{C}1} is the monodromy manifold of the Painlevé VI equation (Oblomkov 2004 Int. Math. Res. Not. 2004 877–912). Here we prove that by considering the limits of the spherical sub-algebras of our new confluent algebras, one obtains the monodromy manifolds of all other Painlevé differential equations. Moreover, we introduce confluent versions of the Zhedanov algebra and prove that each of them (quotiented by their Casimir) is isomorphic to the corresponding spherical sub-algebra of our new confluent Cherednik algebras. We show that in the basic representation our confluent Zhedanov algebras act as symmetries of certain elements of the q-Askey scheme, thus setting a stepping stone towards the solution of the open problem of finding the corresponding quantum algebra for each element of the q-Askey scheme. These results establish a new link between the theory of the Painlevé equations and the theory of the q-Askey scheme making a step towards the construction of a representation theoretic approach for the Painlevé theory.
Confluences of the Painlevé equations, Cherednik algebras and q-Askey scheme
NASA Astrophysics Data System (ADS)
Mazzocco, Marta
2016-09-01
In this paper we produce seven new algebras as confluences of the Cherednik algebra of type \\check {{{{C}1}}} {{C}1} and we characterise their spherical-sub-algebras. The limit of the spherical sub-algebra of the Cherednik algebra of type \\check {{{{C}1}}} {{C}1} is the monodromy manifold of the Painlevé VI equation (Oblomkov 2004 Int. Math. Res. Not. 2004 877-912). Here we prove that by considering the limits of the spherical sub-algebras of our new confluent algebras, one obtains the monodromy manifolds of all other Painlevé differential equations. Moreover, we introduce confluent versions of the Zhedanov algebra and prove that each of them (quotiented by their Casimir) is isomorphic to the corresponding spherical sub-algebra of our new confluent Cherednik algebras. We show that in the basic representation our confluent Zhedanov algebras act as symmetries of certain elements of the q-Askey scheme, thus setting a stepping stone towards the solution of the open problem of finding the corresponding quantum algebra for each element of the q-Askey scheme. These results establish a new link between the theory of the Painlevé equations and the theory of the q-Askey scheme making a step towards the construction of a representation theoretic approach for the Painlevé theory.
NASA Astrophysics Data System (ADS)
Smirnov, Andrey
2010-08-01
New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl( N;?)-case is discussed.
NASA Astrophysics Data System (ADS)
Smirnov, Andrey
2010-08-01
New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.
Egorov, Alexander A
2004-08-31
The vector theory of laser radiation scattering in an integrated optical waveguide with three-dimensional irregularities in the presence of noise is developed. The solution of the electrodynamic problem of laser radiation scattering in an irregular waveguide is obtained by the mode coupling technique using the perturbation theory. An approximate solution of the inhomogeneous three-dimensional wave equation is obtained by the method of Green's functions. The analytic formulas are derived for the radiation fields of propagating and evanescent modes. A physical interpretation is given for the obtained results. The role of noise as an independent depolarising factor (in addition to the classical one) during scattering of light is pointed out. (integrated optical waveguides and devices)
BPS preons and the AdS-M-algebra
NASA Astrophysics Data System (ADS)
Bandos, Igor A.; de Azcárraga, José A.
2008-04-01
We present here the AdS generalization of BPS preons, which were introduced as the hypothetical constituents of M-theory preserving all but one supersymmetries. Our construction, suggested by the relation of `lower dimensional preons' with higher spin theories, can be considered as a deformation of the M-algebraic description of the single supersymmetry broken by a preon, and provides another reason to identify the AdS generalization of the M-algebra, which we call the AdS-M-algebra, with osp(1|32).
Shapes and stability of algebraic nuclear models
NASA Technical Reports Server (NTRS)
Lopez-Moreno, Enrique; Castanos, Octavio
1995-01-01
A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.
PREFACE: Infinite Dimensional Algebras and their Applications to Quantum Integrable Systems
NASA Astrophysics Data System (ADS)
Fring, Andreas; Kulish, Petr P.; Manojlović, Nenad; Nagy, Zoltán; Nunes da Costa, Joana; Samtleben, Henning
2008-05-01
This special issue is centred around the workshop Infinite Dimensional Algebras and Quantum Integrable Systems II—IDAQUIS 2007, held at the University of Algarve, Faro, Portugal in July 2007. It was the second workshop in the IDAQUIS series following a previous meeting at the same location in 2003. The latest workshop gathered around forty experts in the field reviewing recent developments in the theory and applications of integrable systems in the form of invited lectures and in a number of contributions from the participants. All contributions contain significant new results or provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants are also included. The origins of the topic of this issue can be traced back a long way to the early investigations of completely integrable systems of classical mechanics in the fundamental papers by Euler, Lagrange, Jacobi, Liouville, Kowalevski and others. By the end of the nineteenth century all interesting examples seemed to have been exhausted. A revival in the study of integrable systems began with the development of the classical inverse scattering method, or the theory of solitons. Later developments led to the basic geometrical ideas of the theory, of which infinite dimensional algebras are a key ingredient. In a loose sense one may think that all integrable systems possess some hidden symmetry. In the quantum version of these systems the representation theory of these algebras may be exploited in the description of the structure of the Hilbert space of states. Modern examples of field theoretical systems such as conformal field theories, with the Liouville model being a prominent example, affine Toda field theories and the AdS/CFT correspondence are based on algebraic structures like quantum groups, modular doubles, global conformal invariance, Hecke algebras, Kac
Algebraic integrability: a survey.
Vanhaecke, Pol
2008-03-28
We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
Aprepro - Algebraic Preprocessor
2005-08-01
Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.
The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory
NASA Astrophysics Data System (ADS)
Litsey, Sean Christopher
We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog
On Fusion Algebras and Modular Matrices
NASA Astrophysics Data System (ADS)
Gannon, T.; Walton, M. A.
We consider the fusion algebras arising in e.g. Wess-Zumino-Witten conformal field theories, affine Kac-Moody algebras at positive integer level, and quantum groups at roots of unity. Using properties of the modular matrix S, we find small sets of primary fields (equivalently, sets of highest weights) which can be identified with the variables of a polynomial realization of the Ar fusion algebra at level k. We prove that for many choices of rank r and level k, the number of these variables is the minimum possible, and we conjecture that it is in fact minimal for most r and k. We also find new, systematic sources of zeros in the modular matrix S. In addition, we obtain a formula relating the entries of S at fixed points, to entries of S at smaller ranks and levels. Finally, we identify the number fields generated over the rationals by the entries of S, and by the fusion (Verlinde) eigenvalues.
NASA Astrophysics Data System (ADS)
Hiley, B. J.
In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.
A process algebra model of QED
NASA Astrophysics Data System (ADS)
Sulis, William
2016-03-01
The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics.
Gobrecht, Alexia; Bendoula, Ryad; Roger, Jean-Michel; Bellon-Maurel, Véronique
2015-01-01
Visible and Near Infrared (Vis-NIR) Spectroscopy is a powerful non destructive analytical method used to analyze major compounds in bulk materials and products and requiring no sample preparation. It is widely used in routine analysis and also in-line in industries, in-vivo with biomedical applications or in-field for agricultural and environmental applications. However, highly scattering samples subvert Beer-Lambert law's linear relationship between spectral absorbance and the concentrations. Instead of spectral pre-processing, which is commonly used by Vis-NIR spectroscopists to mitigate the scattering effect, we put forward an optical method, based on Polarized Light Spectroscopy to improve the absorbance signal measurement on highly scattering samples. This method selects part of the signal which is less impacted by scattering. The resulted signal is combined in the Absorption/Remission function defined in Dahm's Representative Layer Theory to compute an absorbance signal fulfilling Beer-Lambert's law, i.e. being linearly related to concentration of the chemicals composing the sample. The underpinning theories have been experimentally evaluated on scattering samples in liquid form and in powdered form. The method produced more accurate spectra and the Pearson's coefficient assessing the linearity between the absorbance spectra and the concentration of the added dye improved from 0.94 to 0.99 for liquid samples and 0.84-0.97 for powdered samples. PMID:25467494
Gobrecht, Alexia; Bendoula, Ryad; Roger, Jean-Michel; Bellon-Maurel, Véronique
2015-01-01
Visible and Near Infrared (Vis-NIR) Spectroscopy is a powerful non destructive analytical method used to analyze major compounds in bulk materials and products and requiring no sample preparation. It is widely used in routine analysis and also in-line in industries, in-vivo with biomedical applications or in-field for agricultural and environmental applications. However, highly scattering samples subvert Beer-Lambert law's linear relationship between spectral absorbance and the concentrations. Instead of spectral pre-processing, which is commonly used by Vis-NIR spectroscopists to mitigate the scattering effect, we put forward an optical method, based on Polarized Light Spectroscopy to improve the absorbance signal measurement on highly scattering samples. This method selects part of the signal which is less impacted by scattering. The resulted signal is combined in the Absorption/Remission function defined in Dahm's Representative Layer Theory to compute an absorbance signal fulfilling Beer-Lambert's law, i.e. being linearly related to concentration of the chemicals composing the sample. The underpinning theories have been experimentally evaluated on scattering samples in liquid form and in powdered form. The method produced more accurate spectra and the Pearson's coefficient assessing the linearity between the absorbance spectra and the concentration of the added dye improved from 0.94 to 0.99 for liquid samples and 0.84-0.97 for powdered samples.
Open-closed homotopy algebra in mathematical physics
Kajiura, Hiroshige; Stasheff, Jim
2006-02-15
In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A{sub {infinity}} algebras) by closed strings (L{sub {infinity}} algebras)
Local Algebras of Differential Operators
NASA Astrophysics Data System (ADS)
Church, P. T.; Timourian, J. G.
2002-05-01
There is an increasing literature devoted to the study of boundary value problems using singularity theory. The resulting differential operators are typically Fredholm with index 0, defined on infinite-dimensional spaces, and they have often led to folds, cusps, and even higher-order Morin singularities. In this paper we develop some of the local algebras of germs of such differential Fredholm operators, extending the theory of the finite-dimensional case. We apply this work to nonlinear elliptic boundary value problems: in particular, we make further progress on a question proposed and initially studied by Ruf [1999, J. Differential Equations 151, 111-133]. We also make comments on several problems raised by others.
Locally Compact Quantum Groups. A von Neumann Algebra Approach
NASA Astrophysics Data System (ADS)
Van Daele, Alfons
2014-08-01
In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We start with a von Neumann algebra and a comultiplication on this von Neumann algebra. We assume that there exist faithful left and right Haar weights. Then we develop the theory within this von Neumann algebra setting. In [Math. Scand. 92 (2003), 68-92] locally compact quantum groups are also studied in the von Neumann algebraic context. This approach is independent of the original C^*-algebraic approach in the sense that the earlier results are not used. However, this paper is not really independent because for many proofs, the reader is referred to the original paper where the C^*-version is developed. In this paper, we give a completely self-contained approach. Moreover, at various points, we do things differently. We have a different treatment of the antipode. It is similar to the original treatment in [Ann. Sci. & #201;cole Norm. Sup. (4) 33 (2000), 837-934]. But together with the fact that we work in the von Neumann algebra framework, it allows us to use an idea from [Rev. Roumaine Math. Pures Appl. 21 (1976), 1411-1449] to obtain the uniqueness of the Haar weights in an early stage. We take advantage of this fact when deriving the other main results in the theory. We also give a slightly different approach to duality. Finally, we collect, in a systematic way, several important formulas. In an appendix, we indicate very briefly how the C^*-approach and the von Neumann algebra approach eventually yield the same objects. The passage from the von Neumann algebra setting to the C^*-algebra setting is more or less standard. For the other direction, we use a new method. It is based on the observation that the Haar weights on the C^*-algebra extend to weights on the double dual with central support and that all these supports are the same. Of course, we get the von Neumann algebra by cutting down the double dual with this unique
On vertex algebra representations of the Schrödinger-Virasoro Lie algebra
NASA Astrophysics Data System (ADS)
Unterberger, Jérémie
2009-12-01
The Schrödinger-Virasoro Lie algebra sv is an extension of the Virasoro Lie algebra by a nilpotent Lie algebra formed with a bosonic current of weight 3/2 and a bosonic current of weight 1. It is also a natural infinite-dimensional extension of the Schrödinger Lie algebra, which — leaving aside the invariance under time-translation — has been proved to be a symmetry algebra for many statistical physics models undergoing a dynamics with dynamical exponent z=2. We define in this article general Schrödinger-Virasoro primary fields by analogy with conformal field theory, characterized by a 'spin' index and a (non-relativistic) mass, and construct vertex algebra representations of sv out of a charged symplectic boson and a free boson and its associated vertex operators. We also compute two- and three-point functions of still conjectural massive fields that are defined by an analytic continuation with respect to a formal parameter.
NASA Astrophysics Data System (ADS)
Osmaston, Miles F.
My development of Continuum Theory rests importantly on two mathematical treatments and calculations which I wrote in 1994 and were published in 1998 as Appendices A and B to my PIRT V paper presented in London in 1996. In view of their continuing scientific relevance, this contribution to the V9 conference proceedings is a republication of those Appendices, subject to minimal re-editing. Appendix B, presented first, tackles our 1959 finding that the daylight sky brightness distribution at high altitude shows the presence of an additional contribution whose intensity and distribution which, on careful analysis, I identified as having come from a deflection scattering mechanism due to transmission by an (atmospheric) `particle-tied aether'. Appendix A shows that redshift is one of the consequences of such transmission. The parameters involved are then used to analyse the 1968 radio ground-wave caesium clock redshift observations of Sadeh et al and to extrapolate them to the intergalactic transmission paths pertinent to the cosmic redshift as a transmission effect, not a velocity. It finds this to be a reasonable evaluation within observational uncertainties, notably those of density and degree of ionization. In that case, there being no Big Bang, the temperature is precisely known from the CMBR, identified as synchrotron-type radiation from the randomly moving aether along the path, but slightly elevated where the path has traversed a heat-generating cluster.
Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model
NASA Astrophysics Data System (ADS)
Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang
2015-04-01
In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.
Algebraic description of external and internal attributes of fundamental fermions
NASA Astrophysics Data System (ADS)
Sogami, Ikuo S.
2012-02-01
To describe external and internal attributes of fundamental fermions, a theory of multi-spinor fields is developed on an algebra, a triplet algebra, which consists of all the triple-direct-products of Dirac γ-matrices. The triplet algebra is decomposed into the product of two subalgebras, an external algebra and an internal algebra, which are exclusively related with external and internal characteristic of the multi-spinor field named triplet fields. All elements of the external algebra which is isomorphic to the original Dirac algebra Aγ are invariant under the action of permutation group S3 which works to exchange the order of the Aγ elements in the triple-direct-product. The internal algebra is decomposed into the product of two 42 dimensional algebras, called the family and color algebras, which describe the family and color degrees of freedom. The family and color algebras have fine substructures with "trio plus solo" (3 + 1) conformations which are irreducible under the action of S3. The triplet field has trio plus solo family modes with ordinary tricolor quark and colorless solo lepton components. To incorporate the Weinberg-Salam mechanism, it is required to introduce two types of triplet fields, a left-handed doublet and right-handed singlets of electroweak iso-spin. It is possible to qualify the Yukawa interaction and to make a new interpretation of its coupling constants naturally in an intrinsic mechanism of the triplet field formalism. The ordinary Higgs mechanism leads to the Dirac mass matrices which can explain all data of quark sector within experimental accuracy.
Chiral symmetry and $\pi $-$\pi $ scattering in the Covariant Spectator Theory
Biernat, Elmar P.; Peña, M. T.; Ribeiro, J. E.; Stadler, Alfred; Gross, Franz
2014-11-14
The π-π scattering amplitude calculated with a model for the quark-antiquark interaction in the framework of the Covariant Spectator Theory (CST) is shown to satisfy the Adler zero constraint imposed by chiral symmetry. The CST formalism is established in Minkowski space and our calculations are performed in momentum space. We prove that the axial-vector Ward-Takahashi identity is satisfied by our model. Then we show that, similarly to what happens within the Bethe-Salpeter formalism, application of the axial-vector Ward Takahashi identity to the CST π-π scattering amplitude allows us to sum the intermediate quark-quark interactions to all orders. Thus, the Adler self-consistency zero for π-π scattering in the chiral limit emerges as the result for this sum.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Computer Program For Linear Algebra
NASA Technical Reports Server (NTRS)
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
Algebra for Gifted Third Graders.
ERIC Educational Resources Information Center
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
Semenov, Alexander; Babikov, Dmitri
2016-06-01
Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes.
Pseudo Algebraically Closed Extensions
NASA Astrophysics Data System (ADS)
Bary-Soroker, Lior
2009-07-01
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.
Tensor Algebra Library for NVidia Graphics Processing Units
Liakh, Dmitry
2015-03-16
This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion of the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor operation are assumed to be stored in local RAM of a node or GPU RAM. The main research area where this library can be utilized is the quantum many-body theory (e.g., in electronic structure theory).
Tensor Algebra Library for NVidia Graphics Processing Units
2015-03-16
This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion ofmore » the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor operation are assumed to be stored in local RAM of a node or GPU RAM. The main research area where this library can be utilized is the quantum many-body theory (e.g., in electronic structure theory).« less
Technology Transfer Automated Retrieval System (TEKTRAN)
The energy transport in a vegetated (corn) surface layer is examined by solving the vector radiative transfer equation using a numerical iterative approach. This approach allows a higher order that includes the multiple scattering effects. Multiple scattering effects are important when the optical t...
Assessing Elementary Algebra with STACK
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2007-01-01
This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
Habenschuss, Anton {Tony}; Tsige, Mesfin; Curro, John G.; Grest, Gary S.; Nath, Shyamal
2007-01-01
Wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between the MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.
Habenschuss, Anton {Tony}; Tsige, Mesfin; Curro, John G.; Grest, Gary S.; Nath, Shyamal
2007-01-01
Wide-angle X-ray scattering, molecular dynamics (MD) simulations, and integral equation theory are used to study the structure of poly(diethylsiloxane) (PDES), poly(ethylmethylsiloxane) (PEMS), and poly(dimethylsiloxane) (PDMS) melts. The structure functions of PDES, PEMS, and PDMS are similar, but systematic trends in the intermolecular packing are observed. The local intramolecular structure is extracted from the experimental structure functions. The bond distances and bond angles obtained, including the large Si-O-Si angle, are in good agreement with the explicit atom (EA) and united atom (UA) potentials used in the simulations and theory and from other sources. Very good agreement is found between the MD simulations using the EA potentials and the experimental scattering results. Good agreement is also found between the polymer reference interaction site model (PRISM theory) and the UA MD simulations. The intermolecular structure is examined experimentally using an appropriately weighted radial distribution function and with theory and simulation using intermolecular site/site pair correlation functions. Experiment, simulation, and theory show systematic increases in the chain/chain packing distances in the siloxanes as the number of sites in the pendant side chains is increased.
Semenov, Alexander; Babikov, Dmitri
2015-12-17
The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.
Pawlak Algebra and Approximate Structure on Fuzzy Lattice
Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai
2014-01-01
The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties. PMID:25152922
Pawlak algebra and approximate structure on fuzzy lattice.
Zhuang, Ying; Liu, Wenqi; Wu, Chin-Chia; Li, Jinhai
2014-01-01
The aim of this paper is to investigate the general approximation structure, weak approximation operators, and Pawlak algebra in the framework of fuzzy lattice, lattice topology, and auxiliary ordering. First, we prove that the weak approximation operator space forms a complete distributive lattice. Then we study the properties of transitive closure of approximation operators and apply them to rough set theory. We also investigate molecule Pawlak algebra and obtain some related properties.
Using Group Explorer in teaching abstract algebra
NASA Astrophysics Data System (ADS)
Schubert, Claus; Gfeller, Mary; Donohue, Christopher
2013-04-01
This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in abstract algebra. A total of 26 participants in an undergraduate course studying group theory were surveyed regarding their experiences using Group Explorer. Findings indicate that all participants believed that the software was beneficial to their learning and described their attitudes regarding the software in terms of using the technology and its helpfulness in learning concepts. A multiple regression analysis reveals that representational fluency of concepts with the software correlated significantly with participants' understanding of group concepts yet, participants' attitudes about Group Explorer and technology in general were not significant factors.
ERIC Educational Resources Information Center
Benjamin, Carl; And Others
Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra II. Topics covered include: differencing and complements; real numbers; factoring; fractions; linear equations; exponents and radicals; complex numbers,…
Thinking Visually about Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
Computer Algebra versus Manipulation
ERIC Educational Resources Information Center
Zand, Hossein; Crowe, David
2004-01-01
In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…
ERIC Educational Resources Information Center
Glick, David
1995-01-01
Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
Tsytovich, Vadim; Gusein-zade, Namik; Ignatov, Alexander
2015-07-15
Dust structuring is a natural and universal process in complex plasmas. The scattering of electromagnetic waves by dust structures is governed by the factor of coherency, i.e., the total number of coherent electrons in a single structure. In the present paper, we consider how the factor of coherency changes due to additional pulse electron heating and show that it obeys a hysteresis. After the end of the pulse heating, the scattering intensity differs substantially from that before heating. There are three necessary conditions for scattering hysteresis: first, the radiation wavelength should be larger than the pattern (structure) size; second, the total number of coherent electrons confined by the structure should be large; and third, the heating pulse duration should be shorter than the characteristic time of dust structure formation. We present the results of numerical calculations using existing models of self-consistent dust structures with either positively or negatively charged dust grains. It is shown that, depending on the grain charge and the ionization rate, two types of hysteresis are possible: one with a final increase of the scattering and the other with a final decrease of the scattering. It is suggested that the hysteresis of coherent scattering can be used as a tool in laboratory experiments and that it can be a basic mechanism explaining the observed hysteresis in radar scattering by noctilucent clouds during active experiments on electron heating in mesosphere.
NASA Astrophysics Data System (ADS)
Pecina, P.
2016-08-01
The integro-differential equation for the polarization vector P inside the meteor trail, representing the analytical solution of the set of Maxwell equations, is solved for the case of backscattering of radio waves on meteoric ionization. The transversal and longitudinal dimensions of a typical meteor trail are small in comparison to the distances to both transmitter and receiver and so the phase factor appearing in the kernel of the integral equation is large and rapidly changing. This allows us to use the method of stationary phase to obtain an approximate solution of the integral equation for the scattered field and for the corresponding generalized radar equation. The final solution is obtained by expanding it into the complete set of Bessel functions, which results in solving a system of linear algebraic equations for the coefficients of the expansion. The time behaviour of the meteor echoes is then obtained using the generalized radar equation. Examples are given for values of the electron density spanning a range from underdense meteor echoes to overdense meteor echoes. We show that the time behaviour of overdense meteor echoes using this method is very different from the one obtained using purely numerical solutions of the Maxwell equations. Our results are in much better agreement with the observations performed e. g. by the Ondřejov radar.
NASA Astrophysics Data System (ADS)
Etingof, Pavel; Rains, Eric
2016-10-01
Generalized power sums are linear combinations of ith powers of coordinates. We consider subalgebras of the polynomial algebra generated by generalized power sums, and study when such algebras are Cohen-Macaulay. It turns out that the Cohen-Macaulay property of such algebras is rare, and tends to be related to quantum integrability and representation theory of Cherednik algebras. Using representation theoretic results and deformation theory, we establish Cohen-Macaulayness of the algebra of q, t-deformed power sums defined by Sergeev and Veselov, and of some generalizations of this algebra, proving a conjecture of Brookner, Corwin, Etingof, and Sam. We also apply representation-theoretic techniques to studying m-quasi-invariants of deformed Calogero-Moser systems. In an appendix to this paper, M. Feigin uses representation theory of Cherednik algebras to compute Hilbert series for such quasi-invariants, and show that in the case of one light particle, the ring of quasi-invariants is Gorenstein.
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
The Progressive Development of Early Embodied Algebraic Thinking
ERIC Educational Resources Information Center
Radford, Luis
2014-01-01
In this article I present some results from a 5-year longitudinal investigation with young students about the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning--the theory of…
Phase transitions for rotational states within an algebraic cluster model
NASA Astrophysics Data System (ADS)
López Moreno, E.; Morales Hernández, G. E.; Hess, P. O.; Yépez Martínez, H.
2016-07-01
The ground state and excited, rotational phase transitions are investigated within the Semimicroscopic Algebraic Cluster Model (SACM). The catastrophe theory is used to describe these phase transitions. Short introductions to the SACM and the catastrophe theory are given. We apply the formalism to the case of 16O+α→20Ne.
Unified derivation of exact solutions to the relativistic Coulomb problem: Lie algebraic approach
NASA Astrophysics Data System (ADS)
Panahi, H.; Baradaran, M.; Savadi, A.
2015-10-01
Exact algebraic solutions of the D-dimensional Dirac and Klein-Gordon equations for the Coulomb potential are obtained in a unified treatment. It is shown that two cases are reducible to the same basic equation, which can be solved exactly. Using the Lie algebraic approach, the general exact solutions of the problem are obtained within the framework of representation theory of the sl(2) Lie algebra.
Generalizing the Connes Moscovici Hopf algebra to contain all rooted trees
Agarwala, Susama; Delaney, Colleen
2015-04-15
This paper defines a generalization of the Connes-Moscovici Hopf algebra, H(1), that contains the entire Hopf algebra of rooted trees. A relationship between the former, a much studied object in non-commutative geometry, and the latter, a much studied object in perturbative quantum field theory, has been established by Connes and Kreimer. The results of this paper open the door to study the cohomology of the Hopf algebra of rooted trees.
Benjamin, David; Abanin, Dmitry; Abbamonte, Peter; Demler, Eugene
2013-03-29
We present a microscopic theory of resonant soft-x-ray scattering that accounts for the delocalized character of valence electrons. Unlike past approaches based on local form factors, our functional determinant method treats realistic band structures. This method builds upon earlier theoretical work in mesoscopic physics and accounts for excitonic effects as well as the orthogonality catastrophe arising from interaction between the core hole and the valence band electrons. We show that the two-peak structure observed near the O K edge of stripe-ordered La1.875Ba0.125CuO4 is due to dynamical nesting within the canonical cuprate band structure. Our results provide evidence for reasonably well-defined, high-energy quasiparticles in cuprates and establish resonant soft-x-ray scattering as a bulk-sensitive probe of the electron quasiparticles.
Benjamin, David; Abanin, Dmitry; Abbamonte, Peter; Demler, Eugene
2013-03-29
We present a microscopic theory of resonant soft-x-ray scattering that accounts for the delocalized character of valence electrons. Unlike past approaches based on local form factors, our functional determinant method treats realistic band structures. This method builds upon earlier theoretical work in mesoscopic physics and accounts for excitonic effects as well as the orthogonality catastrophe arising from interaction between the core hole and the valence band electrons. We show that the two-peak structure observed near the O K edge of stripe-ordered La1.875Ba0.125CuO4 is due to dynamical nesting within the canonical cuprate band structure. Our results provide evidence for reasonably well-defined, high-energy quasiparticles in cuprates and establish resonant soft-x-ray scattering as a bulk-sensitive probe of the electron quasiparticles. PMID:23581360
ERIC Educational Resources Information Center
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
Algebraic Modeling of Information Retrieval in XML Documents
NASA Astrophysics Data System (ADS)
Georgiev, Bozhidar; Georgieva, Adriana
2009-11-01
This paper presents an information retrieval approach in XML documents using tools, based on the linear algebra. The well-known transformation languages as XSLT (XPath) are grounded on the features of higher-order logic for manipulating hierarchical trees. The presented conception is compared to existing higher-order logic formalisms, where the queries are realized by both languages XSLT and XPath. The possibilities of the proposed linear algebraic model combined with hierarchy data models permit more efficient solutions for searching, extracting and manipulating semi-structured data with hierarchical structures avoiding the global navigation over the XML tree components. The main purpose of this algebraic model representation, applied to the hierarchical relationships in the XML data structures, is to make the implementation of linear algebra tools possible for XML data manipulations and to eliminate existing problems, related to regular grammars theory and also to avoid the difficulties, connected with higher -order logic (first-order logic, monadic second- order logic etc.).
On the cohomology of Leibniz conformal algebras
NASA Astrophysics Data System (ADS)
Zhang, Jiao
2015-04-01
We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.
Assessing Algebraic Solving Ability: A Theoretical Framework
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
2012-01-01
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
NASA Astrophysics Data System (ADS)
Matsuno, Yoshimasa
2004-02-01
The multisoliton solution of the Benjamin-Ono equation is derived from the system of nonlinear algebraic equations. This finding is unexpected from the scheme of the inverse scattering transform method, which constructs the multisoliton solution through the system of linear algebraic equations. The anlaysis developed here is also applied to the rational multisoliton solution of the Kadomtsev-Petviashvili equation.
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.
ERIC Educational Resources Information Center
Novotna, Jarmila; Hoch, Maureen
2008-01-01
Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…
Renormalization group flows and continual Lie algebras
NASA Astrophysics Data System (ADS)
Bakas, Ioannis
2003-08-01
We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.
Algebraic methods for the solution of some linear matrix equations
NASA Technical Reports Server (NTRS)
Djaferis, T. E.; Mitter, S. K.
1979-01-01
The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.
2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras
NASA Astrophysics Data System (ADS)
Ayupov, Shavkat; Kudaybergenov, Karimbergen
2016-03-01
The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation.
NASA Astrophysics Data System (ADS)
Cardona, Carlos; Gomez, Humberto
2016-06-01
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a mathbb{C}{P}^2 space. We show that for the simplest integrand, namely the n - gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ-algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
Contraction-based classification of supersymmetric extensions of kinematical lie algebras
Campoamor-Stursberg, R.; Rausch de Traubenberg, M.
2010-02-15
We study supersymmetric extensions of classical kinematical algebras from the point of view of contraction theory. It is shown that contracting the supersymmetric extension of the anti-de Sitter algebra leads to a hierarchy similar in structure to the classical Bacry-Levy-Leblond classification.
On an approach for computing the generating functions of the characters of simple Lie algebras
NASA Astrophysics Data System (ADS)
Fernández Núñez, José; García Fuertes, Wifredo; Perelomov, Askold M.
2014-04-01
We describe a general approach to obtain the generating functions of the characters of simple Lie algebras which is based on the theory of the quantum trigonometric Calogero-Sutherland model. We show how the method works in practice by means of a few examples involving some low rank classical algebras.
Liu, Zhe; Jiang, Liwei; Zheng, Yisong
2016-01-01
The diagonal and Hall conductivities of graphene arising from the spin-orbit coupling impurity scattering are theoretically studied. Based on the continuous model, i.e. the massless Dirac equation, we derive analytical expressions of the conductivity tensor from both the Kubo and Boltzmann transport theories. By performing numerical calculations, we find that the Kubo quantum transport result of the diagonal conductivity within the self-consistent Born approximation exhibits an insulating gap around the Dirac point. And in this gap a well-defined quantized spin Hall plateau occurs. This indicates the realization of the quantum spin Hall state of graphene driven by the spin-orbit coupling impurities. In contrast, the semi-classical Boltzmann theory fails to predict such a topological insulating phase. The Boltzmann diagonal conductivity is nonzero even in the insulating gap, in which the Boltzmann spin Hall conductivity does not exhibit any quantized plateau. PMID:27029398