Nonlocal Equations with Measure Data
NASA Astrophysics Data System (ADS)
Kuusi, Tuomo; Mingione, Giuseppe; Sire, Yannick
2015-08-01
We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly degenerate and cover the case of the fractional p-Laplacean operator with measurable coefficients. We introduce a natural function class where we solve the Dirichlet problem, and prove basic and optimal nonlinear Wolff potential estimates for solutions. These are the exact analogs of the results valid in the case of local quasilinear degenerate equations established by Boccardo and Gallouët (J Funct Anal 87:149-169, 1989, Partial Differ Equ 17:641-655, 1992) and Kilpeläinen and Malý (Ann Scuola Norm Sup Pisa Cl Sci (IV) 19:591-613, 1992, Acta Math 172:137-161, 1994). As a consequence, we establish a number of results that can be considered as basic building blocks for a nonlocal, nonlinear potential theory: fine properties of solutions, Calderón-Zygmund estimates, continuity and boundedness criteria are established via Wolff potentials. A main tool is the introduction of a global excess functional that allows us to prove a nonlocal analog of the classical theory due to Campanato (Ann Mat Pura Appl (IV) 69:321-381, 1965). Our results cover the case of linear nonlocal equations with measurable coefficients, and the one of the fractional Laplacean, and are new already in such cases.
Nonlocal electrical diffusion equation
NASA Astrophysics Data System (ADS)
Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.
2016-07-01
In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.
Cusp Formation for a Nonlocal Evolution Equation
NASA Astrophysics Data System (ADS)
Hoang, Vu; Radosz, Maria
2017-02-01
Córdoba et al. (Ann Math 162(3):1377-1389, 2005) introduced a nonlocal active scalar equation as a one-dimensional analogue of the surface-quasigeostrophic equation. It has been conjectured, based on numerical evidence, that the solution forms a cusp-like singularity in finite time. Up until now, no active scalar with nonlocal flux is known for which cusp formation has been rigorously shown. In this paper, we introduce and study a nonlocal active scalar, inspired by the Córdoba-Córdoba-Fontelos equation, and prove that either a cusp- or needle-like singularity forms in finite time.
Chaotic Orbits for Systems of Nonlocal Equations
NASA Astrophysics Data System (ADS)
Dipierro, Serena; Patrizi, Stefania; Valdinoci, Enrico
2017-01-01
We consider a system of nonlocal equations driven by a perturbed periodic potential. We construct multibump solutions that connect one integer point to another one in a prescribed way. In particular, heteroclinic, homoclinic and chaotic trajectories are constructed. This is the first attempt to consider a nonlocal version of this type of dynamical systems in a variational setting and the first result regarding symbolic dynamics in a fractional framework.
Nonlocal diffusion second order partial differential equations
NASA Astrophysics Data System (ADS)
Benedetti, I.; Loi, N. V.; Malaguti, L.; Taddei, V.
2017-02-01
The paper deals with a second order integro-partial differential equation in Rn with a nonlocal, degenerate diffusion term. Nonlocal conditions, such as the Cauchy multipoint and the weighted mean value problem, are investigated. The existence of periodic solutions is also studied. The dynamic is transformed into an abstract setting and the results come from an approximation solvability method. It combines a Schauder degree argument with an Hartman-type inequality and it involves a Scorza-Dragoni type result. The compact embedding of a suitable Sobolev space in the corresponding Lebesgue space is the unique amount of compactness which is needed in this discussion. The solutions are located in bounded sets and they are limits of functions with values in finitely dimensional spaces.
Scaling approach to the nonlocal surface growth equations
NASA Astrophysics Data System (ADS)
Tang, Gang; Ma, Benkun
2001-09-01
The scaling behavior of nonlocal surface growth equations are analyzed using a Flory-type approach introduced by Hentschel and Family [Phys. Rev. Lett. 66 (1991) 1982]. The growth equations studied include the nonlocal Kardar-Parisi-Zhang, nonlocal Sun-Guo-Grant, and nonlocal Lai-Das Sarma-Villain equation. The types of noise involved include white, colored noise and quenched randomness. We find that the obtained scaling exponents in the weak-coupling region can well match the corresponding results of the dynamic renormalizatin group theory. The scaling exponents in the strong-coupling region are also derived.
Nonlocal equation for the superconducting gap parameter
NASA Astrophysics Data System (ADS)
Simonucci, S.; Strinati, G. Calvanese
2017-08-01
The properties are considered in detail of a nonlocal (integral) equation for the superconducting gap parameter, which is obtained by a coarse-graining procedure applied to the Bogoliubov-de Gennes (BdG) equations over the whole coupling-versus-temperature phase diagram associated with the superfluid phase. It is found that the limiting size of the coarse-graining procedure, which is dictated by the range of the kernel of this integral equation, corresponds to the size of the Cooper pairs over the whole coupling-versus-temperature phase diagram up to the critical temperature, even when Cooper pairs turn into composite bosons on the BEC side of the BCS-BEC crossover. A practical method is further implemented to solve numerically this integral equation in an efficient way, which is based on a novel algorithm for calculating the Fourier transforms. Application of this method to the case of an isolated vortex, throughout the BCS-BEC crossover and for all temperatures in the superfluid phase, helps clarifying the nature of the length scales associated with a single vortex and the kinds of details that are in practice disposed off by the coarse-graining procedure on the BdG equations.
Nonlocal conservation laws of the constant astigmatism equation
NASA Astrophysics Data System (ADS)
Hlaváč, Adam; Marvan, Michal
2017-03-01
For the constant astigmatism equation, we construct a system of nonlocal conservation laws (an abelian covering) closed under the reciprocal transformations. The corresponding potentials are functionally independent modulo a Wronskian type relation.
Complete integrability of nonlocal nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Gerdjikov, V. S.; Saxena, A.
2017-01-01
Based on the completeness relation for the squared solutions of the Lax operator L, we show that a subset of nonlocal equations from the hierarchy of nonlocal nonlinear Schrödinger equations (NLS) is a completely integrable system. The spectral properties of the Lax operator indicate that there are two types of soliton solutions. The relevant action-angle variables are parametrized by the scattering data of the Lax operator. The notion of the symplectic basis, which directly maps the variations of the potential of L to the variations of the action-angle variables has been generalized to the nonlocal case. We also show that the inverse scattering method can be viewed as a generalized Fourier transform. Using the trace identities and the symplectic basis, we construct the hierarchy Hamiltonian structures for the nonlocal NLS equations.
Linearization properties, first integrals, nonlocal transformation for heat transfer equation
NASA Astrophysics Data System (ADS)
Orhan, Özlem; Özer, Teoman
2016-08-01
We examine first integrals and linearization methods of the second-order ordinary differential equation which is called fin equation in this study. Fin is heat exchange surfaces which are used widely in industry. We analyze symmetry classification with respect to different choices of thermal conductivity and heat transfer coefficient functions of fin equation. Finally, we apply nonlocal transformation to fin equation and examine the results for different functions.
Nonlocal Symmetries and Exact Solutions for PIB Equation
NASA Astrophysics Data System (ADS)
Xin, Xiang-Peng; Miao, Qian; Chen, Yong
2012-09-01
In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.
Nonlocal Symmetry Reductions for Bosonized Supersymmetric Burgers Equation
NASA Astrophysics Data System (ADS)
Ren, Bo; Lin, Ji; Le, Jia-Yi; Wang, Sheng; Dai, Tian-Zhao
2017-08-01
Based on the bosonization approach, the supersymmetric Burgers (SB) system is transformed to a coupled bosonic system. By solving the bosonized SB (BSB) equation, the difficulties caused by the anticommutative fermionic field of the SB equation can be avoided. The nonlocal symmetry for the BSB equation is obtained by the truncated Painlevé method. By introducing multiple new fields, the finite symmetry transformation for the BSB equation is derived by solving the first Lie’s principle of the prolonged systems. Some group invariant solutions are obtained with the similarity reductions related by the nonlocal symmetry. Supported by the National Natural Science Foundation of China under Grant Nos. 11675146, 11305106, 11472177, 11275129, and the Natural Science Foundation of Zhejiang Province of China under Grant No. LZ15A050001
Localization of Nonlocal Symmetries and Symmetry Reductions of Burgers Equation
NASA Astrophysics Data System (ADS)
Wu, Jian-Wen; Lou, Sen-Yue; Yu, Jun
2017-05-01
The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé method. The auto-Bäcklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained. Supported by the Global Change Research Program China under Grant No. 2015CB953904, the National Natural Science Foundations of China under Grant Nos. 11435005, 11175092, and 11205092, Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No. ZF1213, and K. C. Wong Magna Fund in Ningbo University
Integrable nonlocal nonlinear Schrödinger equation.
Ablowitz, Mark J; Musslimani, Ziad H
2013-02-08
A new integrable nonlocal nonlinear Schrödinger equation is introduced. It possesses a Lax pair and an infinite number of conservation laws and is PT symmetric. The inverse scattering transform and scattering data with suitable symmetries are discussed. A method to find pure soliton solutions is given. An explicit breathing one soliton solution is found. Key properties are discussed and contrasted with the classical nonlinear Schrödinger equation.
On a class of nonlocal wave equations from applications
NASA Astrophysics Data System (ADS)
Beyer, Horst Reinhard; Aksoylu, Burak; Celiker, Fatih
2016-06-01
We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form a system of nonlocal wave equations. We take a novel approach by applying operator theory methods in a systematic way. On the unbounded domain ℝn, we present three main results. As main result 1, we find that the governing operator is a bounded function of the governing operator of classical elasticity. As main result 2, a consequence of main result 1, we prove that the peridynamic solutions strongly converge to the classical solutions by utilizing, for the first time, strong resolvent convergence. In addition, main result 1 allows us to incorporate local boundary conditions, in particular, into peridynamics. This avenue of research is developed in companion papers, providing a remedy for boundary effects. As main result 3, employing spherical Bessel functions, we give a new practical series representation of the solution which allows straightforward numerical treatment with symbolic computation.
Scaling of the Nonlocal Growth Equations with Spatially and Temporally Correlated Noise
NASA Astrophysics Data System (ADS)
Tang, Gang; Ma, Benkun
The Flory-type approach proposed by Hentschel and Family [Phys. Rev. Lett. 66, 1982 (1991)] is generalized to analyze the scaling behavior of the nonlocal surface growth equations with long-range spatially and temporally correlated noise. The scaling exponents in both the weak- and strong-coupling regions are obtained. The growth equations studied include the nonlocal Kardar-Parisi-Zhang, nonlocal Sun-Guo-Grant, and nonlocal Lai-Das Sarma-Villain equation.
Non-local quasi-linear parabolic equations
NASA Astrophysics Data System (ADS)
Amann, H.
2005-12-01
This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal L_p regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona-Malik equation of image processing.
Solitons and dynamics for a general integrable nonlocal coupled nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Song, Cai-Qin; Xiao, Dong-Mei; Zhu, Zuo-Nong
2017-04-01
In this paper, we investigate a general integrable nonlocal coupled nonlinear Schrödinger (NLS) system with the parity-time (PT) symmetry, which contains not only the nonlocal self-phase modulation and the nonlocal cross-phase modulation, but also the nonlocal four-wave mixing terms. This nonlocal coupled NLS system is a nonlocal version of a coupled NLS system. The general N-th Darboux transformation for the nonlocal coupled NLS equation is constructed. By using the Darboux transformation, its soliton solutions are obtained. Dynamics and interactions of different kinds of soliton solutions are discussed.
Chaoticons described by nonlocal nonlinear Schrödinger equation.
Zhong, Lanhua; Li, Yuqi; Chen, Yong; Hong, Weiyi; Hu, Wei; Guo, Qi
2017-01-30
It is shown that the unstable evolutions of the Hermite-Gauss-type stationary solutions for the nonlocal nonlinear Schrödinger equation with the exponential-decay response function can evolve into chaotic states. This new kind of entities are referred to as chaoticons because they exhibit not only chaotic properties (with positive Lyapunov exponents and spatial decoherence) but also soliton-like properties (with invariant statistic width and interaction of quasi-elastic collisions).
Chaoticons described by nonlocal nonlinear Schrödinger equation
Zhong, Lanhua; Li, Yuqi; Chen, Yong; Hong, Weiyi; Hu, Wei; Guo, Qi
2017-01-01
It is shown that the unstable evolutions of the Hermite-Gauss-type stationary solutions for the nonlocal nonlinear Schrödinger equation with the exponential-decay response function can evolve into chaotic states. This new kind of entities are referred to as chaoticons because they exhibit not only chaotic properties (with positive Lyapunov exponents and spatial decoherence) but also soliton-like properties (with invariant statistic width and interaction of quasi-elastic collisions). PMID:28134268
Secondary bifurcation for a nonlocal Allen-Cahn equation
NASA Astrophysics Data System (ADS)
Kuto, Kousuke; Mori, Tatsuki; Tsujikawa, Tohru; Yotsutani, Shoji
2017-09-01
This paper studies the Neumann problem of a nonlocal Allen-Cahn equation in an interval. A main result finds a symmetry breaking (secondary) bifurcation point on the bifurcation curve of solutions with odd-symmetry. Our proof is based on a level set analysis for the associated integral map. A method using the complete elliptic integrals proves the uniqueness of secondary bifurcation point. We also show some numerical simulations concerning the global bifurcation structure.
Integro-differential equation of non-local wave interaction
Engibaryan, N B; Khachatryan, Aghavard Kh
2007-06-30
The integro-differential equation d{sup 2}f/dx{sup 2} + Af = {integral}{sub 0}{sup {infinity}}K(x-t)f(t)dt + g(x) with kernel K(x)={lambda}{integral}{sub a}{sup {infinity}}e{sup -|x|p}G(p)dp, a{>=}0, is considered, in which A>0, {lambda} element of 9-{infinity},{infinity}), G(p){>=}0, 2{integral}{sub a}{sup {infinity}}1/p g(p)dp=1. These equations arise, in particular, in the theory of non-local wave interaction. A factorization method of their analysis and solution is developed. Bibliography: 9 titles.
Symmetry reduction related with nonlocal symmetry for Gardner equation
NASA Astrophysics Data System (ADS)
Ren, Bo
2017-01-01
Based on the truncated Painlevé method or the Möbious (conformal) invariant form, the nonlocal symmetry for the (1+1)-dimensional Gardner equation is derived. The nonlocal symmetry can be localized to the Lie point symmetry by introducing one new dependent variable. Thanks to the localization procedure, the finite symmetry transformations are obtained by solving the initial value problem of the prolonged systems. Furthermore, by using the symmetry reduction method to the enlarged systems, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, Painlevé II solutions are given. Especially, some special concrete soliton-cnoidal interaction solutions are analyzed both in analytical and graphical ways.
NASA Astrophysics Data System (ADS)
Ji, Jia-Liang; Zhu, Zuo-Nong
2017-01-01
Very recently, Ablowitz and Musslimani introduced a new integrable nonlocal nonlinear Schrödinger equation. In this paper, we investigate an integrable nonlocal modified Korteweg-de Vries equation (mKdV) which can be derived from the well-known AKNS system. We construct the Darboux transformation for the nonlocal mKdV equation. Using the Darboux transformation, we obtain its different kinds of exact solutions including soliton, kink, antikink, complexiton, rogue-wave solution, and nonlocalized solution with singularities. It is shown that these solutions possess new properties which are different from the ones for mKdV equation.
NASA Astrophysics Data System (ADS)
Lazar, Omar
2016-11-01
We study a 1D transport equation with nonlocal velocity with subcritical or supercritical dissipation. For all data in the weighted Sobolev space Hk (wλ,κ) ∩L∞, where k = max (0 , 3 / 2 - α) and wλ,κ is a given family of Muckenhoupt weights, we prove a global existence result in the subcritical case α ∈ (1 , 2). We also prove a local existence theorem for large data in H2 (wλ,κ) ∩L∞ in the supercritical case α ∈ (0 , 1). The proofs are based on the use of the weighted Littlewood-Paley theory, interpolation along with some new commutator estimates.
Fault Diagnosis of Rolling Bearing Based on Fast Nonlocal Means and Envelop Spectrum
Lv, Yong; Zhu, Qinglin; Yuan, Rui
2015-01-01
The nonlocal means (NL-Means) method that has been widely used in the field of image processing in recent years effectively overcomes the limitations of the neighborhood filter and eliminates the artifact and edge problems caused by the traditional image denoising methods. Although NL-Means is very popular in the field of 2D image signal processing, it has not received enough attention in the field of 1D signal processing. This paper proposes a novel approach that diagnoses the fault of a rolling bearing based on fast NL-Means and the envelop spectrum. The parameters of the rolling bearing signals are optimized in the proposed method, which is the key contribution of this paper. This approach is applied to the fault diagnosis of rolling bearing, and the results have shown the efficiency at detecting roller bearing failures. PMID:25585105
Second-order envelope equation of graphene electrons
NASA Astrophysics Data System (ADS)
Luo, Ji
2014-10-01
A treatment of graphene's electronic states based on the tight-binding method is presented. Like Dirac equation, this treatment uses envelope functions to eliminate crystal potential. Besides, a density-functional-theory Kohn-Sham (KS) orbital of an isolated carbon atom is employed. By locally expanding envelope functions into second-order polynomials and by involving up to third-nearest atoms in calculating orbital integrals, the second-order envelope equation is obtained. This equation does not contain any experimental data except graphene's crystal structure, and its coefficients are determined through several kinds of integrals of the carbon KS orbital. As an improvement, it leads to more accurate energy dispersion than Dirac equation including the triangular warping effect and asymmetry for electrons and holes, and gives the Fermi velocity which is in good agreement with the experimental value.
Edge envelope equation for a ballistically focused neutralized ion beam
Lemons, D.S.; Thode, L.E.
1980-11-01
An envelope equation for a cold ion beam with overall charge and current neutralization provided by a coflowing electron gas obeying an adiabatic equation of state is derived. The derivation assumes the beam evolves self-similarly with the ion at the edge of a uniform density ion profile. Numerical and approximate analytical solutions are calculated.
A Partial Differential Equation for the Rank One Convex Envelope
NASA Astrophysics Data System (ADS)
Oberman, Adam M.; Ruan, Yuanlong
2017-02-01
A partial differential equation (PDE) for the rank one convex envelope is introduced. The existence and uniqueness of viscosity solutions to the PDE is established. Elliptic finite difference schemes are constructed and convergence of finite difference solutions to the viscosity solution of the PDE is proven. Computational results are presented and laminates are computed from the envelopes. Results include the Kohn-Strang example, the classical four gradient example, and an example with eight gradients which produces nontrivial laminates.
NASA Astrophysics Data System (ADS)
Bishop, S. A.; Ayoola, E. O.; Oghonyon, G. J.
2016-08-01
New results on existence and uniqueness of solution of impulsive quantum stochastic differential equation with nonlocal conditions are established. The nonlocal conditions are completely continuous. The methods applied here are simple extension of the methods applied in the classical case to this noncummutative quantum setting.
Reverse Space-Time Nonlocal Sasa-Satsuma Equation and Its Solutions
NASA Astrophysics Data System (ADS)
Song, Caiqin; Xiao, Dongmei; Zhu, Zuo-nong
2017-05-01
The Sasa-Satsuma equation is an integrable high-order nonlinear Schrödinger (NLS) equation, and also is a complex modified KdV-type equation. It can describe the propagation of femtosecond pulses in optical fibers. Very recently, Ablowitz and Mussliman introduced a class of reverse space-time and reverse time nonlinear integrable equations, including the reverse space nonlocal NLS equation, the real and complex reverse space-time nonlocal mKdV, sine-Gordon, Davey-Stewartson equations, etc. So, what is nonlocal version of high-order NLS? In this paper, we introduce a reverse space-time nonlocal Sasa-Satsuma equation, i.e., a reverse space-time nonlocal high-order NLS equation, and derive its solutions with the binary Darboux transformation method. Periodic solutions, and some localized solutions, such as dark soliton, W-shaped soliton, M-shaped soliton and breather soliton of the reverse space-time nonlocal Sasa-Satsuma equation are constructed.
A note on the nonlocal boundary value problem for a third order partial differential equation
NASA Astrophysics Data System (ADS)
Belakroum, Kheireddine; Ashyralyev, Allaberen; Guezane-Lakoud, Assia
2016-08-01
The nonlocal boundary-value problem for a third order partial differential equation d/3u (t ) d t3 +A d/u (t ) d t =f (t ), 0
Nonlocal operators, parabolic-type equations, and ultrametric random walks
Chacón-Cortes, L. F. Zúñiga-Galindo, W. A.
2013-11-15
In this article, we introduce a new type of nonlocal operators and study the Cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators. Some of these equations are the p-adic master equations of certain models of complex systems introduced by Avetisov, V. A. and Bikulov, A. Kh., “On the ultrametricity of the fluctuation dynamicmobility of protein molecules,” Proc. Steklov Inst. Math. 265(1), 75–81 (2009) [Tr. Mat. Inst. Steklova 265, 82–89 (2009) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Zubarev, A. P., “First passage time distribution and the number of returns for ultrametric random walks,” J. Phys. A 42(8), 085003 (2009); Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic models of ultrametric diffusion in the conformational dynamics of macromolecules,” Proc. Steklov Inst. Math. 245(2), 48–57 (2004) [Tr. Mat. Inst. Steklova 245, 55–64 (2004) (Izbrannye Voprosy Matematicheskoy Fiziki i p-adicheskogo Analiza) (in Russian)]; Avetisov, V. A., Bikulov, A. Kh., and Osipov, V. A., “p-adic description of characteristic relaxation in complex systems,” J. Phys. A 36(15), 4239–4246 (2003); Avetisov, V. A., Bikulov, A. H., Kozyrev, S. V., and Osipov, V. A., “p-adic models of ultrametric diffusion constrained by hierarchical energy landscapes,” J. Phys. A 35(2), 177–189 (2002); Avetisov, V. A., Bikulov, A. Kh., and Kozyrev, S. V., “Description of logarithmic relaxation by a model of a hierarchical random walk,” Dokl. Akad. Nauk 368(2), 164–167 (1999) (in Russian). The fundamental solutions of these parabolic-type equations are transition functions of random walks on the n-dimensional vector space over the field of p-adic numbers. We study some properties of these random walks, including the first passage time.
New Exact Solutions of the CDGSK Equation Related to a Non-local Symmetry
NASA Astrophysics Data System (ADS)
Lou, Senyue; Ruan, Hangyu; Chen, Weizhong; Wang, Zhenli; Chen, Lili
1994-10-01
A non-local symmetry of the Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation has been used for finding exact solution in two different ways. Firstly, using the standard prolongation approach, we obtain the finite Lie Bäcklund transformation and the single soliton solution. Secondly, combining some local symmetries and the nonlocal symmetry, we get the group invariant solution which is described by the Weierstrass elliptic function and is deduced to the so-called interacting soliton for a special parameter.
Imaginary Time Step Method to Solve the Dirac Equation with Nonlocal Potential
Zhang Ying; Liang Haozhao; Meng Jie
2009-08-26
The imaginary time step (ITS) method is applied to solve the Dirac equation with nonlocal potentials in coordinate space. Taking the nucleus {sup 12}C as an example, even with nonlocal potentials, the direct ITS evolution for the Dirac equation still meets the disaster of the Dirac sea. However, following the recipe in our former investigation, the disaster can be avoided by the ITS evolution for the corresponding Schroedinger-like equation without localization, which gives the convergent results exactly the same with those obtained iteratively by the shooting method with localized effective potentials.
NASA Astrophysics Data System (ADS)
Zhang, Yu-Juan; Zhao, Dun; Ma, Wen-Xiu
2017-01-01
We present the inverse scattering transformation for a nonisospectral AKNS hierarchy in which the spectral parameter is determined by an ordinary differential equation with polynomial nonlinearity, and thus, we give a unified treatment for the local and nonlocal nonautonomous Gross-Pitaevskii equations which possess the parity-time ( PT ) symmetric invariance. We find that unlike the local case, the PT -symmetry of the nonlocal Gross-Pitaevskii equation allows two different choices of the symmetry relations of the eigenfunctions which guarantee two different kinds of inverse scattering solutions.
NASA Astrophysics Data System (ADS)
Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.
2014-09-01
In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach
CTE Solvability, Exact Solutions and Nonlocal Symmetries of the Sharma-Tasso-Olver Equation
NASA Astrophysics Data System (ADS)
Pu, Huan; Jia, Man
2015-12-01
In this letter, we prove that the STO equation is CTE solvable and obtain the exact solutions of solitons fission and fusion. We also provide the nonlocal symmetries of the STO equation related to CTE. The nonlocal symmetries are localized by prolonging the related enlarged system. Supported by National Natural Science Foundation of China under Grant Nos. 11205092, 11175092 and 11435005, Ningbo Natural Science Foundation under Grant Nos. 2015A610159 and 2012A610178 and by the Opening Project of Zhejiang Provincial Top Key Discipline of Physics Sciences in Ningbo University under Grant No. xkzw11502. And the authors were sponsored by K. C. Wong Magna Fund in Ningbo University
Dynamical Behavior of Solution in Integrable Nonlocal Lakshmanan—Porsezian—Daniel Equation
NASA Astrophysics Data System (ADS)
Liu, Wei; Qiu, De-Qin; Wu, Zhi-Wei; He, Jing-Song
2016-06-01
The integrable nonlocal Lakshmanan—Porsezian—Daniel (LPD) equation which has the higher-order terms (dispersions and nonlinear effects) is first introduced. We demonstrate the integrability of the nonlocal LPD equation, provide its Lax pair, and present its rational soliton solutions and self-potential function by using the degenerate Darboux transformation. From the numerical plots of solutions, the compression effects of the real refractive index profile and the gain-or-loss distribution produced by δ are discussed. Supported by the National Natural Science Foundation of China under Grant No. 11271210 and the K.C. Wong Magna Fund in Ningbo University
NASA Astrophysics Data System (ADS)
Shen, Wenxian; Shen, Zhongwei
2017-03-01
The present paper is devoted to the investigation of various properties of transition fronts in one-dimensional nonlocal equations in heterogeneous media of ignition type, whose existence has been established by the authors of the present paper in a previous work. It is first shown that transition fronts are continuously differentiable in space with uniformly bounded and uniformly Lipschitz continuous space partial derivative. This is the first time that space regularity of transition fronts in nonlocal equations is ever studied. It is then shown that transition fronts are uniformly steep. Finally, asymptotic stability, in the sense of exponentially attracting front-like initial data, of transition fronts is studied.
Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions
NASA Technical Reports Server (NTRS)
Hodge, Steve L.; Zorumski, William E.; Watson, Willie R.
1995-01-01
The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.
NASA Astrophysics Data System (ADS)
Xie, Dexuan; Jiang, Yi
2016-10-01
The nonlocal dielectric approach has been studied for more than forty years but only limited to water solvent until the recent work of Xie et al. (2013) [20]. As the development of this recent work, in this paper, a nonlocal modified Poisson-Boltzmann equation (NMPBE) is proposed to incorporate nonlocal dielectric effects into the classic Poisson-Boltzmann equation (PBE) for protein in ionic solvent. The focus of this paper is to present an efficient finite element algorithm and a related software package for solving NMPBE. Numerical results are reported to validate this new software package and demonstrate its high performance for protein molecules. They also show the potential of NMPBE as a better predictor of electrostatic solvation and binding free energies than PBE.
Nonlocal Symmetries and Finite Transformations of the Fifth-Order KdV Equation
NASA Astrophysics Data System (ADS)
Hao, Xiazhi; Liu, Yinping; Tang, Xiaoyan; Li, Zhibin
2017-05-01
The nth finite transformations of the fifth-order KdV equation are obtained from the Lie point symmetry approach via localisation of nonlocal symmetries to local ones of the enlarged system. Through the obtained transformations, some periodic and soliton solutions are derived.
Hölder estimates for non-local parabolic equations with critical drift
NASA Astrophysics Data System (ADS)
Chang-Lara, Héctor A.; Dávila, Gonzalo
2016-03-01
In this paper we extend previous results on the regularity of solutions of integro-differential parabolic equations. The kernels are non-necessarily symmetric which could be interpreted as a non-local drift with the same order as the diffusion. We provide a growth lemma and a Harnack inequality which can be used to prove higher regularity estimates.
Nonlocal Symmetry and Interaction Solutions of a Generalized Kadomtsev—Petviashvili Equation
NASA Astrophysics Data System (ADS)
Huang, Li-Li; Chen, Yong; Ma, Zheng-Yi
2016-08-01
A generalized Kadomtsev—Petviashvili equation is studied by nonlocal symmetry method and consistent Riccati expansion (CRE) method in this paper. Applying the truncated Painlevé analysis to the generalized Kadomtsev—Petviashvili equation, some Bäcklund transformations (BTs) including auto-BT and non-auto-BT are obtained. The auto-BT leads to a nonlocal symmetry which corresponds to the residual of the truncated Painlevé expansion. Then the nonlocal symmetry is localized to the corresponding nonlocal group by introducing two new variables. Further, by applying the Lie point symmetry method to the prolonged system, a new type of finite symmetry transformation is derived. In addition, the generalized Kadomtsev—Petviashvili equation is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to be found by other traditional methods. Moreover, figures are given out to show the properties of the explicit analytic interaction solutions. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of under Grant Nos. 11275072 and 11435005, Doctoral Program of Higher Education of China under Grant No. 20120076110024, the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No. 61321064, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, and Zhejiang Provincial Natural Science Foundation of China under Grant No. LY14A010005
Scaling analysis of the anisotropic nonlocal Kardar-Parisi-Zhang equation
NASA Astrophysics Data System (ADS)
Tang, Gang; Ma, Benkun
2002-07-01
The scaling behaviors of the anisotropic nonlocal Kardar-Parisi-Zhang equation are studied by the scaling analysis method introduced by Hentschel and Family. The scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. The scaling exponents in weak-coupling region can well match the results of the dynamic renormalization-group analysis.
Generalized Klein-Gordon and Dirac Equations from Nonlocal Kinetic Approach
NASA Astrophysics Data System (ADS)
El-Nabulsi, Rami Ahmad
2016-09-01
In this note, I generalized the Klein-Gordon and the Dirac equations by using Suykens's nonlocal-in-time kinetic energy approach, which is motivated from Feynman's kinetic energy functional formalism where the position differences are shifted with respect to one another. I proved that these generalized equations are similar to those obtained in literature in the presence of minimal length based on the Quesne-Tkachuk algebra.
NASA Astrophysics Data System (ADS)
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2017-06-01
The one-dimensional Fokker-Planck-Kolmogorov equation with a special type of nonlocal quadratic nonlinearity is represented as a consistent system of differential equations, including a dynamical system describing the evolution of the moments of the unknown function. Lie symmetries are found for the consistent system using methods of classical group analysis. An example of an invariant-group solution obtained with an additional integral constraint imposed on the system is considered.
Modulational instability in nonlinear nonlocal equations of regularized long wave type
NASA Astrophysics Data System (ADS)
Hur, Vera Mikyoung; Pandey, Ashish Kumar
2016-06-01
We study the stability and instability of periodic traveling waves in the vicinity of the origin in the spectral plane, for equations of Benjamin-Bona-Mahony (BBM) and regularized Boussinesq types permitting nonlocal dispersion. We extend recent results for equations of Korteweg-de Vries type and derive modulational instability indices as functions of the wave number of the underlying wave. We show that a sufficiently small, periodic traveling wave of the BBM equation is spectrally unstable to long wavelength perturbations if the wave number is greater than a critical value and a sufficiently small, periodic traveling wave of the regularized Boussinesq equation is stable to square integrable perturbations.
Nonlocal Symmetry and its Applications in Perturbed mKdV Equation
NASA Astrophysics Data System (ADS)
Ren, Bo; Lin, Ji
2016-06-01
Based on the modified direct method, the variable-coefficient perturbed mKdV equation is changed to the constant-coefficient perturbed mKdV equation. The truncated Painlevé method is applied to obtain the nonlocal symmetry of the constant-coefficient perturbed mKdV equation. By introducing one new dependent variable, the nonlocal symmetry can be localized to the Lie point symmetry. Thanks to the localization procedure, the finite symmetry transformation is presented by solving the initial value problem of the prolonged systems. Furthermore, many explicit interaction solutions among different types of solutions such as solitary waves, rational solutions, and Painlevé II solutions are obtained using the symmetry reduction method to the enlarged systems. Two special concrete soliton-cnoidal interaction solutions are studied in both analytical and graphical ways.
Modulated traveling fronts for a nonlocal Fisher-KPP equation: A dynamical systems approach
NASA Astrophysics Data System (ADS)
Faye, Grégory; Holzer, Matt
2015-04-01
We consider a nonlocal generalization of the Fisher-KPP equation in one spatial dimension. As a parameter is varied, the system undergoes a Turing bifurcation. We study the dynamics near this Turing bifurcation. Our results are two-fold. First, we prove the existence of a two-parameter family of bifurcating stationary periodic solutions and derive a rigorous asymptotic approximation of these solutions. We also study the spectral stability of the bifurcating stationary periodic solutions with respect to almost co-periodic perturbations. Second, we restrict to a specific class of exponential kernels for which the nonlocal problem is transformed into a higher order partial differential equation. In this context, we prove the existence of modulated traveling fronts near the Turing bifurcation that describe the invasion of the Turing unstable homogeneous state by the periodic pattern established in the first part. Both results rely on a center manifold reduction to a finite dimensional ordinary differential equation.
Tolman-Oppenheimer-Volkoff equations in nonlocal f(R) gravity
NASA Astrophysics Data System (ADS)
Momeni, Davood; Gholizade, H.; Raza, Muhammad; Myrzakulov, Ratbay
2015-06-01
Nonlocal f(R) gravity was proposed as a powerful alternative to general relativity (GR). This theory has potentially adverse implications for infrared (IR) regime as well as ultraviolet (UV) early epochs. However, there are a lot of powerful features, making it really user-friendly. A scalar-tensor frame comprising two auxiliary scalar fields is used to reduce complex action. However, this is not the case for the modification complex which plays a distinct role in modified theories for gravity. In this work, we study the dynamics of a static, spherically symmetric object. The interior region of space-time had rapidly filled the perfect fluid. However, it is possible to derive a physically based model which relates interior metric to nonlocal f(R). The Tolman-Oppenheimer-Volkoff (TOV) equations would be a set of first-order differential equations from which we can deduce all mathematical (physical) truths and derive all dynamical objects. This set of dynamical equations govern pressure p, density ρ, mass m and auxiliary fields {ψ, ξ}. The full conditional solutions are evaluated and inverted numerically to obtain exact forms of the compact stars Her X-1, SAX J 1808.4-3658 and 4U 1820-30 for nonlocal Starobinsky model of f(◻-1 R) = ◻-1 R+α(◻-1 R)2. The program solves the differential equations numerically using adaptive Gaussian quadrature. An ascription of correctness is supposed to be an empirical equation of state (P)/(Pc) = a (1- e-bρ/ρc) for star which is informative in so far as it excludes an alternative nonlocal approach to compact star formation. This model is most suited for astrophysical observation.
NASA Astrophysics Data System (ADS)
Özen, Kemal
2016-12-01
One of the little-known techniques for ordinary integro-differential equations in literature is Green's functional method, the origin of which dates back to Azerbaijani scientist Seyidali S. Akhiev. According to this method, Green's functional concepts for some simple forms of such equations have been introduced in the several studies. In this study, we extend Green's functional concept to a higher order ordinary integro-differential equation involving generally nonlocal conditions. A novel kind of adjoint problem and Green's functional are constructed for completely nonhomogeneous problem. By means of the obtained Green's functional, the solution to the problem is identified.
NASA Astrophysics Data System (ADS)
Stalin, S.; Senthilvelan, M.; Lakshmanan, M.
2017-08-01
In this paper, we succeed to bilinearize the PT-invariant nonlocal nonlinear Schrödinger (NNLS) equation through a nonstandard procedure and present more general bright soliton solutions. We achieve this by bilinearizing both the NNLS equation and its associated parity transformed complex conjugate equation in a novel way. The obtained one and two soliton solutions are invariant under combined space and time reversal transformations and are more general than the known ones. Further, by considering the two-soliton solution we bring out certain novel interaction properties of the PT-invariant multi-soliton solutions.
NASA Astrophysics Data System (ADS)
Matsuno, Yoshimasa
2004-12-01
We present the new representations of the multiperiodic and multisoliton solutions of the Benjamin-Ono and nonlocal nonlinear Schrödinger equations. The key idea in the analysis is to explore the structure of the determinantal expressions of the solutions. After providing a direct verification of the multiperiodic solution by means of an elementary theory of determinants, we show that the solution admits a representation in terms of solutions for a system of nonlinear algebraic equations. This representation is found to be an analog of the multiperiodic solution of the Korteweg-de Vries equation. We also discuss the long-wave limit of the results associated with the multiperiodic solutions.
A Legendre tau-Spectral Method for Solving Time-Fractional Heat Equation with Nonlocal Conditions
Bhrawy, A. H.; Alghamdi, M. A.
2014-01-01
We develop the tau-spectral method to solve the time-fractional heat equation (T-FHE) with nonlocal condition. In order to achieve highly accurate solution of this problem, the operational matrix of fractional integration (described in the Riemann-Liouville sense) for shifted Legendre polynomials is investigated in conjunction with tau-spectral scheme and the Legendre operational polynomials are used as the base function. The main advantage in using the presented scheme is that it converts the T-FHE with nonlocal condition to a system of algebraic equations that simplifies the problem. For demonstrating the validity and applicability of the developed spectral scheme, two numerical examples are presented. The logarithmic graphs of the maximum absolute errors is presented to achieve the exponential convergence of the proposed method. Comparing between our spectral method and other methods ensures that our method is more accurate than those solved similar problem. PMID:25057507
NASA Astrophysics Data System (ADS)
Tang, Gang; Ma, Benkun
The scaling approach proposed by Hentschel and Family [Phys. Rev. Lett. 66, 1982 (1991)] is generalized to the studies of the scaling of the anisotropic nonlocal Kardar-Parisi-Zhang equation with spatially correlated noise. The scaling exponents in both the weak- and strong-coupling regions are obtained, respectively. The scaling exponents obtained in the weak-coupling region can well match the results of the dynamic renormalization-group analysis.
Regularity of the global attractor for the plate equation with nonlocal nonlinearity in ℝn
NASA Astrophysics Data System (ADS)
Yayla, Sema
2017-07-01
This paper deals with the regularity of the global attractor for the semilinear plate equation with nonlocal nonlinearity. We proved the existence of the global attractor in the phase space H2 (ℝn) × L2 (ℝn) in our earlier work. In this study, we show that the global attractor is a bounded subset of H4 (ℝn) × H2 (ℝn).
Jasra, Ajay; Law, Kody J. H.; Zhou, Yan
2016-01-01
Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are used for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.
General solution of the diffusion equation with a nonlocal diffusive term and a linear force term.
Malacarne, L C; Mendes, R S; Lenzi, E K; Lenzi, M K
2006-10-01
We obtain a formal solution for a large class of diffusion equations with a spatial kernel dependence in the diffusive term. The presence of this kernel represents a nonlocal dependence of the diffusive process and, by a suitable choice, it has the spatial fractional diffusion equations as a particular case. We also consider the presence of a linear external force and source terms. In addition, we show that a rich class of anomalous diffusion, e.g., the Lévy superdiffusion, can be obtained by an appropriated choice of kernel.
a Note on Difference Schemes of Nonlocal Boundary Value Problems for Hyperbolic-Parabolic Equations
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Ozdemir, Yildirim
2010-11-01
A numerical method is proposed for solving multi-dimensional hyperbolic-parabolic differential equations with the nonlocal boundary condition in t and Dirichlet condition in space variables. The first and second orders of accuracy difference schemes are presented. The stability estimates for the solution and its first- and second-orders difference derivatives are established. A procedure of modified Gauss elimination method is used for solving these difference schemes in the case of a one-dimensional hyperbolic-parabolic partial differential equations with variable in x coefficients.
NASA Astrophysics Data System (ADS)
Li-Li, Huang; Yong, Chen
2016-06-01
In this paper, the truncated Painlevé analysis, nonlocal symmetry, Bäcklund transformation of the (2+1)-dimensional modified Bogoyavlenskii-Schiff equation are presented. Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system. In addition, the (2+1)-dimensional modified Bogoyavlenskii-Schiff is proved consistent Riccati expansion (CRE) solvable. As a result, the soliton-cnoidal wave interaction solutions of the equation are explicitly given, which are difficult to find by other traditional methods. Moreover figures are given out to show the properties of the explicit analytic interaction solutions. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and the Fund from Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213).
Internal noise-driven generalized Langevin equation from a nonlocal continuum model.
Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan
2015-08-01
Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.
NASA Astrophysics Data System (ADS)
Beshtokov, M. Kh.
2014-09-01
A nonlocal boundary value problem for a third-order hyperbolic equation with variable coefficients is considered in the one- and multidimensional cases. A priori estimates for the nonlocal problem are obtained in the differential and difference formulations. The estimates imply the stability of the solution with respect to the initial data and the right-hand side on a layer and the convergence of the difference solution to the solution of the differential problem.
Jeong, Darae; Kim, Junseok
2015-11-01
We investigate microphase separation patterns on curved surfaces in three-dimensional space by numerically solving a nonlocal Cahn-Hilliard equation for diblock copolymers. In our model, a curved surface is implicitly represented as the zero level set of a signed distance function. We employ a discrete narrow band grid that neighbors the curved surface. Using the closest point method, we apply a pseudo-Neumann boundary at the boundary of the computational domain. The boundary treatment allows us to replace the Laplace-Beltrami operator by the standard Laplacian operator. In particular, we can apply standard finite difference schemes in order to approximate the nonlocal Cahn-Hilliard equation in the discrete narrow band domain. We employ a type of unconditionally stable scheme, which was introduced by Eyre, and use the Jacobi iterative to solve the resulting implicit discrete system of equations. In addition, we use the minimum number of grid points for the discrete narrow band domain. Therefore, the algorithm is simple and fast. Numerous computational experiments are provided to study microphase separation patterns for diblock copolymers on curved surfaces in three-dimensional space.
On a new nonlocal boundary value problem for an equation of the mixed parabolic-hyperbolic type
NASA Astrophysics Data System (ADS)
Dildabek, Gulnar
2016-12-01
In this work a new nonlocal boundary value problem for an equation of the mixed type is formulated. This equation is parabolic-hyperbolic and belongs to the first kind because the line of type change is not a characteristic of the equation. Non-local condition binds points on boundaries of the parabolic and hyperbolic parts of the domain with each other. This problem is generalization of the well-known problems of Frankl type. A boundary value problem for the heat equation with conditions of the Samarskii-Ionlin type arises in solving this problem. Unlike the existing publications of the other authors related to the theme it is necessary to note that in this papers the nonlocal problems were considered in rectangular domains. But in our formulation of the problem the hyperbolic part of the domain coincides with a characteristic triangle. Unique strong solvability of the formulated problem is proved.
Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
NASA Astrophysics Data System (ADS)
Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemí
2012-08-01
The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, u t = J* u- u := Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on {R^NsetminusΩ} . When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation.
Nonlocal Symmetry, CTE Solvability and Interaction Solutions of Whitham-Broer-Kaup Equations
NASA Astrophysics Data System (ADS)
Zhou, Wei; Lu, Bin
2017-02-01
Whitham-Broer-Kaup (WBK) equations in the shallow water small-amplitude regime is hereby under investigation. Nonlocal symmetry and Bäcklund transformation are presented via the truncated Painlevé expansion. This residual symmetry is localised to Lie point symmetry by the properly enlarged system. The finite symmetry transformation of the prolonged system is computed. Based on the CTE method, WBK equations are linearized and new analytic interaction solutions between solitary waves and cnoidal waves are given with the aid of solutions for the linear equation. Supported by the Key Foundation of Anhui Education Bureau under Grant No. KJ2013A028, the 211 Project of Anhhui University under Grant No. J18520104, Scientific Training Project for University Students, National Natural Science Foundation of China under Grant Nos. 11471015, 11571016, and Natural Science Foundation of Anhui Province under Grant No. 1408085MA02
NASA Astrophysics Data System (ADS)
Mao, Zhiping; Karniadakis, George Em
2017-05-01
We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which, surprisingly, has an analytical solution obtained by a fractional extension of the Hopf-Cole transformation. We use this model and its inviscid limit to develop stable spectral and discontinuous Galerkin spectral element methods by employing the concept of spectral vanishing viscosity (SVV). For the global spectral method, SVV is very effective and the computational cost is O (N2), which is essentially the same as for the standard Burgers equation. We also develop a local discontinuous Galerkin (LDG) spectral element method to improve the accuracy around discontinuities, and we again stabilize the LDG method with the SVV operator. Finally, we solve numerically the inviscid fractional Burgers equation both with the spectral and the spectral element LDG methods. We study systematically the stability and convergence of both methods and determine the effectiveness of each method for different parameters.
NASA Astrophysics Data System (ADS)
Laiho, R.; Safonchik, M.; Traito, K. B.
2007-05-01
We extend the Ginsburg-Landau solution for cutoff function in London equation to low temperatures by solving numerically the quasiclassical Eilenberger equations in mixed state of s -wave superconductors. As a result the nonlocal generalized London equation (NGLE) is obtained. The magnetic field and temperature dependence of the cutoff function parameter k1(B,T) are calculated. Due to Kramer-Pesch effect k1 decreases strongly at low temperatures. It is also found that k1 has a minimum at a value of magnetic field depending on temperature. We reduce the NGLE model to an effective local model and calculate the value of an effective penetration depth λeff(B,T) . The sublinear field dependence of λeff is predicted that agrees with experimental μ SR results for the penetration depth of magnetic field in the s -wave superconductor V3Si and NbSe2 .
NASA Astrophysics Data System (ADS)
Gal, Ciprian G.; Warma, Mahamadi
2016-08-01
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is Hölder continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction-diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings.
Domoshnitsky, Alexander
2014-01-01
The impulsive delay differential equation is considered (Lx)(t) = x′(t) + ∑i=1 m p i(t)x(t − τ i(t)) = f(t), t ∈ [a, b], x(t j) = β j x(t j − 0), j = 1,…, k, a = t 0 < t 1 < t 2 < ⋯
NASA Astrophysics Data System (ADS)
Sinha, Debdeep; Ghosh, Pijush K.
2017-01-01
A two component nonlocal vector nonlinear Schrödinger equation (VNLSE) is considered with a self-induced parity-time-symmetric potential. It is shown that the system possess a Lax pair and an infinite number of conserved quantities and hence integrable. Some of the conserved quantities like number operator, Hamiltonian etc. are found to be real-valued, in spite of the corresponding charge densities being complex. The soliton solution for the same equation is obtained through the method of inverse scattering transformation and the condition of reduction from nonlocal to local case is mentioned.
Lund, S M; Bukh, B
2003-07-23
In typical diagnostic applications, intense ion beams are intercepted by a conducting plate associated with devices used to measure beam phase-space projections. This results in the transverse space-charge field near the plate being shorted out, rendering simple envelope models with constant space-charge strength inaccurate. Here we develop corrected envelope models based on analytical calculations to account for this effect on the space-charge term of the envelope equations, thereby removing a systematic source of error in the equations and enabling more accurate comparisons with experiment. For common intense beam parameters, we find that the correction occurs primarily in the envelope angles and that the effect can be large enough to degrade precision beam matching. Results are verified with 3D self-consistent PIC simulations based on intense beam experiments associated with driver developments for Heavy-Ion Fusion.
NASA Astrophysics Data System (ADS)
Setia, Amit; Prakash, Bijil; Vatsala, Aghalaya S.
2017-01-01
In this paper, a numerical method is proposed to solve the Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions by using Haar wavelets. A collocation based Galerkin's method is applied by using Haar wavelets as basis functions over the interval [0, 1). It converts the Fredholm-Volterra fractional integro-differential equation into a system of m linear equations. On incorporating q nonlocal boundary conditions, it leads to further q equations. All together it will give a system of (m + q) linear equations in (m + q) variables which can be solved. A variety of test examples are considered to illustrate the proposed method. The actual error is also measured with respect to a norm and the results are validated through error bounds.
NASA Astrophysics Data System (ADS)
Shapovalov, A. V.; Trifonov, A. Yu; Lisok, A. L.
2016-01-01
We consider an integro-differential 2-component multidimensional Gross-Pitaevskii equation with a Manakov-type cubic nonlocal nonlinearity. In the framework of the WKB-Maslov semiclassical formalism, we obtain a semiclassically reduced 2-component nonlocal Gross- Pitaevskii equation determining the leading term of the semiclassical asymptotic solution. For the reduced Gross-Pitaevskii equation we construct symmetry operators which transform arbitrary solution of the equation into another solution. Constructing the symmetry operator is based on the Cauchy problem solution technique and uses an intertwining operator which connects two solutions of the reduced Gross-Pitaevskii equation. General structure of the symmetry operator is illustrated with a 1D case for which a family of symmetry operators is found explicitly and a set of exact solutions is generated.
Jasra, Ajay; Law, Kody J. H.; Zhou, Yan
2016-01-01
Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are usedmore » for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.« less
Drogoul, Audric; Veltz, Romain
2017-02-01
In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.
Hopf bifurcation in a nonlocal nonlinear transport equation stemming from stochastic neural dynamics
NASA Astrophysics Data System (ADS)
Drogoul, Audric; Veltz, Romain
2017-02-01
In this work, we provide three different numerical evidences for the occurrence of a Hopf bifurcation in a recently derived [De Masi et al., J. Stat. Phys. 158, 866-902 (2015) and Fournier and löcherbach, Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)] mean field limit of a stochastic network of excitatory spiking neurons. The mean field limit is a challenging nonlocal nonlinear transport equation with boundary conditions. The first evidence relies on the computation of the spectrum of the linearized equation. The second stems from the simulation of the full mean field. Finally, the last evidence comes from the simulation of the network for a large number of neurons. We provide a "recipe" to find such bifurcation which nicely complements the works in De Masi et al. [J. Stat. Phys. 158, 866-902 (2015)] and Fournier and löcherbach [Ann. Inst. H. Poincaré Probab. Stat. 52, 1844-1876 (2016)]. This suggests in return to revisit theoretically these mean field equations from a dynamical point of view. Finally, this work shows how the noise level impacts the transition from asynchronous activity to partial synchronization in excitatory globally pulse-coupled networks.
Universal envelope equation and emittance evolution of high-brightness beam in linac.
Wang, C.-X.; Accelerator Systems Division
2009-01-01
We report a universal beam envelope equation that governs the transverse linear dynamics of high-intensity and high-brightness relativistic beams under constant acceleration in axisymmetric linear accelerators. This dimensionless and almost parameter-free nonlinear equation is useful for understanding scaling properties and for investigating nonlinear behaviors that are beyond analytical analysis. Particularly, we explore emittance compensation in high-brightness beams evolving from the space-charge regime to the thermal-emittance regime, a transition that commonly occurs during acceleration but is not well studied. A new formula is given for correctly computing the rms bunch emittance from slice envelopes, which is different from the commonly used quadratic sum of the thermal emittance and the rms emittance in the envelope phase space.
A non-local evolution equation model of cell–cell adhesion in higher dimensional space
Dyson, Janet; Gourley, Stephen A.; Webb, Glenn F.
2013-01-01
A model for cell–cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell–cell adhesion, J. Theor. Biol. 243 (2006), pp. 98–113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments. AMS Classifications: 35A01; 35B09; 35B40; 35K57; 92C17 PMID:23289870
Multivalley envelope function equations and effective potentials for phosphorus impurity in silicon
NASA Astrophysics Data System (ADS)
Klymenko, M. V.; Rogge, S.; Remacle, F.
2015-11-01
We propose a system of real-space envelope function equations without fitting parameters for modeling the electronic spectrum and wave functions of a phosphorus donor atom embedded in silicon. The approach relies on the Burt-Foreman envelope function representation and leads to coupled effective-mass Schrödinger equations containing smooth effective potentials. These potentials result from the spatial filtering imposed on the exact potential energy matrix elements in the envelope function representation. The corresponding filter function is determined from the definition of the envelope function. The resulting effective potentials and the system of envelope functions jointly reproduce the valley-orbit coupling effect in doped silicon. It is found that including the valley-orbit coupling not only of the 1 s but also for 2 s atomic orbitals, as well as static dielectric screening, is crucial to accurately reproduce experimental data. The measured binding energies are recovered with a maximum relative error of 1.53%. The computed wave functions are in good agreement with experimental measurements of the electron density provided by scanning tunneling microscopy.
Representation of solutions and large-time behavior for fully nonlocal diffusion equations
NASA Astrophysics Data System (ADS)
Kemppainen, Jukka; Siljander, Juhana; Zacher, Rico
2017-07-01
We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: a representation formula for classical solutions a quantitative decay rate at which the solution tends to the fundamental solution optimal L2-decay of mild solutions in all dimensions L2-decay of weak solutions via energy methods. The first result relies on a delicate analysis of the definition of classical solutions. After proving the representation formula we carefully analyze the integral representation to obtain the quantitative decay rates of (ii). Next we use Fourier analysis techniques to obtain the optimal decay rate for mild solutions. Here we encounter the critical dimension phenomenon where the decay rate attains the decay rate of that in a bounded domain for large enough dimensions. Consequently, the decay rate does not anymore improve when the dimension increases. The theory is markedly different from that of the standard caloric functions and this substantially complicates the analysis. Finally, we use energy estimates and a comparison principle to prove a quantitative decay rate for weak solutions defined via a variational formulation. Our main idea is to show that the L2-norm is actually a subsolution to a purely time-fractional problem which allows us to use the known theory to obtain the result.
Wen, Zichao; Yan, Zhenya
2017-05-01
We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schrödinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken and unbroken PT-symmetric phases of linear bounded states and the linear stability of the obtained solitons. Moreover, we numerically explore the dynamical behaviors of solitons and find stable solitons for some given parameters.
An Inhomogeneous Space-Time Patching Model Based on a Nonlocal and Nonlinear Schrödinger Equation
NASA Astrophysics Data System (ADS)
Dantas, Christine C.
2016-10-01
We consider an integrable, nonlocal and nonlinear, Schrödinger equation (NNSE) as a model for building space-time patchings in inhomogeneous loop quantum cosmology (LQC). We briefly review exact solutions of the NNSE, specially those obtained through "geometric equivalence" methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.
NASA Astrophysics Data System (ADS)
Degasperis, A.; Lebedev, D.; Olshanetsky, M.; Pakuliak, S.; Perelomov, A.; Santini, P.
1991-10-01
Two new hierarchies, MILW2 and a two-dimensional nonlocal Toda lattice are constructed. The characteristic property of the first one is the connection with the ILW2 hierarchy by means of gl(2) Miura transformation. On the other hand, MILW2 equations turn out to be symmetry equations for a two-dimensional nonlocal Toda lattice. A new version of the dressing technique with quantized spectral parameter is proposed.
Hong Qin and Ronald C. Davidson
2012-04-25
A class of generalized Kapchinskij-Vladimirskij solutions of the nonlinear Vlasov-Maxwell equations and the associated envelope equations for high-intensity beams in a periodic lattice is derived. It includes the classical Kapchinskij-Vladimirskij solution as a special case. For a given lattice, the distribution functions and the envelope equations are specified by eight free parameters. The class of solutions derived captures a wider range of dynamical envelope behavior for high-intensity beams, and thus provides a new theoretical tool to investigate the dynamics of high-intensity beams.
Sepulveda, Nestor
2011-04-15
Modulated solutions of the nonlocal Gross-Pitaevskii equation are studied at T{ne}0. Stationary states are computed by constructing a stochastic process consisting of a noisy Ginzburg-Landau equation. An order parameter is introduced to quantify the superfluid fraction as a function of the temperature. When the temperature increases the superfluid fraction is shown to vanish. This is explained qualitatively by the thermal appearance of defects that disconnect the system wave function. We also deduce an explicit formula for the introduced order parameter in terms of an Arrhenius law. This allow us to estimate the ''energy of activation'' to create a disconnection in the wave function.
NASA Astrophysics Data System (ADS)
Drugan, W. J.; Willis, J. R.
2016-06-01
A variational formulation employing the minimum potential and complementary energy principles is used to derive a micromechanics-based nonlocal constitutive equation for random linear elastic composite materials, relating ensemble averages of stress and strain in the most general situation when mean fields vary spatially. All information contained in the energy principles is retained; we employ stress polarization trial fields utilizing one-point statistics so that the resulting nonlocal constitutive equation incorporates up through three-point statistics. The variational structure is developed first for arbitrary heterogeneous linear elastic materials, then for randomly inhomogeneous materials, then for general n-phase composite materials, and finally for two-phase composite materials, in which case explicit variational upper and lower bounds on the nonlocal effective modulus tensor operator are derived. For statistically uniform infinite-body composites, these bounds are determined even more explicitly in Fourier transform space. We evaluate these in detail in an example case: longitudinal shear of an aligned fiber or void composite. We determine the full permissible ranges of the terms involving two- and three-point statistics in these bounds, and thereby exhibit explicit results that encompass arbitrary isotropic in-plane phase distributions; we also develop a nonlocal "Milton parameter", the variation of whose eigenvalues throughout the interval [0, 1] describes the full permissible range of the three-point term. Example plots of the new bounds show them to provide substantial improvement over the (two-point) Hashin-Shtrikman bounds on the nonlocal operator tensor, for all permissible values of the two- and three-point parameters. We next discuss further applications of the general nonlocal operator bounds: to any three-dimensional scalar transport problem e.g. conductivity, for which explicit results are given encompassing the full permissible ranges of the
NASA Astrophysics Data System (ADS)
Cuesta, C. M.; Achleitner, F.
2017-01-01
We add a theorem to F. Achleitner, C.M. Cuesta and S. Hittmeir (2014) [1]. In that paper we studied travelling wave solutions of a Korteweg-de Vries-Burgers type equation with a non-local diffusion term. In particular, the proof of existence and uniqueness of these waves relies on the assumption that the exponentially decaying functions are the only bounded solutions of the linearised equation. In this addendum we prove this assumption and thus close the existence and uniqueness proof of travelling wave solutions.
On the asymptotic behavior of a subcritical convection-diffusion equation with nonlocal diffusion
NASA Astrophysics Data System (ADS)
Cazacu, Cristian M.; Ignat, Liviu I.; Pazoto, Ademir F.
2017-08-01
In this paper we consider a subcritical model that involves nonlocal diffusion and a classical convective term. In spite of the nonlocal diffusion, we obtain an Oleinik type estimate similar to the case when the diffusion is local. First we prove that the entropy solution can be obtained by adding a small viscous term μ uxx and letting μ\\to 0 . Then, by using uniform Oleinik estimates for the viscous approximation we are able to prove the well-posedness of the entropy solutions with L 1-initial data. Using a scaling argument and hyperbolic estimates given by Oleinik’s inequality, we obtain the first term in the asymptotic behavior of the nonnegative solutions. Finally, the large time behavior of changing sign solutions is proved using the classical flux-entropy method and estimates for the nonlocal operator.
Igor D. Kaganovich; Oleg Polomarov
2003-05-19
In low-pressure discharges, when the electron mean free path is larger or comparable with the discharge length, the electron dynamics is essentially non-local. Moreover, the electron energy distribution function (EEDF) deviates considerably from a Maxwellian. Therefore, an accurate kinetic description of the low-pressure discharges requires knowledge of the non-local conductivity operator and calculation of the non-Maxwellian EEDF. The previous treatments made use of simplifying assumptions: a uniform density profile and a Maxwellian EEDF. In the present study a self-consistent system of equations for the kinetic description of nonlocal, non-uniform, nearly collisionless plasmas of low-pressure discharges is derived. It consists of the nonlocal conductivity operator and the averaged kinetic equation for calculation of the non-Maxwellian EEDF. The importance of accounting for the non-uniform plasma density profile on both the current density profile and the EEDF is demonstrated.
Solutions of the matched KV envelope equations for a ``smooth'' asymmetric focusing channel
NASA Astrophysics Data System (ADS)
Reiser, Martin; Li, Hui
2004-07-01
In many particle accelerators the applied focusing forces may differ in two or three directions either by design in order to avoid resonances or for other reasons, such as design constraints, bunch compression/expansion, dispersion, etc. At high intensities, space charge effects and related collective forces may cause unwanted emittance growth via instabilities and equipartitioning (relaxation of temperature anisotropy). For the transverse two-dimensional case, such asymmetric (anisotropic) systems are described by the coupled, matched envelope equations of the Kapchinskij-Vladimirskij distribution with different focusing strengths and emittances in the x and y directions, which must be solved numerically for a periodic lattice. In this article, we present results for a "smooth" asymmetric focusing channel, in which case one obtains a set of two coupled algebraic equations for the envelopes X and Y. Though the algebraic equations can easily be solved numerically, the scaling with the physics parameters is usually obscured by the numerical procedures. We derived an approximate solution as well as a general, more accurate solution, both of which represent results that exhibit the scaling with the applied focusing, space-charge, and emittance terms. The accuracy of the approximate solution is in the range of a few percent for a channel with a small degree of asymmetry. The general solution is obtained by solving for the aspect ratio A=Y/X by an iteration method that yields results to any desired degree of accuracy. More importantly, to facilitate the comparison between systems with different particle species and/or operating parameters, the envelope equations in this general treatment are written in dimensionless form. This is accomplished by expressing the envelopes X and Y in terms of the "average radius" as, and by introducing dimensionless parameters, v and w, which measure the degrees of focusing and emittance asymmetries, and the ratios of the space charge to
Bunched beam envelope equations including image effects from a cylindrical pipe
Allen, C.K.; Reiser, M.
1997-06-01
We derive a set of differential equations for the beam envelopes of an axisymmetric, bunched beam inside a perfectly conducting beam pipe. It is found that the beam dynamics are essentially independent of the form of bunch distribution in the free-space situation, however, in the presence of the beam pipe this is no longer the case. Analytic expressions involving infinite summations of Bessel functions are derived for the image potential and image fields of an ellipsoidally symmetric charge distributions in a beam pipe, in particular, the uniform density distribution. We simulate a simple beam transport system to demonstrate the application of these results. {copyright} {ital 1997} {ital The American Physical Society}
NASA Astrophysics Data System (ADS)
Cheng, Wen-Guang; Qiu, De-Qin; Yu, Bo
2017-06-01
This paper is concerned with the fifth-order modified Korteweg-de Vries (fmKdV) equation. It is proved that the fmKdV equation is consistent Riccati expansion (CRE) solvable. Three special form of soliton-cnoidal wave interaction solutions are discussed analytically and shown graphically. Furthermore, based on the consistent tanh expansion (CTE) method, the nonlocal symmetry related to the consistent tanh expansion (CTE) is investigated, we also give the relationship between this kind of nonlocal symmetry and the residual symmetry which can be obtained with the truncated Painlevé method. We further study the spectral function symmetry and derive the Lax pair of the fmKdV equation. The residual symmetry can be localized to the Lie point symmetry of an enlarged system and the corresponding finite transformation group is computed. Supported by National Natural Science Foundation of China under Grant No. 11505090, and Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009
Oxley, M.P.; Cosgriff, E.C.; Allen, L.J.
2005-05-27
We show how an effective nonlocality in imaging can lead to the sampling of a spatial region which is not significantly illuminated by an imaging probe. The nonlocality is embodied in the effective nonlocal potential describing inelastic scattering which occurs when coupled channel Schroedinger equations are reduced to a single integro-differential equation. The context in which this prediction will be illustrated is atomic resolution imaging based on energy-loss spectroscopy in scanning transmission electron microscopy.
Oxley, M P; Cosgriff, E C; Allen, L J
2005-05-27
We show how an effective nonlocality in imaging can lead to the sampling of a spatial region which is not significantly illuminated by an imaging probe. The nonlocality is embodied in the effective nonlocal potential describing inelastic scattering which occurs when coupled channel Schrödinger equations are reduced to a single integro-differential equation. The context in which this prediction will be illustrated is atomic resolution imaging based on energy-loss spectroscopy in scanning transmission electron microscopy.
Ellipticity and the spurious solution problem of k•p envelope equations
NASA Astrophysics Data System (ADS)
Veprek, Ratko G.; Steiger, Sebastian; Witzigmann, Bernd
2007-10-01
We present an explanation to the spurious solution problem affecting the k•p envelope function method, indicating that the problem is mathematically caused by loss of ellipticity of the differential operator. Focusing on direct band gap zinc-blende heterostructures, we derive criteria that must be fulfilled by the input parameters in order to establish ellipticity. Using these criteria, we compare symmetrized operators with Burt-Foreman [B. A. Foreman, Phys. Rev. B 56, R12748 (1997)] operator ordering. We substantiate our arguments with numerical results obtained using linear finite elements. We find that the space of stable input parameters is very narrow and demonstrate that Burt-Foreman operator ordering together with experimental k•p input parameters leads to near-elliptic envelope equations in the 4×4 and 6×6 models, whereas symmetrization yields strong nonellipticity. In the k•p 8×8 model, the procedure of renormalizing parameters of the 4×4 model generally yields parameters producing spurious solutions, even for Burt-Foreman operator ordering. We find that this problem can be resolved by using a smaller optical matrix parameter Ep . This suggests that the parametrization of k•p models for heterostructures of any dimensionality must be reviewed, checking against the mathematical ellipticity of the equation system.
NASA Astrophysics Data System (ADS)
Jin-Yuan, Li; Nian-Qiao, Fang; Ji, Zhang; Yu-Long, Xue; Xue-Mu, Wang; Xiao-Bo, Yuan
2016-04-01
In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given. Project supported by the National Natural Science Foundation of China (Grant No. 41406018).
NASA Astrophysics Data System (ADS)
Su, Ying; Zou, Xingfu
2014-01-01
In this paper, we study the spatial-temporal patterns of the solutions to the diffusive non-local Nicholson's blowflies equations with time delay (maturation time) subject to the no flux boundary condition. We establish the existence of both spatially homogeneous periodic solutions and various spatially inhomogeneous periodic solutions by investigating the Hopf bifurcations at the spatially homogeneous steady state. We also compute the normal form on the centre manifold, by which the bifurcation direction and stability of the bifurcated periodic solutions can be determined. The results show that the bifurcated homogeneous periodic solutions are stable, while the bifurcated inhomogeneous periodic solutions can only be stable on the corresponding centre manifold, implying that generically the model can only allow transient oscillatory patterns. Finally, we present some numerical simulations to demonstrate the theoretic results. For these transient patterns, we derive approximation formulas which are confirmed by numerical simulations.
NASA Astrophysics Data System (ADS)
Zhang, Guo-Bao; Ma, Ruyun
2014-10-01
This paper is concerned with the traveling wave solutions and the spreading speeds for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity, which is motivated by an age-structured population model with time delay. We first prove the existence of traveling wave solution with critical wave speed c = c*. By introducing two auxiliary monotone birth functions and using a fluctuation method, we further show that the number c = c* is also the spreading speed of the corresponding initial value problem with compact support. Then, the nonexistence of traveling wave solutions for c < c* is established. Finally, by means of the (technical) weighted energy method, we prove that the traveling wave with large speed is exponentially stable, when the initial perturbation around the wave is relatively small in a weighted norm.
Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions
ERIC Educational Resources Information Center
Aliev, Nihan; Jahanshahi, Mohammad
2002-01-01
Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…
Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions
ERIC Educational Resources Information Center
Aliev, Nihan; Jahanshahi, Mohammad
2002-01-01
Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…
NASA Technical Reports Server (NTRS)
Hummer, D. G.; Mihalas, Dimitri
1988-01-01
An equation of state for material in stellar envelopes, subject to the limits of temperature less than about 10 to the 7th K and density less than about .01 g/cu cm is presented. The equation makes it possible to express free energy as the sum of several terms representing effects such as partial degeneracy of the electron, Coulomb interactions among charged particles, finite-volume, hard sphere repulsion, and van der Waals attraction. An occupation probability formalism is used to represent the effects of the plasma in establishing a finite partition function. It is shown that the use of the static screened Coulomb potential to calculate level shifts and to estimate the cutoff of the internal partition function is invalid. For most of the parameter space relevant to stellar envelopes, perturbations arising from the plasma ions are shown to be dominant in establishing the internal partition function.
NASA Technical Reports Server (NTRS)
Hummer, D. G.; Mihalas, Dimitri
1988-01-01
An equation of state for material in stellar envelopes, subject to the limits of temperature less than about 10 to the 7th K and density less than about .01 g/cu cm is presented. The equation makes it possible to express free energy as the sum of several terms representing effects such as partial degeneracy of the electron, Coulomb interactions among charged particles, finite-volume, hard sphere repulsion, and van der Waals attraction. An occupation probability formalism is used to represent the effects of the plasma in establishing a finite partition function. It is shown that the use of the static screened Coulomb potential to calculate level shifts and to estimate the cutoff of the internal partition function is invalid. For most of the parameter space relevant to stellar envelopes, perturbations arising from the plasma ions are shown to be dominant in establishing the internal partition function.
Wen, Xiao-Yong; Yan, Zhenya; Yang, Yunqing
2016-06-01
The integrable nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential [M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. Lett. 110, 064105 (2013)] is investigated, which is an integrable extension of the standard nonlinear Schrödinger equation. Its novel higher-order rational solitons are found using the nonlocal version of the generalized perturbation (1,N-1)-fold Darboux transformation. These rational solitons illustrate abundant wave structures for the distinct choices of parameters (e.g., the strong and weak interactions of bright and dark rational solitons). Moreover, we also explore the dynamical behaviors of these higher-order rational solitons with some small noises on the basis of numerical simulations.
A generalized nonlocal vector calculus
NASA Astrophysics Data System (ADS)
Alali, Bacim; Liu, Kuo; Gunzburger, Max
2015-10-01
A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A formulation is developed that provides a more general setting for the nonlocal vector calculus that is independent of particular nonlocal models. It is shown that general nonlocal calculus operators are integral operators with specific integral kernels. General nonlocal calculus properties are developed, including nonlocal integration by parts formula and Green's identities. The nonlocal vector calculus introduced in Du et al. (Math Model Meth Appl Sci 23:493-540, 2013) is shown to be recoverable from the general formulation as a special example. This special nonlocal vector calculus is used to reformulate the peridynamics equation of motion in terms of the nonlocal gradient operator and its adjoint. A new example of nonlocal vector calculus operators is introduced, which shows the potential use of the general formulation for general nonlocal models.
Nonlocal gravity: Conformally flat spacetimes
NASA Astrophysics Data System (ADS)
Bini, Donato; Mashhoon, Bahram
2016-04-01
The field equations of the recent nonlocal generalization of Einstein’s theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein’s field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of NLG.
Sinha, Debdeep; Ghosh, Pijush K
2015-04-01
A class of nonlocal nonlinear Schrödinger equations (NLSEs) is considered in an external potential with a space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization of a recently introduced integrable nonlocal NLSE with self-induced potential that is parity-time-symmetric in the corresponding stationary problem. Exact soliton solutions are obtained for the inhomogeneous and/or nonautonomous nonlocal NLSE by using similarity transformation, and the method is illustrated with a few examples. It is found that only those transformations are allowed for which the transformed spatial coordinate is odd under the parity transformation of the original one. It is shown that the nonlocal NLSE without the external potential and a (d+1)-dimensional generalization of it admits all the symmetries of the (d+1)-dimensional Schrödinger group. The conserved Noether charges associated with the time translation, dilatation, and special conformal transformation are shown to be real-valued in spite of being non-Hermitian. Finally, the dynamics of different moments are studied with an exact description of the time evolution of the "pseudowidth" of the wave packet for the special case in which the system admits a O(2,1) conformal symmetry.
NASA Astrophysics Data System (ADS)
Sinha, Debdeep; Ghosh, Pijush K.
2015-04-01
A class of nonlocal nonlinear Schrödinger equations (NLSEs) is considered in an external potential with a space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization of a recently introduced integrable nonlocal NLSE with self-induced potential that is parity-time-symmetric in the corresponding stationary problem. Exact soliton solutions are obtained for the inhomogeneous and/or nonautonomous nonlocal NLSE by using similarity transformation, and the method is illustrated with a few examples. It is found that only those transformations are allowed for which the transformed spatial coordinate is odd under the parity transformation of the original one. It is shown that the nonlocal NLSE without the external potential and a (d +1 )-dimensional generalization of it admits all the symmetries of the (d +1 )-dimensional Schrödinger group. The conserved Noether charges associated with the time translation, dilatation, and special conformal transformation are shown to be real-valued in spite of being non-Hermitian. Finally, the dynamics of different moments are studied with an exact description of the time evolution of the "pseudowidth" of the wave packet for the special case in which the system admits a O (2 ,1 ) conformal symmetry.
Hong Qin, Moses Chung, and Ronald C. Davidson
2009-11-20
In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high- intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.
Acausality in nonlocal gravity theory
NASA Astrophysics Data System (ADS)
Zhang, Ying-li; Koyama, Kazuya; Sasaki, Misao; Zhao, Gong-Bo
2016-03-01
We investigate the nonlocal gravity theory by deriving nonlocal equations of motion using the traditional variation principle in a homogeneous background. We focus on a class of models with a linear nonlocal modification term in the action. It is found that the resulting equations of motion contain the advanced Green's function, implying that there is an acausality problem. As a consequence, a divergence arises in the solutions due to contributions from the future infinity unless the Universe will go back to the radiation dominated era or become the Minkowski spacetime in the future. We also discuss the relation between the original nonlocal equations and its biscalar-tensor representation and identify the auxiliary fields with the corresponding original nonlocal terms. Finally, we show that the acusality problem cannot be avoided by any function of nonlocal terms in the action.
Nonlocal effective gravitational field equations and the running of Newton's constant G
Hamber, H.W.; Williams, R.M.
2005-08-15
Nonperturbative studies of quantum gravity have recently suggested the possibility that the strength of gravitational interactions might slowly increase with distance. Here a set of generally covariant effective field equations are proposed, which are intended to incorporate the gravitational, vacuum-polarization induced, running of Newton's constant G. One attractive feature of this approach is that, from an underlying quantum gravity perspective, the resulting long-distance (or large time) effective gravitational action inherits only one adjustable parameter {xi}, having the units of a length, arising from dimensional transmutation in the gravitational sector. Assuming the above scenario to be correct, some simple predictions for the long-distance corrections to the classical standard model Robertson-Walker metric are worked out in detail, with the results formulated as much as possible in a model-independent framework. It is found that the theory, even in the limit of vanishing renormalized cosmological constant, generally predicts an accelerated power-law expansion at later times t{approx}{xi}{approx}1/H.
NASA Astrophysics Data System (ADS)
Mashhoon, Bahram
2017-05-01
Relativity theory is based on a postulate of locality, which means that the past history of the observer is not directly taken into account. This book argues that the past history should be taken into account. In this way, nonlocality 1R 2i1nr-in the sense of history dependence-is introduced into relativity theory. The deep connection between inertia and gravitation suggests that gravity could be nonlocal, and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein's theory of gravitation has recently been developed. A significant consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. According to nonlocal gravity theory, what astronomers attribute to dark matter should instead be due to the nonlocality of gravitation. Nonlocality dominates on the scale of galaxies and beyond. Memory fades with time; therefore, the nonlocal aspect of gravity becomes weaker as the universe expands. The implications of nonlocal gravity are explored in this book for gravitational lensing, gravitational radiation, the gravitational physics of the Solar System and the internal dynamics of nearby galaxies, as well as clusters of galaxies. This approach is extended to nonlocal Newtonian cosmology, where the attraction of gravity fades with the expansion of the universe. Thus far, scientists have only compared some of the consequences of nonlocal gravity with astronomical observations.
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Montobbio, Michele; Nardelli, Giuseppe
2007-12-01
An analytic approach to phenomenological models inspired by cubic string field theory is introduced and applied to some examples. We study a class of actions for a minimally coupled, homogeneous scalar field whose energy density contains infinitely many time derivatives. These nonlocal systems are systematically localized and an algorithm to find cosmological solutions of the dynamical equations is provided. Our formalism is able to define the nonlocal field in regions of the parameter space which are inaccessible by standard methods. Also, problems related to nonlocality are reinterpreted under a novel perspective and naturally overcome. We consider phenomenological models living on a Friedmann-Robertson-Walker background with power-law scale factor, both in four dimensions and on a high-energy braneworld. The quest for solutions unravels general features of nonlocal dynamics indicating several future directions of investigation.
NASA Astrophysics Data System (ADS)
Grinevich, P. G.; Santini, P. M.
2016-10-01
Written in the evolutionary form, the multidimensional integrable dispersionless equations, exactly like the soliton equations in 2+1 dimensions, become nonlocal. In particular, the Pavlov equation is brought to the form v t = v x v y - ∂ x -1 ∂ y [ v y + v x 2], where the formal integral ∂ x -1 becomes the asymmetric integral - int_x^∞ {dx'} . We show that this result could be guessed using an apparently new integral geometry lemma. It states that the integral of a sufficiently general smooth function f( X, Y) over a parabola in the plane ( X, Y) can be expressed in terms of the integrals of f( X, Y) over straight lines not intersecting the parabola. We expect that this result can have applications in two-dimensional linear tomography problems with an opaque parabolic obstacle.
Rolling Tachyon in Nonlocal Cosmology
Joukovskaya, L.
2007-11-20
Nonlocal cosmological models derived from String Field Theory are considered. A new method for constructing rolling tachyon solutions in the FRW metric in two field configuration is proposed and solutions of the Friedman equations with nonlocal operator are presented. The cosmological properties of these solutions are discussed.
Nonlocality Without Nonlocality
NASA Astrophysics Data System (ADS)
Weinstein, Steven
2009-08-01
Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ ( SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all.
NASA Astrophysics Data System (ADS)
Antoine, Xavier; Tang, Qinglin; Zhang, Yong
2016-11-01
In this paper, we propose some efficient and robust numerical methods to compute the ground states and dynamics of Fractional Schrödinger Equation (FSE) with a rotation term and nonlocal nonlinear interactions. In particular, a newly developed Gaussian-sum (GauSum) solver is used for the nonlocal interaction evaluation [31]. To compute the ground states, we integrate the preconditioned Krylov subspace pseudo-spectral method [4] and the GauSum solver. For the dynamics simulation, using the rotating Lagrangian coordinates transform [14], we first reformulate the FSE into a new equation without rotation. Then, a time-splitting pseudo-spectral scheme incorporated with the GauSum solver is proposed to simulate the new FSE. In parallel to the numerical schemes, we also prove some existence and nonexistence results for the ground states. Dynamical laws of some standard quantities, including the mass, energy, angular momentum and the center of mass, are stated. The ground states properties with respect to the fractional order and/or rotating frequencies, dynamics involving decoherence and turbulence together with some interesting phenomena are reported.
Kostin, A B
2013-10-31
We study the inverse problem for a parabolic equation of recovering the source, that is, the right-hand side F(x,t)=h(x,t)f(x), where the function f(x) is unknown. To find f(x), along with the initial and boundary conditions, we also introduce an additional condition of nonlocal observation of the form ∫{sub 0}{sup T}u(x,t) dμ(t)=χ(x). We prove the Fredholm property for the problem stated in this way, and obtain sufficient conditions for the existence and uniqueness of a solution. These conditions are of the form of readily verifiable inequalities and put no restrictions on the value of T>0 or the diameter of the domain Ω under consideration. The proof uses a priori estimates and the qualitative properties of solutions of initial-boundary value problems for parabolic equations. Bibliography: 40 titles.
Nonlocal and quasilocal field theories
NASA Astrophysics Data System (ADS)
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
Zhou, Xiangyu; Ghione, Giovanni; Bertazzi, Francesco Goano, Michele; Bellotti, Enrico
2014-07-21
We present a multiband envelope-function model for wurtzite nanostructures based on a rigorous numerical procedure to determine operator ordering and band parameters from nonlocal empirical pseudopotential calculations. The proposed approach, implemented within a finite-element scheme, leads to well-posed, numerically stable envelope equations that accurately reproduce full-Brillouin-zone subband dispersions of quantum systems. Although demonstrated here for III-nitride nonlocal empirical pseudopotentials, the model provides a general theoretical framework applicable to ab initio electronic structures of wurtzite semiconductors.
NASA Astrophysics Data System (ADS)
Giaccari, Stefano; Modesto, Leonardo
2017-09-01
We propose an N =1 supersymmetric extension for a class of weakly nonlocal four-dimensional gravitational theories. The construction is done in the superspace where the off-shell supersymmetry is manifest. The tree-level perturbative unitarity is explicitly proved both in superfield formalism and in field components. For the minimal nonlocal supergravity the spectrum is the same as in the local theory and in particular it is ghost free. The supersymmetric extension of the nonlocal Starobinsky theory is found as a straightforward application of the formalism.
Frustrated Brownian Motion of Nonlocal Solitary Waves
Folli, V.; Conti, C.
2010-05-14
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.
Michel, N.
2008-02-15
Demonstrating the completeness of wave function solutions of the radial Schroedinger equation is a very difficult task. Existing proofs, relying on operator theory, are often very abstract and far from intuitive comprehension. However, it is possible to obtain rigorous proofs amenable to physical insight, if one restricts the considered class of Schroedinger potentials. One can mention, in particular, unbounded potentials yielding a purely discrete spectrum and short-range potentials. However, those possessing a Coulomb tail, very important for physical applications, have remained problematic due to their long-range character. The method proposed in this paper allows to treat them correctly, provided that the non-Coulomb part of potentials vanishes after a finite radius. Nonlocality of potentials can also be handled. The main idea in the proposed demonstration is that regular solutions behave like sine/cosine functions for large momenta, so that their expansions verify Fourier transform properties. The highly singular point at k=0 of long-range potentials is dealt with properly using analytical properties of Coulomb wave functions. Lebesgue measure theory is avoided, rendering the demonstration clear from a physical point of view.
Nonlinear Landau damping of wave envelopes in a quantum plasma
NASA Astrophysics Data System (ADS)
Chatterjee, Debjani; Misra, A. P.
2016-10-01
The nonlinear theory of Landau damping of electrostatic wave envelopes (WEs) is revisited in a quantum electron-positron pair plasma. Starting from a Wigner-Moyal equation coupled to the Poisson equation and applying the multiple scale technique, we derive a nonlinear Schrödinger (NLS) equation which governs the evolution of electrostatic WEs. It is shown that the coefficients of the NLS equation, including the nonlocal nonlinear term, which appears due to the resonant particles having a group velocity of the WEs, are significantly modified by the particle dispersion. The effects of the quantum parameter H (the ratio of the plasmon energy to the thermal energy densities), associated with the particle dispersion, are examined on the Landau damping rate of carrier waves, as well as on the modulational instability of WEs. It is found that the Landau damping rate and the decay rate of the solitary wave amplitude are greatly reduced compared to their classical values (H = 0).
Deser, S; Woodard, R P
2007-09-14
We explore nonlocally modified models of gravity, inspired by quantum loop corrections, as a mechanism for explaining current cosmic acceleration. These theories enjoy two major advantages: they allow a delayed response to cosmic events, here the transition from radiation to matter dominance, and they avoid the usual level of fine-tuning; instead, emulating Dirac's dictum, the required large numbers come from the large time scales involved. Their solar system effects are safely negligible, and they may even prove useful to the black hole information problem.
Origin of Dynamical Quantum Non-locality
NASA Astrophysics Data System (ADS)
Pachon, Cesar E.; Pachon, Leonardo A.
2014-03-01
Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two ``flavours'': a kinematic non-locality- arising from the structure of the Hilbert space- and a dynamical non-locality- arising from the quantum equations of motion-. Kinematic non-locality is unable to induce any change in the probability distributions, so that the ``action-at-a-distance'' cannot manifest. Conversely, dynamical non-locality does create explicit changes in probability, though in a ``causality-preserving'' manner. The origin of non-locality of quantum measurements and its relations to the fundamental postulates of quantum mechanics, such as the uncertainty principle, have been only recently elucidated. Here we trace the origin of dynamical non-locality to the superposition principle. This relation allows us to establish and identify how the uncertainty and the superposition principles determine the non-local character of the outcome of a quantum measurement. Being based on group theoretical and path integral formulations, our formulation admits immediate generalizations and extensions to to, e.g., quantum field theory. This work was supported by the Departamento Administrativo de Ciencia, Tecnologia e Innovacion -COLCIENCIAS- of Colombia under the grant number 111556934912.
NASA Astrophysics Data System (ADS)
Zidour, M.; Daouadji, T. H.; Benrahou, K. H.; Tounsi, A.; Adda Bedia, El A.; Hadji, L.
2014-03-01
On the basis of the nonlocal elasticity theory, the Timoshenko beam model is utilized to investigate the elastic buckling of chiral single-walled carbon nanotubes (SWCNTs) under axial compression. Based on the governing equations of the nonlocal Timoshenko beam model, an analytical solution for nonlocal critical buckling loads is obtained. The influence of a nonlocal small-scale coefficient, the vibration mode number, the chirality of SWWCNTs, and their aspect ratio on the nonlocal critical buckling loads is studied and discussed.
Quantum nonlocality does not exist.
Tipler, Frank J
2014-08-05
Quantum nonlocality is shown to be an artifact of the Copenhagen interpretation, in which each observed quantity has exactly one value at any instant. In reality, all physical systems obey quantum mechanics, which obeys no such rule. Locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the many-worlds interpretation (MWI). Using the MWI, I show that the quantum side of Bell's inequality, generally believed nonlocal, is really due to a series of three measurements (not two as in the standard, oversimplified analysis), all three of which have only local effects. Thus, experiments confirming "nonlocality" are actually confirming the MWI. The mistaken interpretation of nonlocality experiments depends crucially on a question-begging version of the Born interpretation, which makes sense only in "collapse" versions of quantum theory, about the meaning of the modulus of the wave function, so I use the interpretation based on the MWI, namely that the wave function is a world density amplitude, not a probability amplitude. This view allows the Born interpretation to be derived directly from the Schrödinger equation, by applying the Schrödinger equation to both the observed and the observer.
Nonlocal study of ultimate plasmon hybridization.
Raza, Søren; Wubs, Martijn; Bozhevolnyi, Sergey I; Mortensen, N Asger
2015-03-01
Within our recently proposed generalized nonlocal optical response (GNOR) model, where nonlocal response is included by taking into account both convective and diffusive currents of the conduction electrons, we revisit the fundamental problem of an optically excited plasmonic dimer. We consider the transition from separated dimers via touching dimers to finally overlapping dimers. In particular, we focus on the touching case, showing a fundamental limit on the hybridization of the bonding plasmon modes due to nonlocality. Using transformation optics, we determine a simple analytical equation for the resonance energies.
On a nonlocal model of image segmentation
NASA Astrophysics Data System (ADS)
Gajewski, Herbert; Gärtner, Klaus
2005-07-01
We understand an image as binary grey ‘alloy’ of a black and a white component and use a nonlocal phase separation model to describe image segmentation. The model consists in a degenerate nonlinear parabolic equation with a nonlocal drift term additionally to the familiar Perona-Malik model. We formulate conditions for the model parameters to guarantee global existence of a unique solution that tends exponentially in time to a unique steady state. This steady state is solution of a nonlocal nonlinear elliptic boundary value problem and allows a variational characterization. Numerical examples demonstrate the properties of the model.
Quantum ring solitons and nonlocal effects in plasma wake field excitations
Fedele, R.; Tanjia, F.; De Nicola, S.; Jovanovic, D.; Shukla, P. K.
2012-10-15
A theoretical investigation of the quantum transverse beam motion for a cold relativistic charged particle beam travelling in a cold, collisionless, strongly magnetized plasma is carried out. This is done by taking into account both the individual quantum nature of the beam particles (single-particle uncertainty relations and spin) and the self consistent interaction generated by the plasma wake field excitation. By adopting a fluid model of a strongly magnetized plasma, the analysis is carried out in the overdense regime (dilute beams) and in the long beam limit. It is shown that the quantum description of the collective transverse beam dynamics is provided by a pair of coupled nonlinear governing equations. It comprises a Poisson-like equation for the plasma wake potential (driven by the beam density) and a 2D spinorial Schroedinger equation for the wave function, whose squared modulus is proportional to the beam density, that is obtained in the Hartree's mean field approximation, after disregarding the exchange interactions. The analysis of this pair of equations, which in general exhibits a strong nonlocal character, is carried out analytically as well as numerically in both the linear and the nonlinear regimes, showing the existence of the quantum beam vortices in the form of Laguerre-Gauss modes and ring envelope solitons, respectively. In particular, when the relation between the plasma wake field response and the beam probability density is strictly local, the pair of the governing equations is reduced to the 2D Gross-Pitaevskii equation that allows one to establish the conditions for the self focusing and collapse. These conditions include the quantum nature of the beam particles. Finally, when the relation between the plasma wake field response and the beam probability density is moderately nonlocal, the above pair of equations permits to follow the spatio-temporal evolution of a quantum ring envelope soliton. Such a structure exhibits small or violent
Palatini formulation of non-local gravity
NASA Astrophysics Data System (ADS)
Briscese, F.; Pucheu, M. L.
We derive the dynamical equations for a non-local gravity model in the Palatini formalism and we discuss some of the properties of this model. We have show that, in some specific case, the vacuum solutions of general relativity are also vacuum solutions of the non-local model, so we conclude that, at least in this case, the singularities of Einstein’s gravity are not removed.
NASA Astrophysics Data System (ADS)
Filk, Thomas
2013-04-01
In this article I investigate several possibilities to define the concept of "temporal non-locality" within the standard framework of quantum theory. In particular, I analyze the notions of "temporally non-local states", "temporally non-local events" and "temporally non-local observables". The idea of temporally non-local events is already inherent in the standard formalism of quantum mechanics, and Basil Hiley recently defined an operator in order to measure the degree of such a temporal non-locality. The concept of temporally non-local states enters as soon as "clock-representing states" are introduced in the context of special and general relativity. It is discussed in which way temporally non-local measurements may find an interesting application for experiments which test temporal versions of Bell inequalities.
Boundary fluxes for nonlocal diffusion
NASA Astrophysics Data System (ADS)
Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.
Pacemakers in large arrays of oscillators with nonlocal coupling
NASA Astrophysics Data System (ADS)
Jaramillo, Gabriela; Scheel, Arnd
2016-02-01
We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be approximated by a continuous nonlocal evolution equation. We concentrate on the case of heterogeneities with positive average and show that steady solutions to the nonlocal problem exist. In particular, we show that these heterogeneities act as a wave source. This effect is not possible in 3 dimensional systems, such as the complex Ginzburg-Landau equation, where the wavenumber of weak sources decays at infinity. To obtain our results we use a series of isomorphisms to relate the nonlocal problem to the viscous eikonal equation. We then use Fredholm properties of the Laplace operator in Kondratiev spaces to obtain solutions to the eikonal equation, and by extension to the nonlocal problem.
Nonlocal heat transport in a stochastic magnetic field
Rax, J.M.; White, R.B.
1991-12-01
Heat transport in a stochastic magnetic field configuration is shown to be nonlocal. Collisional transport processes, in such a disordered media, cannot always be reduced to a standard diffusion process, and the concept of a diffusion coefficient is meaningless for a wide range of typical tokamak parameters. In the nonlocal regime the relaxation of a gradient is described by an integral equation, involving a nonlocal propagator. This propagator is calculated, and the relation to previous results is elucidated. 15 refs.
NASA Technical Reports Server (NTRS)
Mihalas, Dimitri; Hummer, D. G.; Mihalas, Barbara Weibel; Daeppen, Werner
1990-01-01
The free-energy minimization technique in the form developed in the preceding papers in this series is employed to evaluate thermodynamic quantities and ionization fractions on a fine temperature and density grid for six astrophysical mixtures of 15 elements. The mixtures range from that appropriate to super-metal-rich stars, through solar abundance, to that for extreme Population II objects. In this paper, the results for solar abundances are summarized in a form that is illustrative and which facilitates comparison with the results from other equation of state calculations.
Effects of nonlocality on transfer reactions
NASA Astrophysics Data System (ADS)
Titus, Luke
Nuclear reactions play a key role in the study of nuclei away from stability. Single-nucleon transfer reactions involving deuterons provide an exceptional tool to study the single-particle structure of nuclei. Theoretically, these reactions are attractive as they can be cast into a three-body problem composed of a neutron, proton, and the target nucleus. Optical potentials are a common ingredient in reactions studies. Traditionally, nucleon-nucleus optical potentials are made local for convenience. The effects of nonlocal potentials have historically been included approximately by applying a correction factor to the solution of the corresponding equation for the local equivalent interaction. This is usually referred to as the Perey correction factor. In this thesis, we have systematically investigated the effects of nonlocality on (p,d) and (d,p) transfer reactions, and the validity of the Perey correction factor. We implemented a method to solve the single channel nonlocal equation for both bound and scattering states. We also developed an improved formalism for nonlocal interactions that includes deuteron breakup in transfer reactions. This new formalism, the nonlocal adiabatic distorted wave approximation, was used to study the effects of including nonlocality consistently in ( d,p) transfer reactions. For the (p,d) transfer reactions, we solved the nonlocal scattering and bound state equations using the Perey-Buck type interaction, and compared to local equivalent calculations. Using the distorted wave Born approximation we construct the T-matrix for (p,d) transfer on 17O, 41Ca, 49Ca, 127 Sn, 133Sn, and 209Pb at 20 and 50 MeV. Additionally we studied (p,d) reactions on 40Ca using the the nonlocal dispersive optical model. We have also included nonlocality consistently into the adiabatic distorted wave approximation and have investigated the effects of nonlocality on on (d,p) transfer reactions for deuterons impinged on 16O, 40Ca, 48Ca, 126Sn, 132Sn, 208Pb at 10
Quantum nonlocality does not exist
Tipler, Frank J.
2014-01-01
Quantum nonlocality is shown to be an artifact of the Copenhagen interpretation, in which each observed quantity has exactly one value at any instant. In reality, all physical systems obey quantum mechanics, which obeys no such rule. Locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the many-worlds interpretation (MWI). Using the MWI, I show that the quantum side of Bell’s inequality, generally believed nonlocal, is really due to a series of three measurements (not two as in the standard, oversimplified analysis), all three of which have only local effects. Thus, experiments confirming “nonlocality” are actually confirming the MWI. The mistaken interpretation of nonlocality experiments depends crucially on a question-begging version of the Born interpretation, which makes sense only in “collapse” versions of quantum theory, about the meaning of the modulus of the wave function, so I use the interpretation based on the MWI, namely that the wave function is a world density amplitude, not a probability amplitude. This view allows the Born interpretation to be derived directly from the Schrödinger equation, by applying the Schrödinger equation to both the observed and the observer. PMID:25015084
Breather solitons in highly nonlocal media
NASA Astrophysics Data System (ADS)
Alberucci, Alessandro; Jisha, Chandroth P.; Assanto, Gaetano
2016-12-01
We investigate the breathing of optical spatial solitons in highly nonlocal media. We use a generalization of the Ehrenfest theorem (1990 Am. J. Phys. 58 742) leading to a fourth-order ordinary differential equation, the latter ruling the beam width evolution in propagation. In actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell (1997 Science 276 1538) cannot accurately describe the dynamics of self-confined beams: the transverse size oscillations have a period which not only depends on power, but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.
Definitions of multipartite nonlocality
NASA Astrophysics Data System (ADS)
Bancal, Jean-Daniel; Barrett, Jonathan; Gisin, Nicolas; Pironio, Stefano
2013-07-01
In a multipartite setting, it is possible to distinguish quantum states that are genuinely n-way entangled from those that are separable with respect to some bipartition. Similarly, the nonlocal correlations that can arise from measurements on entangled states can be classified into those that are genuinely n-way nonlocal, and those that are local with respect to some bipartition. Svetlichny introduced an inequality intended as a test for genuine tripartite nonlocality. This work introduces two alternative definitions of n-way nonlocality, which we argue are better motivated both from the point of view of the study of nature, and from the point of view of quantum information theory. We show that these definitions are strictly weaker than Svetlichny's, and introduce a series of suitable Bell-type inequalities for the detection of three-way nonlocality. Numerical evidence suggests that all three-way entangled pure quantum states can produce three-way nonlocal correlations.
NASA Astrophysics Data System (ADS)
Mashhoon, Bahram
2014-12-01
A brief account of the present status of the recent nonlocal generalization of Einstein's theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenbock's torsion and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline-Kuhn approach to modified gravity. To account for the observational data regarding dark matter, nonlocality is associated with a characteristic length scale of order 1 kpc. The confrontation of nonlocal gravity with observation is briefly discussed.
Quantum Nonlocality and Reality
NASA Astrophysics Data System (ADS)
Bell, Mary; Gao, Shan
2016-09-01
Preface; Part I. John Stewart Bell: The Physicist: 1. John Bell: the Irish connection Andrew Whitaker; 2. Recollections of John Bell Michael Nauenberg; 3. John Bell: recollections of a great scientist and a great man Gian-Carlo Ghirardi; Part II. Bell's Theorem: 4. What did Bell really prove? Jean Bricmont; 5. The assumptions of Bell's proof Roderich Tumulka; 6. Bell on Bell's theorem: the changing face of nonlocality Harvey R. Brown and Christopher G. Timpson; 7. Experimental tests of Bell inequalities Marco Genovese; 8. Bell's theorem without inequalities: on the inception and scope of the GHZ theorem Olival Freire, Jr and Osvaldo Pessoa, Jr; 9. Strengthening Bell's theorem: removing the hidden-variable assumption Henry P. Stapp; Part III. Nonlocality: Illusions or Reality?: 10. Is any theory compatible with the quantum predictions necessarily nonlocal? Bernard d'Espagnat; 11. Local causality, probability and explanation Richard A. Healey; 12. Bell inequality and many-worlds interpretation Lev Vaidman; 13. Quantum solipsism and non-locality Travis Norsen; 14. Lessons of Bell's theorem: nonlocality, yes; action at a distance, not necessarily Wayne C. Myrvold; 15. Bell non-locality, Hardy's paradox and hyperplane dependence Gordon N. Fleming; 16. Some thoughts on quantum nonlocality and its apparent incompatibility with relativity Shan Gao; 17. A reasonable thing that just might work Daniel Rohrlich; 18. Weak values and quantum nonlocality Yakir Aharonov and Eliahu Cohen; Part IV. Nonlocal Realistic Theories: 19. Local beables and the foundations of physics Tim Maudlin; 20. John Bell's varying interpretations of quantum mechanics: memories and comments H. Dieter Zeh; 21. Some personal reflections on quantum non-locality and the contributions of John Bell Basil J. Hiley; 22. Bell on Bohm Sheldon Goldstein; 23. Interactions and inequality Philip Pearle; 24. Gravitation and the noise needed in objective reduction models Stephen L. Adler; 25. Towards an objective
Nonlocal teleparallel cosmology.
Bahamonde, Sebastian; Capozziello, Salvatore; Faizal, Mir; Nunes, Rafael C
2017-01-01
Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + [Formula: see text] observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction.
Operational Framework for Nonlocality
NASA Astrophysics Data System (ADS)
Gallego, Rodrigo; Würflinger, Lars Erik; Acín, Antonio; Navascués, Miguel
2012-08-01
Because of the importance of entanglement for quantum information purposes, a framework has been developed for its characterization and quantification as a resource based on the following operational principle: entanglement among N parties cannot be created by local operations and classical communication, even when N-1 parties collaborate. More recently, nonlocality has been identified as another resource, alternative to entanglement and necessary for device-independent quantum information protocols. We introduce an operational framework for nonlocality based on a similar principle: nonlocality among N parties cannot be created by local operations and allowed classical communication even when N-1 parties collaborate. We then show that the standard definition of multipartite nonlocality, due to Svetlichny, is inconsistent with this operational approach: according to it, genuine tripartite nonlocality could be created by two collaborating parties. We finally discuss alternative definitions for which consistency is recovered.
A nonlocal inhomogeneous dispersal process
NASA Astrophysics Data System (ADS)
Cortázar, C.; Coville, J.; Elgueta, M.; Martínez, S.
This article in devoted to the study of the nonlocal dispersal equation u(x,t)=∫R J({x-y}/{g(y)}){u(y,t)}/{g(y)} dy-u(x,t) in R×[0,∞), and its stationary counterpart. We prove global existence for the initial value problem, and under suitable hypothesis on g and J, we prove that positive bounded stationary solutions exist. We also analyze the asymptotic behavior of the finite mass solutions as t→∞, showing that they converge locally to zero.
Opacities for Stellar Envelopes
NASA Astrophysics Data System (ADS)
Seaton, M. J.; Yan, Y.; Mihalas, D.; Pradhan, A. K.
1994-02-01
We define stellar envelopes to be those regions of stellar interiors in which atoms exist and are not markedly perturbed by the plasma environment. Availability of accurate and extensive atomic data is a prime requirement for the calculation of envelope opacities. For envelopes we adopt the criterion of mass density p < 0.01 ρ≥g cm-3. We present radiative Rosseland mean opacities for envelopes obtained using atomic data calculated in an international collaboration referred to as the Opacity Project, or OP. Equations of state are calculated using an occupation-probability formalism. To a good approximation, ionization equilibria and level populations in envelopes depend only on the temperature T and electron density Ne and are insensitive to chemical mixtures. Monochromatic opacities for all abundant chemical elements are therefore calculated on a grid of (T, Ne) values and are archived. Rosseland mean opacities are then readily calculated for any chemical mixture. Tables of Rosseland means, for any required mixtures and as functions of ρ and T, are available on request in computer-readable form. The present, op, results are compared with those from another recent study, referred to as OPAL, by C. A. Iglesias and F. A. Rogers at the Lawrence Livermore National Laboratory. The agreement between the OP and OPAL calculations is generally good, although there are some differences. Both calculations give results larger than those obtained in earlier work, by factors of up to 3 or more.
Spatial optical solitons in highly nonlocal media
NASA Astrophysics Data System (ADS)
Alberucci, Alessandro; Jisha, Chandroth P.; Smyth, Noel F.; Assanto, Gaetano
2015-01-01
We theoretically investigate the propagation of bright spatial solitary waves in highly nonlocal media possessing radial symmetry in a three-dimensional cylindrical geometry. Focusing on a thermal nonlinearity, modeled by a Poisson equation, we show how the profile of the light-induced waveguide strongly depends on the extension of the nonlinear medium in the propagation direction as compared to the beamwidth. We demonstrate that self-trapped beams undergo oscillations in size, either periodically or aperiodically, depending on the input waist and power. The—usually neglected—role of the longitudinal nonlocality as well as the detrimental effect of absorptive losses are addressed.
Nonlocality from Local Contextuality
NASA Astrophysics Data System (ADS)
Liu, Bi-Heng; Hu, Xiao-Min; Chen, Jiang-Shan; Huang, Yun-Feng; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can; Cabello, Adán
2016-11-01
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.
Nonlocality from Local Contextuality.
Liu, Bi-Heng; Hu, Xiao-Min; Chen, Jiang-Shan; Huang, Yun-Feng; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can; Cabello, Adán
2016-11-25
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.
NASA Astrophysics Data System (ADS)
Lu, Yanfei; Lekszycki, Tomasz
2016-10-01
During fracture healing, a series of complex coupled biological and mechanical phenomena occurs. They include: (i) growth and remodelling of bone, whose Young's modulus varies in space and time; (ii) nutrients' diffusion and consumption by living cells. In this paper, we newly propose to model these evolution phenomena. The considered features include: (i) a new constitutive equation for growth simulation involving the number of sensor cells; (ii) an improved equation for nutrient concentration accounting for the switch between Michaelis-Menten kinetics and linear consumption regime; (iii) a new constitutive equation for Young's modulus evolution accounting for its dependence on nutrient concentration and variable number of active cells. The effectiveness of the model and its predictive capability are qualitatively verified by numerical simulations (using COMSOL) describing the healing of bone in the presence of damaged tissue between fractured parts.
Transfer reaction code with nonlocal interactions
NASA Astrophysics Data System (ADS)
Titus, L. J.; Ross, A.; Nunes, F. M.
2016-10-01
We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, (d , N) or (N , d) , including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of A(d , N) B or B(N , d) A. Details on the implementation of the T-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided. This code is suitable to be applied for deuteron induced reactions in the range of Ed =10-70 MeV, and provides cross sections with 4% accuracy.
Transfer reaction code with nonlocal interactions
Titus, L. J.; Ross, A.; Nunes, F. M.
2016-07-14
Here, we present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, (d,N) or (N,d), including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are dif- ferential angular distributions for the cross sections of A(d,N)B or B(N,d)A. Details on the implementation of the T-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided. This code is suitable to be applied for deuteron induced reactions in the range of E_{d} = 10–70 MeV, and provides cross sections with 4% accuracy.
Effectively nonlocal metric-affine gravity
NASA Astrophysics Data System (ADS)
Golovnev, Alexey; Koivisto, Tomi; Sandstad, Marit
2016-03-01
In metric-affine theories of gravity such as the C-theories, the spacetime connection is associated to a metric that is nontrivially related to the physical metric. In this article, such theories are rewritten in terms of a single metric, and it is shown that they can be recast as effectively nonlocal gravity. With some assumptions, known ghost-free theories with nonsingular and cosmologically interesting properties may be recovered. Relations between different formulations are analyzed at both perturbative and nonperturbative levels, taking carefully into account subtleties with boundary conditions in the presence of integral operators in the action, and equivalences between theories related by nonlocal redefinitions of the fields are verified at the level of equations of motion. This suggests a possible geometrical interpretation of nonlocal gravity as an emergent property of non-Riemannian spacetime structure.
Nonlocal continuum theories of beams for the analysis of carbon nanotubes
NASA Astrophysics Data System (ADS)
Reddy, J. N.; Pang, S. D.
2008-01-01
The equations of motion of the Euler-Bernoulli and Timoshenko beam theories are reformulated using the nonlocal differential constitutive relations of Eringen [International Journal of Engineering Science 10, 1-16 (1972)]. The equations of motion are then used to evaluate the static bending, vibration, and buckling responses of beams with various boundary conditions. Numerical results are presented using the nonlocal theories to bring out the effect of the nonlocal behavior on deflections, buckling loads, and natural frequencies of carbon nanotubes.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators.
Belenchia, Alessio; Benincasa, Dionigi M T; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-22
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators
NASA Astrophysics Data System (ADS)
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-01
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Multipartite nonlocality distillation
Hsu, Li-Yi; Wu, Keng-Shuo
2010-11-15
The stronger nonlocality than that allowed in quantum theory can provide an advantage in information processing and computation. Since quantum entanglement is distillable, can nonlocality be distilled in the nonsignalling condition? The answer is positive in the bipartite case. In this article the distillability of the multipartite nonlocality is investigated. We propose a distillation protocol solely exploiting xor operations on output bits. The probability-distribution vectors and matrix are introduced to tackle the correlators. It is shown that only the correlators with extreme values can survive the distillation process. As the main result, the amplified nonlocality cannot maximally violate any Bell-type inequality. Accordingly, a distillability criterion in the postquantum region is proposed.
Solitary Alfven wave envelopes and the modulational instability
Kennel, C.F.
1987-06-01
The derivative nonlinear Schroedinger equation describes the modulational instability of circularly polarized dispersive Alfven wave envelopes. It also may be used to determine the properties of finite amplitude localized stationary wave envelopes. Such envelope solitons exist only in conditions of modulational stability. This leaves open the question of whether, and if so, how, the modulational instability produces envelope solitons. 12 refs.
Geometric reduction of dynamical nonlocality in nanoscale quantum circuits
NASA Astrophysics Data System (ADS)
Strambini, E.; Makarenko, K. S.; Abulizi, G.; de Jong, M. P.; van der Wiel, W. G.
2016-01-01
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young’s double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for quantum information processing. Here, we present a fundamentally different pathway of losing dynamical nonlocality, demonstrating that the detailed geometry of the detection scheme is crucial to preserve nonlocality. By means of a solid-state quantum-interference experiment we quantify this effect in a diffusive system. We show that interference is not only affected by decoherence, but also by a loss of dynamical nonlocality based on a local reduction of the number of quantum conduction channels of the interferometer. With our measurements and theoretical model we demonstrate that this mechanism is an intrinsic property of quantum dynamics. Understanding the geometrical constraints protecting nonlocality is crucial when designing quantum networks for quantum information processing.
Geometric reduction of dynamical nonlocality in nanoscale quantum circuits.
Strambini, E; Makarenko, K S; Abulizi, G; de Jong, M P; van der Wiel, W G
2016-01-06
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young's double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for quantum information processing. Here, we present a fundamentally different pathway of losing dynamical nonlocality, demonstrating that the detailed geometry of the detection scheme is crucial to preserve nonlocality. By means of a solid-state quantum-interference experiment we quantify this effect in a diffusive system. We show that interference is not only affected by decoherence, but also by a loss of dynamical nonlocality based on a local reduction of the number of quantum conduction channels of the interferometer. With our measurements and theoretical model we demonstrate that this mechanism is an intrinsic property of quantum dynamics. Understanding the geometrical constraints protecting nonlocality is crucial when designing quantum networks for quantum information processing.
Geometric reduction of dynamical nonlocality in nanoscale quantum circuits
Strambini, E.; Makarenko, K. S.; Abulizi, G.; de Jong, M. P.; van der Wiel, W. G.
2016-01-01
Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young’s double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for quantum information processing. Here, we present a fundamentally different pathway of losing dynamical nonlocality, demonstrating that the detailed geometry of the detection scheme is crucial to preserve nonlocality. By means of a solid-state quantum-interference experiment we quantify this effect in a diffusive system. We show that interference is not only affected by decoherence, but also by a loss of dynamical nonlocality based on a local reduction of the number of quantum conduction channels of the interferometer. With our measurements and theoretical model we demonstrate that this mechanism is an intrinsic property of quantum dynamics. Understanding the geometrical constraints protecting nonlocality is crucial when designing quantum networks for quantum information processing. PMID:26732751
Nonlocal effects in metallic nanoparticles: The kinetic approach outlook
NASA Astrophysics Data System (ADS)
Tomchuk, Petro M.; Butenko, Danylo
2017-02-01
For the metallic nanoparticles, smaller than the free electron path, an impact of the particle’s surface on the nonlocal effects emerging is shown. Light-induced current inside the particle begins to depend on the spatial derivatives of the field that leads to modification of Maxwell’s equations. Consequently, the results of Mie theory as well as definitions of the dielectric function and optical conductivity should be revisited. For the sphere-shaped nanoparticle, the explicit expression for the high-frequency current with account of nonlocality is obtained. The dependence of the nonlocal contribution on the light frequency and particle’s size is discussed.
Nonlocal optical response of metal nanostructures with arbitrary shape.
McMahon, J. M.; Gray, S. K.; Schatz, G. C.; Northwestern Univ.
2009-08-28
We present an implementation of Maxwell's equations that incorporates the spatially nonlocal response of materials, an effect necessary to describe the optical properties of structures with features less than 10 nm. For the first time it is possible to investigate the nonlocal optical response of structures without spherical or planar shape, and outside of the electrostatic limit. As an illustration, we calculate the optical properties of Au nanowires and show that nonlocal effects are particularly important in structures with apex features, even for arbitrarily large sizes.
Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems
D’Elia, M. E-mail: mdelia@sandia.gov; Gunzburger, M.
2016-04-15
The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the control and the parameter function as the control variable. The analysis makes use of a nonlocal vector calculus that allows one to define a variational formulation of the nonlocal problem. In a manner analogous to the local partial differential equations counterpart, we demonstrate, for certain kernel functions, the existence of at least one optimal solution in the space of admissible parameters. We introduce a Galerkin finite element discretization of the optimal control problem and derive a priori error estimates for the approximate state and control variables. Using one-dimensional numerical experiments, we illustrate the theoretical results and show that by using nonlocal models it is possible to estimate non-smooth and discontinuous diffusion parameters.
NASA Astrophysics Data System (ADS)
Bénisti, Didier
2016-10-01
This paper addresses the linear and nonlinear three-dimensional propagation of an electron wave in a collisionless plasma that may be inhomogeneous, nonstationary, anisotropic, and even weakly magnetized. The wave amplitude, together with any hydrodynamic quantity characterizing the plasma (density, temperature, etc.) is supposed to vary very little within one wavelength or one wave period. Hence, the geometrical optics limit is assumed, and the wave propagation is described by a first order differential equation. This equation explicitly accounts for three-dimensional effects, plasma inhomogeneity, Landau damping, and the collisionless dissipation and electron acceleration due to trapping. It is derived by mixing results obtained from a direct resolution of the Vlasov-Poisson system and from a variational formalism involving a nonlocal Lagrangian density. In a one-dimensional situation, abrupt transitions are predicted in the coefficients of the wave equation. They occur when the state of the electron plasma wave changes, from a linear wave to a wave with trapped electrons. In a three dimensional geometry, the transitions are smoother, especially as regards the nonlinear Landau damping rate, for which a very simple effective and accurate analytic expression is provided.
Nonlocal chaotic phase synchronization
NASA Astrophysics Data System (ADS)
Zhan, Meng; Zheng, Zhi-Gang; Hu, Gang; Peng, Xi-Hong
2000-09-01
A novel synchronization behavior, nonlocal chaotic phase synchronization, is investigated. For two coupled Rossler oscillators with only one forced by an injected periodic signal, the phase of the unforced oscillator can be locked to the phase of the periodic signal while the forced one is well unlocked by the signal; in a chain of coupled chaotic oscillators with nearest coupling, the phase of an oscillator (or a cluster) can be locked to another nonneighbor one. Moreover, the mechanism underlying the transition to nonlocal synchronization is discussed in detail.
Nonlocal Boltzmann theory of plasma channels
NASA Astrophysics Data System (ADS)
Yu, S. S.; Melendez, R. E.
1983-01-01
The mathematical framework for the Lawrence Livermore National Lab. (LLNL) code NUTS is developed. This code is designed to study the evolution of an electron beam generated plasma channel at all pressures. The Boltzmann treatment of the secondary electrons presented include all inertial, nonlocal, electric and magnetic effects, as well as effects of atomic collisions. Field equations are advanced simultaneously and self-consistently with the evolving plasma currents.
Application of nonlocal models to nano beams. Part II: Thickness length scale effect.
Kim, Jun-Sik
2014-10-01
Applicability of nonlocal models to nano-beams is discussed in terms of the Eringen's nonlocal Euler-Bernoulli (EB) beam model. In literature, most work has taken the axial coordinate derivative in the Laplacian operator presented in nonlocal elasticity. This causes that the non-locality always makes the beam soften as compared to the local counterpart. In this paper, the thickness scale effect is solely considered to investigate if the nonlocal model can simulate stiffening effect. Taking the thickness derivative in the Laplacian operator leads to the presence of a surface stress state. The governing equation derived is compared to that of the EB model with the surface stress. The results obtained reveal that the nonlocality tends to decrease the bending moment stiffness whereas to increase the bending rigidity in the governing equation. This tendency also depends on the surface conditions.
A Class of High Order Nonlocal Operators
NASA Astrophysics Data System (ADS)
Tian, Xiaochuan; Du, Qiang
2016-12-01
We study a class of nonlocal operators that may be seen as high order generalizations of the well known nonlocal diffusion operators. We present properties of the associated nonlocal functionals and nonlocal function spaces including nonlocal versions of Sobolev inequalities such as the nonlocal Poincaré and nonlocal Gagliardo-Nirenberg inequalities. Nonlocal characterizations of high order Sobolev spaces in the spirit of Bourgain-Brezis-Mironescu are provided. Applications of nonlocal calculus of variations to the well-posedness of linear nonlocal models of elastic beams and plates are also considered.
Duc Cao; Richard Metcalf
2010-07-01
The Safeguards Envelope is a strategy to determine a set of specific operating parameters within which nuclear facilities may operate to maximize safeguards effectiveness without sacrificing safety or plant efficiency. This paper details advanced statistical techniques that will be applied to real plant process monitoring (PM) data from the Idaho Chemical Processing Plant (ICPP). In a simulation based on this data, multi-tank and multi-attribute correlations were tested against synthetic diversion scenarios. Kernel regression smoothing was used to fit a curve to the historical data, and multivariable, residual analysis and cumulative sum techniques set parameters for operating conditions. Diversion scenarios were created and tested, showing improved results when compared with a previous study utilizing only one-variable Z-testing. A brief analysis of the impact of the safeguards optimization on the rest of plant efficiency, criticality concerns, and overall requirements is presented.
ERIC Educational Resources Information Center
Hobson, Art
2012-01-01
Nonlocality arises from the unified "all or nothing" interactions of a spatially extended field quantum such as a photon or an electron. In the double-slit experiment with light, for example, each photon comes through both slits and arrives at the viewing screen as an extended but unified energy bundle or "field quantum." When the photon interacts…
ERIC Educational Resources Information Center
Hobson, Art
2012-01-01
Nonlocality arises from the unified "all or nothing" interactions of a spatially extended field quantum such as a photon or an electron. In the double-slit experiment with light, for example, each photon comes through both slits and arrives at the viewing screen as an extended but unified energy bundle or "field quantum." When the photon interacts…
NASA Astrophysics Data System (ADS)
Lim, C. W.; Zhang, G.; Reddy, J. N.
2015-05-01
In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory. In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed. It is based on the nonlocal effects of the strain field and first gradient strain field. This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational
A radial basis function Galerkin method for inhomogeneous nonlocal diffusion
Lehoucq, Richard B.; Rowe, Stephen T.
2016-02-01
We introduce a discretization for a nonlocal diffusion problem using a localized basis of radial basis functions. The stiffness matrix entries are assembled by a special quadrature routine unique to the localized basis. Combining the quadrature method with the localized basis produces a well-conditioned, sparse, symmetric positive definite stiffness matrix. We demonstrate that both the continuum and discrete problems are well-posed and present numerical results for the convergence behavior of the radial basis function method. As a result, we explore approximating the solution to anisotropic differential equations by solving anisotropic nonlocal integral equations using the radial basis function method.
Electrodynamics of memory-dependent nonlocal elastic continua
NASA Astrophysics Data System (ADS)
Eringen, A. Cemal
1984-11-01
Balance laws and constitutive equations are given for elastic continua with memory of past motions and electromagnetic fields. Nonlinear, finite-linear, and linear constitutive equations are obtained and restricted by the second law of thermodynamics. Memory-dependent nonlocal piezoelectricity, piezomagnetism, heat and electric conduction, viscoelasticity, and other allied physical phenomena are in the domain of the general theory. The theory is applied to discuss infrared dispersion and lattice vibrations, natural optical activity, anomalous skin effect, and superconductivity, indicating the power and the potential of the nonlocal theory.
NASA Astrophysics Data System (ADS)
Tala-Tebue, E.; Tsobgni-Fozap, D. C.; Kenfack-Jiotsa, A.; Kofane, T. C.
2014-06-01
Using the Jacobi elliptic functions and the alternative ( G'/ G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.
NASA Astrophysics Data System (ADS)
Chambolle, Antonin; Morini, Massimiliano; Ponsiglione, Marcello
2015-12-01
This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of nonlocal generalized mean curvatures and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows. We then introduce a class of generalized perimeters, whose first variation is an admissible generalized curvature. Within this class, we implement a minimizing movements scheme and we prove that it approximates the viscosity solution of the corresponding level set PDE. We also describe several examples and applications. Besides recovering and presenting in a unified way existence, uniqueness, and approximation results for several geometric motions already studied and scattered in the literature, the theory developed in this paper also allows us to establish new results.
Revealing hidden genuine tripartite nonlocality
NASA Astrophysics Data System (ADS)
Paul, Biswajit; Mukherjee, Kaushiki; Sarkar, Debasis
2016-11-01
Nonlocal correlations arising from measurements on tripartite entangled states can be classified into two groups, one genuinely three-way nonlocal and other local with respect to some bipartition. Still, whether a genuinely tripartite entangled quantum state can exhibit genuine three-way nonlocality remains a challenging problem as far as measurement context is concerned. Here we introduce an approach in this regard. We consider three tripartite quantum states, none of which is genuinely three-way nonlocal in a specific Bell scenario (three parties, two measurements per party, two outcomes per measurement), but they can exhibit genuine three-way nonlocality when the initial states are subjected to stochastic local operations and classical communication. So, genuine three-way nonlocality is a resource which can be revealed by using a sequence of measurements.
Causality, Nonlocality, and Negative Refraction.
Forcella, Davide; Prada, Claire; Carminati, Rémi
2017-03-31
The importance of spatial nonlocality in the description of negative refraction in electromagnetic materials has been put forward recently. We develop a theory of negative refraction in homogeneous and isotropic media, based on first principles, and that includes nonlocality in its full generality. The theory shows that both dissipation and spatial nonlocality are necessary conditions for the existence of negative refraction. It also provides a sufficient condition in materials with weak spatial nonlocality. These fundamental results should have broad implications in the theoretical and practical analyses of negative refraction of electromagnetic and other kinds of waves.
Structure of nonlocality of plasma turbulence
NASA Astrophysics Data System (ADS)
Gürcan, Ö. D.; Vermare, L.; Hennequin, P.; Berionni, V.; Diamond, P. H.; Dif-Pradalier, G.; Garbet, X.; Ghendrih, P.; Grandgirard, V.; McDevitt, C. J.; Morel, P.; Sarazin, Y.; Storelli, A.; Bourdelle, C.; the Tore Supra Team
2013-07-01
Various indications on the weakly nonlocal character of turbulent plasma transport both from experimental fluctuation measurements from Tore Supra and observations from the full-f, flux-driven gyrokinetic code GYSELA are reported. A simple Fisher equation model of this weakly nonlocal dynamics can be formulated in terms of an evolution equation for the turbulent entropy density, which contains the basic phenomenon of radial turbulence spreading in addition to avalanche-like dynamics via coupling to profile modulations. A derivation of this model, which contains the so-called beach effect, a diffusive and convective flux components for the flux of turbulence intensity, in addition to linear group propagation is given, starting from the drift-kinetic equation. The proposed model has the form of a transport equation for turbulence intensity, and may be considered as an addition to transport modelling. The kinetic fluxes given, can be computed using model closures, or local gyrokinetics. The model is also used in a particular setup that represents the near edge region as a relatively stable zone between the core and edge region where the energy injection is locally more substantial. It is observed that with constant, physical coefficients, the model gives a convincing qualitative profile of fluctuation intensity when the turbulence is coming from the core region with either a group velocity or a convective flux.
Elevated temperature envelope forming
NASA Technical Reports Server (NTRS)
Burg, Bruce M. (Inventor); Gane, David H. (Inventor); Starowski, Robert M. (Inventor)
1992-01-01
Elevated temperature envelope forming includes enclosing a part blank and form tool within an envelope sealed against the atmosphere, heat treating the combination while forming pressure holds the envelope and part against the form tool, and allowing part cool down to occur in an inert atmosphere with forming pressure removed. The forming pressure is provided by evacuating the envelope and may be aided by differential force applied between the envelope and the form tool.
Transfer reaction code with nonlocal interactions
Titus, L. J.; Ross, A.; Nunes, F. M.
2016-07-14
We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, (d,N)(d,N) or (N,d)(N,d), including nonlocal nucleon–target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of A(d,N)BA(d,N)B or B(N,d)AB(N,d)A. Details on the implementation of the TT-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided. This code is suitable to be applied for deuteron induced reactions in the range of View the MathML sourceEd=10–70MeV, and provides cross sections with 4% accuracy.
Transfer reaction code with nonlocal interactions
Titus, L. J.; Ross, A.; Nunes, F. M.
2016-07-14
We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, (d,N)(d,N) or (N,d)(N,d), including nonlocal nucleon–target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of A(d,N)BA(d,N)B or B(N,d)AB(N,d)A. Details on the implementation of the TT-matrix to obtain the final cross sections within the adiabatic distorted wave approximation method are also provided.more » This code is suitable to be applied for deuteron induced reactions in the range of View the MathML sourceEd=10–70MeV, and provides cross sections with 4% accuracy.« less
Nonlocal conservation laws for strings
Balachandran, A.P.; Stern, A.
1982-09-15
A finite number of nonlocal conservation laws are found in the Nambu-Goto string model. An infinite number of conserved currents may be obtained by embedding the string in more than 3+1 space-time dimensions. These currents resemble the nonlocal currents found in two-dimensional chiral models.
NASA Astrophysics Data System (ADS)
Senno, Gabriel; Bendersky, Ariel; Figueira, Santiago
2016-07-01
The concepts of randomness and non-locality are intimately intertwined outcomes of randomly chosen measurements over entangled systems exhibiting non-local correlations are, if we preclude instantaneous influence between distant measurement choices and outcomes, random. In this paper, we survey some recent advances in the knowledge of the interplay between these two important notions from a quantum information science perspective.
Nonlocal models in continuum mechanics
Johnson, N.L.; Phan-Thien, N.
1993-09-01
The recent appearance of nonlocal methods is examined in the light of traditional continuum mechanics. A comparison of nonlocal approaches in the fields of solid and fluid mechanics reveals that no consistent definition of a nonlocal theory has been used. We suggest a definition based on the violation of the principle of local action in continuum mechanics. From the consideration of the implications of a nonlocal theory based on this definition, we conclude that constitutive relations with nonlocal terms can confuse the traditional separation of the roles between conservation laws and constitutive relations. The diversity of motivations for the nonlocal approaches are presented, resulting primarily from deficiencies in numerical solutions to practical problems. To illustrate these concepts, the history of nonlocal terms in the field of viscoelastic fluids is reviewed. A specific example of a viscoelastic constitutive relation that contains a stress diffusion term is applied to a simple shear flow and found not to be a physical description of any known fluid. We conclude by listing questions that should be asked of nonlocal approaches.
The nonlocal elastomagnetoelectrostatics of disordered micropolar media
Kabychenkov, A. F.; Lisiovskii, F. V.
2016-08-15
The interactions of electric, magnetic, and elastic subsystems in nonlinear disordered micropolar media that possess a bending–torsion tensor and an nonsymmetric strain tensor have been studied in the framework of phenomenological elastomagnetoelectrostatics. A system of nonlinear equations for determining the ground state of these media has been obtained by the variational method. It is shown that nonuniform external and internal rotations not only create elastic stresses, but also generate additional electric and magnetic fields, while nonuniform elastic stresses and external fields induce internal rotations. The nonlocal character of the micropolar media significantly influences elementary excitations and nonlinear dynamic processes.
Leading-order nonlocal kinetic energy in peridynamics for consistent energetics and wave dispersion
NASA Astrophysics Data System (ADS)
Dayal, Kaushik
2017-08-01
This work considers the approximation of peridynamics by strain-gradient models in the linear, one-dimensional setting. Strain-gradient expansions that approximate the peridynamic dispersion relation using Taylor series are compared to strain-gradient models that approximate the peridynamic elastic energy. The dynamic and energetic expansions differ from each other, and neither captures an important feature of peridynamics that mimics atomic-scale dynamics, namely that the frequency of short waves is bounded and non-zero. The paper next examines peridynamics as the limit model along a sequence of strain-gradient models that consistently approximate both the energetics and the dispersion properties of peridynamics. Formally examining the limit suggests that the inertial term in the dynamical equation of peridynamics - or equivalently, the peridynamic kinetic energy - is necessarily nonlocal in space to balance the spatial nonlocality in the elastic energy. The nonlocality in the kinetic energy is of leading-order in the following sense: classical elasticity is the zeroth-order theory in both the kinetically nonlocal peridynamics and the classical peridynamics, but once nonlocality in the elastic energy is introduced, it must be balanced by nonlocality in the kinetic energy at the same order. In that sense, the kinetic nonlocality is not a higher-order correction; rather, the kinetic nonlocality is essential for consistent energetics and dynamics even in the simplest setting. The paper then examines the implications of kinetically nonlocal peridynamics in the context of stationary and propagating discontinuities of the kinematic fields.
Hermite-Gaussian Vector soliton in strong nonlocal media
NASA Astrophysics Data System (ADS)
Wang, Qing; Li, JingZhen
2014-12-01
The propagation of two mutually incoherent Hermite-Gaussian (HG) beams in strong nonlocal media was studied. We obtained the evolution equations for the parameters of the two beams and found the condition of forming a HG Vector soliton by variational approach. The numerical result, which accords with the analytical solution very well, shows that a series of vector solitons which consisted of different-order HG beam pairs can be formed in strong nonlocal media. In addition, we found that the phase shifts are not only related to the total incident power, but also related to the orders of the two HG beams.
Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid.
Sahin, Buyukdagli; Ralf, Blossey
2014-07-16
We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.
Extent of multiparticle quantum nonlocality
Jones, Nick S.; Linden, Noah; Massar, Serge
2005-04-01
It is well known that entangled quantum states are nonlocal: the corrrelations between local measurements carried out on these states cannot be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are more nonlocal than bipartite ones in the sense that even some nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely, we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalizes work of Svetlichny and others in which it was showed that a particular class of classical nonlocal models, the 'separable' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition.
Spatial equation for water waves
NASA Astrophysics Data System (ADS)
Dyachenko, A. I.; Zakharov, V. E.
2016-02-01
A compact spatial Hamiltonian equation for gravity waves on deep water has been derived. The equation is dynamical and can describe extreme waves. The equation for the envelope of a wave train has also been obtained.
Nonlocal Transport in the Reversed Field Pinch
Spizzo, G.; White, R. B.; Cappello, S.; Marrelli, L.
2009-09-21
Several heuristic models for nonlocal transport in plasmas have been developed, but they have had a limited possibility of detailed comparision with experimental data. Nonlocal aspects introduced by the existence of a known spectrum of relatively stable saturated tearing modes in a low current reversed field pinch offers a unique possibility for such a study. A numerical modelling of the magnetic structure and associated particle transport is carried out for the reversed-field pinch experiment at the Consorzio RFX, Padova, Italy. A reproduction of the tearing mode spectrum with a guiding center code1 reliably reproduces the observed soft X-ray tomography. Following particle trajectories in the stochastic magnetic field shows the transport across the unperturbed flux surfaces to be due to a spectrum of Levy flights, with the details of the spectrum position dependent. The resulting transport is subdiffusive, and cannot be described by Rechester-Rosenbluth diffusion, which depends on a random phase approximation. If one attempts to fit the local transport phenomenologically, the subdiffusion can be fit with a combination of diffusion and inward pinch2. It is found that whereas passing particles explore the stochastic field and hence participate in Levy flights, the trapped particles experience normal neoclassical diffusion. A two fluid nonlocal Montroll equation is used to model this transport, with a Levy flight defined as the motion of an ion during the period that the pitch has one sign. The necessary input to the Montroll equation consists of a time distribution for the Levy flights, given by the pitch angle scattering operator, and a distribution of the flight distances, determined numerically using a guiding center code. Results are compared to experiment. The relation of this formulation to fractional kinetics is also described.
Theoretical Foundations of Incorporating Local Boundary Conditions into Nonlocal Problems
NASA Astrophysics Data System (ADS)
Aksoylu, Burak; Beyer, Horst Reinhard; Celiker, Fatih
2017-08-01
We study nonlocal equations from the area of peridynamics on bounded domains. We present four main results. In our recent paper, we have discovered that, on R, the governing operator in peridynamics, which involves a convolution, is a bounded function of the classical (local) governing operator. Building on this, as main result 1, we construct an abstract convolution operator on bounded domains which is a generalization of the standard convolution based on integrals. The abstract convolution operator is a function of the classical operator, defined by a Hilbert basis available due to the purely discrete spectrum of the latter. As governing operator of the nonlocal equation we use a function of the classical operator, this allows us to incorporate local boundary conditions into nonlocal theories. As main result 2, we prove that the solution operator can be uniquely decomposed into a Hilbert-Schmidt operator and a multiple of the identity operator. As main result 3, we prove that Hilbert-Schmidt operators provide a smoothing of the input data in the sense a square integrable function is mapped into a function that is smooth up to boundary of the domain. As main result 4, for the homogeneous nonlocal wave equation, we prove that continuity is preserved by time evolution. Namely, the solution is discontinuous if and only if the initial data is discontinuous. As a consequence, discontinuities remain stationary.
Linear delta-f simulations of nonlocal electron heat transport
NASA Astrophysics Data System (ADS)
Brunner, S.; Valeo, E.; Krommes, J. A.
2000-07-01
Nonlocal electron heat transport calculations are carried out by making use of some of the techniques developed previously for extending the δf method to transport time scale simulations [S. Brunner, E. Valeo, and J. Krommes, Phys. Plasmas 6, 4504 (1999)]. By considering the relaxation of small amplitude temperature perturbations of an homogeneous Maxwellian background, only the linearized Fokker-Planck equation has to be solved, and direct comparisons can be made with the equivalent, nonlocal hydrodynamic approach [V. Yu. Bychenkov et al., Phys. Rev. Lett. 75, 4405 (1995)]. A quasineutrality-conserving algorithm is derived for computing the self-consistent electric fields driving the return currents. In the low-collisionality regime, results illustrate the importance of taking account of nonlocality in both space and time.
Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Reza Barati, Mohammad
2016-09-01
In this work, a size-dependent curved beam model is developed to take into account the effects of nonlocal stresses on the buckling behavior of curved magneto-electro-elastic FG nanobeams for the first time. The governing differential equations are derived based on the principle of virtual work and Euler-Bernoulli beam theory. The power-law function is employed to describe the spatially graded magneto-electro-elastic properties. By extending the radius of the curved nanobeam to infinity, the results of straight nonlocal FG beams can be rendered. The effects of magnetic potential, electric voltage, opening angle, nonlocal parameter, power-law index and slenderness ratio on buckling loads of curved MEE-FG nanobeams are studied.
Torsional wave propagation in multiwalled carbon nanotubes using nonlocal elasticity
NASA Astrophysics Data System (ADS)
Arda, Mustafa; Aydogdu, Metin
2016-03-01
Torsional wave propagation in multiwalled carbon nanotubes is studied in the present work. Governing equation of motion of multiwalled carbon nanotube is obtained using Eringen's nonlocal elasticity theory. The effect of van der Waals interaction coefficient is considered between inner and outer nanotubes. Dispersion relations are obtained and discussed in detail. Effect of nonlocal parameter and van der Waals interaction to the torsional wave propagation behavior of multiwalled carbon nanotubes is investigated. It is obtained that torsional van der Waals interaction between adjacent tubes can change the rotational direction of multiwalled carbon nanotube as in-phase or anti-phase. The group and escape velocity of the waves converge to a limit value in the nonlocal elasticity approach.
Modelling population growth with delayed nonlocal reaction in 2-dimensions.
Liang, Dong; Wu, Jianhong; Zhang, Fan
2005-01-01
In this paper, we consider the population growth of a single species living in a two-dimensional spatial domain. New reaction-difusion equation models with delayed nonlocal reaction are developed in two-dimensional bounded domains combining diferent boundary conditions. The important feature of the models is the reflection of the joint efect of the difusion dynamics and the nonlocal maturation delayed efect. We consider and ana- lyze numerical solutions of the mature population dynamics with some wellknown birth functions. In particular, we observe and study the occurrences of asymptotically stable steady state solutions and periodic waves for the two-dimensional problems with nonlocal delayed reaction. We also investigate numerically the efects of various parameters on the period, the peak and the shape of the periodic wave as well as the shape of the asymptotically stable steady state solution.
Valley Hall effect and nonlocal transport in strained graphene
NASA Astrophysics Data System (ADS)
Zhang, Xian-Peng; Huang, Chunli; Cazalilla, Miguel A.
2017-06-01
Graphene subject to high levels of shear strain leads to strong pseudo-magnetic fields resulting in the emergence of pseudo-Landau levels. Here we show that, with modest levels of strain, graphene can also sustain a classical valley Hall effect (VHE) that can be detected in nonlocal transport measurements. We provide a theory of the strain-induced VHE starting from the quantum Boltzmann equation. This allows us to show that, averaging over short-range impurity configurations destroys quantum coherence between valleys, leaving the elastic scattering time and inter-valley scattering rate as the only parameters characterizing the transport theory. Using the theory, we compute the nonlocal resistance of a Hall bar device in the diffusive regime. Our theory is also relevant for the study of moderate strain effects in the (nonlocal) transport properties of other two-dimensional materials and van der Walls heterostructures.
Nonlocal anomalous Hall effect
NASA Astrophysics Data System (ADS)
Zhang, Shulei; Vignale, Giovanni
Anomalous Hall effect (AHE) is a distinctive transport property of ferromagnetic metals arising from spin orbit coupling (SOC) in concert with spontaneous spin polarization. Nonetheless, recent experiments have shown that the effect also appears in a nonmagnetic metal in contact with a magnetic insulator. The main puzzle lies in the apparent absence of spin polarized electrons in the non-magnetic metal. Here, we theoretically demonstrate that the scattering of electrons from a rough metal-insulator interface is generally spin-dependent, which results in mutual conversion between spin and charge currents flowing in the plane of the layer. It is the current-carrying spin polarized electrons and the spin Hall effect in the bulk of the metal layer that conspire to generate the AH current. This novel AHE differs from the conventional one only in the spatial separation of the SOC and the magnetization, so we name it as nonlocal AHE. In contrast to other previously proposed mechanisms (e.g., spin Hall AHE and magnetic proximity effect (MPE)), the nonlocal AHE appears on the first order of spin Hall angle and does not rely on the induced moments in the metal layer, which make it experimentally detectable by contrasting the AH current directions of two layered structures such as Pt/Cu/YIG and β -Ta/Cu/YIG (with a thin inserted Cu layer to eliminate the MPE). We predict that the directions of the AH currents in these two trilayers would be opposite since the spin Hall angles of Pt and β -Ta are of opposite signs. Work supported by NSF Grants DMR-1406568.
NASA Astrophysics Data System (ADS)
Du, Qiang; Yang, Jiang
2017-03-01
This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simple ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge-Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge-Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen-Cahn equations, nonlocal Cahn-Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.
Aspects of nonlocality in quantum field theory, quantum gravity and cosmology
NASA Astrophysics Data System (ADS)
Barvinsky, A. O.
2015-02-01
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter (dS) cosmological evolution at an arbitrary value of Λ — a model of dark energy with the dynamical scale selected by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of a scalar mediated gravity and the short distance general relativistic limit in a special metric frame related by a nonlocal conformal transformation to the original metric.
Zhang, Jianming; Yang, Yang
2015-03-10
According to Hamilton’s principle, a new mathematical model and analytical solutions for nonlocal Timoshenko beam model (ANT) is established based on nonlocal elastic continuum theory when shear deformation and nonlocal effect are considered. The new ANT equilibrium equations and boundary conditions are derived for bending analysis of carbon nanotubes (CNTs) with simply supported, clamped and cantilever. The ANT deflection solutions demonstrate that the CNT stiffness is enhanced by the presence of nonlocal stress effects. Furthermore, the new ANT model concluded verifiable bending behaviors for a cantilever CNT with point load at the free end, which depends on the strength of nonlocal stress. Therefore, this new model will gives a better prediction for mechanical behaviors of nanostructures.
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Reza Barati, Mohammad
2017-01-01
In this research, vibration characteristics of a flexoelectric nanobeam in contact with Winkler-Pasternak foundation is investigated based on the nonlocal elasticity theory considering surface effects. This nonclassical nanobeam model contains flexoelectric effect to capture coupling of strain gradients and electrical polarizations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, flexoelectric and surface effects are omitted. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying a Galerkin-based solution. Natural frequencies are verified with those of previous papers on nanobeams. It is illustrated that flexoelectricity, nonlocality, surface stresses, elastic foundation and boundary conditions affects considerably the vibration frequencies of piezoelectric nanobeams.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
NASA Astrophysics Data System (ADS)
Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.
2005-11-01
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
On locally and nonlocally related potential systems
NASA Astrophysics Data System (ADS)
Cheviakov, Alexei F.; Bluman, George W.
2010-07-01
For any partial differential equation (PDE) system, a local conservation law yields potential equations in terms of some potential variable, which normally is a nonlocal variable. The current paper examines situations when such a potential variable is a local variable, i.e., is a function of the independent and dependent variables of a given PDE system, and their derivatives. In the case of two independent variables, a simple necessary and sufficient condition is presented for the locality of such a potential variable, and this is illustrated by several examples. As a particular example, two-dimensional reductions of equilibrium equations for fluid and plasma dynamics are considered. It is shown that such reductions with respect to helical, axial, and translational symmetries have conservation laws which yield local potential variables. This leads to showing that the well-known Johnson-Frieman-Kruskal-Oberman (JFKO) and Bragg-Hawthorne (Grad-Shafranov) equations are locally related to the corresponding helically and axially symmetric PDE systems of fluid/plasma dynamics. For the axially symmetric case, local symmetry classifications and arising invariant solutions are compared for the original PDE system and the Bragg-Hawthorne (potential) equation. The potential equation is shown to have additional symmetries, denoted as restricted symmetries. Restricted symmetries leave invariant a family of solutions of a given PDE system but not the whole solution manifold, and hence are not symmetries of the given PDE system. Corresponding reductions are shown to yield solutions, which are not obtained as invariant solutions from local symmetry reduction.
Complementarity of genuine multipartite Bell nonlocality
NASA Astrophysics Data System (ADS)
Sami, Sasha; Chakrabarty, Indranil; Chaturvedi, Anubhav
2017-08-01
We introduce a feature of no-signaling (Bell) nonlocal theories: namely, when a system of multiple parties manifests genuine nonlocal correlation, then there cannot be arbitrarily high nonlocal correlation among any subset of the parties. We call this feature complementarity of genuine multipartite nonlocality. We use Svetlichny's criterion for genuine multipartite nonlocality and nonlocal games to derive the complementarity relations under no-signaling constraints. We find that the complementarity relations are tightened for the much stricter quantum constraints. We compare this notion with the well-known notion of monogamy of nonlocality. As a consequence, we obtain tighter nontrivial monogamy relations that take into account genuine multipartite nonlocality. Furthermore, we provide numerical evidence showcasing this feature using a bipartite measure and several other well-known tripartite measures of nonlocality.
Nonlocal electron transport in magnetized plasmas with arbitrary atomic number
Bennaceur-Doumaz, D.; Bendib, A.
2006-09-15
The numerical solution of the steady-state electron Fokker-Planck equation perturbed with respect to a global equilibrium is presented in magnetized plasmas with arbitrary atomic number Z. The magnetic field is assumed to be constant and the electron-electron collisions are described by the Landau collision operator. The solution is derived in the Fourier space and in the framework of the diffusive approximation which captures the spatial nonlocal effects. The transport coefficients are deduced and used to close a complete set of nonlocal electron fluid equations. This work improves the results of A. Bendib et al. [Phys. Plasmas 9, 1555 (2002)] and of A. V. Brantov et al. [Phys. Plasmas 10, 4633 (2003)] restricted to the local and nonlocal high-Z plasma approximations, respectively. The influence of the magnetic field on the nonlocal effects is discussed. We propose also accurate numerical fits of the relevant transport coefficients with respect to the collisionality parameter {lambda}{sub ei}/L and the atomic number Z, where L is the typical scale length and {lambda}{sub ei} is the electron-ion mean-free-path.
Nonlocal wave turbulence in non-Abelian plasmas
NASA Astrophysics Data System (ADS)
Mehtar-Tani, Yacine
2017-10-01
We investigate driven wave turbulence in non-Abelian plasmas, in the framework of kinetic theory where both elastic and inelastic processes are considered in the small angle approximation. The gluon spectrum, that forms in the presence of a steady source, is shown to be controlled by nonlocal interactions in momentum space, in contrast to the universal Kolmogorov-Zakharov spectra. Assuming strongly nonlocal interactions, we show that inelastic processes are dominant in the IR and cause a thermal bath to form below the forcing scale, as a result of a detailed balance between radiation and absorption of soft gluons by the hard ones. Above the forcing scale, the inelastic collision term reduces to an inhomogeneous diffusion-like equation yielding a spectrum that spreads to the UV as t 1 / 2, similarly to elastic processes. Due to nonlocal interactions the non-universal turbulent spectrum is not steady and flattens when time goes on toward the thermal distribution. This analysis is complemented by numerical simulations, where we observe that in the explored time interval the spectral exponent of the nonlocal turbulent cascade is close to -2 in agreement with simulations of classical Yang-Mills equations.
Nonlocal optical response in metallic nanostructures.
Raza, Søren; Bozhevolnyi, Sergey I; Wubs, Martijn; Asger Mortensen, N
2015-05-13
This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response.
Nonlocal Anomalous Hall Effect.
Zhang, Steven S-L; Vignale, Giovanni
2016-04-01
The anomalous Hall (AH) effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator [yttrium iron garnet (YIG)], even when precautions are taken to ensure that there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin-Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect-the only difference being the spatial separation of the spin-orbit interaction and the magnetization. For this reason we name this effect the nonlocal anomalous Hall effect and predict that its sign will be determined by the sign of the spin-Hall angle in the metal. The AH conductivity that we calculate from our theory is in order of magnitude agreement with the measured values in Pt/YIG structures.
Bipartite units of nonlocality
Forster, Manuel; Wolf, Stefan
2011-10-15
Imagine a task in which a group of separated players aim to simulate a statistic that violates a Bell inequality. Given measurement choices the players shall announce an output based solely on the results of local operations--which they can discuss before the separation--on shared random data and shared copies of a so-called unit correlation. In the first part of this paper we show that in such a setting the simulation of any bipartite correlation, not containing the possibility of signaling, can be made arbitrarily accurate by increasing the number of shared Popescu-Rohrlich (PR) boxes. This establishes the PR box as a simple asymptotic unit of bipartite nonlocality. In the second part we study whether this property extends to the multipartite case. More generally, we ask if it is possible for separated players to asymptotically reproduce any nonsignaling statistic by local operations on bipartite unit correlations. We find that nonadaptive strategies are limited by a constant accuracy and that arbitrary strategies on n resource correlations make a mistake with a probability greater or equal to c/n, for some constant c.
Nonlocal Anomalous Hall Effect
NASA Astrophysics Data System (ADS)
Zhang, Steven S.-L.; Vignale, Giovanni
2016-04-01
The anomalous Hall (AH) effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator [yttrium iron garnet (YIG)], even when precautions are taken to ensure that there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin-Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect—the only difference being the spatial separation of the spin-orbit interaction and the magnetization. For this reason we name this effect the nonlocal anomalous Hall effect and predict that its sign will be determined by the sign of the spin-Hall angle in the metal. The AH conductivity that we calculate from our theory is in order of magnitude agreement with the measured values in Pt /YIG structures.
Nonlocal Intracranial Cavity Extraction
Manjón, José V.; Eskildsen, Simon F.; Coupé, Pierrick; Romero, José E.; Collins, D. Louis; Robles, Montserrat
2014-01-01
Automatic and accurate methods to estimate normalized regional brain volumes from MRI data are valuable tools which may help to obtain an objective diagnosis and followup of many neurological diseases. To estimate such regional brain volumes, the intracranial cavity volume (ICV) is often used for normalization. However, the high variability of brain shape and size due to normal intersubject variability, normal changes occurring over the lifespan, and abnormal changes due to disease makes the ICV estimation problem challenging. In this paper, we present a new approach to perform ICV extraction based on the use of a library of prelabeled brain images to capture the large variability of brain shapes. To this end, an improved nonlocal label fusion scheme based on BEaST technique is proposed to increase the accuracy of the ICV estimation. The proposed method is compared with recent state-of-the-art methods and the results demonstrate an improved performance both in terms of accuracy and reproducibility while maintaining a reduced computational burden. PMID:25328511
Contact of boundary-value problems and nonlocal problems in mathematical models of heat transfer
NASA Astrophysics Data System (ADS)
Lyashenko, V.; Kobilskaya, O.
2015-10-01
In this paper the mathematical models in the form of nonlocal problems for the two-dimensional heat equation are considered. Relation of a nonlocal problem and a boundary value problem, which describe the same physical heating process, is investigated. These problems arise in the study of the temperature distribution during annealing of the movable wire and the strip by permanent or periodically operating internal and external heat sources. The first and the second nonlocal problems in the mobile area are considered. Stability and convergence of numerical algorithms for the solution of a nonlocal problem with piecewise monotone functions in the equations and boundary conditions are investigated. Piecewise monotone functions characterize the heat sources and heat transfer conditions at the boundaries of the area that is studied. Numerous experiments are conducted and temperature distributions are plotted under conditions of internal and external heat sources operation. These experiments confirm the effectiveness of attracting non-local terms to describe the thermal processes. Expediency of applying nonlocal problems containing nonlocal conditions - thermal balance conditions - to such models is shown. This allows you to define heat and mass transfer as the parameters of the process control, in particular heat source and concentration of the substance.
Rose, Annkatrin; Patel, Shalaka; Meier, Iris
2004-01-01
This review summarizes our present knowledge about the composition and function of the plant nuclear envelope. Compared with animals or yeast, our molecular understanding of the nuclear envelope in higher plants is in its infancy. However, fundamental differences in the structure and function of the plant and animal nuclear envelope have already been found. Here, we compare and contrast these differences with respect to nuclear pore complexes, targeting of Ran signaling to the nuclear envelope, inner nuclear envelope proteins, and the role and fate of the nuclear envelope during mitosis. Further investigation of the emerging fundamental differences as well as the similarities between kingdoms might illuminate why there appears to be more than one blueprint for building a nucleus.
Nonlocal Measurements via Quantum Erasure.
Brodutch, Aharon; Cohen, Eliahu
2016-02-19
Nonlocal observables play an important role in quantum theory, from Bell inequalities and various postselection paradoxes to quantum error correction codes. Instantaneous measurement of these observables is known to be a difficult problem, especially when the measurements are projective. The standard von Neumann Hamiltonian used to model projective measurements cannot be implemented directly in a nonlocal scenario and can, in some cases, violate causality. We present a scheme for effectively generating the von Neumann Hamiltonian for nonlocal observables without the need to communicate and adapt. The protocol can be used to perform weak and strong (projective) measurements, as well as measurements at any intermediate strength. It can also be used in practical situations beyond nonlocal measurements. We show how the protocol can be used to probe a version of Hardy's paradox with both weak and strong measurements. The outcomes of these measurements provide a nonintuitive picture of the pre- and postselected system. Our results shed new light on the interplay between quantum measurements, uncertainty, nonlocality, causality, and determinism.
The inverse scattering problem at fixed angular momentum for nonlocal separable interactions
NASA Technical Reports Server (NTRS)
Chadan, K.
1972-01-01
The problem of inverse scattering at fixed angular momentum is considered. The problem is particularized to the case of nonlocal separable interactions. A brief survey of the inverse problem for nonlocal separable interactions is presented. This problem can be solved exactly by integration. It amounts to solving singular integral equations of the Hilbert-Mushkhelishvili type, which have been studied extensively in the past and appear in many areas of physics, including theory of elasticity and dispersions relations in high energy physics.
A nonlocal fluid closure for antiparallel reconnection
NASA Astrophysics Data System (ADS)
Ng, J.; Hakim, A.; Bhattacharjee, A.
2016-12-01
The integration of kinetic effects in fluid models is an important problem in global simulations of the Earth's magnetosphere and space weather modelling. In particular, it has been shown that ion kinetics play an important role in the dynamics of large reconnecting systems, and that fluid models can account of some of these effects[1,2] . Here we introduce a new fluid model and closure for collisionless magnetic reconnection and more general applications. Taking moments of the kinetic equation, we evolve the full pressure tensor for electrons and ions, which includes the off diagonal terms necessary for reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework [3]. Using the island coalescence problem as a test, we show how the nonlocal ion closure improves on the typical collisional closures used for ten-moment models and circumvents the need for a colllisional free parameter. Finally, we extend the closure to study guide-field reconnection and discuss the implementation of a twenty-moment model.[1] A. Stanier et al. Phys Rev Lett (2015)[2] J. Ng et al. Phys Plasmas (2015)[3] G. Hammett et al. Phys Rev Lett (1990)
A nonlocal fluid closure for antiparallel reconnection
NASA Astrophysics Data System (ADS)
Ng, Jonathan; Hakim, A.; Bhattacharjee, A.
2016-10-01
The integration of kinetic effects in fluid models is an important problem in global simulations of the Earth's magnetosphere and space weather modelling. In particular, it has been shown that ion kinetics play an important role in the dynamics of large reconnecting systems, and that fluid models can account of some of these effects. Here we introduce a new fluid model and closure for collisionless magnetic reconnection and more general applications. Taking moments of the kinetic equation, we evolve the full pressure tensor for electrons and ions, which includes the off diagonal terms necessary for reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework. Using the island coalescence problem as a test, we show how the nonlocal ion closure improves on the typical collisional closures used for ten-moment models and circumvents the need for a colllisional free parameter. Finally, we extend the closure to study guide-field reconnection and discuss the implementation of a twenty-moment model. Supported by: NSF Grant No. AGS-1338944, DOE Contract DE-AC02-09CH11466.
Generating tripartite nonlocality from bipartite resources
NASA Astrophysics Data System (ADS)
Su, Zhaofeng
2017-01-01
Nonlocality is an important resource for quantum information processing. Tripartite nonlocality is more difficult to produce in experiments than bipartite ones. In this paper, we analyze a simple setting to generate tripartite nonlocality from two classes of bipartite resources, namely two-qubit entangled pure states and Werner states. Upper bounds on the tripartite nonlocality, characterized by the maximal violation of Svetlichny inequalities, are given, and the optimal measurements to achieve these bounds are provided.
Cryptographic quantum bound on nonlocality
NASA Astrophysics Data System (ADS)
Ishizaka, Satoshi
2017-02-01
Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some boundaries between quantum and postquantum nonlocal correlations, where the obtainable information reaches the maximum limit. We show that no-signaling resources of pure partially entangled states produce randomness (or noise) in the communication bits, and achievement of the maximum limit is impossible, i.e., the information causality principle is insufficient for the full identification of the quantum boundaries already for bipartite settings. The nonlocality inequalities such as so-called the Tsirelson inequality are extended to show how such randomness affects the strength of nonlocal correlations. As a result, a relation followed by most of quantum correlations in the simplest Bell scenario is revealed. The extended inequalities reflect the cryptographic principle such that a completely scrambled message cannot carry information.
Propagation of in-plane wave in viscoelastic monolayer graphene via nonlocal strain gradient theory
NASA Astrophysics Data System (ADS)
Xiao, Weiwei; Li, Li; Wang, Meng
2017-06-01
The behaviors of monolayer graphene sheet have attracted increasing attention of many scientists and researchers. In this study, the propagation behaviors of in-plane wave in viscoelastic monolayer graphene are investigated. The constitutive equation and governing equation for in-plane wave propagation is developed by employing Hamilton's principle and nonlocal strain gradient theory. By solving the governing equation of motion, the closed-form dispersion relation between phase velocity and wave number is derived and an asymptotic phase velocity can be acquired. The effects of wave number, material length scale parameter, nonlocal parameter and damping coefficient on in-plane wave propagation behaviors are discussed in the numerical studies. It is found that, when exciting wavelengths or structural dimensions become comparable to the material length scale parameters and nonlocal parameters, the scaling effects on wave propagation behaviors are significant. For nanoscaled graphene sheet, the effects of nonlocal parameter, material length scale parameter and damping coefficient on phase velocity are tiny at low wave numbers while significant at high wave numbers. The phase velocity would increase with the increase of material length scale parameter or the decrease of nonlocal parameter and damping coefficient. Furthermore, results indicate that the asymptotic phase velocity can be increase by increasing material length scale parameter or decreasing nonlocal parameter.
NASA Astrophysics Data System (ADS)
Norouzzadeh, A.; Ansari, R.
2017-04-01
Stress-strain relation in Eringen's nonlocal elasticity theory was originally formulated within the framework of an integral model. Due to difficulty of working with that integral model, the differential model of nonlocal constitutive equation is widely used for nanostructures. However, paradoxical results may be obtained by the differential model for some boundary and loading conditions. Presented in this article is a finite element analysis of Timoshenko nano-beams based on the integral model of nonlocal continuum theory without employing any simplification in the model. The entire procedure of deriving equations of motion is carried out in the matrix form of representation, and hence, they can be easily used in the finite element analysis. For comparison purpose, the differential counterparts of equations are also derived. To study the outcome of analysis based on the integral and differential models, some case studies are presented in which the influences of boundary conditions, nonlocal length scale parameter and loading factor are analyzed. It is concluded that, in contrast to the differential model, there is no paradox in the numerical results of developed integral model of nonlocal continuum theory for different situations of problem characteristics. So, resolving the mentioned paradoxes by means of a purely numerical approach based on the original integral form of nonlocal elasticity theory is the major contribution of present study.
Effects of nonlocal hydromechanics in a flow in thin channels
NASA Astrophysics Data System (ADS)
Aydagulov, R. R.; Ganiev, O. R.
2017-04-01
An approach to viscous friction is described as nonlocal momentum exchange between different layers of a fluid. The Navier-Stokes equations are replaced by pseudo-differential equations hyperbolic in time. In this case, instead of zero velocity on the boundary, a nonlocal nonlinear boundary condition is set in the form of the velocity dependence of the coefficient before the intensity of the momentum exchange with the boundary. The non-newtonian character of the viscosity of water is shown in experiments with thin insulin needles and explained by the nonlinear character of the momentum exchange of water with the boundary. The calculations agree very well both with our experiments and with the experiments of other authors. Calculations show that the flow decreases more than one-and-a-half times in comparison with the Poiseuille flow for channels with a diameter of 360-390 μm, which is confirmed in experiments.
NASA Astrophysics Data System (ADS)
Firouz-Abadi, R. D.; Fotouhi, M. M.; Haddadpour, H.
2012-06-01
A nonlocal continuum shell model is developed to study the stability of nanocones under combined loading: external pressure and compression force. The nonlinear governing equations of motion of nanocone are obtained using Hamilton's principle and the external loads are considered as prestress. Based on Eringen's nonlocal elasticity theory the small-scale effect is accounted in the governing equations of motion. To obtain the critical loads, the equations are solved using Galerkin technique and the effect of small-scale parameter and geometry on the stability of nanocone is studied.
Strong Local-Nonlocal Coupling for Integrated Fracture Modeling
Littlewood, David John; Silling, Stewart A.; Mitchell, John A.; Seleson, Pablo D.; Bond, Stephen D.; Parks, Michael L.; Turner, Daniel Z.; Burnett, Damon J.; Ostien, Jakob; Gunzburger, Max
2015-09-01
Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling," completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for
Fidelity based measurement induced nonlocality
NASA Astrophysics Data System (ADS)
Muthuganesan, R.; Sankaranarayanan, R.
2017-09-01
In this paper, we propose measurement induced nonlocality (MIN) using a metric based on fidelity to capture global nonlocal effect of a quantum state due to locally invariant projective measurements. This quantity is a remedy for local ancilla problem in the original definition of MIN. We present an analytical expression of the proposed version of MIN for pure bipartite state and 2 × n dimensional mixed state. We also provide an upper bound of the MIN for general mixed state. Finally, we compare this quantity with MINs based on Hilbert-Schmidt norm and skew information for higher dimensional Werner and isotropic states.
Maxwell-Garnett effective medium theory: Quantum nonlocal effects
Moradi, Afshin
2015-04-15
We develop the Maxwell-Garnett theory for the effective medium approximation of composite materials with metallic nanoparticles by taking into account the quantum spatial dispersion effects in dielectric response of nanoparticles. We derive a quantum nonlocal generalization of the standard Maxwell-Garnett formula, by means the linearized quantum hydrodynamic theory in conjunction with the Poisson equation as well as the appropriate additional quantum boundary conditions.
Structure formation in a nonlocally modified gravity model
Park, Sohyun; Dodelson, Scott
2013-01-01
We study a nonlocally modified gravity model proposed by Deser and Woodard which gives an explanation for current cosmic acceleration. By deriving and solving the equations governing the evolution of the structure in the Universe, we show that this model predicts a pattern of growth that differs from standard general relativity (+dark energy) at the 10-30% level. These differences will be easily probed by the next generation of galaxy surveys, so the model should be tested shortly.
NASA Astrophysics Data System (ADS)
Ghafarian, M.; Ariaei, A.
2016-08-01
The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique to solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.
Ghafarian, M.; Ariaei, A.
2016-08-07
The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique to solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.
Non-local rheology for dense granular flows in avalanches
NASA Astrophysics Data System (ADS)
Izzet, Adrien; Clement, Eric; Andreotti, Bruno
A local constitutive relation was proposed to describe dense granular flows (GDR MiDi, EPJE 2004). It provides a rather good prediction of the flowing regime but does not foresee the existence of a ``creep regime'' as observed by Komatsu et al. (PRL 2001). In the context of a 2D shear cell, a relaxation length for the velocity profile was measured (Bouzid et al., PRL 2013) which confirmed the existence of a flow below the standard Coulomb yield threshold. A correction for the local rheology was proposed. To test further this non-local constitutive relation, we built an inclined narrow channel within which we monitor the flow from the side. We managed to observe the ``creep regime'' over five orders of magnitude in velocity and fit the velocity profiles in the depth with an asymptotic solution of the non-local equation. However, the boundary condition at the free surface needs to be selected in order to calibrate the non-local rheology over the whole range of stresses in the system. In this perspective, we complement the experimental results with 2D simulations of hard and frictional discs on an inclined plane in which we introduce a surface friction force proportional to the effective pressure in the granular. We analyze these results in the light of the non-local rheology.
Nonlocal elasticity tensors in dislocation and disclination cores
Taupin, V.; Gbemou, K.; Fressengeas, C.; ...
2017-01-07
We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli tensors adequately reflect the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum andmore » moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.« less
Nonlocal elasticity tensors in dislocation and disclination cores
NASA Astrophysics Data System (ADS)
Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.
2017-03-01
Nonlocal elastic constitutive laws are introduced for crystals containing defects such as dislocations and disclinations. In addition to pointwise elastic moduli tensors adequately reflecting the elastic response of defect-free regions by relating stresses to strains and couple-stresses to curvatures, elastic cross-moduli tensors relating strains to couple-stresses and curvatures to stresses within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic stress/couple stress fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. The convoluted cross-moduli bring the following results: (i) Nonlocal stresses and couple stresses oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple stress fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-stress and couple stress fields of grain boundaries in nanocrystalline configurations.
Vibration analysis of defective graphene sheets using nonlocal elasticity theory
NASA Astrophysics Data System (ADS)
Namin, S. F. Asbaghian; Pilafkan, R.
2017-09-01
Many papers have studied the free vibration of graphene sheets. However, all this papers assumed their atomic structure free of any defects. Nonetheless, they actually contain some defects including single vacancy, double vacancy and Stone-Wales defects. This paper, therefore, investigates the free vibration of defective graphene sheets, rather than pristine graphene sheets, via nonlocal elasticity theory. Governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defective graphene sheets. Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different defect types are inspected for graphene sheets with clamped or simply-supported boundary conditions on all sides. It is shown that the natural frequencies of graphene sheets decrease by introducing defects to the atomic structure. Furthermore, it is found that the number of missing atoms, shapes and distributions of structural defects play a significant role in the vibrational behavior of graphene. The effect of vacancy defect reconstruction is also discussed in this paper.
Learning Non-Local Dependencies
ERIC Educational Resources Information Center
Kuhn, Gustav; Dienes, Zoltan
2008-01-01
This paper addresses the nature of the temporary storage buffer used in implicit or statistical learning. Kuhn and Dienes [Kuhn, G., & Dienes, Z. (2005). Implicit learning of nonlocal musical rules: implicitly learning more than chunks. "Journal of Experimental Psychology-Learning Memory and Cognition," 31(6) 1417-1432] showed that people could…
Nonlocal response of hyperbolic metasurfaces.
Correas-Serrano, D; Gomez-Diaz, J S; Tymchenko, M; Alù, A
2015-11-16
We analyze and model the nonlocal response of ultrathin hyperbolic metasurfaces (HMTSs) by applying an effective medium approach. We show that the intrinsic spatial dispersion in the materials employed to realize the metasurfaces imposes a wavenumber cutoff on the hyperbolic isofrequency contour, inversely proportional to the Fermi velocity, and we compare it with the cutoff arising from the structure granularity. In the particular case of HTMSs implemented by an array of graphene nanostrips, we find that graphene nonlocality can become the dominant mechanism that closes the hyperbolic contour - imposing a wavenumber cutoff at around 300k(0) - in realistic configurations with periodicity L<π/(300k(0)), thus providing a practical design rule to implement HMTSs at THz and infrared frequencies. In contrast, more common plasmonic materials, such as noble metals, operate at much higher frequencies, and therefore their intrinsic nonlocal response is mainly relevant in hyperbolic metasurfaces and metamaterials with periodicity below a few nm, being very weak in practical scenarios. In addition, we investigate how spatial dispersion affects the spontaneous emission rate of emitters located close to HMTSs. Our results establish an upper bound set by nonlocality to the maximum field confinement and light-matter interactions achievable in practical HMTSs, and may find application in the practical development of hyperlenses, sensors and on-chip networks.
Learning Non-Local Dependencies
ERIC Educational Resources Information Center
Kuhn, Gustav; Dienes, Zoltan
2008-01-01
This paper addresses the nature of the temporary storage buffer used in implicit or statistical learning. Kuhn and Dienes [Kuhn, G., & Dienes, Z. (2005). Implicit learning of nonlocal musical rules: implicitly learning more than chunks. "Journal of Experimental Psychology-Learning Memory and Cognition," 31(6) 1417-1432] showed that people could…
Interaction trajectory of solitons in nonlinear media with an arbitrary degree of nonlocality
Dai, Zhiping; Yang, Zhenjun; Ling, Xiaohui; Zhang, Shumin; Pang, Zhaoguang
2016-03-15
The interaction trajectory of solitons in nonlocal nonlinear media is investigated. A simple differential equation describing the interaction trajectories is derived based on the light ray equation. Numerical calculations are carried out to illustrate the interaction trajectories with different parameters. The results show that the degree of nonlocality greatly affects the interaction of solitons. For a strongly nonlocal case, the interaction trajectory can be described by a cosine function. Analytical expressions describing the trajectory and the oscillation period are obtained. For generally and weakly nonlocal cases, the interaction trajectories still oscillate periodically, however it is no longer sinusoidal and the oscillation period increases with the nonlocal degree decreasing. In addition, the trajectory of two solitons launched with a relative angle at the entrance plane is investigated. It is found that there exists a critical angle. When the initial relative angle is larger than the critical angle, the two solitons do not collide on propagation. The influence of the degree of nonlocality on the critical angle is also discussed.
D'Elia, Marta; Perego, Mauro; Bochev, Pavel B.; Littlewood, David John
2015-12-21
We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result, the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.
D'Elia, Marta; Perego, Mauro; Bochev, Pavel B.; ...
2015-12-21
We develop and analyze an optimization-based method for the coupling of nonlocal and local diffusion problems with mixed volume constraints and boundary conditions. The approach formulates the coupling as a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the nonlocal and local domains, and the controls are virtual volume constraints and boundary conditions. When some assumptions on the kernel functions hold, we prove that the resulting optimization problem is well-posed and discuss its implementation using Sandia’s agile software components toolkit. As a result,more » the latter provides the groundwork for the development of engineering analysis tools, while numerical results for nonlocal diffusion in three-dimensions illustrate key properties of the optimization-based coupling method.« less
CTE Solvability, Nonlocal Symmetry and Explicit Solutions of Modified Boussinesq System
NASA Astrophysics Data System (ADS)
Ren, Bo; Cheng, Xue-Ping
2016-07-01
A consistent tanh expansion (CTE) method is used to study the modified Boussinesq equation. It is proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by the Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependent variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initial value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among solitons and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wave interaction behaviors are studied both in analytical and graphical ways. Supported by the National Natural Science Foundation of China under Grant Nos. 11305106 and 11505154
Rayleigh-type waves in nonlocal micropolar solid half-space.
Khurana, Aarti; Tomar, S K
2017-01-01
Propagation of Rayleigh type surface waves in nonlocal micropolar elastic solid half-space has been investigated. Two modes of Rayleigh-type waves are found to propagate under certain approximations. Frequency equations of these Rayleigh type modes and their conditions of existence have been derived. These frequency equations are found to be dispersive in character due to the presence of micropolarity and nonlocality parameters in the medium. One of the frequency equations is a counterpart of the classical Rayleigh waves and the other is new and has appeared due to micropolarity of the medium. Phase speeds of these waves are computed numerically for Magnesium crystal and their variation against wavenumber are presented graphically. Comparisons have been made between the phase speeds of Rayleigh type waves through nonlocal micropolar, local micropolar and elastic solid half-spaces.
Non-local dynamics governing the self-induced motion of a planar vortex filament
NASA Astrophysics Data System (ADS)
Van Gorder, Robert A.
2015-06-01
While the Hasimoto planar vortex filament is one of the few exact solutions to the local induction approximation (LIA) approximating the self-induced motion of a vortex filament, it is natural to wonder whether such a vortex filament solution would exist for the non-local Biot-Savart dynamics exactly governing the filament motion, and if so, whether the non-local effects would drastically modify the solution properties. Both helical vortex filaments and vortex rings are known to exist under both the LIA and non-local Biot-Savart dynamics; however, the planar filament is a bit more complicated. In the present paper, we demonstrate that a planar vortex filament solution does exist for the non-local Biot-Savart formulation, provided that a specific non-linear integral equation (governing the spatial structure of such a filament) has a non-trivial solution. By using the Poincaré-Lindstedt method, we are able to obtain an accurate analytical approximation to the solution of this integral equation under physically reasonable assumptions. To obtain these solutions, we approximate local effects near the singularity of the integral equation using the LIA and non-local effects using the Biot-Savart formulation. Mathematically, the results constitute an analytical solution to an interesting nonlinear singular integro-differential equation in space and time variables. Physically, these results show that planar vortex filaments exist and maintain their forms under the non-local Biot-Savart formulation, as one would hope. Due to the regularization approach utilized, we are able to compare the structure of the planar filaments obtained under both LIA and Biot-Savart formulations in a rather straightforward manner, in order to determine the role of the non-locality on the structure of the planar filament.
Soteriades, Andreas Diomedes; Stott, Alistair William; Moreau, Sindy; Charroin, Thierry; Blanchard, Melanie; Liu, Jiayi; Faverdin, Philippe
2016-01-01
We aimed at quantifying the extent to which agricultural management practices linked to animal production and land use affect environmental outcomes at a larger scale. Two practices closely linked to farm environmental performance at a larger scale are farming intensity, often resulting in greater off-farm environmental impacts (land, non-renewable energy use etc.) associated with the production of imported inputs (e.g. concentrates, fertilizer); and the degree of self-sufficiency, i.e. the farm’s capacity to produce goods from its own resources, with higher control over nutrient recycling and thus minimization of losses to the environment, often resulting in greater on-farm impacts (eutrophication, acidification etc.). We explored the relationship of these practices with farm environmental performance for 185 French specialized dairy farms. We used Partial Least Squares Structural Equation Modelling to build, and relate, latent variables of environmental performance, intensification and self-sufficiency. Proxy indicators reflected the latent variables for intensification (milk yield/cow, use of maize silage etc.) and self-sufficiency (home-grown feed/total feed use, on-farm energy/total energy use etc.). Environmental performance was represented by an aggregate ‘eco-efficiency’ score per farm derived from a Data Envelopment Analysis model fed with LCA and farm output data. The dataset was split into two spatially heterogeneous (bio-physical conditions, production patterns) regions. For both regions, eco-efficiency was significantly negatively related with milk yield/cow and the use of maize silage and imported concentrates. However, these results might not necessarily hold for intensive yet more self-sufficient farms. This requires further investigation with latent variables for intensification and self-sufficiency that do not largely overlap- a modelling challenge that occurred here. We conclude that the environmental ‘sustainability’ of intensive dairy
Soteriades, Andreas Diomedes; Stott, Alistair William; Moreau, Sindy; Charroin, Thierry; Blanchard, Melanie; Liu, Jiayi; Faverdin, Philippe
2016-01-01
We aimed at quantifying the extent to which agricultural management practices linked to animal production and land use affect environmental outcomes at a larger scale. Two practices closely linked to farm environmental performance at a larger scale are farming intensity, often resulting in greater off-farm environmental impacts (land, non-renewable energy use etc.) associated with the production of imported inputs (e.g. concentrates, fertilizer); and the degree of self-sufficiency, i.e. the farm's capacity to produce goods from its own resources, with higher control over nutrient recycling and thus minimization of losses to the environment, often resulting in greater on-farm impacts (eutrophication, acidification etc.). We explored the relationship of these practices with farm environmental performance for 185 French specialized dairy farms. We used Partial Least Squares Structural Equation Modelling to build, and relate, latent variables of environmental performance, intensification and self-sufficiency. Proxy indicators reflected the latent variables for intensification (milk yield/cow, use of maize silage etc.) and self-sufficiency (home-grown feed/total feed use, on-farm energy/total energy use etc.). Environmental performance was represented by an aggregate 'eco-efficiency' score per farm derived from a Data Envelopment Analysis model fed with LCA and farm output data. The dataset was split into two spatially heterogeneous (bio-physical conditions, production patterns) regions. For both regions, eco-efficiency was significantly negatively related with milk yield/cow and the use of maize silage and imported concentrates. However, these results might not necessarily hold for intensive yet more self-sufficient farms. This requires further investigation with latent variables for intensification and self-sufficiency that do not largely overlap- a modelling challenge that occurred here. We conclude that the environmental 'sustainability' of intensive dairy farming
Nonlocality as a function of PDE type
NASA Astrophysics Data System (ADS)
Maker, David
2007-08-01
Here we postulate a geometrical 2D closed path invariant ds=ds t+ds Φ (geometrical interpretation) with the observer's own 2D ds=ds t+ds Φ then giving a total direct sum 2⊕2=4 degrees of freedom for the resulting (observer translation) Dirac equation pde and its ψ. There are several, more or less technical, ways of stating the consequences of that new "observer interpretation" Dirac equation pde. Two such ways are "wave function collapse," and in a more common sense vein "Bertlmann's socks." Note that wavefunction collapse to ψ then (and experimental nonlocality implications) is the "observables translation" of that fundamental postulate and so not itself postulated. Also that geometrical postulate does not allow a Bohmian hidden variable interpretation because of its fundamental nature (i.e., we cannot go any deeper). For example that postulate states no x or p that we would be certain of in some hidden variable context. Thus we can ignore here the straw man arguments of J.S. Bell that are in response to Bohmian hidden variable theories only. Thus there cannot result Bell's kink at θ=0 in the correlation function between the polarization measurements on the two ends of an EPR experimental apparatus (Bell, 1987). Recall this kink required correlating in a hidden variable, classical statistical mechanical context, with resulting superluminal implications. Also note here the "observer interpretation" boundary condition conservation of angular momentum of the initial singlet state for our 4D Dirac pde results in this being a time independent solution to this pde. Thus wave function collapse to the measured value in no way implies superluminal communication. In laymen terms it is just the Bertlmann's socks common sense fact that we knew before hand about the original singlet state of the central emitter, no superluminal communication between the left and right ends of the Aspect apparatus was required to know about this. Thus our new observer representation
A new nonlocal nonlinear diffusion of image processing
NASA Astrophysics Data System (ADS)
Guidotti, Patrick
A novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing. The equation can be viewed as a new paradigm for the regularization of the well-known Perona-Malik equation. The regularization is implemented via nonlinearity intensity reduction through fractional derivatives. Well-posedness in the weak setting is established. Global existence and convergence to the average holds in the purely diffusive limit whereas an interesting dynamic behavior is engendered by the presence of nontrivial equilibria as the intensity of the nonlinearity is increased and comes close to the one of Perona-Malik.
NASA Astrophysics Data System (ADS)
Xiong, D. R.; Deng, L.; Zhang, C.
2015-08-01
Starting from hydrodynamic equations, we have established a set of hydrodynamic equations for average flow and a set of dynamic equations of auto- and cross-correlations of turbulent velocity and temperature fluctuations, following the classic Reynold's treatment of turbulence. The combination of the two sets of equations leads to a complete and self-consistent mathematical expressions ready for the calculations of stellar structure and oscillations. In this paper, non-locality and anisotropy of turbulent convection are concisely presented, together with defining and calibrating of the three convection parameters (c1, c2 and c3) included in the algorithm. With the non-local theory of convection, the structure of the convective envelope and the major characteristics of non-adiabatic linear oscillations are demonstrated by numerical solutions. Great effort has been exercised to the choice of convection parameters and pulsation instabilities of the models, the results of which show that within large ranges of all three parameters (c1, c2 and c3) the main properties of pulsation stability keep unchanged.
Nonlocal Structures: Bilocal Photon
NASA Astrophysics Data System (ADS)
Clapp, Roger E.
1980-01-01
As a starting point, it is postulated that all particles and fields are built from a single primitive field, which must then be a massless fermion with a σ spin of one-half. Two helicities are embodied in a τ spin of one-half. The vacuum is an open Fermi sea whose height is a wave number κ. Elementary particles are structures having the form of standing-wave systems floating on the vacuum sea, with the height κ providing both the scale of inner structural size and the mass unit for the elementary particle mass spectrum. A bilocal photon starts with a function describing two primitive quanta with parallel σ spin and opposite τ spin. A centroid-time wave equation then couples-in an infinite set of orthogonal functions. The introduction of an operator Q λ permits the reduction of the infinite secular determinant to a finite six-by-six determinant. Solutions (for the infinite expansion) are obtained describing photons with right-handed and left-handed polarizations. Superpositions of these give linearly polarized photons. Electric and magnetic field vectors, satisfying the vacuum Maxwell equations, are obtained from a bilocal Hertz vector given by п= (2/κ3 c)(∂/∂ t r)∇rΨ(1,2), where Ψ(1,2) is the bilocal wave function, and tr and r are the relative time and relative position variables.
Evidence for nonlocal electrodynamics in planar Josephson junctions.
Boris, A A; Rydh, A; Golod, T; Motzkau, H; Klushin, A M; Krasnov, V M
2013-09-13
We study the temperature dependence of the critical current modulation I(c)(H) for two types of planar Josephson junctions: a low-Tc Nb/CuNi/Nb and a high-Tc YBa2Cu3O(7-δ) bicrystal grain-boundary junction. At low T both junctions exhibit a conventional behavior, described by the local sine-Gordon equation. However, at elevated T the behavior becomes qualitatively different: the I(c)(H) modulation field ΔH becomes almost T independent and neither ΔH nor the critical field for the penetration of Josephson vortices vanish at Tc. Such an unusual behavior is in good agreement with theoretical predictions for junctions with nonlocal electrodynamics. We extract absolute values of the London penetration depth λ from our data and show that a crossover from local to nonlocal electrodynamics occurs with increasing T when λ(T) becomes larger than the electrode thickness.
Pattern transitions and complexity for a nonlocal logistic map
NASA Astrophysics Data System (ADS)
Barbosa, Fernando V.; Penna, André A. L.; Ferreira, Rogelma M. S.; Novais, Keila L. V.; da Cunha, Jefferson A. R.; Oliveira, Fernando A.
2017-05-01
We examine the pattern solutions in a generalized nonlocal logistic map that includes spatial kernels in both growth and competition terms. We show that this map includes as a particular case the nonlocal Fisher-Kolmogorov equation, and we demonstrate the existence of three kinds of stationary nonlinear solutions: one uniform, one cosine type that we refer to as wavelike solution, and another in the form of Gaussian. We also obtain analytical expressions that describe the nonlinear pattern behavior in the system, and we establish the stability criterion. We define thermodynamics quantities such as entropy and the order parameter. Based on this, the pattern-no-pattern and pattern-pattern transitions are properly analyzed. We show that these pattern solutions may be related to the recently observed peak adding phenomenon in nonlinear optics.
Chaudhury, Kunal N; Singer, Amit
2012-11-01
In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.
Activation of nonlocal quantum resources.
Navascués, Miguel; Vértesi, Tamás
2011-02-11
We find two two-qubit bipartite states ρ1, ρ2 such that arbitrarily many copies of one or the other cannot exhibit nonlocal correlations in a two-setting-two-outcome Bell scenario. However, the bipartite state ρ1 ⊗ ρ2 violates the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).] by an amount of 2.023. We also identify a CHSH-local state ρ such that ρ⊗2 is CHSH inequality-violating. The tools employed can be easily adapted to find instances of nonlocality activation in arbitrary Bell scenarios.
Nonlocality and conflicting interest games.
Pappa, Anna; Kumar, Niraj; Lawson, Thomas; Santha, Miklos; Zhang, Shengyu; Diamanti, Eleni; Kerenidis, Iordanis
2015-01-16
Nonlocality enables two parties to win specific games with probabilities strictly higher than allowed by any classical theory. Nevertheless, all known such examples consider games where the two parties have a common interest, since they jointly win or lose the game. The main question we ask here is whether the nonlocal feature of quantum mechanics can offer an advantage in a scenario where the two parties have conflicting interests. We answer this in the affirmative by presenting a simple conflicting interest game, where quantum strategies outperform classical ones. Moreover, we show that our game has a fair quantum equilibrium with higher payoffs for both players than in any fair classical equilibrium. Finally, we play the game using a commercial entangled photon source and demonstrate experimentally the quantum advantage.
Certifying nonlocality from separable marginals
NASA Astrophysics Data System (ADS)
Vértesi, Tamás; Laskowski, Wiesław; Pál, Károly F.
2014-01-01
Imagine three parties, Alice, Bob, and Charlie, who share a state of three qubits such that all two-party reduced states A-B, A-C, and B-C are separable. Suppose that they have information only about these marginals but not about the global state. According to recent results, there exists an example for a set of three separable two-party reduced states that is only compatible with an entangled global state. In this paper, we show a stronger result by exhibiting separable two-party reduced states A-B, A-C, and B-C, such that any global state compatible with these marginals is nonlocal. Hence, we obtain that nonlocality of multipartite states can be certified from information only about separable marginals.
Temporal nonlocality in bistable perception
NASA Astrophysics Data System (ADS)
Atmanspacher, Harald; Filk, Thomas
2012-12-01
A novel conceptual framework for theoretical psychology is presented and illustrated for the example of bistable perception. A basic formal feature of this framework is the non-commutativity of operations acting on mental states. A corresponding model for the bistable perception of ambiguous stimuli, the Necker-Zeno model, is sketched and some empirical evidence for it so far is described. It is discussed how a temporal nonlocality of mental states, predicted by the model, can be understood and tested.
Beam envelope calculations in general linear coupled lattices
Chung, Moses; Qin, Hong; Groening, Lars; Xiao, Chen; Davidson, Ronald C.
2015-01-15
The envelope equations and Twiss parameters (β and α) provide important bases for uncoupled linear beam dynamics. For sophisticated beam manipulations, however, coupling elements between two transverse planes are intentionally introduced. The recently developed generalized Courant-Snyder theory offers an effective way of describing the linear beam dynamics in such coupled systems with a remarkably similar mathematical structure to the original Courant-Snyder theory. In this work, we present numerical solutions to the symmetrized matrix envelope equation for β which removes the gauge freedom in the matrix envelope equation for w. Furthermore, we construct the transfer and beam matrices in terms of the generalized Twiss parameters, which enables calculation of the beam envelopes in arbitrary linear coupled systems.
Nonlocal distillation based on multisetting Bell inequality
NASA Astrophysics Data System (ADS)
Ye, Xiang-Jun; Deng, Dong-Ling; Chen, Jing-Ling
2012-12-01
Inspired by the recent works of Foster [Phys. Rev. Lett.0031-900710.1103/PhysRevLett.102.120401 102, 120401 (2009)] and Brunner [Phys. Rev. Lett.0031-900710.1103/PhysRevLett.102.160403 102, 160403 (2009)], we present a nonlocality distillation protocol for two three-level (qutrit) systems in the framework of generalized nonsignaling theories. Our protocol is based on a three-setting Bell inequality. It works efficiently for a specific class of three-input-three-output nonlocal boxes. In the asymptotic limit, all these nonlocal boxes can be distilled to the maximally nonlocal box defined by the inequality and nonsignaling constraints. Then we introduce a contracting protocol that reduces these boxes to the so-called “correlated nonlocal boxes.” As a result, our three-input-three-output nonlocal boxes also make communication complexity trivial and appear very unlikely to exist in nature.
Detrimental nonlocality in luminescence measurements
NASA Astrophysics Data System (ADS)
Pluska, Mariusz; Czerwinski, Andrzej
2017-08-01
Luminescence studies are used to investigate the local properties of various light-emitting materials. A critical issue of these studies is presented that the signals often lack all advantages of luminescence-studies of high locality, and may originate from an extended spatial region of even a few millimeters in size or the whole sample, i.e., places other than intended for investigation. This is a key problem for research and development in photonics. Due to this nonlocality, information indicating defects, irregularities, nonuniformities and inhomogeneities is lost. The issue refers to typical structures with a strong built-in electric field. Such fields exist intentionally in most photonic structures and occur unintentionally in many other materials investigated by applied physics. We reveal [using test samples prepared with focused ion beam (FIB) on an AlGaAs/GaAs laser heterostructure with an InGaAs quantum well (QW)] that nonlocality increases at low temperatures. This is contrary to the widely expected outcome, as low-temperature luminescence measurements are usually assumed to be free from disturbances. We explain many effects observed due to nonlocality in luminescence studies and prove that separation of the investigated area by focused ion beam milling is a practical solution enabling truly local luminescence measurements. All conclusions drawn using the example of cathodoluminescence are useful for other luminescence techniques.
Circumplanetary disc or circumplanetary envelope?
NASA Astrophysics Data System (ADS)
Szulágyi, J.; Masset, F.; Lega, E.; Crida, A.; Morbidelli, A.; Guillot, T.
2016-08-01
We present three-dimensional simulations with nested meshes of the dynamics of the gas around a Jupiter mass planet with the JUPITER and FARGOCA codes. We implemented a radiative transfer module into the JUPITER code to account for realistic heating and cooling of the gas. We focus on the circumplanetary gas flow, determining its characteristics at very high resolution (80 per cent of Jupiter's diameter). In our nominal simulation where the temperature evolves freely by the radiative module and reaches 13000 K at the planet, a circumplanetary envelope was formed filling the entire Roche lobe. Because of our equation of state is simplified and probably overestimates the temperature, we also performed simulations with limited maximal temperatures in the planet region (1000, 1500, and 2000 K). In these fixed temperature cases circumplanetary discs (CPDs) were formed. This suggests that the capability to form a CPD is not simply linked to the mass of the planet and its ability to open a gap. Instead, the gas temperature at the planet's location, which depends on its accretion history, plays also fundamental role. The CPDs in the simulations are hot and cooling very slowly, they have very steep temperature and density profiles, and are strongly sub-Keplerian. Moreover, the CPDs are fed by a strong vertical influx, which shocks on the CPD surfaces creating a hot and luminous shock-front. In contrast, the pressure supported circumplanetary envelope is characterized by internal convection and almost stalled rotation.
Planet formation with envelope enrichment: new insights on planetary diversity
NASA Astrophysics Data System (ADS)
Venturini, Julia; Alibert, Yann; Benz, Willy
2016-12-01
Aims: We compute for the first time self-consistent models of planet growth that include the effect of envelope enrichment. The change in envelope metallicity is assumed to be the result of planetesimal disruption or icy pebble sublimation. Methods: We solved internal structure equations taking into account global energy conservation for the envelope to compute in situ planetary growth. We considered different opacities and equations of state suited for a wide range of metallicities. Results: We find that envelope enrichment speeds up the formation of gas giants. It also explains naturally the formation of low- and intermediate-mass objects with large fractions of H-He ( 20-30% in mass). High-opacity models explain the metallicity of the giant planets of the solar system well, while low-opacity models are suited to explain the formation of low-mass objects with thick H-He envelopes and gas giants with sub-solar envelope metallicities. We find good agreement between our models and the estimated water abundance for WASP-43b. For HD 189733b, HD 209458b, and WASP-12b we predict fractions of water higher than what is estimated from observations by at least a factor 2. Conclusions: Envelope enrichment by icy planetesimals is the natural scenario to explain the formation of a wide variety of objects, ranging from mini-Neptunes to gas giants. We predict that the total and envelope metallicity decrease with planetary mass.
Unified criteria for multipartite quantum nonlocality
Cavalcanti, E. G.; He, Q. Y.; Reid, M. D.; Wiseman, H. M.
2011-09-15
Wiseman and co-workers [H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett. 98, 140402, (2007)] proposed a distinction among the nonlocality classes of Bell's nonlocality, Einstein-Podolsky-Rosen (EPR) paradox or steering, and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.
Nonlocality and entanglement in the XY model
Batle, J.; Casas, M.
2010-12-15
Nonlocality and quantum entanglement constitute two special features of quantum systems of paramount importance in quantum-information theory (QIT). Essentially regarded as identical or equivalent for many years, they constitute different concepts. Describing nonlocality by means of the maximal violation of two Bell inequalities, we study both entanglement and nonlocality for two and three spins in the XY model. Our results shed light on the description of nonlocality and the possible information-theoretic task limitations of entanglement in an infinite quantum system.
Siebert, Julien; Alonso, Sergio; Bär, Markus; Schöll, Eckehard
2014-05-01
A one-component bistable reaction-diffusion system with asymmetric nonlocal coupling is derived as a limiting case of a two-component activator-inhibitor reaction-diffusion model with differential advection. The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusion system are then compared to the previously studied case of a system with symmetric nonlocal coupling. We carry out a linear stability analysis of the spatially homogeneous steady states of the model and numerical simulations of the model to show how the asymmetric nonlocal coupling controls and alters the steady states and the front dynamics in the system. In a second step, a third fast reaction-diffusion equation is included which induces the formation of more complex patterns. A linear stability analysis predicts traveling waves for asymmetric nonlocal coupling, in contrast to a stationary Turing patterns for a system with symmetric nonlocal coupling. These findings are verified by direct numerical integration of the full equations with nonlocal coupling.
FRACTIONAL CRYSTALLIZATION FEED ENVELOPE
HERTING DL
2008-03-19
Laboratory work was completed on a set of evaporation tests designed to establish a feed envelope for the fractional crystallization process. The feed envelope defines chemical concentration limits within which the process can be operated successfully. All 38 runs in the half-factorial design matrix were completed successfully, based on the qualitative definition of success. There is no feed composition likely to be derived from saltcake dissolution that would cause the fractional crystallization process to not meet acceptable performance requirements. However, some compositions clearly would provide more successful operation than other compositions.
Thongyothee, Chawis Chucheepsakul, Somchai
2013-12-28
This paper is concerned with postbuckling behaviors of nanorods subjected to an end concentrated load. One end of the nanorod is clamped while the other end is fixed to a support that can slide in the slot. The governing equation is developed from static equilibrium and geometrical conditions by using the exact curvature corresponding to the elastica theory. The nonlocal elasticity, the effect of surface stress, and their combined effects are taken into account in Euler–Bernoulli beam theory. Differential equations in this problem can be solved numerically by using the shooting-optimization technique for the postbuckling loads and the buckled configurations. The results show that nanorods with the nonlocal elasticity effect undergo increasingly large deformation while the effect of surface stress in combination with nonlocal elasticity decreases the deflection of nanorods under the same postbuckling load.
A Transport Model for Non-Local Heating of Electrons in ICP Reactors
NASA Technical Reports Server (NTRS)
Chang, C. H.; Bose, Deepak; Arnold, James O. (Technical Monitor)
1998-01-01
A new model has been developed for non-local heating of electrons in ICP reactors, based on a hydrodynamic approach. The model has been derived using the electron momentum conservation in azimuthal direction with electromagnetic and frictional forces respectively as driving force and damper of harmonic oscillatory motion of electrons. The resulting transport equations include the convection of azimuthal electron momentum in radial and axial directions, thereby accounting for the non-local effects. The azimuthal velocity of electrons and the resulting electrical current are coupled to the Maxwell's relations, thus forming a self-consistent model for non-local heating. This model is being implemented along with a set of Navier-Stokes equations for plasma dynamics and gas flow to simulate low-pressure (few mTorr's) ICP discharges. Characteristics of nitrogen plasma in a TCP 300mm etch reactor is being studied. The results will be compared against the available Langmuir probe measurements.
Caulfield, Michael; Cupo, Albert; Dean, Hansi; Hoffenberg, Simon; King, C. Richter; Klasse, P. J.; Marozsan, Andre; Moore, John P.; Sanders, Rogier W.; Ward, Andrew; Wilson, Ian; Julien, Jean-Philippe
2017-08-22
The present application relates to novel HIV-1 envelope glycoproteins, which may be utilized as HIV-1 vaccine immunogens, and antigens for crystallization, electron microscopy and other biophysical, biochemical and immunological studies for the identification of broad neutralizing antibodies. The present invention encompasses the preparation and purification of immunogenic compositions, which are formulated into the vaccines of the present invention.
MacLennan, Donald A.; Turner, Brian P.; Gitsevich, Aleksandr; Bass, Gary K.; Dolan, James T.; Kipling, Kent; Kirkpatrick, Douglas A.; Leng, Yongzhang; Levin, Izrail; Roy, Robert J.; Shanks, Bruce; Smith, Malcolm; Trimble, William C.; Tsai, Peter
2001-01-01
A jacketed lamp bulb envelope includes a ceramic cup having an open end and a partially closed end, the partially closed end defining an aperture, a lamp bulb positioned inside the ceramic cup abutting the aperture, and a reflective ceramic material at least partially covering a portion of the bulb not abutting the aperture. The reflective ceramic material may substantially fill an interior volume of the ceramic cup not occupied by the bulb. The ceramic cup may include a structural feature for aiding in alignment of the jacketed lamp bulb envelope in a lamp. The ceramic cup may include an external flange about a periphery thereof. One example of a jacketed lamp bulb envelope includes a ceramic cup having an open end and a closed end, a ceramic washer covering the open end of the ceramic cup, the washer defining an aperture therethrough, a lamp bulb positioned inside the ceramic cup abutting the aperture, and a reflective ceramic material filling an interior volume of the ceramic cup not occupied by the bulb. A method of packing a jacketed lamp bulb envelope of the type comprising a ceramic cup with a lamp bulb disposed therein includes the steps of filling the ceramic cup with a flowable slurry of reflective material, and applying centrifugal force to the cup to pack the reflective material therein.
Pushing the endogenous envelope
Henzy, Jamie E.; Johnson, Welkin E.
2013-01-01
The majority of retroviral envelope glycoproteins characterized to date are typical of type I viral fusion proteins, having a receptor binding subunit associated with a fusion subunit. The fusion subunits of lentiviruses and alpha-, beta-, delta- and gammaretroviruses have a very conserved domain organization and conserved features of secondary structure, making them suitable for phylogenetic analyses. Such analyses, along with sequence comparisons, reveal evidence of numerous recombination events in which retroviruses have acquired envelope glycoproteins from heterologous sequences. Thus, the envelope gene (env) can have a history separate from that of the polymerase gene (pol), which is the most commonly used gene in phylogenetic analyses of retroviruses. Focusing on the fusion subunits of the genera listed above, we describe three distinct types of retroviral envelope glycoproteins, which we refer to as gamma-type, avian gamma-type and beta-type. By tracing these types within the ‘fossil record’ provided by endogenous retroviruses, we show that they have surprisingly distinct evolutionary histories and dynamics, with important implications for cross-species transmissions and the generation of novel lineages. These findings validate the utility of env sequences in contributing phylogenetic signal that enlarges our understanding of retrovirus evolution. PMID:23938755
NASA Astrophysics Data System (ADS)
Kukushkin, A. B.
1996-11-01
The nonlocal transport approach is formulated, based on anomalous cross-field energy transport (ACFET) by the longitudinal/tranverse EM waves of the mean free path of the order and much larger than plasma characteristic size and, correspondingly, on integral equation in space variables. Self-consistency of this approach is shown in interpreting those observed phenomena of nonlocality whose interpretation in "local", diffusion-like approaches gives instant jumps of thermal diffusivities in a large part of plasma volume. The modelling is carried out of the initial stage of recently observed phenomena of fast nonlocal energy transport: (i) net inward flux of energy during off-axis heating (vs. ECRH experiments on D-III-D); (ii) prompt rise of temperature in the core in "cold pulse" experiments (fast cooling of the periphery) on TEXT and TFTR; (iii) fast "volumetric" response of energy transport to plasma edge behavior during L-H transitions (in JET and JT-60U). The results suggest (a) universal and transparent physical explanation of the mechanism of nonlocal inward energy flux, which is lost in diffusion-like approaches, and (b) necessity to append existing numerical codes with nonlocal transport term, an integral in space variables.
Conformal symmetry and nonlinear extensions of nonlocal gravity
NASA Astrophysics Data System (ADS)
Cusin, Giulia; Foffa, Stefano; Maggiore, Michele; Mancarella, Michele
2016-04-01
We study two nonlinear extensions of the nonlocal R □-2R gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing □-2 with (-□+R /6 )-2, which is the operator that enters the action for a conformally-coupled scalar field, or replacing □-2 with the inverse of the Paneitz operator, which is a four-derivative operator that enters in the effective action induced by the conformal anomaly. We show that the former modification gives an interesting and viable cosmological model, with a dark energy equation of state today wDE≃-1.01 , which very closely mimics Λ CDM and evolves asymptotically into a de Sitter solution. The model based on the Paneitz operator seems instead excluded by the comparison with observations. We also review some issues about the causality of nonlocal theories, and we point out that these nonlocal models can be modified so to nicely interpolate between Starobinski inflation in the primordial universe and accelerated expansion in the recent epoch.
Two dimensional non-local transport across zonal shear flows
NASA Astrophysics Data System (ADS)
Kullberg, A.; Del-Castillo-Negrete, D.; Morales, G. J.; Maggs, J. E.
2011-10-01
The standard diffusive model assumes that the fluxes are entirely determined by the local value of the gradient. Although this paradigm has had considerable success, there are situations in which this prescription (i.e. Fick's law) does not hold; instead, the flux at a point may depend on the gradients throughout the entire spatial domain. Examples of this type of transport include perturbative experiments in tokamaks, numerical simulations of turbulent plasmas, and generalized random walk theoretical models. This presentation describes recent results on non-local transport in the presence of zonal shear flows. The study is based on a 2-dimensional equation that has a poloidal zonal flow coupled to a radial non-local transport channel. This work extends upon previous research by incorporating a cylindrical, 2-dimensional (albeit azimuthally averaged), non-local radial transport operator. Numerical results relating to several aspects of transport across the zonal shear flow are presented, including a numerical study of the creation of resonant traveling thermal waves inside the flow by an oscillating heat source, and the propagation of cold pulses across the zonal flow. In the case of thermal waves, resonance occurs when the source frequency matches the rotational angular frequency of the flow.
Nonlocal problems in thin domains
NASA Astrophysics Data System (ADS)
Pereira, Marcone C.; Rossi, Julio D.
2017-08-01
In this paper we consider nonlocal problems in thin domains. First, we deal with a nonlocal Neumann problem, that is, we study the behavior of the solutions to f (x) =∫Ω1×Ω2Jɛ (x - y) (uɛ (y) -uɛ (x)) dy with Jɛ (z) = J (z1 , ɛz2) and Ω =Ω1 ×Ω2 ⊂RN =R N1 ×R N2 a bounded domain. We find that there is a limit problem, that is, we show that uɛ →u0 as ɛ → 0 in Ω and this limit function verifies ∫Ω2 f (x1 ,x2) dx2 = |Ω2 |∫Ω1 J (x1 -y1 , 0) (U0 (y1) -U0 (x1)) dy1, with U0 (x1) =∫Ω2u0 (x1 ,x2) dx2. In addition, we deal with a double limit when we add to this model a rescale in the kernel with a parameter that controls the size of the support of J. We show that this double limit exhibits some interesting features. We also study a nonlocal Dirichlet problem f (x) =∫RNJɛ (x - y) (uɛ (y) -uɛ (x)) dy, x ∈ Ω, with uɛ (x) ≡ 0, x ∈RN ∖ Ω, and deal with similar issues. In this case the limit as ɛ → 0 is u0 = 0 and the double limit problem commutes and also gives v ≡ 0 at the end.
On the preservation of cooperation in two-strategy games with nonlocal interactions.
Aydogmus, Ozgur; Zhou, Wen; Kang, Yun
2017-03-01
Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions based on an integro-differential replicator equation. By defining the invasion speed and minimal traveling wave speed for the derived model, we study the effects of the payoffs, the selection pressure and the spatial parameter on the preservation of cooperation. One of our most interesting findings is that, for the Prisoners Dilemma games in which the defection is the only evolutionary stable strategy for unstructured populations, analyses on its asymptotic speed of propagation suggest that, in contrast with spatially homogeneous games, the cooperators can invade the habitat under proper conditions. Other two-strategy evolutionary spatial games are also explored. Both our theoretical and numerical studies show that the nonlocal spatial interaction favors diversity in strategies in a population and is able to preserve cooperation in a competing environment. A real data application in a virus mutation study echoes our theoretical observations. In addition, we compare the results of our model to the partial differential equation approach to demonstrate the importance of including non-local interaction component in evolutionary game models.
Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter
2015-01-01
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581
Multipole vector solitons in nonlocal nonlinear media.
Kartashov, Yaroslav V; Torner, Lluis; Vysloukh, Victor A; Mihalache, Dumitru
2006-05-15
We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.
Non-local in time formulations for reactive transport
NASA Astrophysics Data System (ADS)
Carrera, J.; Willmann, M.; Sanchez-Vila, X.; Silva, O.; Saaltink, M.; Bea, S. A.
2009-04-01
The rate at which equilibrium chemical reactions occur is driven by mixing-induced chemical disequilibrium. At the field scale, mixing is poorly represented by an Advection Dispersion type equation (ADE). Instead, non-local in time variants have been proposed to represent effective transport dynamics. These include formulations such as the Multi-Rate Mass Transfer (MRMT) or Continuous Time Random Walk (CTRW) methods, which have been successful in representing breakthrough curves (BTCs) of conservative solutes at intermediate scales. The original formulation of these equations is not amenable to reactive transport, which requires local (in space and time) concentrations. However, such original formulations can be easily localized, which allows using these formulations for general solutions. The objective of our work is, first, to test whether non-local transport models derived from conservative solutes observations, can be used to describe effective reactive transport in heterogeneous media. To this end, we use a numerical approach to obtain the spatial and temporal distribution of mineral precipitation in a binary system at equilibrium in a heterogeneous aquifer. We then compare these reaction rates to those corresponding to an equivalent (i.e. same conservative BTC) homogenized media with transport characterized by a non-local in time equation involving a memory function (MRMT). We find an excellent agreement between the two models in terms of cumulative precipitated mass, and depending on the local heterogeneous structure the match is acceptable for the reaction rate. These results indicate that mass transfer models are an excellent tool for upscaling mixing controlled reactive transport.
Nonlocal Galileons and self-acceleration
NASA Astrophysics Data System (ADS)
Gabadadze, Gregory; Yu, Siqing
2017-05-01
A certain class of nonlocal theories eliminates an arbitrary cosmological constant (CC) from a universe that can be perceived as our world. Dark energy then cannot be explained by a CC; it could however be due to massive gravity. We calculate the new corrections, which originate from the nonlocal terms that eliminate the CC, to the decoupling limit Lagrangian of massive gravity. The new nonlocal terms also have internal field space Galilean symmetry and are referred here as ;nonlocal Galileons.; We then study a self-accelerated solution and show that the new nonlocal terms change the perturbative stability analysis. In particular, small fluctuations are now stable and non-superluminal for some simple parameter choices, whereas for the same choices the pure massive gravity fluctuations are unstable. We also study stable spherically symmetric solutions on this background.
Nonlocal thermal transport in solar flares
NASA Technical Reports Server (NTRS)
Karpen, Judith T.; Devore, C. Richard
1987-01-01
A flaring solar atmosphere is modeled assuming classical thermal transport, locally limited thermal transport, and nonlocal thermal transport. The classical, local, and nonlocal expressions for the heat flux yield significantly different temperature, density, and velocity profiles throughout the rise phase of the flare. Evaporation of chromospheric material begins earlier in the nonlocal case than in the classical or local calculations, but reaches much lower upward velocities. Much higher coronal temperatures are achieved in the nonlocal calculations owing to the combined effects of delocalization and flux limiting. The peak velocity and momentum are roughly the same in all three cases. A more impulsive energy release influences the evolution of the nonlocal model more than the classical and locally limited cases.
Hyperbolic metamaterial lens with hydrodynamic nonlocal response.
Yan, Wei; Mortensen, N Asger; Wubs, Martijn
2013-06-17
We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we propose to measure the near-field distribution of a hyperbolic metamaterial lens.
Ivanov, V. V.; Kukushkin, A. B.
1997-05-05
The importance of nonlocal effects in radiative transfer in continuous spectra is shown in numerical modelling of space profiles of plasma temperature and Bremsstrahlung total power losses in a layer of adiabatically compressed hot dense plasma, via comparing the results of the exact, integral equation formalism and widely used approach of radiation temperature diffusion with Rosseland mean diffusion coefficient.
Fronts under arrest: Nonlocal boundary dynamics in biology.
McCalla, Scott G; von Brecht, James H
2016-12-01
We introduce a minimal geometric partial differential equation framework to understand pattern formation from interacting, counterpropagating fronts. Our approach concentrates on the interfaces between different states in a system, and relies on both nonlocal interactions and mean-curvature flow to track their evolution. As an illustration, we use this approach to describe a phenomenon in bacterial colony formation wherein sibling colonies can arrest each other's growth. This arrested motion leads to static separations between healthy, growing colonies. As our minimal model faithfully recovers the geometry of these competing colonies, it captures and elucidates the key leading-order mechanisms responsible for such patterned growth.
Nonlinear analysis of lipid tubules by nonlocal beam model.
Shen, Hui-Shen
2011-05-07
Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for lipid tubules. The lipid tubule is modeled as a nonlocal micro/nano-beam which contains small scale effect. The material properties are assumed to be size-dependent. The governing equation is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of lipid tubules. In contrast, it increases the nonlinear to linear frequency ratios slightly for the lipid tubule with immovable end conditions.
Fronts under arrest: Nonlocal boundary dynamics in biology
NASA Astrophysics Data System (ADS)
McCalla, Scott G.; von Brecht, James H.
2016-12-01
We introduce a minimal geometric partial differential equation framework to understand pattern formation from interacting, counterpropagating fronts. Our approach concentrates on the interfaces between different states in a system, and relies on both nonlocal interactions and mean-curvature flow to track their evolution. As an illustration, we use this approach to describe a phenomenon in bacterial colony formation wherein sibling colonies can arrest each other's growth. This arrested motion leads to static separations between healthy, growing colonies. As our minimal model faithfully recovers the geometry of these competing colonies, it captures and elucidates the key leading-order mechanisms responsible for such patterned growth.
Nonlocal String Tachyon as a Model for Cosmological Dark Energy
Aref'eva, Irina Ya.
2006-03-29
There are many different phenomenological models describing the cosmological dark energy and accelerating Universe by choosing adjustable functions. In this paper we consider a specific model of scalar tachyon field which is derived from the NSR string field theory and study its cosmological applications. We find that in the effective field theory approximation the equation of state parameter w < -1, i.e. one has a phantom Universe. It is shown that due to nonlocal effects there is no quantum instability that the usual phantom models suffer from. Moreover due to a flip effect of the potential the Universe does not enter to a future singularity.
NASA Astrophysics Data System (ADS)
Challamel, Noël; Grazide, Cécile; Picandet, Vincent; Perrot, Arnaud; Zhang, Yingyan
2016-06-01
This study focuses on heat conduction in unidimensional lattices also known as microstructured rods. The lattice thermal properties can be representative of concentrated thermal interface phases in one-dimensional segmented rods. The exact solution of the linear time-dependent spatial difference equation associated with the lattice problem is presented for some given initial and boundary conditions. This exact solution is compared to the quasicontinuum approximation built by continualization of the lattice equations. A rational-based asymptotic expansion of the pseudo-differential problem leads to an equivalent nonlocal-type Fourier's law. The differential nonlocal Fourier's law is analysed with respect to thermodynamic models available in the literature, such as the Guyer-Krumhansl-type equation. The length scale of the nonlocal heat law is calibrated with respect to the lattice spacing. An error analysis is conducted for quantifying the efficiency of the nonlocal model to capture the lattice evolution problem, as compared to the local model. The propagation of error with the nonlocal model is much slower than that in its local counterpart. A two-dimensional thermal lattice is also considered and approximated by a two-dimensional nonlocal heat problem. It is shown that nonlocal and continualized heat equations both approximate efficiently the two-dimensional thermal lattice response. These extended continuous heat models are shown to be good candidates for approximating the heat transfer behaviour of microstructured rods or membranes.
Percolation transitions with nonlocal constraint.
Shim, Pyoung-Seop; Lee, Hyun Keun; Noh, Jae Dong
2012-09-01
We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose r-neighbors share any exclusive pair. The r-neighbor of a node x is defined as a set of at most N(r) neighbors of x, where N is the total number of nodes. The parameter r controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean-field universality class for r<1/2. On the other hand, for r>1/2, the system undergoes a peculiar phase transition from a nonpercolating phase to a quasicritical phase where the largest cluster size G scales as G~N(α) with α=0.74(1). In the marginal case with r=1/2, the model displays a percolation transition that does not belong to the mean-field universality class.
Diagnostics of nonlocal plasmas: advanced techniques
NASA Astrophysics Data System (ADS)
Mustafaev, Alexander; Grabovskiy, Artiom; Strakhova, Anastasiya; Soukhomlinov, Vladimir
2014-10-01
This talk generalizes our recent results, obtained in different directions of plasma diagnostics. First-method of flat single-sided probe, based on expansion of the electron velocity distribution function (EVDF) in series of Legendre polynomials. It will be demonstrated, that flat probe, oriented under different angles with respect to the discharge axis, allow to determine full EVDF in nonlocal plasmas. It is also shown, that cylindrical probe is unable to determine full EVDF. We propose the solution of this problem by combined using the kinetic Boltzmann equation and experimental probe data. Second-magnetic diagnostics. This method is implemented in knudsen diode with surface ionization of atoms (KDSI) and based on measurements of the magnetic characteristics of the KDSI in presence of transverse magnetic field. Using magnetic diagnostics we can investigate the wide range of plasma processes: from scattering cross-sections of electrons to plasma-surface interactions. Third-noncontact diagnostics method for direct measurements of EVDF in remote plasma objects by combination of the flat single-sided probe technique and magnetic polarization Hanley method.
The neglected nonlocal effects of deforestation
NASA Astrophysics Data System (ADS)
Winckler, Johannes; Reick, Christian; Pongratz, Julia
2017-04-01
Deforestation changes surface temperature locally via biogeophysical effects by changing the water, energy and momentum balance. Adding to these locally induced changes (local effects), deforestation at a given location can cause changes in temperature elsewhere (nonlocal effects). Most previous studies have not considered local and nonlocal effects separately, but investigated the total (local plus nonlocal) effects, for which global deforestation was found to cause a global mean cooling. Recent modeling and observational studies focused on the isolated local effects: The local effects are relevant for local living conditions, and they can be obtained from in-situ and satellite observations. Observational studies suggest that the local effects of potential deforestation cause a warming when averaged globally. This contrast between local warming and total cooling indicates that the nonlocal effects of deforestation are causing a cooling and thus counteract the local effects. It is still unclear how the nonlocal effects depend on the spatial scale of deforestation, and whether they still compensate the local warming in a more realistic spatial distribution of deforestation. To investigate this, we use a fully coupled climate model and separate local and nonlocal effects of deforestation in three steps: Starting from a forest world, we simulate deforestation in one out of four grid boxes using a regular spatial pattern and increase the number of deforestation grid boxes step-wise up to three out of four boxes in subsequent simulations. To compare these idealized spatial distributions of deforestation to a more realistic case, we separate local and nonlocal effects in a simulation where deforestation is applied in regions where it occurred historically. We find that the nonlocal effects scale nearly linearly with the number of deforested grid boxes, and the spatial distribution of the nonlocal effects is similar for the regular spatial distribution of deforestation
NASA Astrophysics Data System (ADS)
Ansari, R.; Sahmani, S.
2012-04-01
The free vibration response of single-walled carbon nanotubes (SWCNTs) is investigated in this work using various nonlocal beam theories. To this end, the nonlocal elasticity equations of Eringen are incorporated into the various classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Reddy beam theory (RBT) to consider the size-effects on the vibration analysis of SWCNTs. The generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations of each nonlocal beam theory corresponding to four commonly used boundary conditions. Then molecular dynamics (MD) simulation is implemented to obtain fundamental frequencies of nanotubes with different chiralities and values of aspect ratio to compare them with the results obtained by the nonlocal beam models. Through the fitting of the two series of numerical results, appropriate values of nonlocal parameter are derived relevant to each type of chirality, nonlocal beam model, and boundary conditions. It is found that in contrast to the chirality, the type of nonlocal beam model and boundary conditions make difference between the calibrated values of nonlocal parameter corresponding to each one.
Quantum Nonlocal Boxes Exhibit Stronger Distillability
NASA Astrophysics Data System (ADS)
Høyer, Peter; Rashid, Jibran
2013-06-01
The hypothetical nonlocal box (NLB) proposed by Popescu and Rohrlich allows two spatially separated parties, Alice and Bob, to exhibit stronger than quantum correlations. If the generated correlations are weak, they can sometimes be distilled into a stronger correlation by repeated applications of the NLB. Motivated by the limited distillability of NLBs, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (qNLBs). We propose a new protocol for distillation and show that it asymptotically distills a class of correlated quantum nonlocal boxes to the value (1)/(2)(3√ {3}+1) ≈ 3.098076, whereas in contrast, the optimal non-adaptive parity protocol for classical nonlocal boxes asymptotically distills only to the value 3.0. We show that our protocol is an optimal non-adaptive protocol for 1, 2 and 3 qNLB copies by constructing a matching dual solution for the associated primal semidefinite program (SDP). We conclude that qNLBs are a stronger resource for nonlocality than NLBs. The main premise that develops from this conclusion is that the NLB model is not the strongest resource to investigate the fundamental principles that limit quantum nonlocality. As such, our work provides strong motivation to reconsider the status quo of the principles that are known to limit nonlocal correlations under the framework of qNLBs rather than NLBs.
NASA Astrophysics Data System (ADS)
Wu, Chih-Ping; Li, Wei-Chen
2017-05-01
A three-dimensional (3D) asymptotic formulation is developed for the buckling analysis of simply-supported, single-layered nanoplates/graphene sheets (SLNP and SLGS) embedded in an elastic medium and under biaxial compressive loads. In the formulation, the Eringen nonlocal elasticity theory is used to capture the small length scale effect, and the interaction between the SLNP/SLGS and its surrounding medium is simulated using a Pasternak-type foundation. After performing the mathematical processes of nondimensionalization, asymptotic expansion and successive integration, we finally obtain recursive sets of governing equations for various order problems. The nonlocal classical plate theory (CPT) is derived as a first-order approximation of the 3D nonlocal elasticity theory, and the governing equations for higher-order problems retain the same differential operators as those of nonlocal CPT, although with different nonhomogeneous terms. Some accurate nonlocal elasticity solutions of the critical load parameters of simply-supported, biaxially-loaded SLNP/SLGS with and without being embedded in the elastic medium are given to demonstrate the performance of the 3D asymptotic nonlocal elasticity theory.
Nonlocal effects and countermeasures in cascading failures.
Witthaut, Dirk; Timme, Marc
2015-09-01
We study the propagation of cascading failures in complex supply networks with a focus on nonlocal effects occurring far away from the initial failure. It is shown that a high clustering and a small average path length of a network generally suppress nonlocal overloads. These properties are typical for many real-world networks, often called small-world networks, such that cascades propagate mostly locally in these networks. Furthermore, we analyze the spatial aspects of countermeasures based on the intentional removal of additional edges. Nonlocal actions are generally required in networks that have a low redundancy and are thus especially vulnerable to cascades.
Local renormalizable gauge theories from nonlocal operators
Capri, M.A.L. Lemes, V.E.R. Sobreiro, R.F. Sorella, S.P. Thibes, R.
2008-03-15
The possibility that nonlocal operators might be added to the Yang-Mills action is investigated. We point out that there exists a class of nonlocal operators which lead to renormalizable gauge theories. These operators turn out to be localizable by means of the introduction of auxiliary fields. The renormalizability is thus ensured by the symmetry content exhibited by the resulting local theory. The example of the nonlocal operator Tr{integral}A{sub {mu}}1/(D{sup 2}) A{sub {mu}} is analyzed in detail. A few remarks on the possible role that these operators might have for confining theories are outlined.
Bell-type inequalities for nonlocal resources
NASA Astrophysics Data System (ADS)
Brunner, Nicolas; Scarani, Valerio; Gisin, Nicolas
2006-11-01
We present bipartite Bell-type inequalities which allow the two partners to use some nonlocal resource. Such inequalities can only be violated if the parties use a resource which is more nonlocal than the one permitted by the inequality. We introduce a family of N-input nonlocal machines, which are generalizations of the well-known PR (Popescu-Rohrlich) box. Then we construct Bell-type inequalities that cannot be violated by strategies that use one of these new machines. Finally we discuss implications for the simulation of quantum states.
Non-locality of experimental qutrit pairs
NASA Astrophysics Data System (ADS)
Bernhard, C.; Bessire, B.; Montina, A.; Pfaffhauser, M.; Stefanov, A.; Wolf, S.
2014-10-01
The insight due to John Bell that the joint behavior of individually measured entangled quantum systems cannot be explained by shared information remains a mystery to this day. We describe an experiment, and its analysis, displaying non-locality of entangled qutrit pairs. The non-locality of such systems, as compared to qubit pairs, is of particular interest since it potentially opens the door for tests of bipartite non-local behavior independent of probabilistic Bell inequalities, but of deterministic nature. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.
Local, nonlocal quantumness and information theoretic measures
NASA Astrophysics Data System (ADS)
Agrawal, Pankaj; Sazim, Sk; Chakrabarty, Indranil; Pati, Arun K.
2016-08-01
It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by information theoretic quantities such as quantum discord, but not by the conventional measures of entanglement. We argue that a state displays quantumness, that can be of local and nonlocal origin. Information theoretic measures not only characterize the nonlocal quantumness, but also the local quantumness, such as the “local superposition”. This can be a reason, why such measures are nonzero, when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of local quantumness, nonlocal quantumness and classical mixedness of a state.
Experimental test of nonlocal causality
Ringbauer, Martin; Giarmatzi, Christina; Chaves, Rafael; Costa, Fabio; White, Andrew G.; Fedrizzi, Alessandro
2016-01-01
Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell’s local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect. PMID:27532045
Experimental test of nonlocal causality.
Ringbauer, Martin; Giarmatzi, Christina; Chaves, Rafael; Costa, Fabio; White, Andrew G; Fedrizzi, Alessandro
2016-08-01
Explaining observations in terms of causes and effects is central to empirical science. However, correlations between entangled quantum particles seem to defy such an explanation. This implies that some of the fundamental assumptions of causal explanations have to give way. We consider a relaxation of one of these assumptions, Bell's local causality, by allowing outcome dependence: a direct causal influence between the outcomes of measurements of remote parties. We use interventional data from a photonic experiment to bound the strength of this causal influence in a two-party Bell scenario, and observational data from a Bell-type inequality test for the considered models. Our results demonstrate the incompatibility of quantum mechanics with a broad class of nonlocal causal models, which includes Bell-local models as a special case. Recovering a classical causal picture of quantum correlations thus requires an even more radical modification of our classical notion of cause and effect.
Nonlocal quantum gravity: A review
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Rachwał, Lesław
We hereby review a class of quantum gravitational theories based on weakly nonlocal analytic classical actions. The most general action is characterized by two nonpolynomial entire functions (form-factors) in terms quadratic in curvature. The form-factors avert the presence of poltergeists, that plague any local higher derivative theory of gravity and improve the high-energy behavior of loop amplitudes. For pedagogical purposes, it is proved that the theory is super-renormalizable in any dimension, i.e. only one-loop divergences survive, and is asymptotically free. Furthermore, due to dimensional reasons, in odd dimensions, there are no counterterms for pure gravity and the theory turns out to be finite. Moreover, we show that it is always possible to choose the additional terms in the action (higher in curvature) in such a way to make the full theory UV-finite and therefore, scale-invariant in quantum realm, also in even dimension.
Film edge nonlocal spin valves.
McCallum, Andrew T; Johnson, Mark
2009-06-01
Spintronics is a new paradigm for integrated digital electronics. Recently established as a niche for nonvolatile magnetic random access memory (MRAM), it offers new functionality while demonstrating low-power and high-speed performance. However, to reach high density spintronic technology must make a transition to the nanometer scale. Prototype devices are presently made using a planar geometry and have an area determined by the lithographic feature size, currently about 100 nm. Here we present a new nonplanar geometry in which one lateral dimension is given by a film thickness, on the order of 10 nm. With this new approach, cell sizes can shrink by an order of magnitude. The geometry is demonstrated with a nonlocal spin valve, where we study devices with an injector/detector separation much less than the spin diffusion length.
Nonlocal advantage of quantum coherence
NASA Astrophysics Data System (ADS)
Mondal, Debasis; Pramanik, Tanumoy; Pati, Arun Kumar
2017-01-01
A bipartite state is said to be steerable if and only if it does not have a single-system description, i.e., the bipartite state cannot be explained by a local hidden state model. Several steering inequalities have been derived using different local uncertainty relations to verify the ability to control the state of one subsystem by the other party. Here, we derive complementarity relations between coherences measured on mutually unbiased bases using various coherence measures such as the l1-norm, relative entropy, and skew information. Using these relations, we derive conditions under which a nonlocal advantage of quantum coherence can be achieved and the state is steerable. We show that not all steerable states can achieve such an advantage.
Experimental many-pairs nonlocality
NASA Astrophysics Data System (ADS)
Poh, Hou Shun; Cerè, Alessandro; Bancal, Jean-Daniel; Cai, Yu; Sangouard, Nicolas; Scarani, Valerio; Kurtsiefer, Christian
2017-08-01
Collective measurements on large quantum systems together with a majority voting strategy can lead to a violation of the Clauser-Horne-Shimony-Holt Bell inequality. In the presence of many entangled pairs, this violation decreases quickly with the number of pairs and vanishes for some critical pair number that is a function of the noise present in the system. Here we show that a different binning strategy can lead to a more substantial Bell violation when the noise is sufficiently small. Given the relation between the critical pair number and the source noise, we then present an experiment where the critical pair number is used to quantify the quality of a high visibility photon pair source. Our results demonstrate nonlocal correlations using collective measurements operating on clusters of more than 40 photon pairs.
The Gardner category and nonlocal conservation laws for N=1 Super KdV
Andrea, S.; Restuccia, A.; Sotomayor, A.
2005-10-01
The nonlocal conserved quantities of the N=1 Super KdV are obtained using a Gardner map. A fermionic substitution semigroup and the resulting Gardner category are defined and several propositions concerning their algebraic structure are obtained. This algebraic framework makes it possible to define general transformations between different nonlinear SUSY differential equations. A SUSY ring extension is then introduced to deal with the nonlocal conserved quantities of SKdV. The algebraic version of the nonlocal conserved quantities is solved in terms of the exponential function applied to the D{sup -1} of the local conserved quantities of SKdV. Finally the same formulas are shown to work for rapidly decreasing superfields.
Frequency analysis of curved nano-sandwich structure based on a nonlocal model
NASA Astrophysics Data System (ADS)
Rahmani, O.; Hosseini, S. A. H.; Hayati, H.
2016-04-01
In this paper, we study the vibration of curved nano-sandwich (CNS) with considering the influence of core shear based on the Eringen nonlocal theory. The equation of motion is derived and exact solution for the natural frequencies of CNS is presented. The proposed nonlocal model includes a material length scale parameter that can capture the size effect in CNS beam. The effects of important parameters, such as the thickness to length ratio, nonlocal parameter and mode number on the frequencies of CNS are investigated. The result of our research shows that as the opening angle increases, the amount of natural frequencies decrease. We have additionally validate, our results against previous research works which showed good agreement.
Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics.
Horikis, Theodoros P; Frantzeskakis, Dimitrios J
2017-06-16
Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2+1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y-, X-, and H-shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.
Radial vibration of free anisotropic nanoparticles based on nonlocal continuum mechanics.
Ghavanloo, Esmaeal; Fazelzadeh, S Ahmad
2013-02-22
Radial vibration of spherical nanoparticles made of materials with anisotropic elasticity is theoretically investigated using nonlocal continuum mechanics. The anisotropic elastic model is reformulated using the nonlocal differential constitutive relations of Eringen. The nonlocal differential equation of radial motion is derived in terms of radial displacement. Cubic, hexagonal, trigonal and tetragonal symmetries of the elasticity are discussed. The suggested model is justified by a good agreement between the results given by the present model and available experimental data. Furthermore, the model is used to elucidate the effect of small scale on the vibration of several nanoparticles. Our results show that the small scale is essential for the radial vibration of the nanoparticles when the nanoparticle radius is smaller than 1.5 nm.
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Reza Barati, Mohammad; Haghi, Parisa
2016-11-01
In this paper, the thermo-elastic wave propagation analysis of a temperature-dependent functionally graded (FG) nanobeam supported by Winkler-Pasternak elastic foundation is studied using nonlocal elasticity theory. The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function. The temperature field has a nonlinear distribution called heat conduction across the nanobeam thickness. Temperature-dependent material properties change gradually in the spatial coordinate according to the Mori-Tanaka model. The governing equations of the wave propagation of the refined FG nanobeam are derived by using Hamilton's principle. The analytic dispersion relation of the embedded nonlocal functionally graded nanobeam is obtained by solving an eigenvalue problem. Numerical examples show that the wave characteristics of the functionally graded nanobeam are related to the temperature distribution, elastic foundation parameters, nonlocality and material composition.
NASA Astrophysics Data System (ADS)
Mehralian, Fahimeh; Tadi Beni, Yaghoub; Karimi Zeverdejani, Mehran
2017-06-01
Featured by two small length scale parameters, nonlocal strain gradient theory is utilized to investigate the free vibration of nanotubes. A new size-dependent shell model formulation is developed by using the first order shear deformation theory. The governing equations and boundary conditions are obtained using Hamilton's principle and solved for simply supported boundary condition. As main purpose of this study, since the values of two small length scale parameters are still unknown, they are calibrated by the means of molecular dynamics simulations (MDs). Then, the influences of different parameters such as nonlocal parameter, scale factor, length and thickness on vibration characteristics of nanotubes are studied. It is also shown that increase in thickness and decrease in length parameters intensify the effect of nonlocal parameter and scale factor.
Entanglement and quantum nonlocality demystified
NASA Astrophysics Data System (ADS)
Kupczynski, Marian
2012-12-01
Quantum nonlocality is presented often as the most remarkable and inexplicable phenomenon known to modern science. It has been known already for a long time that the probabilistic models used to prove Bell and Clauser-Horn-Shimony-Holt inequalities (BI-CHSH) for spin polarization correlation experiments (SPCE) are incompatible with the experimental protocols of SPCE. In particular these models use the same common probability space, joint probability distributions and/or conditional independence to describe coincidence experiments in incompatible experimental settings. Strangely enough these results are not known or simply neglected. This is why we will once again reanalyze Bell locality assumptions and show that they have nothing to do with the notion of Einsteinian locality therefore their violation should not be called quantum nonlocality but rather quantum non-Kolmogorovness or quantum contextuality. Moreover if local variables describing the measuring instruments are correctly taken into account then BI-CHSH can no longer be proven and one can easily construct non-signaling probabilistic models able to reproduce the predictions of QT. The violation of BI-CHSH is considered usually as a proof that a quantum state is entangled. Since BI-CHSH are violated also in some experiments from outside the domain of quantum physics therefore the entanglement is not exclusively a quantum phenomenon. In order to further demystify these notions we show that one can prepare two macroscopic systems in such a way that simple realizable local experiments on these systems violate BI. In view of these arguments the further testing of BI-CHSH inequalities in search for the loopholes does not seem to be necessary.
Model scattering envelopes of young stellar objects. II - Infalling envelopes
NASA Technical Reports Server (NTRS)
Whitney, Barbara A.; Hartmann, Lee
1993-01-01
We present scattered light images for models of young stellar objects surrounded by dusty envelopes. The envelopes are assumed to have finite angular momentum and are falling in steady flow onto a disk. The model envelopes include holes, such as might be created by energetic bipolar flows. We calculate images using the Monte Carlo method to follow the light scattered in the dusty envelope and circumstellar disk, assuming that the photons originate from the central source. Adopting typical interstellar medium dust opacities and expected mass infall rates for protostars of about 10 exp -6 solar mass/yr, we find that detectable amounts of optical radiation can escape from envelopes falling into a disk as small as about 10-100 AU, depending upon the viewing angle and the size of the bipolar flow cavity. We suggest that the extended optical and near-IR light observed around several young stars is scattered by dusty infalling envelopes rather than disks.
Model scattering envelopes of young stellar objects. II - Infalling envelopes
NASA Technical Reports Server (NTRS)
Whitney, Barbara A.; Hartmann, Lee
1993-01-01
We present scattered light images for models of young stellar objects surrounded by dusty envelopes. The envelopes are assumed to have finite angular momentum and are falling in steady flow onto a disk. The model envelopes include holes, such as might be created by energetic bipolar flows. We calculate images using the Monte Carlo method to follow the light scattered in the dusty envelope and circumstellar disk, assuming that the photons originate from the central source. Adopting typical interstellar medium dust opacities and expected mass infall rates for protostars of about 10 exp -6 solar mass/yr, we find that detectable amounts of optical radiation can escape from envelopes falling into a disk as small as about 10-100 AU, depending upon the viewing angle and the size of the bipolar flow cavity. We suggest that the extended optical and near-IR light observed around several young stars is scattered by dusty infalling envelopes rather than disks.
Moving nonradiating kinks in nonlocal φ4 and φ4-φ6 models.
Alfimov, G L; Medvedeva, E V
2011-11-01
We explore the existence of moving nonradiating kinks in nonlocal generalizations of φ(4) and φ(4)-φ(6) models. These models are described by nonlocal nonlinear Klein-Gordon equation, u(tt)-Lu+F(u)=0, where L is a Fourier multiplier operator of a specific form and F(u) includes either just a cubic term (φ(4) case) or cubic and quintic (φ(4)-φ(6) case) terms. The general mechanism responsible for the discretization of kink velocities in the nonlocal model is discussed. We report numerical results obtained for these models. It is shown that, contrary to the traditional φ(4) model, the nonlocal φ(4) model does not admit moving nonradiating kinks but admits solitary waves that do not exist in the local model. At the same time the nonlocal φ(4)-φ(6) model describes moving nonradiating kinks. The set of velocities allowed for these kinks is discrete with the highest possible velocity c(1). This set of velocities is unambiguously determined by the parameters of the model. Numerical simulations show that a kink launched at the velocity c higher than c(1) starts to decelerate, and its velocity settles down to the highest value of the discrete spectrum c(1).
Nonlocal-integro-differential modeling of vibration of elastically supported nanorods
NASA Astrophysics Data System (ADS)
Kiani, Keivan
2016-09-01
In the previously established nonlocal continuum-based models, small characteristic length was commonly incorporated into the mass matrix and the driving force vector which is a bit in contradiction with our sense regarding these factors. Herein, a nonlocal-integro-differential version of the constitutive relations is employed for the bulk and the surface layer of the nanorod. By adopting Hamilton's principle, integro-partial differential equations of motion of elastically supported nanorods are established accounting for both nonlocality and surface energy effects. Then, these are solved by an efficient meshless methodology. For fixed-fixed and fixed-free nanorods, modal analysis of the problem is also performed and the explicit expressions of the mass and stiffness matrices are derived. For these special cases, the obtained results by the meshless technique are successfully verified with those of the modal solution. In the newly developed numerical model, the small-scale parameter is only incorporated into the stiffness matrix which gives us a more realistic sense about the nonlocality effect. Subsequently, the roles of the surface energy, small-scale parameter, elastic supports, and kernel function on natural frequencies of the nanostructure are discussed and explained. This work can be considered as a pivotal step towards a more reasonable nonlocal modeling of vibration of nanoscale structures.
Nonlinear Analysis of Airship Envelop Aerolasticity
NASA Astrophysics Data System (ADS)
Liu, J. M.; Lu, C. J.; Xue, L. P.
The large airship in flow field is a flexible body with low rigidity. The distribution of the peripheral flow field around the airship is closely related to its shape. It is essentially one of the Fluid-structure Interaction problems. Based on this, this paper aims at the numerical simulation of nonlinear airship envelop aeroelasticity by means of coupling aerodynamics and structure using an iteration method. The three-dimensional flow around the airship was studied numerically by means of SIMPLE method based on the Finite Volume Method. Two approaches, the linear method whose equilibrium equations are based on the membrance theory of thin shell and the nonlinear method which uses a nonlinear finite element method to account for the large deformation of the airship envelop, are introduced for geometrically deformation of the airship shape. A thin plate spline method is adopted as the interface of exchanging information between the fluid and structure models.
Refrigerated cryogenic envelope
Loudon, John D.
1976-11-16
An elongated cryogenic envelope including an outer tube and an inner tube coaxially spaced within said inner tube so that the space therebetween forms a vacuum chamber for holding a vacuum. The inner and outer tubes are provided with means for expanding or contracting during thermal changes. A shield is located in the vacuum chamber intermediate the inner and outer tubes; and, a refrigeration tube for directing refrigeration to the shield is coiled about at least a portion of the inner tube within the vacuum chamber to permit the refrigeration tube to expand or contract along its length during thermal changes within said vacuum chamber.
Family of nonlocal bound entangled states
NASA Astrophysics Data System (ADS)
Yu, Sixia; Oh, C. H.
2017-03-01
Bound entanglement, being entangled yet not distillable, is essential to our understanding of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we construct this kind of nonlocal bound entangled state for all finite dimensions larger than two, making possible their experimental demonstration in most general systems. We propose a Bell inequality, based on a Hardy-type argument for nonlocality, and a steering inequality to identify their nonlocality. We also provide a family of entanglement witnesses to detect their entanglement beyond the Bell inequality and the steering inequality.
Plasmonic nanostructures: local versus nonlocal response
NASA Astrophysics Data System (ADS)
Toscano, Giuseppe; Wubs, Martijn; Xiao, Sanshui; Yan, Min; Öztürk, Z. Fatih; Jauho, Antti-Pekka; Mortensen, N. A.
2010-08-01
We study the importance of taking the nonlocal optical response of metals into account for accurate determination of optical properties of nanoplasmonic structures. Here we focus on the computational physics aspects of this problem, and in particular we report on the nonlocal-response package that we wrote for state-of the art numerical software, enabling us to take into account the nonlocal material response of metals for any arbitrarily shaped nanoplasmonic structures, without much numerical overhead as compared to the standard local response. Our method is a frequency-domain method, and hence it is sensitive to possible narrow resonances that may arise due to strong electronic quantum confinement in the metal. This feature allows us to accurately determine which geometries are strongly affected by nonlocal response, for example regarding applications based on electric field enhancement properties for which metal nanostructures are widely used.
Symmetric states: Their nonlocality and entanglement
Wang, Zizhu; Markham, Damian
2014-12-04
The nonlocality of permutation symmetric states of qubits is shown via an extension of the Hardy paradox and the extension of the associated inequality. This is achieved by using the Majorana representation, which is also a powerful tool in the study of entanglement properties of symmetric states. Through the Majorana representation, different nonlocal properties can be linked to different entanglement properties of a state, which is useful in determining the usefulness of different states in different quantum information processing tasks.
Experimental falsification of Leggett's nonlocal variable model.
Branciard, Cyril; Ling, Alexander; Gisin, Nicolas; Kurtsiefer, Christian; Lamas-Linares, Antia; Scarani, Valerio
2007-11-23
Bell's theorem guarantees that no model based on local variables can reproduce quantum correlations. Also, some models based on nonlocal variables, if subject to apparently "reasonable" constraints, may fail to reproduce quantum physics. In this Letter, we introduce a family of inequalities, which use a finite number of measurement settings, and which therefore allow testing Leggett's nonlocal model versus quantum physics. Our experimental data falsify Leggett's model and are in agreement with quantum predictions.
NASA Astrophysics Data System (ADS)
Alibubin, M. U.; Sunarto, A.; Sulaiman, J.
2016-06-01
In this paper, we present the concept of Half-sweep Accelerated OverRelaxation (HSAOR) iterative method with a nonlocal discretization scheme for solving nonlinear two-point boundary value problems. Second order finite difference scheme has been used to derive the half-sweep finite difference (HSFD) approximations of the problems. Then, the nonlocal discretization scheme is applied in order to transform the system of nonlinear approximation equations into the corresponding system of linear equations. Numerical results showed that HSAOR method is superior compared to Full-sweep Gauss-seidel (FSGS), Full-sweep Successive OverRelaxation (FSSOR) and Full-sweep Accelerated Over Relaxation (FSAOR) methods.
NASA Astrophysics Data System (ADS)
Orazov, Issabek; Besbaev, Gani A.
2016-12-01
In the present work we investigate a nonlocal boundary problem for the Laplace equation in a half-disk, with opposite flows at the part of the boundary. The difference of this problem is the impossibility of direct applying of the Fourier method (separation of variables). Because the corresponding spectral problem for the ordinary differential equation has the system of eigenfunctions not forming a basis. A special system of functions based on these eigenfunctions is constructed. This system has already formed the basis. This fact is used for solving the nonlocal boundary problem. The existence and the uniqueness of classical solution of the problem are proved.
Inverse energy cascade in nonlocal helical shell models of turbulence
NASA Astrophysics Data System (ADS)
De Pietro, Massimo; Biferale, Luca; Mailybaev, Alexei A.
2015-10-01
Following the exact decomposition in eigenstates of helicity for the Navier-Stokes equations in Fourier space [F. Waleffe, Phys. Fluids A 4, 350 (1992), 10.1063/1.858309], we introduce a modified version of helical shell models for turbulence with nonlocal triadic interactions. By using both an analytical argument and numerical simulation, we show that there exists a class of models, with a specific helical structure, that exhibits a statistically stable inverse energy cascade, in close analogy with that predicted for the Navier-Stokes equations restricted to the same helical interactions. We further support the idea that turbulent energy transfer is the result of a strong entanglement among triads possessing different transfer properties.
A nonlocal approach to the cosmological constant problem
NASA Astrophysics Data System (ADS)
Carroll, Sean M.; Remmen, Grant N.
2017-06-01
We construct a model in which the cosmological constant is canceled from the gravitational equations of motion. Our model relies on two key ingredients: a nonlocal constraint on the action, which forces the spacetime average of the Lagrangian density to vanish, and a dynamical way for this condition to be satisfied classically with arbitrary matter content. We implement the former condition with a spatially constant Lagrange multiplier associated with the volume form and the latter by including a free four-form gauge field strength in the action. These two features are enough to remove the cosmological constant from the Einstein equation. The model is consistent with all cosmological and experimental bounds on modification of gravity and allows for both cosmic inflation and the present epoch of acceleration.
Robust non-local median filter
NASA Astrophysics Data System (ADS)
Matsuoka, Jyohei; Koga, Takanori; Suetake, Noriaki; Uchino, Eiji
2017-04-01
This paper describes a novel image filter with superior performance on detail-preserving removal of random-valued impulse noise superimposed on natural gray-scale images. The non-local means filter is in the limelight as a way of Gaussian noise removal with superior performance on detail preservation. By referring the fundamental concept of the non-local means, we had proposed a non-local median filter as a specialized way for random-valued impulse noise removal so far. In the non-local processing, the output of a filter is calculated from pixels in blocks which are similar to the block centered at a pixel of interest. As a result, aggressive noise removal is conducted without destroying the detailed structures in an original image. However, the performance of non-local processing decreases enormously in the case of high noise occurrence probability. A cause of this problem is that the superimposed noise disturbs accurate calculation of the similarity between the blocks. To cope with this problem, we propose an improved non-local median filter which is robust to the high level of corruption by introducing a new similarity measure considering possibility of being the original signal. The effectiveness and validity of the proposed method are verified in a series of experiments using natural gray-scale images.
Robust non-local median filter
NASA Astrophysics Data System (ADS)
Matsuoka, Jyohei; Koga, Takanori; Suetake, Noriaki; Uchino, Eiji
2017-01-01
This paper describes a novel image filter with superior performance on detail-preserving removal of random-valued impulse noise superimposed on natural gray-scale images. The non-local means filter is in the limelight as a way of Gaussian noise removal with superior performance on detail preservation. By referring the fundamental concept of the non-local means, we had proposed a non-local median filter as a specialized way for random-valued impulse noise removal so far. In the non-local processing, the output of a filter is calculated from pixels in blocks which are similar to the block centered at a pixel of interest. As a result, aggressive noise removal is conducted without destroying the detailed structures in an original image. However, the performance of non-local processing decreases enormously in the case of high noise occurrence probability. A cause of this problem is that the superimposed noise disturbs accurate calculation of the similarity between the blocks. To cope with this problem, we propose an improved non-local median filter which is robust to the high level of corruption by introducing a new similarity measure considering possibility of being the original signal. The effectiveness and validity of the proposed method are verified in a series of experiments using natural gray-scale images.
Simulation of random envelope processes.
NASA Technical Reports Server (NTRS)
Yang, J.-N.
1972-01-01
Efficient and practical methods of simulating stationary and nonstationary random envelope processes are presented. The stationary envelope processes are simulated by using the fast Fourier transform while the nonstationary envelope processes are simulated as the square root of the sum of a series of cosine functions and a series of sine functions with random phase angles. Typical applications of the envelope simulation are the simulations of peaks and troughs which play an important role in the analyses of the first excursion probability, fatigue and crack propagation. In particular, applications to the crack propagation under random loadings are demonstrated in detail.
Envelope solitons in three-component degenerate relativistic quantum plasmas
NASA Astrophysics Data System (ADS)
Islam, S.; Sultana, S.; Mamun, A. A.
2017-09-01
The criteria for the formation of envelope solitons and their basic features in a three-component degenerate relativistic quantum plasma (DRQP) system (containing relativistically degenerate electrons, non-degenerate inertial light nuclei, and stationary heavy nuclei) are theoretically investigated. The nonlinear Schrödinger equation is derived by employing the multi-scale perturbation technique. The envelope solitons are found to be associated with the modified ion-acoustic waves in which the inertia (restoring force) is provided by the mass density of light nuclei (degenerate pressure of cold electrons). The basic features of these envelope solitons, which are found to formed in such a DRQP system, and their modulational instability criteria (on the basis of the plasma parameters associated with the degenerate pressure of electrons, number densities of degenerate electrons, inertial light nuclei, and stationary heavy nuclei) are identified. The numerical simulations are also performed to confirm the stability of the envelope solitons predicted here by analytical analysis.
Periodic envelopes of waves over non-uniform depth
NASA Astrophysics Data System (ADS)
Rajan, Girish K.; Bayram, Saziye; Henderson, Diane M.
2016-04-01
The envelope of narrow-banded, periodic, surface-gravity waves propagating in one dimension over water of finite, non-uniform depth may be modeled by the Djordjević and Redekopp ["On the development of packets of surface gravity waves moving over an uneven bottom," Z. Angew. Math. Phys. 29, 950-962 (1978)] equation (DRE). Here we find five approximate solutions of the DRE that are in the form of Jacobi-elliptic functions and discuss them within the framework of ocean swell. We find that in all cases, the maximum envelope-amplitude decreases/increases when the wave group propagates on water of decreasing/increasing depth. In the limit of the elliptic modulus approaching one, three of the solutions reduce to the envelope soliton solution. In the limit of the elliptic modulus approaching zero, two of the solutions reduce to an envelope-amplitude that is uniform in an appropriate reference frame.
SOUND-SPEED INVERSION OF THE SUN USING A NONLOCAL STATISTICAL CONVECTION THEORY
Zhang Chunguang; Deng Licai; Xiong Darun; Christensen-Dalsgaard, Jorgen
2012-11-01
Helioseismic inversions reveal a major discrepancy in sound speed between the Sun and the standard solar model just below the base of the solar convection zone. We demonstrate that this discrepancy is caused by the inherent shortcomings of the local mixing-length theory adopted in the standard solar model. Using a self-consistent nonlocal convection theory, we construct an envelope model of the Sun for sound-speed inversion. Our solar model has a very smooth transition from the convective envelope to the radiative interior, and the convective energy flux changes sign crossing the boundaries of the convection zone. It shows evident improvement over the standard solar model, with a significant reduction in the discrepancy in sound speed between the Sun and local convection models.
NASA Astrophysics Data System (ADS)
Stehno, Martin P.
Spin-based solid-state quantum computing requires the creation of spatially separated, spin-entangled quantum states. The correlated electronic states in a conventional superconductor can serve as an abundant source of entangled spin-singlet electrons provided Cooper pairs can be split without losing wavefunction coherence. In Cooper pair-splitter devices the electrodes (or quantum dots) are coupled to a superconductor with a separation of less than or equal to the superconducting coherence length. At such distances coherent nonlocal subgap transport takes place. It involves Cooper pair splitting among other theoretically predicted transport processes. In this dissertation we investigate signatures of coherence in nonlocal transport. We focus on current correlation measurements in normal metal-superconductor-normal metal (NSN) devices with transparent interfaces for which higher-order processes such as correlated Andreev reflections at both interfaces are predicted to contribute. We verify the distance dependence of nonlocal transport in a superconducting wire to which several normal metal electrodes are attached and obtain a good agreement between the decay length of the nonlocal voltage signal and the theoretical value for the coherence length in the superconductor. To reveal the coherent nature of nonlocal transport we perform a series of experiments involving shot noise and nonlocal current correlation measurements in mesoscopic NSN devices. We extend the model of incoherent shot noise in diffusive normal metal-superconductor (NS) contacts and identify the magnitude of the local self-consistent gap in our devices. We find that the onset of nonequilibrium transport in the superconductor coincides with a steep increase in the nonlocal resistance. We determine the barrier strength at the NS interface by comparing the dynamic resistance to numerical calculations of the contact resistance based on the Keldysh-Usadel equations. The main finding of our work are
Slater's nonlocal exchange potential and beyond
NASA Astrophysics Data System (ADS)
Howard, I. A.; March, N. H.
The local density approximation (LDA) to the exchange potential Vx(r), namely the ρ1/3 electron gas form, was already transcended in Slater's 1951 paper. Here, using Dirac's 1930 form for the exchange energy density γx(r), the Slater (Sl) nonlocal exchange potential V Slx(r) is defined by 2γx(r)/ρ(r). In spherical atomic ions, say the Be or Ne-like series, this form V Slx(r) already has the correct behavior in both r → 0 and r → ∞ limits when known properties of the exchange energy density γx(r) and the ground-state electron density ρ(r) are invoked. As examples, some emphasis will first be given to the use of the so-called 1/Z expansion in such spherical atomic ions, for which analytic results can be obtained for both γx(r) and ρ(r) as the atomic number Z becomes large. The usefulness of the 1/Z expansion is directly demonstrated for the U atomic ion with 18 electrons by comparison with the optimized effective potential prediction. A rather general integral equation for the exchange potential is then proposed. Finally, without appeal to large Z, two-level systems are considered, with specific reference to the Be atom and to the LiH molecule. In all cases treated, the Slater potential V Slx(r) is a valuable starting point, even though it needs appreciable quantitative corrections reflecting directly atomic shell structure.
Kunkri, Samir; Choudhary, Sujit K.; Ahanj, Ali; Joag, Pramod
2006-02-15
Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardy's nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardy's argument.
NASA Astrophysics Data System (ADS)
Kunkri, Samir; Choudhary, Sujit K.; Ahanj, Ali; Joag, Pramod
2006-02-01
Here we deal with a nonlocality argument proposed by Cabello, which is more general than Hardy’s nonlocality argument, but still maximally entangled states do not respond. However, for most of the other entangled states, maximum probability of success of this argument is more than that of the Hardy’s argument.
Envelope Modes of Beams with Angular Momentum
Barnard, J J; Losic, B
2000-08-21
For a particle beam propagating in an alternating gradient focusing system, envelope equations are often employed to describe the evolution of the beam radii in the two directions transverse to the direction of propagation, and aligned with the principle axes of the alternating gradient system. When the beams have zero net angular momentum and when the alternating gradient focusing is approximated by a continuous focusing system, there are two normal modes to the envelope equations: the 'breathing' mode and a 'quadrupole' mode. In the former, the two radii oscillate in phase, and in the latter the radii oscillate 180 degrees out of phase. In this paper, we extend the analysis to include beams that have a finite angular momentum. We perturb the moment equations of ref. [1], wherein it was assumed that space charge is a distributed in a uniform density ellipse. Two additional modes are obtained. The breathing mode remains, but the quadrupole mode is split into two modes, and a new low frequency mode appears. We calculate the frequencies and eigenmodes of these four modes as a function of tune depression and a dimensionless net angular momentum. These modes can be excited by rotational errors of the quadrupoles in an alternating gradient focusing channel.
NASA Astrophysics Data System (ADS)
Ghadiri, Majid; Shafiei, Navvab; Akbarshahi, Amir
2016-07-01
This paper is proposed to study the free vibration of a rotating Timoshenko nanobeam based on the nonlocal theory considering thermal and surface elasticity effects. The governing equations and the related boundary conditions are derived using the Hamilton's principle. In order to solve the problem, generalized differential quadrature method is applied to discretize the governing differential equations corresponding to clamped-simply and clamped-free boundary conditions. In this article, the influences of some parameters such as nonlocal parameter, angular velocity, thickness of the nanobeam, and thermal and surface elasticity effects on the free vibration of the rotating nanobeam are investigated, and the results are compared for different boundary conditions. The results show that the surface effect and the nonlocal parameter and the temperature changes have significant roles, and they should not be ignored in the vibrational study of rotating nanobeams. Also, the angular velocity and the hub radius have more significant roles than temperature change effects on the nondimensional frequency. It is found that the nonlocal parameter behavior and the temperature change behavior on the frequency are different in the first mode for the rotating cantilever nanobeam.
Self-localized states for electron transfer in nonlocal continuum deformable media
NASA Astrophysics Data System (ADS)
Cisneros-Ake, Luis A.
2016-08-01
We consider the problem of electron transport in a deformable continuum medium subjected to an external harmonic substrate potential. We then consider the quasi-stationary state of the full problem to find a Gross-Pitaevskii type equation with a nonlocal external potential, which is solved by variational and numerical means (considered as the exact solution) to find the parameter conditions for the existence of self-localized solutions. The variational approach predicts a threshold on the on-site or nonlocality parameter where localized solutions cease to exist from the Non-Linear Schrödinger soliton limit. A numerical continuation of stationary state solutions in the corresponding discrete system is used to confirm the prediction of the turning value in the on-site term. We finally study the full stationary state and make use of an approximation, proposed by Briedis et al. [17], for the nonlocal term, corresponding to strong nonlocalities, to find analytic expressions for self-localized states in terms of the series solutions of a nonlinear modified Bessel equation.
Optical scheme for simulating post-quantum nonlocality distillation.
Chu, Wen-Jing; Yang, Ming; Pan, Guo-Zhu; Yang, Qing; Cao, Zhuo-Liang
2016-11-28
An optical scheme for simulating nonlocality distillation is proposed in post-quantum regime. The nonlocal boxes are simulated by measurements on appropriately pre- and post-selected polarization entangled photon pairs, i.e. post-quantum nonlocality is simulated by exploiting fair-sampling loophole in a Bell test. Mod 2 addition on the outputs of two nonlocal boxes combined with pre- and post-selection operations constitutes the key operation of simulating nonlocality distillation. This scheme provides a possible tool for the experimental study on the nonlocality in post-quantum regime and the exact physical principle precisely distinguishing physically realizable correlations from nonphysical ones.
Wavefunction Collapse via a Nonlocal Relativistic Variational Principle
Harrison, Alan K.
2012-06-18
Since the origin of quantum theory in the 1920's, some of its practitioners (and founders) have been troubled by some of its features, including indeterminacy, nonlocality and entanglement. The 'collapse' process described in the Copenhagen Interpretation is suspect for several reasons, and the act of 'measurement,' which is supposed to delimit its regime of validity, has never been unambiguously defined. In recent decades, nonlocality and entanglement have been studied energetically, both theoretically and experimentally, and the theory has been reinterpreted in imaginative ways, but many mysteries remain. We propose that it is necessary to replace the theory by one that is explicitly nonlinear and nonlocal, and does not distinguish between measurement and non-measurement regimes. We have constructed such a theory, for which the phase of the wavefunction plays the role of a hidden variable via the process of zitterbewegung. To capture this effect, the theory must be relativistic, even when describing nonrelativistic phenomena. It is formulated as a variational principle, in which Nature attempts to minimize the sum of two spacetime integrals. The first integral tends to drive the solution toward a solution of the standard quantum mechanical wave equation, and also enforces the Born rule of outcome probabilities. The second integral drives the collapse process. We demonstrate that the new theory correctly predicts the possible outcomes of the electron two-slit experiment, including the infamous 'delayed-choice' variant. We observe that it appears to resolve some long-standing mysteries, but introduces new ones, including possible retrocausality (a cause later than its effect). It is not clear whether the new theory is deterministic.
Nonlocal electrodynamics in Weyl semimetals
NASA Astrophysics Data System (ADS)
Rosenstein, B.; Kao, H. C.; Lewkowicz, M.
2017-02-01
Recently synthesized three-dimensional materials with Dirac spectrum exhibit peculiar electric transport qualitatively different from its two-dimensional analog, graphene. By neglecting impurity scattering, the real part of the conductivity is strongly frequency dependent, while the imaginary part is nonzero unlike in undoped, clean graphene. The Coulomb interaction between electrons is unscreened as in a dielectric and hence is long range. We demonstrate that the interaction correction renders the electrodynamics nonlocal on a mesoscopic scale. The longitudinal conductivity σL and the transverse conductivity σT are different in the long-wavelength limit and consequently the standard local Ohm's law description does not apply. This leads to several remarkable effects in optical response. The p -polarized light generates in these materials bulk plasmons as well as the transversal waves. At a specific frequency the two modes coincide, a phenomenon impossible in a local medium. For any frequency there is a Brewster angle where total absorption occurs, turning the Weyl semimetals opaque. The effect of the surface, including the Fermi arcs, is discussed.
NASA Astrophysics Data System (ADS)
Thompson, Ian
2010-11-01
In all direct reactions to probe the structure of exotic nuclei at FRIB, optical potentials will be needed in the entrance and exit channels. At high energies Glauber approximations may be useful, but a low energies (5 to 20 MeV/nucleon) other approaches are required. Recent work of the UNEDF project [1] has shown that reaction cross sections at these energies can be accounted for by calculating all inelastic and transfer channels reachable by one particle-hole transitions from the elastic channel. In this model space, we may also calculate the two-step dynamic polarization potential (DPP) that adds to the bare folded potential to form the complex optical potential. Our calculations of the DPP, however, show that its non-localities are very significant, as well as the partial-wave dependence of both its real and imaginary components. The Perey factors (the wave function ratio to that from an equivalent local potential) are more than 20% different from unity, especially for partial waves inside grazing. These factors combine to suggest a reexamination of the validity of local and L-independent fitted optical potentials, especially for capture reactions that are dominated by low partial waves. Prepared by LLNL under Contract DE-AC52-07NA27344. [1] G.P.A. Nobre, F.S. Dietrich, J.E. Escher, I.J. Thompson, M. Dupuis, J. Terasaki and J. Engel, submitted to Phys. Rev. Letts., 2010.
Eshraghi, Iman; Jalali, Seyed K.; Pugno, Nicola Maria
2016-01-01
Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs. PMID:28773911
Eshraghi, Iman; Jalali, Seyed K; Pugno, Nicola Maria
2016-09-21
Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Barati, Mohammad Reza
2016-09-01
This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment. The theory contains two scale parameters corresponding to both nonlocal and strain gradient effects. A quasi-3D sinusoidal beam theory considering shear and normal deformations is employed to present the formulation. Mori-Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton's principle is employed to obtain the governing equations of nanobeam accounting for thickness stretching effect. These equations are solved analytically to find the wave frequencies and phase velocities of the FG nanobeam. It is indicated that wave dispersion behavior of FG nanobeams is significantly affected by temperature rise, nonlocality, length scale parameter and material composition.
Fast Moreau envelope computation I
NASA Astrophysics Data System (ADS)
Lucet, Yves
2006-11-01
The present article summarizes the state of the art algorithms to compute the discrete Moreau envelope, and presents a new linear-time algorithm, named NEP for NonExpansive Proximal mapping. Numerical comparisons between the NEP and two existing algorithms: The Linear-time Legendre Transform (LLT) and the Parabolic Envelope (PE) algorithms are performed. Worst-case time complexity, convergence results, and examples are included. The fast Moreau envelope algorithms first factor the Moreau envelope as several one-dimensional transforms and then reduce the brute force quadratic worst-case time complexity to linear time by using either the equivalence with Fast Legendre Transform algorithms, the computation of a lower envelope of parabolas, or, in the convex case, the non expansiveness of the proximal mapping.
Time dependent wave envelope finite difference analysis of sound propagation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1984-01-01
A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.
Maximally nonlocal theories cannot be maximally random.
de la Torre, Gonzalo; Hoban, Matty J; Dhara, Chirag; Prettico, Giuseppe; Acín, Antonio
2015-04-24
Correlations that violate a Bell inequality are said to be nonlocal; i.e., they do not admit a local and deterministic explanation. Great effort has been devoted to study how the amount of nonlocality (as measured by a Bell inequality violation) serves to quantify the amount of randomness present in observed correlations. In this work we reverse this research program and ask what do the randomness certification capabilities of a theory tell us about the nonlocality of that theory. We find that, contrary to initial intuition, maximal randomness certification cannot occur in maximally nonlocal theories. We go on and show that quantum theory, in contrast, permits certification of maximal randomness in all dichotomic scenarios. We hence pose the question of whether quantum theory is optimal for randomness; i.e., is it the most nonlocal theory that allows maximal randomness certification? We answer this question in the negative by identifying a larger-than-quantum set of correlations capable of this feat. Not only are these results relevant to understanding quantum mechanics' fundamental features, but also put fundamental restrictions on device-independent protocols based on the no-signaling principle.
Group-theoretical interpretation of the Korteweg-de Vries type equations
NASA Astrophysics Data System (ADS)
Perelomov, A. M.
1981-07-01
The Korteweg-de Vries equation is studied in the frame of the group-theoretical approach. Analogous equations have been obtained for which the multi-dimensional Schrödinger equation (with nonlocal potential) is of the same importance as the one-dimensional Schrödinger equation in the theory of the Korteweg-de Vries equation.
Group-theoretical interpretation of the Korteweg-de Vries type equations
NASA Astrophysics Data System (ADS)
Berezin, F. A.; Perelomov, A. M.
1980-06-01
The Korteweg-de Vries equation is studied within the group-theoretical framework. Analogous equations are obtained for which the many-dimensional Schrödinger equation (with nonlocal potential) plays the same role as the one-dimensional Schrödinger equation does in the theory of the Korteweg-de Vries equation.
Different kinds of chimera death states in nonlocally coupled oscillators.
Premalatha, K; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M
2016-05-01
We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multichimera death state, type I periodic chimera death (PCD) state, and type II periodic chimera death state. We also find that the number of periodic domains in both types of PCD states decreases exponentially with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase reduction. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of a multichimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.
Different kinds of chimera death states in nonlocally coupled oscillators
NASA Astrophysics Data System (ADS)
Premalatha, K.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
2016-05-01
We investigate the significance of nonisochronicity parameter in a network of nonlocally coupled Stuart-Landau oscillators with symmetry breaking form. We observe that the presence of nonisochronicity parameter leads to structural changes in the chimera death region while varying the strength of the interaction. This gives rise to the existence of different types of chimera death states such as multichimera death state, type I periodic chimera death (PCD) state, and type II periodic chimera death state. We also find that the number of periodic domains in both types of PCD states decreases exponentially with an increase of coupling range and obeys a power law under nonlocal coupling. Additionally, we also analyze the structural changes of chimera death states by reducing the system of dynamical equations to a phase model through the phase reduction. We also briefly study the role of nonisochronicity parameter on chimera states, where the existence of a multichimera state with respect to the coupling range is pointed out. Moreover, we also analyze the robustness of the chimera death state to perturbations in the natural frequencies of the oscillators.
Bright nonlocal quadratic solitons induced by boundary confinement
NASA Astrophysics Data System (ADS)
Zheng, Yizhou; Gao, Yan; Wang, Jing; Lv, Fang; Lu, Daquan; Hu, Wei
2017-01-01
Under the Dirichlet boundary conditions, a family of bright quadratic solitons exists in the regime where the second harmonic can be regarded as the refractive index of the fundamental wave with an oscillatory nonlocal response. By simplifying the governing equations into the Snyder-Mitchell mode, the approximate analytical solutions are obtained. Taking them as the initial guess and using a numerical code, we found two branches of bright solitons, of which the beam width increases (branch I) and decreases (branch II) with the increase of the sample size, respectively. If the nonlocality is fixed and the sample size is varied, the soliton width varies piecewise and approximately periodically. In each period, solitons only exist in a small range of sample size. Single-hump fundamental wave solitons with the same beam width in narrower samples can be, if the second harmonics are connected smoothly, jointed to be a multihump soliton in a wider sample whose size is the sum of those for the narrower ones. The dynamical simulation shows that the found solitons are unstable.
NASA Astrophysics Data System (ADS)
Kiani, Keivan
2011-10-01
The potential applications of nanoplates in energy storage, chemical and biological sensors, solar cells, field emission, and transporting of nanocars have been attracted the attentions of the nanotechnology community to them during recent years. Herein, the later application of nanoplates from nonlocal elastodynamic point of view is of interest. To this end, dynamic response of a nanoplate subjected to a moving nanoparticle is examined within the context of nonlocal continuum theory of Eringen. The fully simply supported nanoplate is modeled based on the nonlocal Kirchhoff, Mindlin, and higher-order plate theories. The non-dimensional equations of motion of the nonlocal plate models are established. The effects of moving nanoparticle's weight and existing friction between the surfaces of the moving nanoparticle and nanoplate on the in-plane and out-of-plane vibrations of the nanoplate are incorporated into the formulations of the proposed models. The eigen function expansion and the Laplace transform methods are employed for discretization of the governing equations in the spatial and the time domains, respectively. The analytical expressions of the dynamic deformation field associated with each nonlocal plate theory are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight path (an opened path) as well as an ellipse path (a closed path). The dynamic in-plane forces and moments of each nonlocal plate model are also derived. Furthermore, the critical velocity and the critical angular velocity of the moving nanoparticle for the proposed models are expressed analytically for the aforementioned paths. Part II of this work consists in a comprehensive parametric study where the effects of influential parameters on dynamic response of the proposed nonlocal plate models are scrutinized in some detail.
NASA Astrophysics Data System (ADS)
Yang, Yang; Zhang, Lixiang; Lim, C. W.
2011-04-01
This paper is concerned with the characteristics of wave propagation in double-walled carbon nanotubes (DWCNTs). The DWCNTs is simulated with a Timoshenko beam model based on the nonlocal continuum elasticity theory, referred to as an analytically nonlocal Timoshenko-beam (ANT) model. The governing equations of the DWCNTs beam consist of a set of four equations that are derived from the variational principle of the beam with high-order boundary conditions at the both ends, in which the effects of the nano-scale nonlocality and the van der Waals interaction between inner and outer tubes are inclusive. The characteristics of the wave propagation in the DWCNTs beam were analyzed with the new ANT model proposed and the comparisons with the partially nonlocal Timoshenko-beam (PNT) models in publication were made in details. The results show that the nonlocal effects of the ANT model proposed in the present study on the wave propagations are more significant because it is in stronger stiffness enhancement to the DWCNTs beam.
Covariant nonlocal chiral quark models with separable interactions
Dumm, D. Gomez; Grunfeld, A. G.; Scoccola, N. N.
2006-09-01
We present a comparative analysis of chiral quark models which include nonlocal covariant four-fermion couplings. We consider two alternative ways of introducing the nonlocality, as well as various shapes for the momentum-dependent form factors governing the effective interactions. In all cases we study the behavior of model parameters and analyze numerical results for constituent quark masses and quark propagator poles. Advantages of these covariant nonlocal schemes over instantaneous nonlocal schemes and the standard NJL model are pointed out.
Tuning quantum nonlocal effects in graphene plasmonics
NASA Astrophysics Data System (ADS)
Lundeberg, Mark B.; Gao, Yuanda; Asgari, Reza; Tan, Cheng; Van Duppen, Ben; Autore, Marta; Alonso-González, Pablo; Woessner, Achim; Watanabe, Kenji; Taniguchi, Takashi; Hillenbrand, Rainer; Hone, James; Polini, Marco; Koppens, Frank H. L.
2017-07-01
The response of electron systems to electrodynamic fields that change rapidly in space is endowed by unique features, including an exquisite spatial nonlocality. This can reveal much about the materials’ electronic structure that is invisible in standard probes that use gradually varying fields. Here, we use graphene plasmons, propagating at extremely slow velocities close to the electron Fermi velocity, to probe the nonlocal response of the graphene electron liquid. The near-field imaging experiments reveal a parameter-free match with the full quantum description of the massless Dirac electron gas, which involves three types of nonlocal quantum effects: single-particle velocity matching, interaction-enhanced Fermi velocity, and interaction-reduced compressibility. Our experimental approach can determine the full spatiotemporal response of an electron system.
Tuning quantum nonlocal effects in graphene plasmonics.
Lundeberg, Mark B; Gao, Yuanda; Asgari, Reza; Tan, Cheng; Van Duppen, Ben; Autore, Marta; Alonso-González, Pablo; Woessner, Achim; Watanabe, Kenji; Taniguchi, Takashi; Hillenbrand, Rainer; Hone, James; Polini, Marco; Koppens, Frank H L
2017-07-14
The response of electron systems to electrodynamic fields that change rapidly in space is endowed by unique features, including an exquisite spatial nonlocality. This can reveal much about the materials' electronic structure that is invisible in standard probes that use gradually varying fields. Here, we use graphene plasmons, propagating at extremely slow velocities close to the electron Fermi velocity, to probe the nonlocal response of the graphene electron liquid. The near-field imaging experiments reveal a parameter-free match with the full quantum description of the massless Dirac electron gas, which involves three types of nonlocal quantum effects: single-particle velocity matching, interaction-enhanced Fermi velocity, and interaction-reduced compressibility. Our experimental approach can determine the full spatiotemporal response of an electron system. Copyright © 2017, American Association for the Advancement of Science.
Black hole information, unitarity, and nonlocality
Giddings, Steven B.
2006-11-15
The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. The leading contender is nonlocality. Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. Suggestions that such dynamics arise from ultra-Planckian modes in Hawking's derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. However, no simultaneous description of modes that have fallen into the black hole and outgoing Hawking modes can be given without appearance of a large kinematic invariant, or other dependence on ultra-Planckian physics. This indicates that a reliable argument for information loss has not been constructed, and that strong gravitational dynamics is important. Such dynamics has been argued to be fundamentally nonlocal in extreme situations, such as those required to investigate the fate of information.
Hardy's criterion of nonlocality for mixed states
Ghirardi, GianCarlo; Marinatto, Luca
2006-03-15
We generalize Hardy's proof of nonlocality to the case of bipartite mixed statistical operators, and we exhibit a necessary condition which has to be satisfied by any given mixed state {sigma} in order that a local and realistic hidden variable model exists which accounts for the quantum mechanical predictions implied by {sigma}. Failure of this condition will imply both the impossibility of any local explanation of certain joint probability distributions in terms of hidden variables and the nonseparability of the considered mixed statistical operator. Our result can be also used to determine the maximum amount of noise, arising from imperfect experimental implementations of the original Hardy's proof of nonlocality, in presence of which it is still possible to put into evidence the nonlocal features of certain mixed states.
Nonlocal Markovian models for image denoising
NASA Astrophysics Data System (ADS)
Salvadeo, Denis H. P.; Mascarenhas, Nelson D. A.; Levada, Alexandre L. M.
2016-01-01
Currently, the state-of-the art methods for image denoising are patch-based approaches. Redundant information present in nonlocal regions (patches) of the image is considered for better image modeling, resulting in an improved quality of filtering. In this respect, nonlocal Markov random field (MRF) models are proposed by redefining the energy functions of classical MRF models to adopt a nonlocal approach. With the new energy functions, the pairwise pixel interaction is weighted according to the similarities between the patches corresponding to each pair. Also, a maximum pseudolikelihood estimation of the spatial dependency parameter (β) for these models is presented here. For evaluating this proposal, these models are used as an a priori model in a maximum a posteriori estimation to denoise additive white Gaussian noise in images. Finally, results display a notable improvement in both quantitative and qualitative terms in comparison with the local MRFs.
Slits, plates, and Poisson-Boltzmann theory in a local formulation of nonlocal electrostatics.
Paillusson, Fabien; Blossey, Ralf
2010-11-01
Polar liquids like water carry a characteristic nanometric length scale, the correlation length of orientation polarizations. Continuum theories that can capture this feature commonly run under the name of "nonlocal" electrostatics since their dielectric response is characterized by a scale-dependent dielectric function ε(q), where q is the wave vector; the Poisson(-Boltzmann) equation then turns into an integro-differential equation. Recently, "local" formulations have been put forward for these theories and applied to water, solvated ions, and proteins. We review the local formalism and show how it can be applied to a structured liquid in slit and plate geometries, and solve the Poisson-Boltzmann theory for a charged plate in a structured solvent with counterions. Our results establish a coherent picture of the local version of nonlocal electrostatics and show its ease of use when compared to the original formulation.
Effect of Nonlocal Thermal Electron Transport on the Symmetry of Polar-Drive Experiments
NASA Astrophysics Data System (ADS)
Delettrez, J. A.; Collins, T. J. B.; Radha, P. B.; Michel, D. T.; Cao, D.; Moses, G.
2013-10-01
A nonlocal, multigroup diffusion model for thermal electron transport has been added to the 2-D hydrodynamic code DRACO. This model has been applied to simulations of polar-drive (PD) experiments on the OMEGA Laser System and the National Ignition Facility. When compared with the simulation with flux-limited diffusion transport, the nonlocal transport under the same laser illumination pattern increases the drive at the equator, resulting in an increase of the amplitude of modes two to six at end of target acceleration. The increased drive is caused by the larger heat flux at the equator than near the pole, which results from the coronal temperature being driven purposely high to compensate for the oblique illumination when using the flux-limiter model. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.
Ziółkowski, Andrzej
2014-12-15
Nonlinear light propagation in photorefractive media can be analyzed by numerical methods. The presented numerical approach has regard to the effects of time nonlocality. Two algorithms are presented, and compared in terms of physical results and computing times. The possibility to address the issue of time nonlocality in two ways is attributed to the fact that, it is possible to completely separate carrier dynamics evaluation and wave equation calculation. This in turn, allows to choose a short integration time for carrier dynamics and a longer one to solve the wave equation. The tests of the methods were carried out for a one-carrier model that describes most of photorefractive media, and for a model with bipolar transport and hot electron effect, used in descriptions of semiconductor materials.
Nami, Mohammad Rahim
2013-01-01
Summary In this article, a new higher order shear deformation theory based on trigonometric shear deformation theory is developed. In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates. In the present theory, the transverse shear stresses satisfy the traction free boundary conditions of the rectangular plates and these stresses can be calculated from the constitutive equations. The effects of different parameters such as nonlocal parameter and aspect ratio are investigated on both nondimensional deflections and deflection ratios. It may be important to mention that the present formulations are general and can be used for isotropic, orthotropic and anisotropic nanoplates. PMID:24455455
Manifestly local formulation of nonlocal approach to the cosmological constant problem
NASA Astrophysics Data System (ADS)
Oda, Ichiro
2017-05-01
We present a manifestly local and general coordinate invariant formulation of a nonlocal approach to the cosmological constant problem which has been recently proposed by Carroll and Remmen. To do that, we need to introduce a topological term involving a new 3-form gauge field. The equations of motion for this new 3-form gauge field lead to a constant Lagrange multiplier parameter and the resulting action becomes equivalent to that of Carroll and Remmen. In our formulation, nonlocal information is encoded via the procedure of taking the space-time average at the stage of the equations of motion. Consequently, our theory evades a no-go theorem by Weinberg and provides a new solution to the cosmological constant problem in almost exactly the same way as the original proposal by Carroll et al.
NASA Astrophysics Data System (ADS)
Rajabi, K.; Hosseini-Hashemi, Sh
2017-07-01
In this study, the free vibration analysis of first-order shear-deformable orthotropic nanoplates are conducted in the frameworks of the nonlocal strain gradient elasticity theory. The equations of motion and also the associated boundary conditions are derived using the extended Hamilton’s principle. The multi-term extended Kantorovich method (MTEKM) in conjunction with the generalized differential quadrature method (GDQM) is employed to solve the equations of motion. For clamped and simply supported boundary conditions the problem is solved. In addition, a modified Mindlin plate model is introduced by excluding the nonlocality in the shear constitutive equations. Numerical results have shown that the two material length scale parameters have opposite effects on the frequency response of the nanoplate. Also, the excluding the nonlocality in the shear constitutive equations is associated with the stiffness-softening phenomenon.
Multifamily Envelope Leakage Model
Faakye, Omari; Griffiths, Dianne
2015-05-08
“The cost for blower testing is high, because it is labor intensive, and it may disrupt occupants in multiple units. This high cost and disruption deter program participants, and dissuade them from pursuing energy improvements that would trigger air leakage testing, such as improvements to the building envelope.” This statement found in a 2012 report by Heschong Mahone Group for several California interests emphasizes the importance of reducing the cost and complexity of blower testing in multifamily buildings. Energy efficiency opportunities are being bypassed. The cost of single blower testing is on the order of $300. The cost for guarded blower door testing—the more appropriate test for assessing energy savings opportunities—could easily be six times that, and that’s only if you have the equipment and simultaneous access to multiple apartments. Thus, the proper test is simply not performed. This research seeks to provide an algorithm for predicting the guarded blower door test result based upon a single, total blower door test.
Masonry building envelope analysis
NASA Astrophysics Data System (ADS)
McMullan, Phillip C.
1993-04-01
Over the past five years, infrared thermography has proven an effective tool to assist in required inspections on new masonry construction. However, with more thermographers providing this inspection service, establishing a standard for conducting these inspections is imperative. To attempt to standardize these inspections, it is important to understand the nature of the inspection as well as the context in which the inspection is typically conducted. The inspection focuses on evaluating masonry construction for compliance with the design specifications with regard to structural components and thermal performance of the building envelope. The thermal performance of the building includes both the thermal resistance of the material as well as infiltration/exfiltration characteristics. Given that the inspections occur in the 'field' rather than the controlled environment of a laboratory, there are numerous variables to be considered when undertaking this type of inspection. Both weather and site conditions at the time of the inspection can vary greatly. In this paper we will look at the variables encountered during recent inspections. Additionally, the author will present the standard which was employed in collecting this field data. This method is being incorporated into a new standard to be included in the revised version of 'Guidelines for Specifying and Performing Infrared Inspections' developed by the Infraspection Institute.
Envelope glycoprotein of arenaviruses.
Burri, Dominique J; da Palma, Joel Ramos; Kunz, Stefan; Pasquato, Antonella
2012-10-17
Arenaviruses include lethal human pathogens which pose serious public health threats. So far, no FDA approved vaccines are available against arenavirus infections, and therapeutic options are limited, making the identification of novel drug targets for the development of efficacious therapeutics an urgent need. Arenaviruses are comprised of two RNA genome segments and four proteins, the polymerase L, the envelope glycoprotein GP, the matrix protein Z, and the nucleoprotein NP. A crucial step in the arenavirus life-cycle is the biosynthesis and maturation of the GP precursor (GPC) by cellular signal peptidases and the cellular enzyme Subtilisin Kexin Isozyme-1 (SKI-1)/Site-1 Protease (S1P) yielding a tripartite mature GP complex formed by GP1/GP2 and a stable signal peptide (SSP). GPC cleavage by SKI-1/S1P is crucial for fusion competence and incorporation of mature GP into nascent budding virion particles. In a first part of our review, we cover basic aspects and newer developments in the biosynthesis of arenavirus GP and its molecular interaction with SKI-1/S1P. A second part will then highlight the potential of SKI-1/S1P-mediated processing of arenavirus GPC as a novel target for therapeutic intervention to combat human pathogenic arenaviruses.
Towards an emerging understanding of non-locality phenomena and non-local transport
NASA Astrophysics Data System (ADS)
Ida, K.; Shi, Z.; Sun, H. J.; Inagaki, S.; Kamiya, K.; Rice, J. E.; Tamura, N.; Diamond, P. H.; Dif-Pradalier, G.; Zou, X. L.; Itoh, K.; Sugita, S.; Gürcan, O. D.; Estrada, T.; Hidalgo, C.; Hahm, T. S.; Field, A.; Ding, X. T.; Sakamoto, Y.; Oldenbürger, S.; Yoshinuma, M.; Kobayashi, T.; Jiang, M.; Hahn, S. H.; Jeon, Y. M.; Hong, S. H.; Kosuga, Y.; Dong, J.; Itoh, S.-I.
2015-01-01
In this paper, recent progress on experimental analysis and theoretical models for non-local transport (non-Fickian fluxes in real space) is reviewed. The non-locality in the heat and momentum transport observed in the plasma, the departures from linear flux-gradient proportionality, and externally triggered non-local transport phenomena are described in both L-mode and improved-mode plasmas. Ongoing evaluation of ‘fast front’ and ‘intrinsically non-local’ models, and their success in comparisons with experimental data, are discussed
Non-locality Sudden Death in Tripartite Systems
Jaeger, Gregg; Ann, Kevin
2009-03-10
Bell non-locality sudden death is the disappearance of non-local properties in finite times under local phase noise, which decoheres states only in the infinite-time limit. We consider the relationship between decoherence, disentanglement, and Bell non-locality sudden death in bipartite and tripartite systems in specific large classes of state preparation.
Reversed rainbow with a nonlocal metamaterial
Morgado, Tiago A. Marcos, João S.; Silveirinha, Mário G.; Costa, João T.; Costa, Jorge R.; Fernandes, Carlos A.
2014-12-29
One of the intriguing potentials of metamaterials is the possibility to realize a nonlocal electromagnetic reaction, such that the effective medium response at a given point is fundamentally entangled with the macroscopic field distribution at long distances. Here, it is experimentally and numerically verified that a microwave nonlocal metamaterial formed by crossed metallic wires enables a low-loss broadband anomalous material response such that the refractive index decreases with frequency. Notably, it is shown that an electromagnetic beam refracted by our metamaterial prism creates a reversed microwave rainbow.
Experimental nonlocal and surreal Bohmian trajectories.
Mahler, Dylan H; Rozema, Lee; Fisher, Kent; Vermeyden, Lydia; Resch, Kevin J; Wiseman, Howard M; Steinberg, Aephraim
2016-02-01
Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed "surreal" when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.
Experimental nonlocal and surreal Bohmian trajectories
Mahler, Dylan H.; Rozema, Lee; Fisher, Kent; Vermeyden, Lydia; Resch, Kevin J.; Wiseman, Howard M.; Steinberg, Aephraim
2016-01-01
Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed “surreal” when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality. PMID:26989784
Compressive Sensing via Nonlocal Smoothed Rank Function
Fan, Ya-Ru; Liu, Jun; Zhao, Xi-Le
2016-01-01
Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction. PMID:27583683
Observational viability and stability of nonlocal cosmology
Deser, S.; Woodard, R.P. E-mail: woodard@phys.ufl.edu
2013-11-01
We show that the nonlocal gravity models, proposed to explain current cosmic acceleration without dark energy, pass two essential tests: first, they can be defined so as not to alter the, observationally correct, general relativity predictions for gravitationally bound systems. Second, they are stable, ghost-free, with no additional excitations beyond those of general relativity. In this they differ from their, ghostful, localized versions. The systems' initial value constraints are the same as in general relativity, and our nonlocal modifications never convert the original gravitons into ghosts.
Compressive Sensing via Nonlocal Smoothed Rank Function.
Fan, Ya-Ru; Huang, Ting-Zhu; Liu, Jun; Zhao, Xi-Le
2016-01-01
Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction.
Nonlocal Coulomb drag in Weyl semimetals
NASA Astrophysics Data System (ADS)
Baum, Yuval; Stern, Ady
2017-02-01
Nonlocality is one of the most striking signatures of the topological nature of Weyl semimetals. We propose to probe the nonlocality in these materials via a measurement of a magnetic-field-dependent Coulomb drag between two sheets of graphene which are separated by a three-dimensional slab of Weyl semimetal. We predict a mechanism of Coulomb drag, based on cyclotron orbits that are split between opposite surfaces of the semimetal. In the absence of impurity scattering between different Weyl nodes, this mechanism does not decay with the thickness of the semimetal.
Reversed rainbow with a nonlocal metamaterial
NASA Astrophysics Data System (ADS)
Morgado, Tiago A.; Marcos, João S.; Costa, João T.; Costa, Jorge R.; Fernandes, Carlos A.; Silveirinha, Mário G.
2014-12-01
One of the intriguing potentials of metamaterials is the possibility to realize a nonlocal electromagnetic reaction, such that the effective medium response at a given point is fundamentally entangled with the macroscopic field distribution at long distances. Here, it is experimentally and numerically verified that a microwave nonlocal metamaterial formed by crossed metallic wires enables a low-loss broadband anomalous material response such that the refractive index decreases with frequency. Notably, it is shown that an electromagnetic beam refracted by our metamaterial prism creates a reversed microwave rainbow.
Erasing nonlocal like two photon interference
NASA Astrophysics Data System (ADS)
Olindo, C.; Sagioro, M. A.; Pádua, S.; Monken, C. H.
2015-12-01
Over the years, since the 1980s, various two photon interference experiments have been reported with photon pairs generated by parametric down conversion. Some of them have shown local interference features and non-local ones. An experiment is shown here which joins the two features at the same time in a Hong-Ou-Mandel interferometer. However, the non-local effects are lost if the photons' arrival time difference at the beam splitter is much larger than the pulse length of the pump beam that generates the photon pair.
Envelope solitons of acoustic plate modes and surface waves.
Mayer, Andreas P; Kovalev, Alexander S
2003-06-01
The problem of the existence of evelope solitons in elastic plates and at solid surfaces covered by an elastic film is revisited with special attention paid to nonlinear long-wave short-wave interactions. Using asymptotic expansions and multiple scales, conditions for the existence of envelope solitons are established and it is shown how their parameters can be expressed in terms of the elastic moduli and mass densities of the materials involved. In addition to homogeneous plates, weak periodic modulation of the plate's material parameters are also considered. In the case of wave propagation in an elastic plate, modulations of weakly nonlinear carrier waves are governed by a coupled system of partial differential equations consisting of evolution equations for the complex amplitude of the carrier wave (the nonlinear Schrödinger equation for envelope solitons and the Mills-Trullinger equations for gap solitons), and the wave equation for long-wavelength acoustic plate modes. In contrast to this situation, envelope solitons of surface acoustic waves in a layered structure are normally described by the nonlinear Schrödinger equation alone. However, at higher orders of the carrier wave amplitude, the envelope soliton is found to be accompanied by a quasistatic long-wavelength strain field, which may be localized at the surface with penetration depth into the substrate of the order of the inverse amplitude or which may radiate energy into the bulk. A new set of modulation equations is derived for the resonant case of the carrier wave's group velocity being equal to the phase velocity of long-wavelength Rayleigh waves of the uncoated substrate.
Elliptic Hermite-Gaussian soliton in anisotropic strong nonlocal media
NASA Astrophysics Data System (ADS)
Wang, Qing; Li, JingZhen
2016-01-01
The propagation of elliptic Hermite-Gaussian (HG) beam in strong nonlocal media with elliptic Gaussian-shaped response function was studied by variational approach as well as numerical simulate. The evolution equations of the beam widths in x- and y-directions are obtained and the elliptic HG soliton is found. For forming such a soliton, the ratio of the square of the beam width must be proportional to the ratio of the characteristic length of the material, and the initial power should be equal to the two critical powers in x- and y-directions. For the anisotropic nonlinearity of the media, the instability of the high-order elliptic HG beam is increase as the increase of the order.
Cosmological solutions of a nonlocal model with a perfect fluid
Elizalde, Emilio; Pozdeeva, Ekaterina O.; Vernov, Sergey Yu.; Zhang, Ying-li E-mail: pozdeeva@www-hep.sinp.msu.ru E-mail: yingli@yukawa.kyoto-u.ac.jp
2013-07-01
A nonlocal gravity model which does not assume the existence of a new dimensional parameter in the action and includes a function f(□{sup −1}R), with □ the d'Alembertian operator, is studied. By specifying an exponential form for the function f and including a matter sector with a constant equation of state parameter, all available power-law solutions in the Jordan frame are obtained. New power-law solutions in the Einstein frame are also probed. Furthermore, the relationship between power-law solutions in both frames, established through conformal transformation, is substantially clarified. The correspondence between power-law solutions in these two frames is proven to be a very useful tool in order to obtain new solutions in the Einstein frame.
Commutative deformations of general relativity: nonlocality, causality, and dark matter
NASA Astrophysics Data System (ADS)
de Vegvar, P. G. N.
2017-01-01
Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on commutative manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter fields are utilized to generate self-consistent Abelian Drinfeld twists in a background independent manner and their continuous and discrete symmetries are examined. There is negligible experimental effect on the standard model of particles. While baryonic twist producing matter would begin to behave acausally for rest masses above {˜ }1-10 TeV, other possibilities are viable dark matter candidates or a right-handed neutrino. First order deformed Maxwell equations are derived and yield immeasurably small cosmological dispersion and produce a propagation horizon only for photons at or above Planck energies. This model incorporates dark matter without any appeal to extra dimensions, supersymmetry, strings, grand unified theories, mirror worlds, or modifications of Newtonian dynamics.
NASA Astrophysics Data System (ADS)
Mehralian, Fahimeh; Tadi Beni, Yaghoub; Karimi Zeverdejani, Mehran
2017-09-01
The present paper is concerned with the applicability of nonlocal strain gradient theory for axial buckling analysis of nanotubes. The first order shear deformation theory with the von Kármán geometrical nonlinearity is utilized to establish theoretical formulations. The governing equations and boundary conditions are derived using the minimum potential energy principle. As main purpose of this study, the small length scale parameters are calibrated for the axial buckling problem of carbon nanotubes (CNTs) using molecular dynamics (MDs) simulations. Further the influences of different geometrical and material parameters, such as length and thickness ratio as well as small length scale parameters on the buckling response of nanotubes are studied. It is indicated that the effect of small length scale parameters on the critical buckling load becomes more prominent by increasing thickness and decreasing length ratio. Moreover, the calibrated small length scale parameters presented herein would be useful for the purpose of applying the nonlocal strain gradient theory for the analysis of nanotubes. The calibrated nonlocal strain gradient theory presented herein should be useful for researchers who are using the nonlocal strain gradient shell theories for analysis of micro/nanotubes.
NASA Astrophysics Data System (ADS)
Soleimani, Ahmad; Naei, Mohammad Hasan; Mashhadi, Mahmoud Mosavi
In this paper, the first order shear deformation theory (FSDT) is used to investigate the postbuckling behavior of orthotropic single-layered graphene sheet (SLGS) under in-plane loadings. Nonlocal elasticity theory and von-Karman nonlinear model in combination with the isogeometric analysis (IGA) have been applied to study the postbuckling characteristics of SLGSs. In contrast to the classical model, the nonlocal continuum model developed in this work considers the size-effects on the postbuckling characteristics of SLGSs. FSDT takes into account effects of shear deformations through-the-thickness of plate. Geometric imperfection which is defined as a very small transverse displacement of the mid-plane is applied on undeformed nanoplate to create initial deviation in graphene sheet from being perfectly flat. Nonlinear governing equations of motion for SLGS are derived from the principle of virtual work and a variational formulation. At the end, the results are presented as the postbuckling equilibrium paths of SLGS. The influence of various parameters such as edge length, nonlocal parameter, compression ratio, boundary conditions and aspect ratio on the postbuckling path is investigated. The results of this work show the high accuracy of nonlocal FSDT-based analysis for postbuckling behavior of graphene sheets.
NASA Astrophysics Data System (ADS)
Saffari, Shahab; Hashemian, Mohammad; Toghraie, Davood
2017-09-01
Based on nonlocal Timoshenko beam theory, dynamic stability of functionally graded (FG) nanobeam under axial and thermal loading was investigated. Surface stress effects were implemented according to Gurtin-Murdoch continuum theory. Using power law distribution for FGM and von Karman geometric nonlinearity, governing equations were derived based on Hamilton's principle. The developed nonlocal models have the capability of interpreting small scale effects. Pasternak elastic medium was employed to represent the interaction of the FG nanobeam and the surrounding elastic medium. A parametric study was conducted to focus influences of the static load factor, temperature change, gradient index, nonlocal parameter, slenderness ratio, surface effect and springs constants of the elastic medium on the dynamic instability region (DIR) of the FG beam with simply-supported boundary conditions. It was found that differences between DIRs predicted by local and nonlocal beam theories are significant for beams with lower aspect ratio. Moreover, it was observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origin of the DIR to higher excitation frequency zone and leads to further stability. Considering surface stress effects shifts the DIR of FG beam to higher frequency zone, also increasing the gradient index enhances the frequency of DIR.
NASA Technical Reports Server (NTRS)
Tiwari, S. N.; Jha, M. K.
1993-01-01
Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations. Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions. The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are obtained numerically by employing the method of variation of parameters. The results are compared under local and nonlocal thermodynamic equilibrium conditions at different temperature and pressure conditions. Both gray and nongray studies are conducted extensively for all molecular gases considered. The particular gases selected for this investigation are CO, NO, OH, CO2, H2O, and CH4. The temperature and pressure range considered are 300-2000 K and 0.1-10 atmosphere, respectively. In general, results demonstrate that the gray gas approximation overestimates the effect of radiative interaction for all conditions. The conditions of NLTE, however, result in underestimation of radiative interactions. The method developed for this study can be extended to solve complex problems of radiative heat transfer involving nonequilibrium phenomena.
Isolation of bacteria envelope proteins.
Quan, Shu; Hiniker, Annie; Collet, Jean-François; Bardwell, James C A
2013-01-01
Proteomic analysis on cell envelope proteins from Gram-negative bacteria requires specific isolation techniques. We found that conventional extraction methods such as osmotic shock cause extracts to be heavily contaminated with soluble cytoplasmic proteins. These cytoplasmic protein contaminants constitute the major signal in proteomic analysis and can overwhelm the signals coming from genuine envelope components. After extensive testing of various protocols for the preparation of envelope contents, we found that a modified version of the method of Oliver and Beckwith consistently produces the cleanest extract of periplasmic and outer membrane proteins.We have designated this very simple method TSE extraction because it uses a Tris-sucrose solution supplemented with EDTA.Cytoplasmic and inner membrane protein contaminants are not evident on 1D SDS polyacrylamide gels and contribute to less than 6% of total signal in very sensitive mass spectrometry analysis. This straightforward method is therefore ideal for -analyzing specific proteomic changes in the cell envelope.
NASA Astrophysics Data System (ADS)
Liang, Lin-mei; Li, Cheng-zu
2005-02-01
This Letter presents nonlocality without inequalities for two-qubit mixed states. This Letter was mainly sparked by Cabello's work [Phys. Rev. A 65 (2003) 032108] and is an extension of our recent work [Phys. Lett. A 318 (2003) 300].
Budini, Adrian A.
2006-11-15
In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the structure of a classical rate equation. The system dynamics may develop strong nonlocal effects such as the dependence of the stationary properties with the system initialization. These equations are derived from alternative microscopic interactions, such as complex environments described in a generalized Born-Markov approximation and tripartite system-environment interactions, where extra unobserved degrees of freedom mediates the entanglement between the system and a Markovian reservoir. Conditions that guarantee the completely positive condition of the solution map are found. Quantum stochastic processes that recover the system dynamics in average are formulated. We exemplify our results by analyzing the dynamical action of nontrivial structured dephasing and depolarizing reservoirs over a single qubit.
Consequences and applications of the completeness of Hardy's nonlocality
NASA Astrophysics Data System (ADS)
Mansfield, Shane
2017-02-01
Logical nonlocality is completely characterized by Hardy's "paradox" in (2 ,2 ,l ) and (2 ,k ,2 ) scenarios. We consider a variety of consequences and applications of this fact. (i) Polynomial algorithms may be given for deciding logical nonlocality in these scenarios. (ii) Bell states are the only entangled two-qubit states which are not logically nonlocal under projective measurements. (iii) It is possible to witness Hardy nonlocality with certainty in a simple tripartite quantum system. (iv) Noncommutativity of observables is necessary and sufficient for enabling logical nonlocality.
29 CFR 780.320 - Nonlocal minors.
Code of Federal Regulations, 2010 CFR
2010-07-01
... That Is Exempted From the Minimum Wage and Overtime Pay Requirements Under Section 13(a)(6) Statutory... 29 Labor 3 2010-07-01 2010-07-01 false Nonlocal minors. 780.320 Section 780.320 Labor Regulations Relating to Labor (Continued) WAGE AND HOUR DIVISION, DEPARTMENT OF LABOR STATEMENTS OF GENERAL POLICY OR...
Nonlocality and entanglement via the Unruh effect
Tian, Zehua; Wang, Jieci; Jing, Jiliang
2013-05-15
Modeling the qubit by a two-level semiclassical detector coupled to a massless scalar field, we investigate how the Unruh effect affects the nonlocality and entanglement of two-qubit and three-qubit states when one of the entangled qubits is accelerated. Two distinct differences with the results of free field model in non-inertial frames are (i) for the two-qubit state, the CHSH inequality cannot be violated for sufficiently large but finite acceleration, furthermore, the concurrence will experience “sudden death”; and (ii) for the three-qubit state, not only does the entanglement vanish in the infinite acceleration limit, but also the Svetlichny inequality cannot be violated in the case of large acceleration. -- Highlights: ► We compare entanglement and nonlocality of two-level detector model with that of free field model in noninertial frame. ► Two-qubit state entanglement experiences “sudden death”. ► Three-qubit state entanglement vanishes in the infinite acceleration limit. ► Bipartite nonlocal correlations vanish for finite values of the acceleration. ► Tripartite nonlocal correlations vanish for finite values of the acceleration as well.
Nonlocality as Evidence for a Multiverse Cosmology
NASA Astrophysics Data System (ADS)
Tipler, Frank J.
We show that observations of quantum nonlocaltiy can be interpreted as purely local phenomena, provided one assumes that the cosmos is a multiverse. Conversely, the observation of quantum nonlocality can be interpreted as observation evidence for a multiverse cosmology, just as observation of the setting of the Sun can be interpreted as evidence for the Earth's rotation.
29 CFR 780.320 - Nonlocal minors.
Code of Federal Regulations, 2011 CFR
2011-07-01
... That Is Exempted From the Minimum Wage and Overtime Pay Requirements Under Section 13(a)(6) Statutory... 29 Labor 3 2011-07-01 2011-07-01 false Nonlocal minors. 780.320 Section 780.320 Labor Regulations Relating to Labor (Continued) WAGE AND HOUR DIVISION, DEPARTMENT OF LABOR STATEMENTS OF GENERAL POLICY OR...
29 CFR 780.320 - Nonlocal minors.
Code of Federal Regulations, 2014 CFR
2014-07-01
... That Is Exempted From the Minimum Wage and Overtime Pay Requirements Under Section 13(a)(6) Statutory... 29 Labor 3 2014-07-01 2014-07-01 false Nonlocal minors. 780.320 Section 780.320 Labor Regulations Relating to Labor (Continued) WAGE AND HOUR DIVISION, DEPARTMENT OF LABOR STATEMENTS OF GENERAL POLICY OR...
29 CFR 780.320 - Nonlocal minors.
Code of Federal Regulations, 2013 CFR
2013-07-01
... That Is Exempted From the Minimum Wage and Overtime Pay Requirements Under Section 13(a)(6) Statutory... 29 Labor 3 2013-07-01 2013-07-01 false Nonlocal minors. 780.320 Section 780.320 Labor Regulations Relating to Labor (Continued) WAGE AND HOUR DIVISION, DEPARTMENT OF LABOR STATEMENTS OF GENERAL POLICY OR...
29 CFR 780.320 - Nonlocal minors.
Code of Federal Regulations, 2012 CFR
2012-07-01
... That Is Exempted From the Minimum Wage and Overtime Pay Requirements Under Section 13(a)(6) Statutory... 29 Labor 3 2012-07-01 2012-07-01 false Nonlocal minors. 780.320 Section 780.320 Labor Regulations Relating to Labor (Continued) WAGE AND HOUR DIVISION, DEPARTMENT OF LABOR STATEMENTS OF GENERAL POLICY OR...
Measurement-induced Nonlocality for Gaussian States
NASA Astrophysics Data System (ADS)
Ma, Ruifen; Hou, Jinchuan; Qi, Xiaofei
2017-04-01
We establish an analytic formula of measurement-induced nonlocality (MIN) for two-mode squeezed thermal states and mixed thermal states. Different from the quantum discord case, we show that there is no Gaussian version of MIN by Gaussian positive operator valued measurements.
Spiraling multivortex solitons in nonlocal nonlinear media.
Buccoliero, Daniel; Desyatnikov, Anton S; Krolikowski, Wieslaw; Kivshar, Yuri S
2008-01-15
We demonstrate the existence of a broad class of higher-order rotating spatial solitons in nonlocal nonlinear media. We employ the generalized Hermite-Laguerre-Gaussian ansatz for constructing multivortex soliton solutions and study numerically their dynamics and stability. We discuss in detail the tripole soliton carrying two spiraling phase dislocations, or self-trapped optical vortices.
Nonlocal optical response of plasmonic nanowire metamaterials
NASA Astrophysics Data System (ADS)
Wells, Brian Michael
Nanowire metamaterials are a class of composite photonic media formed by an array of aligned plasmonic nanowires embedded in a dielectric matrix. Depending on exact composition, geometry, and excitation wavelength, nanowire structures are known to exhibit elliptical, hyperbolic, or epsilon-near-zero (ENZ) responses. In the ENZ regime, optical response of the composite becomes strongly nonlocal. Excitation of an additional wave, caused by nonlocality, has been experimentally demonstrated in nanowire-based metamaterials. In this thesis, a computational study of the nonlocal optical response in plasmonic nanowire arrays has been conducted to better understand such materials. The results of this computational study were used to develop an analytical technique that provides an adequate description of the optical response of wire based metamaterials. This formalism combines the local and nonlocal effective-medium theories often used to describe the optics of nanowire composites. It provides insight into the origin of the additional wave and allows implementation of additional boundary conditions. This approach can be straightforwardly extended to describe the optics for numerious plasmonic structures.
Resonant and nonlocal properties of phononic metasolids
NASA Astrophysics Data System (ADS)
Torrent, Daniel; Pennec, Yan; Djafari-Rouhani, Bahram
2015-11-01
We derive a general theory of effective properties in metasolids based on phononic crystals with low frequency resonances. We demonstrate that in general these structures need to be described by means of a frequency-dependent and nonlocal anisotropic mass density, stiffness tensor and a third-rank coupling tensor, which shows that they behave like a nonlocal Willis medium. The effect of nonlocality and coupling tensor manifest themselves for some particular resonances, whereas they become negligible for other resonances. Considering the example of a two-dimensional phononic crystal, consisting of triangular arrangements of cylindrical shells in an elastic matrix, we show that its mass density tensor is strongly resonant and anisotropic presenting both positive and negative divergent values, while becoming scalar in the quasistatic limit. Moreover, it is found that the negative value of transverse component of the mass density is induced by a dipolar resonance, while that of the vertical component is induced by a monopolar one. Finally, the dispersion relation obtained by the effective parameters of the crystal is compared with the band structure, showing good agreement for the low-wave-number region, although the nonlocal effects are important given the existence of some resonant values of the wave number.
The electroneutrality constraint in nonlocal models
NASA Astrophysics Data System (ADS)
Lees, Eitan; Rokkam, Srujan; Shanbhag, Sachin; Gunzburger, Max
2017-09-01
We develop a nonlocal Nernst-Planck model for reaction and diffusion in multicomponent ionic systems. We apply the model to the one-dimensional liquid junction problem, in which two electrolytic solutions of different ionic concentrations are brought into contact via a permeable membrane. Transport of ions through the membrane induces an electric field which is modeled using two separate nonlocal conditions: charge conservation and Gauss' law. We investigate how well they satisfy the criterion of strict electroneutrality which stipulates that the net charge at each point in the domain is zero, by considering four different initial scenarios. Charge conservation and Gauss' law yield similar results for most practical scenarios in which the initial condition satisfies strict electroneutrality. However, Gauss' law has two important advantages over charge conservation: (i) it is numerically more stable and can be applied even when the concentration of all the charged species drops to zero and (ii) computationally, it is significantly cheaper. Further, this study provides insights on the prescription of electroneutrality conditions necessary to handle the physics of evolving charges in nonlocal peridynamic models that are aimed at modeling nonlocal reaction-diffusion or corrosion-type processes.
Nonlocal dynamics of dissipative phononic fluids
NASA Astrophysics Data System (ADS)
Nemati, Navid; Lee, Yoonkyung E.; Lafarge, Denis; Duclos, Aroune; Fang, Nicholas
2017-06-01
We describe the nonlocal effective properties of a two-dimensional dissipative phononic crystal made by periodic arrays of rigid and motionless cylinders embedded in a viscothermal fluid such as air. The description is based on a nonlocal theory of sound propagation in stationary random fluid/rigid media that was proposed by Lafarge and Nemati [Wave Motion 50, 1016 (2013), 10.1016/j.wavemoti.2013.04.007]. This scheme arises from a deep analogy with electromagnetism and a set of physics-based postulates including, particularly, the action-response procedures, whereby the effective density and bulk modulus are determined. Here, we revisit this approach, and clarify further its founding physical principles through presenting it in a unified formulation together with the two-scale asymptotic homogenization theory that is interpreted as the local limit. Strong evidence is provided to show that the validity of the principles and postulates within the nonlocal theory extends to high-frequency bands, well beyond the long-wavelength regime. In particular, we demonstrate that up to the third Brillouin zone including the Bragg scattering, the complex and dispersive phase velocity of the least-attenuated wave in the phononic crystal which is generated by our nonlocal scheme agrees exactly with that reproduced by a direct approach based on the Bloch theorem and multiple scattering method. In high frequencies, the effective wave and its associated parameters are analyzed by treating the phononic crystal as a random medium.
Testing nonlocal realism with entangled coherent states
Paternostro, Mauro; Jeong, Hyunseok
2010-03-15
We investigate the violation of nonlocal realism using entangled coherent states (ECSs) under nonlinear operations and homodyne measurements. We address recently proposed Leggett-type inequalities, including a class of optimized incompatibility inequalities proposed by Branciard et al. [Nature Phys. 4, 681 (2008)], and thoroughly assess the effects of detection inefficiency.
Radiative accelerations in stellar envelopes
NASA Astrophysics Data System (ADS)
Seaton, M. J.
1997-08-01
In stars which are sufficiently quiescent, changes in the relative abundances of the chemical elements can result from gravitational settling and from levitation produced by radiation pressure forces, usually expressed as radiative accelerations g_rad. Those changes can affect the structure of such stars, due to modifications in opacities, and can lead to marked peculiarities in observed atmospheric abundances. It is necessary to consider diffusive movements both in the atmospheres and in much deeper layers of the stellar envelopes. For the envelopes the equation of radiative transfer can be solved in a diffusion approximation and, for an element k in ionization stage j, one obtains expressions for g_rad(j, k) proportional to the total radiative flux, to the Rosseland-mean opacity kappa_R (which may depend on the abundance of k), and to a dimensionless quantity gamma(j, k) which, due to saturation effects, can be sensitive to the abundance of k. The radiative accelerations are required for each ionization stage, because the diffusion coefficients depend on j. Using atomic data obtained in the course of the work of the Opacity Project (OP), we calculate kappa_R and gamma(j, k) for the chemical elements C, N, O, Ne, Na, Mg, Al, Si, S, Ar, Ca, Cr, Mn, Fe and Ni. We start from standard Solar system abundances, and then vary the abundance of one element at a time (element k) by a factor chi. The following results are obtained and are available at the Centre de Donnees astronomiques de Strasbourg (CDS). (1) Files stages.zz (where zz specifies the nuclear charge of the selected element k) containing values of kappa_R and gamma(j, k) on a mesh of values of (T, N_e, chi), where T is temperature, and N_e is electron density. We include derivatives of kappa_R and gamma(j, k) with respect to chi, which are used for making interpolations. (2) A code add.f which reads a file stages.zz and writes a file acc.zz containing values of gamma(k) obtained on summing the gamma(j, k
Measuring non-local Lagrangian peak bias
NASA Astrophysics Data System (ADS)
Biagetti, Matteo; Chan, Kwan Chuen; Desjacques, Vincent; Paranjape, Aseem
2014-06-01
We investigate non-local Lagrangian bias contributions involving gradients of the linear density field, for which we have predictions from the excursion set peak formalism. We begin by writing down a bias expansion which includes all the bias terms, including the non-local ones. Having checked that the model furnishes a reasonable fit to the halo mass function, we develop a one-point cross-correlation technique to measure bias factors associated with χ2-distributed quantities. We validate the method with numerical realizations of peaks of Gaussian random fields before we apply it to N-body simulations. We focus on the lowest (quadratic) order non-local contributions -2χ _{10}(k_1\\cdot k_2) and χ _{01}[3(k_1\\cdot k_2)^2-k_1^2 k_2^2], where k_1, k_2 are wave modes. We can reproduce our measurement of χ10 if we allow for an offset between the Lagrangian halo centre-of-mass and the peak position. The sign and magnitude of χ10 is consistent with Lagrangian haloes sitting near linear density maxima. The resulting contribution to the halo bias can safely be ignored for M = 1013 M⊙ h-1, but could become relevant at larger halo masses. For the second non-local bias χ01 however, we measure a much larger magnitude than predicted by our model. We speculate that some of this discrepancy might originate from non-local Lagrangian contributions induced by non-spherical collapse.
NASA Astrophysics Data System (ADS)
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
NASA Astrophysics Data System (ADS)
Colli, Pierluigi; Gilardi, Gianni; Sprekels, Jürgen
2016-06-01
This paper investigates a nonlocal version of a model for phase separation on an atomic lattice that was introduced by P. Podio-Guidugli (2006) [36]. The model consists of an initial-boundary value problem for a nonlinearly coupled system of two partial differential equations governing the evolution of an order parameter ρ and the chemical potential μ. Singular contributions to the local free energy in the form of logarithmic or double-obstacle potentials are admitted. In contrast to the local model, which was studied by P. Podio-Guidugli and the present authors in a series of recent publications, in the nonlocal case the equation governing the evolution of the order parameter contains in place of the Laplacian a nonlocal expression that originates from nonlocal contributions to the free energy and accounts for possible long-range interactions between the atoms. It is shown that just as in the local case the model equations are well posed, where the technique of proving existence is entirely different: it is based on an application of Tikhonov's fixed point theorem in a rather unusual separable and reflexive Banach space.
Simulating the onset of grazing envelope evolution of binary stars
NASA Astrophysics Data System (ADS)
Shiber, Sagiv; Kashi, Amit; Soker, Noam
2017-02-01
We present the first three-dimensional gas-dynamical simulations of the grazing envelope evolution (GEE) of stars, with the goal of exploring the basic flow properties and the role of jets at the onset of the GEE. In the simulated runs, a secondary main-sequence star grazes the envelope of the primary asymptotic giant branch (AGB) star. The orbit is circular at the radius of the AGB primary star on its equator. We inject two opposite jets perpendicular to the equatorial plane from the location of the secondary star, and follow the evolution for several orbital periods. We explore the flow pattern by which the jets eject the outskirts of the AGB envelope. After one orbit, the jets start to interact with gas ejected in previous orbits and inflate hot low-density bubbles.
Line response functions in nonlocal thermodynamic equilibrium. Isotropic case
NASA Astrophysics Data System (ADS)
Milić, I.; van Noort, M.
2017-05-01
Context. Response functions provide us with a quantitative measure of sensitivity of the emergent spectrum to perturbations in the solar atmosphere and are thus the method of choice for interpreting spectropolarimetric observations. For the lines formed in the solar chromosphere, it is necessary to compute these responses taking into account nonlocal thermodynamic equilibrium (NLTE) effects. Aims: We show how to analytically compute the response of the level populations in NLTE to a change of a given physical quantity at a given depth in the atmosphere. These responses are then used to compute opacity and emissivity responses, which are then propagated to obtain the response of the emergent intensity. Methods: Our method is based on the derivative of the rate equations, where we explicitly incorporate spatial coupling in the radiative rate terms. After considering and collecting all interdependencies, the problem reduces to a linear system of equations with a dimension equal to the product of the number of spatial points and the number of energy levels. Results: We compare analytically computed response functions with those obtained using a finite difference approach and find very good agreement. In addition, a more accurate way of propagating opacity and emissivity perturbations through the numerical solution of the radiative transfer equation was developed. Conclusions: This method allows for the fast evaluation of the response of the emergent spectrum to perturbations of a given quantity at a given depth, and thus is a significant step towards more efficient NLTE inversions.
NASA Astrophysics Data System (ADS)
Zhen, Ya-Xin
2017-02-01
In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.
NASA Astrophysics Data System (ADS)
Mohammadimehr, M.; Mohammadi-Dehabadi, A. A.; Maraghi, Z. Khoddami
2017-04-01
In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.
Implicit for local effects and explicit for nonlocal effects is unconditionallly stable.
Anitescu, M.; Layton, W. J.; Pahlevani, F.; Mathematics and Computer Science; Univ. of Pittsburgh
2004-01-01
A combination of implicit and explicit timestepping is analyzed for a system of ordinary differential equations (ODEs) motivated by ones arising from spatial discretizations of evolutionary partial differential equations (PDEs). Loosely speaking, the method we consider is implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numerical scheme are proved by the energy method and by algebraic techniques. This stability result is surprising because usually when different methods are combined, the stability properties of the least stable method plays a determining role in the combination.
Lipschitz regularity of solutions for mixed integro-differential equations
NASA Astrophysics Data System (ADS)
Barles, Guy; Chasseigne, Emmanuel; Ciomaga, Adina; Imbert, Cyril
We establish new Hölder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's method. We thus extend the Hölder regularity results recently obtained by Barles, Chasseigne and Imbert (2011). In addition, we deal with a new class of nonlocal equations that we term mixed integro-differential equations. These equations are particularly interesting, as they are degenerate both in the local and nonlocal term, but their overall behavior is driven by the local-nonlocal interaction, e.g. the fractional diffusion may give the ellipticity in one direction and the classical diffusion in the complementary one.
Hidden variables and nonlocality in quantum mechanics
NASA Astrophysics Data System (ADS)
Hemmick, Douglas Lloyd
1997-05-01
Most physicists hold a skeptical attitude toward a 'hidden variables' interpretation of quantum theory, despite David Bohm's successful construction of such a theory and John S. Bell's strong arguments in favor of the idea. The first reason for doubt concerns certain mathematical theorems (von Neumann's, Gleason's, Kochen and Specker's, and Bell's) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed 'impossible', in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second concern is that the most sophisticated example of a hidden variables theory-that of David Bohm-exhibits non-locality, i.e., consequences of events at one place can propagate to other places instantaneously. However, neither the mathematical theorems in question nor the attribute of nonlocality detract from the importance of a hidden variables interpretation of quantum theory. Nonlocality is present in quantum mechanics itself, and is a required characteristic of any theory that agrees with the quantum mechanical predictions. We first discuss the earliest analysis of hidden variables-that of von Neumann's theorem-and review John S. Bell's refutation of von Neumann's 'impossibility proof'. We recall and elaborate on Bell's arguments regarding the theorems of Gleason, and Kochen and Specker. According to Bell, these latter theorems do not imply that hidden variables interpretations are untenable, but instead that such theories must exhibit contextuality, i.e., they must allow for the dependence of measurement results on the characteristics of both measured system and measuring apparatus. We demonstrate a new way to understand the implications of both Gleason's theorem and Kochen and Specker's theorem by noting that they prove a result we call
Role of retardation in three-dimensional relativistic equations
NASA Astrophysics Data System (ADS)
Lahiff, A. D.; Afnan, I. R.
1997-11-01
Equal-time Green's function is used to derive a three-dimensional integral equation from the Bethe-Salpeter equation. The resultant equation, in the absence of antiparticles, is identical to the use of time-ordered diagrams, and has been used within the framework of φ2σ coupling to study the role of energy dependence and nonlocality when the two-body potential is the sum of σ exchange and crossed σ exchange. The results show that nonlocality and energy dependence make a substantial contribution to both the on-shell and off-shell amplitudes.
Effect of local noise for achieving nonlocal advantage of quantum coherence
NASA Astrophysics Data System (ADS)
Du, Ming-Ming; Wang, Dong; Ye, Liu
2017-09-01
In this paper, we investigate steering, Bell nonlocality and nonlocal advantage of quantum coherence for entangled pure states. We find that there are nonlocal states which cannot achieve a nonlocal advantage of quantum coherence. In addition, we explore the effect of local noise for achieving nonlocal advantage of quantum coherence. It shows that, with the increase in noise parameter, it is difficult to achieve nonlocal advantage of quantum coherence and when the noise parameter is beyond a certain value, nonlocal advantage of quantum coherence cannot be achieved. Compared with steering and Bell nonlocality, the effect of local noise for achieving nonlocal advantage of quantum coherence is dominated.
Classification of scalar and dyadic nonlocal optical response models.
Wubs, M
2015-11-30
Nonlocal optical response is one of the emerging effects on the nanoscale for particles made of metals or doped semiconductors. Here we classify and compare both scalar and tensorial nonlocal response models. In the latter case the nonlocality can stem from either the longitudinal response, the transverse response, or both. In phenomenological scalar models the nonlocal response is described as a smearing out of the commonly assumed infinitely localized response, as characterized by a distribution with a finite width. Here we calculate explicitly whether and how tensorial models, such as the hydrodynamic Drude model and generalized nonlocal optical response theory, follow this phenomenological description. We find considerable differences, for example that nonlocal response functions, in contrast to simple distributions, assume negative and complex values. Moreover, nonlocal response regularizes some but not all diverging optical near fields. We identify the scalar model that comes closest to the hydrodynamic model. Interestingly, for the hydrodynamic Drude model we find that actually only one third (1/3) of the free-electron response is smeared out nonlocally. In that sense, nonlocal response is stronger for transverse and scalar nonlocal response models, where the smeared-out fractions are 2/3 and 3/3, respectively. The latter two models seem to predict novel plasmonic resonances also below the plasma frequency, in contrast to the hydrodynamic model that predicts standing pressure waves only above the plasma frequency.
NASA Astrophysics Data System (ADS)
Bakhshi Khaniki, H.; Hosseini-Hashemi, Sh
2017-06-01
This paper presents the buckling behavior of tapered small-scale beams in the framework of nonlocal strain gradient theory. Three different types of cross-sectional variation are proposed—width variation, thickness variation and a combination of both. The Euler-Bernoulli beam model, nonlocal strain gradient theory and Hamilton’s principle are employed to achieve the governing equations of small-scale beams. A generalized differential quadrature method is used to solve the governing equations for all three nonuniformity models. In order to comprehend the influence of a nonuniform cross section, a parametric study is presented and the effects of strain gradient, nonlocal elasticity and all three types of nonuniformity on the critical buckling load are presented. It is shown that such nonuniformities have a significant effect on the buckling behavior of small-scale beams. Accordingly, with the wide application of tapered small-scale beams in many devices, this study could be a step forward in understanding, predicting and controlling such behaviors.
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Dabbagh, Ali
2017-02-01
Main object of the present research is an exact investigation of wave propagation responses of smart rotating magneto-electro-elastic (MEE) graded nanoscale plates. In addition, effective material properties of functionally graded (FG) nanoplate are presumed to be calculated using the power-law formulations. Also, it has been tried to cover both softening and stiffness-hardening behaviors of nanostructures by the means of employing nonlocal strain gradient theory (NSGT). Due to increasing the accuracy of the presented model in predicting shear deformation effects, a refined higher-order plate theory is introduced. In order to cover the most enormous circumstances, maximum amount of load generated by plate’s rotation is considered. Furthermore, utilizing a developed form of Hamilton’s principle, containing magneto-electric effects, the nonlocal governing equations of MEE-FG rotating nanoplates are derived. An analytical solution is obtained to solve the governing equations and validity of the solution method is proven by comparing results from present method with those of former attempts. At last, outcomes are plotted in the framework of some figures to show the influences of various parameters such as wave number, nonlocality, length scale parameter, magnetic potential, electric voltage, gradient index and angular velocity on wave frequency, phase velocity and escape frequency of the examined nanoplate.
Nonlocal effect on optic spectrum of a periodic dielectric-metal stack.
Paredes-Juárez, Alejandro; Iakushev, Denis A; Flores-Desirena, Benito; Makarov, Nykolay M; Pérez-Rodríguez, Felipe
2014-04-07
On the basis of the formalism of the Boltzmann kinetic equation for the distribution function of the conduction electrons, the photonic band structure of binary dielectric-metal superlattice is theoretically studied. Using the constitutive nonlocal relation between the electrical current density and the electric field inside the metallic layer, the dispersion equation for photonic eigenmodes in the periodic stack is analytically expressed in terms of the surface impedances at the interfaces of the metal and dielectric layers. In the case of very thin metallic layers, the optic spectrum for the superlattice exhibits narrow pass bands as a result of the strong contrast between the impedances of the dielectric and the metal. The narrow pass bands are attributed to Fabry-Perot resonances in the relatively-thick dielectric layer. The metal nonlocality is well pronounced in the infrared and, therefore, the nonlocal effect upon the photonic band structure of the superlattice can be strong when the Fabry-Perot resonance bands are in that frequency range. Our results for the photonic spectrum have been compared with those obtained within the local Drude-Lorentz model. Noticeably differences not only in the the magnitude, but also in the sign of the real part of the Bloch wave number in the Fabry-Perot resonance bands, have been found.
On computing the trace of the kernel of the homogeneous Fredholm's equation
Velazquez-Arcos, J. M.; Vargas, C. A.; Fernandez-Chapou, J. L.; Salas-Brito, A. L.
2008-10-15
A method for computing the trace of the kernel of the homogeneous Fredholm's equation for resonant states arising from nonlocal potentials is proposed. We show that this integral formulation is convergent.
NASA Astrophysics Data System (ADS)
Dildabek, Gulnar; Orazov, Isabek
2016-08-01
In the present paper, we investigate a nonlocal boundary problem for the Laplace equation in a half-disk, with opposite flows at the part of the boundary. The difference of this problem is the impossibility of direct applying of the Fourier method (separation of variables). Because the corresponding spectral problem for the ordinary differential equation has the system of eigenfunctions not forming a basis. A special system of functions based on these eigenfunctions is constructed. This system has already formed the basis. This new basis is used for solving the nonlocal boundary value problem. The existence and the uniqueness of the classical solution of the problem are proved.
Shock Waves Propagation in Scope of the Nonlocal Theory of Dynamical Plasticity
NASA Astrophysics Data System (ADS)
Khantuleva, Tatyana A.
2004-07-01
From the point of view of the modern statistical mechanics the problems on shock compression of solids require a reformulation in terms of highly nonequilibrium effects arising inside the wave front. The self-organization during the multiscale and multistage momentum and energy exchange are originated by the correlation function. The theory of dynamic plasticity has been developed by the author on the base of the self-consistent nonlocal hydrodynamic approach had been applied to the shock wave propagation in solids. Nonlocal balance equations describe both the reversible wave type transport at the initial stage and the diffusive (dissipative) one in the end. The involved inverse influence of the mesoeffects on the wave propagation makes the formulation of problems self-consistent and involves a concept of the cybernetic control close-loop.
Vibration analysis of single-walled carbon peapods based on nonlocal Timoshenko beam theory
NASA Astrophysics Data System (ADS)
Ghadiri, Majid; Hajbarati, Hamid; Safi, Mohsen
2017-04-01
In this article, vibration behavior of single-walled carbon nanotube encapsulating C60 molecules is studied using the Eringen's nonlocal elasticity theory within the frame work of Timoshenko beam theory. The governing equation and boundary conditions are derived using Hamilton's principle. It is considered that the nanopeapod is embedded in an elastic medium and the C60 molecules are modeled as lumped masses attached to the nanobeam. The Galerkin's method is applied to determine the natural frequency of the nanobeam with clamped-clamped boundary conditions. Effects of nonlocality, foundation stiffness, and ratio of the fullerenes' mass to the nanotube's mass on the natural frequencies are investigated. In addition, by vanishing effects of shear deformation and rotary inertia, the results based on Euler-Bernoulli beam theory are presented.
NASA Astrophysics Data System (ADS)
Del Sorbo, D.; Feugeas, J.-L.; Nicolaï, Ph.; Olazabal-Loumé, M.; Dubroca, B.; Guisset, S.; Touati, M.; Tikhonchuk, V.
2015-08-01
Hydrodynamic simulations of high-energy-density plasmas require a detailed description of energy fluxes. For low and intermediate atomic number materials, the leading mechanism is the electron transport, which may be a nonlocal phenomenon requiring a kinetic modeling. In this paper, we present and test the results of a nonlocal model based on the first angular moments of a simplified Fokker-Planck equation. This multidimensional model is closed thanks to an entropic relation (the Boltzman H-theorem). It provides a better description of the electron distribution function, thus enabling studies of small scale kinetic effects within the hydrodynamic framework. Examples of instabilities of electron plasma and ion-acoustic waves, driven by the heat flux, are presented and compared with the classical formula.
Non-local Effects in a Stratified Glow Discharge With Dusty Particles
Sukhinin, G. I.; Fedoseev, A. V.; Ramazanov, T. S.; Amangaliyeva, R. Zh.; Dosbolayev, M. K.; Jumabekov, A. N.
2008-09-07
The work is aimed to describe non-local effects in the positive column of a low pressure stratified DC glow discharge in argon with dusty particles in a vertical cylindrical discharge tube. The numerical calculations of plasma parameters in the axis of the discharge tube were performed with the help of hybrid model based on the solution of non-local Boltzmann equation for EEDF. Distributions of optical emission from striations were measured experimentally. It is shown that in a stratified positive column the EEDF is not Maxwellian and even non-monotonous. Also, the effect of displacing of optical emission distribution relative to the electric field is shown both by numerical simulation and experimental measurements.
Strong nonlocal coupling stabilizes localized structures: an analysis based on front dynamics.
Fernandez-Oto, C; Clerc, M G; Escaff, D; Tlidi, M
2013-04-26
We investigate the effect of strong nonlocal coupling in bistable spatially extended systems by using a Lorentzian-like kernel. This effect through front interaction drastically alters the space-time dynamics of bistable systems by stabilizing localized structures in one and two dimensions, and by affecting the kinetics law governing their behavior with respect to weak nonlocal and local coupling. We derive an analytical formula for the front interaction law and show that the kinetics governing the formation of localized structures obeys a law inversely proportional to their size to some power. To illustrate this mechanism, we consider two systems, the Nagumo model describing population dynamics and nonlinear optics model describing a ring cavity filled with a left-handed material. Numerical solutions of the governing equations are in close agreement with analytical predictions.
A hybridizable discontinuous Galerkin method for solving nonlocal optical response models
NASA Astrophysics Data System (ADS)
Li, Liang; Lanteri, Stéphane; Mortensen, N. Asger; Wubs, Martijn
2017-10-01
We propose Hybridizable Discontinuous Galerkin (HDG) methods for solving the frequency-domain Maxwell's equations coupled to the Nonlocal Hydrodynamic Drude (NHD) and Generalized Nonlocal Optical Response (GNOR) models, which are employed to describe the optical properties of nano-plasmonic scatterers and waveguides. Brief derivations for both the NHD model and the GNOR model are presented. The formulations of the HDG method for the 2D TM mode are given, in which we introduce two hybrid variables living only on the skeleton of the mesh. The local field solutions are expressed in terms of the hybrid variables in each element. Two conservativity conditions are globally enforced to make the problem solvable and to guarantee the continuity of the tangential component of the electric field and the normal component of the current density. Numerical results show that the proposed HDG methods converge at optimal rate. We benchmark our implementation and demonstrate that the HDG method has the potential to solve complex nanophotonic problems.
Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models
NASA Astrophysics Data System (ADS)
Ma, Li-Hong; Ke, Liao-Liang; Wang, Yi-Ze; Wang, Yue-Sheng
2017-02-01
This paper makes the first attempt to investigate the dispersion behavior of waves in magneto-electro-elastic (MEE) nanobeams. The Euler nanobeam model and Timoshenko nanobeam model are developed in the formulation based on the nonlocal theory. By using the Hamilton's principle, we derive the governing equations which are then solved analytically to obtain the dispersion relations of MEE nanobeams. Results are presented to highlight the influences of the thermo-electro-magnetic loadings and nonlocal parameter on the wave propagation characteristics of MEE nanobeams. It is found that the thermo-electro-magnetic loadings can lead to the occurrence of the cut-off wave number below which the wave can't propagate in MEE nanobeams.
Free vibrations of a cantilevered SWCNT with distributed mass in the presence of nonlocal effect.
De Rosa, M A; Lippiello, M; Martin, H D
2015-01-01
The Hamilton principle is applied to deduce the free vibration frequencies of a cantilever single-walled carbon nanotube (SWCNT) in the presence of an added mass, which can be distributed along an arbitrary part of the span. The nonlocal elasticity theory by Eringen has been employed, in order to take into account the nanoscale effects. An exact formulation leads to the equations of motion, which can be solved to give the frequencies and the corresponding vibration modes. Moreover, two approximate semianalytical methods are also illustrated, which can provide quick parametric relationships. From a more practical point of view, the problem of detecting the mass of the attached particle has been solved by calculating the relative frequency shift due to the presence of the added mass: from it, the mass value can be easily deduced. The paper ends with some numerical examples, in which the nonlocal effects are thoroughly investigated.
Del Sorbo, D.; Feugeas, J.-L.; Nicolaï, Ph.; Olazabal-Loumé, M.; Dubroca, B.; Guisset, S.; Touati, M.; Tikhonchuk, V.
2015-08-15
Hydrodynamic simulations of high-energy-density plasmas require a detailed description of energy fluxes. For low and intermediate atomic number materials, the leading mechanism is the electron transport, which may be a nonlocal phenomenon requiring a kinetic modeling. In this paper, we present and test the results of a nonlocal model based on the first angular moments of a simplified Fokker-Planck equation. This multidimensional model is closed thanks to an entropic relation (the Boltzman H-theorem). It provides a better description of the electron distribution function, thus enabling studies of small scale kinetic effects within the hydrodynamic framework. Examples of instabilities of electron plasma and ion-acoustic waves, driven by the heat flux, are presented and compared with the classical formula.
Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam
NASA Astrophysics Data System (ADS)
Azimi, Majid; Mirjavadi, Seyed Sajad; Shafiei, Navvab; Hamouda, A. M. S.
2017-01-01
The free vibration analysis of rotating axially functionally graded nanobeams under an in-plane nonlinear thermal loading is provided for the first time in this paper. The formulations are based on Timoshenko beam theory through Hamilton's principle. The small-scale effect has been considered using the nonlocal Eringen's elasticity theory. Then, the governing equations are solved by generalized differential quadrature method. It is supposed that the thermal distribution is considered as nonlinear, material properties are temperature dependent, and the power-law form is the basis of the variation of the material properties through the axial of beam. Free vibration frequencies obtained are cantilever type of boundary conditions. Presented numerical results are validated by comparing the obtained results with the published results in the literature. The influences of the nonlocal small-scale parameter, angular velocity, hub radius, FG index and also thermal effects on the frequencies of the FG nanobeams are investigated in detail.
Envelope Inflation or Stellar Wind?
NASA Astrophysics Data System (ADS)
Ro, S.; Matzner, C. D.
We an optically-thick, transonic, steady wind model for a H-free Wolf-Rayet star. A bifurcation is found across a critical mass loss rate Mb. Slower winds M < Mb extend by several hydrostatic stellar radii, reproduce features of envelope in ation from Petrovic et al. (2006) and Gräfener et al. (2012), and are energetically unbound. This work is of particular interest for extended envelopes and winds, radiative hydrodynamic instabilities (eg. wind stagnation, clumping, etc.), and NLTE atmospheric models.
Personnel occupied woven envelope robot
NASA Technical Reports Server (NTRS)
Wessling, F. C.
1986-01-01
The use of nonmetallic or fabric structures for space application is considered. The following structures are suggested: (1) unpressurized space hangars; (2) extendable tunnels for soft docking; and (3) manned habitat for space stations, storage facilities, and work structures. The uses of the tunnel as a passageway: for personnel and equipment, eliminating extravehicular activity, for access to a control cabin on a space crane and between free flyers and the space station are outlined. The personnal occupied woven envelope robot (POWER) device is shown. The woven envelope (tunnel) acts as part of the boom of a crane. Potential applications of POWER are outlined. Several possible deflection mechanisms and design criteria are determined.
Carbon chemistry of circumstellar envelopes
NASA Technical Reports Server (NTRS)
Bieging, John H.
1990-01-01
The chemical composition of envelopes surrounding cool evolved stars, as determined from microwave spectroscopic observations, is reviewed. Emphasis is placed on recent observations with the new large mm-wavelength telescopes and interferometer arrays, and on new theoretical work, especially concerning ion-molecule chemistry of carbon-bearing in these envelopes. Thermal (as opposed to maser) emission lines are discussed. Much progress has been made in the past few years in the theoretical understanding of these objects. It is already clear, however, that observations with the new generation of mm-telescopes will require substantial improvements in the theoretical models to achieve a thorough understanding of the data now becoming available.
Bifurcations in Kuramoto-Sivashinsky equations
NASA Astrophysics Data System (ADS)
Kashchenko, S. A.
2017-07-01
We consider the local dynamics of the classical Kuramoto-Sivashinsky equation and its generalizations and study the problem of the existence and asymptotic behavior of periodic solutions and tori. The most interesting results are obtained in the so-called infinite-dimensional critical cases. Considering these cases, we construct special nonlinear partial differential equations that play the role of normal forms and whose nonlocal dynamics thus determine the behavior of solutions of the original boundary value problem.
Non-local geometry inside Lifshitz horizon
NASA Astrophysics Data System (ADS)
Hu, Qi; Lee, Sung-Sik
2017-07-01
Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U( N ) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.
Nonlocal polarization interferometer for entanglement detection
Williams, Brian P.; Humble, Travis S.; Grice, Warren P.
2014-10-30
We report a nonlocal interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer's unique correlation dependence on the antidiagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. The interferometer consists of two spatially separated balanced Mach-Zehnder or Sagnac interferometers that share a polarization-entangled source. Correlations between these interferometers exhibit nonlocal interference, while single-photon interference is suppressed. This interferometer also allows for a unique version of the Clauser-Horne-Shimony-Holt Bell test where the local reality is the photon polarization. In conclusion, we present the relevant theory and experimental results.
Nonlocal neurology: beyond localization to holonomy.
Globus, G G; O'Carroll, C P
2010-11-01
The concept of local pathology has long served neurology admirably. Relevant models include self-organizing nonlinear brain dynamics, global workspace and dynamic core theories. However such models are inconsistent with certain clinical phenomena found in Charles Bonnet syndrome, disjunctive agnosia and schizophrenia, where there is disunity of content within the unity of consciousness. This is contrasted with the split-brain case where there is disunity of content and disunity of consciousnesses. The development of quantum brain theory with it nonlocal mechanisms under the law of the whole ("holonomy") offers new possibilities for explaining disintegration within unity. Dissipative quantum brain dynamics and its approach to the binding problem, memory and consciousness are presented. A nonlocal neurology armed with a holonomic understanding might see more deeply into what clinical neurology has always aspired to: the patient as a whole. Copyright © 2010 Elsevier Ltd. All rights reserved.
Nonlocal polarization interferometer for entanglement detection
Williams, Brian P.; Humble, Travis S.; Grice, Warren P.
2014-10-30
We report a nonlocal interferometer capable of detecting entanglement and identifying Bell states statistically. This is possible due to the interferometer's unique correlation dependence on the antidiagonal elements of the density matrix, which have distinct bounds for separable states and unique values for the four Bell states. The interferometer consists of two spatially separated balanced Mach-Zehnder or Sagnac interferometers that share a polarization-entangled source. Correlations between these interferometers exhibit nonlocal interference, while single-photon interference is suppressed. This interferometer also allows for a unique version of the Clauser-Horne-Shimony-Holt Bell test where the local reality is the photon polarization. In conclusion, wemore » present the relevant theory and experimental results.« less
Affine Non-Local Means Image Denoising.
Fedorov, Vadim; Ballester, Coloma
2017-05-01
This paper presents an extension of the Non-Local Means denoising method, that effectively exploits the affine invariant self-similarities present in the images of real scenes. Our method provides a better image denoising result by grounding on the fact that in many occasions similar patches exist in the image but have undergone a transformation. The proposal uses an affine invariant patch similarity measure that performs an appropriate patch comparison by automatically and intrinsically adapting the size and shape of the patches. As a result, more similar patches are found and appropriately used. We show that this image denoising method achieves top-tier performance in terms of PSNR, outperforming consistently the results of the regular Non-Local Means, and that it provides state-of-the-art qualitative results.
Absolute nonlocality via distributed computing without communication
NASA Astrophysics Data System (ADS)
Czekaj, Ł.; Pawłowski, M.; Vértesi, T.; Grudka, A.; Horodecki, M.; Horodecki, R.
2015-09-01
Understanding the role that quantum entanglement plays as a resource in various information processing tasks is one of the crucial goals of quantum information theory. Here we propose an alternative perspective for studying quantum entanglement: distributed computation of functions without communication between nodes. To formalize this approach, we propose identity games. Surprisingly, despite no signaling, we obtain that nonlocal quantum strategies beat classical ones in terms of winning probability for identity games originating from certain bipartite and multipartite functions. Moreover we show that, for a majority of functions, access to general nonsignaling resources boosts success probability two times in comparison to classical ones for a number of large enough outputs. Because there are no constraints on the inputs and no processing of the outputs in the identity games, they detect very strong types of correlations: absolute nonlocality.
EPR paradox, quantum nonlocality and physical reality
NASA Astrophysics Data System (ADS)
Kupczynski, M.
2016-03-01
Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced
Nonlocality Induces Chains of Nested Dissipative Solitons.
Javaloyes, J; Marconi, M; Giudici, M
2017-07-21
Dissipative solitons often behave as quasiparticles, and they may form molecules characterized by well-defined bond distances. We show that pointwise nonlocality may lead to a new kind of molecule where bonds are not rigid. The elements of this molecule can shift mutually one with respect to the others while remaining linked together, in a manner similar to interlaced rings in a chain. We report experimental observations of these chains of nested dissipative solitons in a time-delayed laser system.
Nonlocality Induces Chains of Nested Dissipative Solitons
NASA Astrophysics Data System (ADS)
Javaloyes, J.; Marconi, M.; Giudici, M.
2017-07-01
Dissipative solitons often behave as quasiparticles, and they may form molecules characterized by well-defined bond distances. We show that pointwise nonlocality may lead to a new kind of molecule where bonds are not rigid. The elements of this molecule can shift mutually one with respect to the others while remaining linked together, in a manner similar to interlaced rings in a chain. We report experimental observations of these chains of nested dissipative solitons in a time-delayed laser system.
Switching non-local vector median filter
NASA Astrophysics Data System (ADS)
Matsuoka, Jyohei; Koga, Takanori; Suetake, Noriaki; Uchino, Eiji
2016-04-01
This paper describes a novel image filtering method that removes random-valued impulse noise superimposed on a natural color image. In impulse noise removal, it is essential to employ a switching-type filtering method, as used in the well-known switching median filter, to preserve the detail of an original image with good quality. In color image filtering, it is generally preferable to deal with the red (R), green (G), and blue (B) components of each pixel of a color image as elements of a vectorized signal, as in the well-known vector median filter, rather than as component-wise signals to prevent a color shift after filtering. By taking these fundamentals into consideration, we propose a switching-type vector median filter with non-local processing that mainly consists of a noise detector and a noise removal filter. Concretely, we propose a noise detector that proactively detects noise-corrupted pixels by focusing attention on the isolation tendencies of pixels of interest not in an input image but in difference images between RGB components. Furthermore, as the noise removal filter, we propose an extended version of the non-local median filter, we proposed previously for grayscale image processing, named the non-local vector median filter, which is designed for color image processing. The proposed method realizes a superior balance between the preservation of detail and impulse noise removal by proactive noise detection and non-local switching vector median filtering, respectively. The effectiveness and validity of the proposed method are verified in a series of experiments using natural color images.
Pattern formation in a model of competing populations with nonlocal interactions
NASA Astrophysics Data System (ADS)
Segal, B. L.; Volpert, V. A.; Bayliss, A.
2013-06-01
We analyze and compute an extension of a previously developed population model based on the well-known diffusive logistic equation with nonlocal interaction, to a system involving competing species. Our model involves a system of nonlinear integro-differential equations, with the nonlocal interaction characterized by convolution integrals of the population densities against specified kernel functions. The extent of the nonlocal coupling is characterized by a parameter δ so that when δ→0 the problem becomes local. We consider critical points of the model, i.e., spatially homogeneous equilibrium solutions. There is generally one critical point in the first quadrant (i.e., both population densities positive), denoting coexistence of the two species. We show that this solution can be destabilized by the nonlocal coupling and obtain general conditions for stability of this critical point as a function of δ, the specific kernel function and parameters of the model. We study the nonlinear behavior of the model and show that the populations can evolve to localized cells, or islands. We find that the stability transition is supercritical. Near the stability boundary solutions are small amplitude, nearly sinusoidal oscillations, however, when δ increases large amplitude, nonlinear states are found. We find a multiplicity of stable, steady state patterns. We further show that with a stepfunction kernel function the structure of these islands, a highly nonlinear phenomenon, can be described analytically. Finally, we analyze the role of the kernel function and show that for some choices of kernel function the resulting population islands can exhibit tip-splitting behavior and island amplitude modulation.
Continuous time random walks for non-local radial solute transport
NASA Astrophysics Data System (ADS)
Dentz, Marco; Kang, Peter K.; Le Borgne, Tanguy
2015-08-01
This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer
Connection between Bell nonlocality and Bayesian game theory.
Brunner, Nicolas; Linden, Noah
2013-01-01
In 1964, Bell discovered that quantum mechanics is a nonlocal theory. Three years later, in a seemingly unconnected development, Harsanyi introduced the concept of Bayesian games. Here we show that, in fact, there is a deep connection between Bell nonlocality and Bayesian games, and that the same concepts appear in both fields. This link offers interesting possibilities for Bayesian games, namely of allowing the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signalling boxes. This will lead to novel joint strategies, impossible to achieve classically. We characterize games for which nonlocal resources offer a genuine advantage over classical ones. Moreover, some of these strategies represent equilibrium points, leading to the notion of quantum/no-signalling Nash equilibrium. Finally, we describe new types of question in the study of nonlocality, namely the consideration of nonlocal advantage given a set of Bell expressions.
Gap solitons under competing local and nonlocal nonlinearities
NASA Astrophysics Data System (ADS)
Kuo, Kuan-Hsien; Lin, Yuanyao; Lee, Ray-Kuang; Malomed, Boris A.
2011-05-01
We analyze the existence, bifurcations, and shape transformations of one-dimensional gap solitons (GSs) in the first finite band gap induced by a periodic potential built into materials with local self-focusing and nonlocal self-defocusing nonlinearities. Originally stable on-site GS modes become unstable near the upper edge of the band gap with the introduction of the nonlocal self-defocusing nonlinearity with a small nonlocality radius. Unstable off-site GSs bifurcate into a new branch featuring single-humped, double-humped, and flat-top modes due to the competition between local and nonlocal nonlinearities. The mechanism underlying the complex bifurcation pattern and cutoff effects (termination of some bifurcation branches) is illustrated in terms of the shape transformation under the action of the varying degree of the nonlocality. The results of this work suggest a possibility of optical-signal processing by means of the competing nonlocal and local nonlinearities.
Nonlocal transport in dual-gated bilayer graphene
NASA Astrophysics Data System (ADS)
Shimazaki, Yuya; Yamamoto, Michihisa; Watanabe, Kenji; Taniguchi, Takashi; Tarucha, Seigo
2014-03-01
We report nonlocal transport measurement of biased bilayer graphene. Dual gated bilayer graphene Hall bars sandwiched between two h-BN insulating layers were prepared using the transfer technique with PMMA thin flims. We measured both local and non-local transport at temperatures between 1.5 K and 200 K. We found enhancement of the nonlocal resistance near the charge neutrality point when we increase the perpendicular electric field. Observed nonlocal resistance at 70K is much larger than what is expected as the Ohmic contribution from van der Pauw formula with measured local resistivity. This observation indicates additional contribution to the nonlocal transport in biased bilayer graphene. We present temperature and displacement field dependence of the nonlocal resistance and discuss its origin in terms of valley Hall effect and transport through disordered edge states.
NON-LOCALITY OF HYDRODYNAMIC AND MAGNETOHYDRODYNAMIC TURBULENCE
Cho, Jungyeon
2010-12-20
We compare non-locality of interactions between different scales in hydrodynamic (HD) turbulence and magnetohydrodynamic (MHD) turbulence in a strongly magnetized medium. We use three-dimensional incompressible direct numerical simulations to evaluate non-locality of interactions. Our results show that non-locality in MHD turbulence is much more pronounced than that in HD turbulence. Roughly speaking, non-local interactions count for more than 10% of total interactions in our MHD simulation on a grid of 512{sup 3} points. However, there is no evidence that non-local interactions are important in our HD simulation with the same numerical resolution. We briefly discuss how non-locality affects the energy spectrum.
Connection between Bell nonlocality and Bayesian game theory
NASA Astrophysics Data System (ADS)
Brunner, Nicolas; Linden, Noah
2013-07-01
In 1964, Bell discovered that quantum mechanics is a nonlocal theory. Three years later, in a seemingly unconnected development, Harsanyi introduced the concept of Bayesian games. Here we show that, in fact, there is a deep connection between Bell nonlocality and Bayesian games, and that the same concepts appear in both fields. This link offers interesting possibilities for Bayesian games, namely of allowing the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signalling boxes. This will lead to novel joint strategies, impossible to achieve classically. We characterize games for which nonlocal resources offer a genuine advantage over classical ones. Moreover, some of these strategies represent equilibrium points, leading to the notion of quantum/no-signalling Nash equilibrium. Finally, we describe new types of question in the study of nonlocality, namely the consideration of nonlocal advantage given a set of Bell expressions.
Nonlocal Gravity and Structure in the Universe
Dodelson, Scott; Park, Sohyun
2014-08-26
The observed acceleration of the Universe can be explained by modifying general relativity. One such attempt is the nonlocal model of Deser and Woodard. Here we fix the background cosmology using results from the Planck satellite and examine the predictions of nonlocal gravity for the evolution of structure in the universe, confronting the model with three tests: gravitational lensing, redshift space distortions, and the estimator of gravity $E_G$. Current data favor general relativity (GR) over nonlocal gravity: fixing primordial cosmology with the best fit parameters from Planck leads to weak lensing results favoring GR by 5.9 sigma; redshift space distortions measurements of the growth rate preferring GR by 7.8 sigma; and the single measurement of $E_G$ favoring GR, but by less than 1-sigma. The significance holds up even after the parameters are allowed to vary within Planck limits. The larger lesson is that a successful modified gravity model will likely have to suppress the growth of structure compared to general relativity.
Halo clustering with nonlocal non-Gaussianity
Schmidt, Fabian; Kamionkowski, Marc
2010-11-15
We show how the peak-background split (PBS) can be generalized to predict the effect of nonlocal primordial non-Gaussianity on the clustering of halos. Our approach is applicable to arbitrary primordial bispectra. We show that the scale dependence of halo clustering predicted in the peak-background split agrees with that of the local-biasing model on large scales. On smaller scales, k > or approx. 0.01h Mpc{sup -1}, the predictions diverge, a consequence of the assumption of separation of scales in the peak-background split. Even on large scales, PBS and local biasing do not generally agree on the amplitude of the effect outside of the high-peak limit. The scale dependence of the biasing - the effect that provides strong constraints to the local-model bispectrum - is far weaker for the equilateral and self-ordering-scalar-field models of non-Gaussianity. The bias scale dependence for the orthogonal and folded models is weaker than in the local model ({approx}k{sup -1}), but likely still strong enough to be constraining. We show that departures from scale-invariance of the primordial power spectrum may lead to order-unity corrections, relative to predictions made assuming scale-invariance--to the non-Gaussian bias in some of these nonlocal models for non-Gaussianity. An Appendix shows that a nonlocal model can produce the local-model bispectrum, a mathematical curiosity we uncovered in the course of this investigation.
Nonlocal modeling of granular flows down inclines.
Kamrin, Ken; Henann, David L
2015-01-07
Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused on driven steady-flow problems. For layers thicker than the stopping height, the theoretical flow profiles display a thickness-dependent shape whose features are in agreement with previous discrete particle simulations. We also address the issue of the Froude number of the flows, which has been shown experimentally to collapse as a function of the ratio of layer thickness to stopping height. While the collapse is not obvious, two explanations emerge leading to a revisiting of the history of inertial rheology, which the nonlocal model references for its homogeneous flow response.
Nonlocal Studies of the Magnetorotational Instability
NASA Astrophysics Data System (ADS)
Bhattacharjee, A.; Ebrahimi, F.; Lefebvre, B.; Vandenberg, A.
2010-11-01
Viewed from the perspective of nonlocal studies of plasmas with sheared flows, the magnetorotational instability (MRI) is an important member of a larger family of shear- driven instabilities in a magnetized disk. A comprehensive analytical and numerical approach to these instabilities was first developed by Hameiri (1976) and Bondeson and coworkers (1987) with applications to fusion plasmas, and more recently applied by Keppens and cooworkers (2002) to Keplerian disks. The general framework uncovers a number of new features that must be included in our understanding of the linear as well as well as nonlinear evolution of the MRI. These include (1) overstability due the presence of compressibility for non-axisymmetric modes, and (2) the presence of an infinite sequence of discrete unstable modes accumulating toward the edge of the slow wave continuum at the Doppler-shifted frequency, regardless of the pressure gradient. For linear studies of these nonlocal instabilities, we present numerical results from a linear eignemode solver, and compare the predictions with NIMROD. We then use NIMROD to examine the consequences of these nonlocal instabilities for the nonlinear evolution of the MRI, where coupling to non-axisymmetric modes has already been shown to play an important role in the saturation of the instability.
On the Nonlocality of the Coulomb Gauge External Field Problem
NASA Astrophysics Data System (ADS)
Hraskó, Péter
The apparent nonlocality of the Coulomb gauge external field problem in electrodynamics is illustrated with an example in which nonlocality is especially striking. Explanation of this apparent nonlocal behaviour based on a purely local picture is given. A gauge invariant decomposition of the Lorentz-force into two terms with clear physical meanings is pointed out. Based on this decomposition derivation of the Aharonov-Bohm effect in terms of field strengths alone is given.
On the nonlocality of the Coulomb gauge external field problem
NASA Astrophysics Data System (ADS)
Hraskó, Péter
2016-10-01
The apparent nonlocality of the Coulomb gauge external field problem in electrodynamics is illustrated with an example in which nonlocality is especially striking. Explanation of this apparent nonlocal behaviour based on a purely local picture is given. A gauge invariant decomposition of the Lorentz-force into two terms with clear physical meanings is pointed out. Based on this decomposition derivation of the Aharonov-Bohm effect in terms of field strengths alone is given.
Exact solutions for a coupled nonlocal model of nanobeams
Marotti de Sciarra, Francesco E-mail: raffaele.barretta@unina.it; Barretta, Raffaele E-mail: raffaele.barretta@unina.it
2014-10-06
BERNOULLI-EULER nanobeams under concentrated forces/couples with the nonlocal constitutive behavior proposed by ERINGEN do not exhibit small-scale effects. A new model obtained by coupling the ERINGEN and gradient models is formulated in the present note. A variational treatment is developed by imposing suitable thermodynamic restrictions for nonlocal models and the ensuing differential and boundary conditions of elastic equilibrium are provided. The nonlocal elastostatic problem is solved in a closed-form for nanocantilever and clamped nanobeams.
Stability of Schwarzschild singularity in non-local gravity
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo
2017-10-01
In a previous work, it was shown that all Ricci-flat spacetimes are exact solutions for a large class of non-local gravitational theories. Here we prove that, for a subclass of non-local theories, the Schwarzschild singularity is stable under linear perturbations. Thus, non-locality may be not enough to cure all the singularities of general relativity. Finally, we show that the Schwarzschild solution can be generated by the gravitational collapse of a thin shell of radiation.
Proposal for revealing quantum nonlocality via local contextuality.
Cabello, Adán
2010-06-04
Two distant systems can exhibit quantum nonlocality even though the correlations between them admit a local model. This nonlocality can be revealed by testing extra correlations between successive measurements on one of the systems which do not admit a noncontextual model whatever the reduced state of this system is. This shows that quantum contextuality plays a fundamental role in quantum nonlocality, and allows an experimental test of the Kochen-Specker with locality theorem.
Cosmological evolution of generalized non-local gravity
NASA Astrophysics Data System (ADS)
Zhang, Xue; Wu, Ya-Bo; Li, Song; Liu, Yu-Chen; Chen, Bo-Hai; Chai, Yun-Tian; Shu, Shuang
2016-07-01
We construct a class of generalized non-local gravity (GNLG) model which is the modified theory of general relativity (GR) obtained by adding a term m2n-2 R□-nR to the Einstein-Hilbert action. Concretely, we not only study the gravitational equation for the GNLG model by introducing auxiliary scalar fields, but also analyse the classical stability and examine the cosmological consequences of the model for different exponent n. We find that the half of the scalar fields are always ghost-like and the exponent n must be taken even number for a stable GNLG model. Meanwhile, the model spontaneously generates three dominant phases of the evolution of the universe, and the equation of state parameters turn out to be phantom-like. Furthermore, we clarify in another way that exponent n should be even numbers by the spherically symmetric static solutions in Newtonian gauge. It is worth stressing that the results given by us can include ones in refs. [28, 34] as the special case of n=2.
Visibility to discern local from nonlocal dynamic processes
NASA Astrophysics Data System (ADS)
Brú, A.; Gómez-Castro, D.; Nuño, J. C.
2017-04-01
We compare using visibility the usual Kardar-Parisi-Zhang (KPZ) universality class and a fractional Edward-Wilkinson (EWf) equation with correlated noise, which share the same kinetic roughening exponents. The KPZ universality class is described by an equation in terms of the usual derivatives, uncorrelated noise and therefore is intrinsically local. The second model includes fractional powers of the Laplace operator and correlated noise, both of which are nonlocal. From their scaling properties, one could be tempted to conclude that both dynamics belong to the same universality class, specifically, to the KPZ universality class. However, this is a wrong conclusion that calls the attention against the indiscriminate application of this approach in real systems without taking into consideration basic physical assumptions (e.g. locality). These examples reveal the necessity of finding new algorithms for detecting characteristics that remain unnoticed to classical scaling analysis, where only the two first moments of the interface distribution (mean and variance) are used to classify the dynamics. We show that visibility and, in particular, the kinetic roughening exponents of the visibility interface, are able to distinguish between these two dynamics which are confused by standard techniques.
Nonuniform dynamic gratings in photorefractive media with nonlocal response.
Bugaychuk, S; Kovács, L; Mandula, G; Polgár, K; Rupp, R A
2003-04-01
The amplitude of the phase dynamic grating is a nonuniform space distributed in photorefractive crystals with nonlocal response as a result of energy transfer between the interacted waves. The dynamical process of grating formation in the case of transmission two- and four-wave mixing is described by the damped sine-Gordon equation that governs the soliton propagation. A stationary soliton solution for the grating amplitude profile was obtained. Experiments on observation of a nonuniform distribution of the grating amplitude through the crystal volume are presented. It is experimentally shown that the changes of the grating amplitude profile in dependence of input intensity ratio match the solutions of the damped sine-Gordon equation in steady state. The diffraction efficiency of energy transfer is determined by the value of the integral under the grating amplitude profile. The soliton profile is altered with changing input intensity ratio of recorded beams. It provides the effect of diffraction efficiency management by changing the half-width and the position of the soliton. The theory predicts a multisoliton behavior in reversible media with strong amplification gain that leads to auto-oscillations of output wave intensities.
Survey on nonlocal games and operator space theory
Palazuelos, Carlos; Vidick, Thomas
2016-01-15
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Circumferential nonlocal effect on the buckling and vibration of nanotubes
NASA Astrophysics Data System (ADS)
Wang, Cheng Yuan; Li, Xiao Hu; Luo, Ying
2016-04-01
The nonlocal beam theories are widely used to study the mechanics of cylindrical nanotubes (NTs). The one-dimensional models however are unable to account for the nonlocal effect in the circumferential direction, which may substantially affect the applicability of the nonlocal beam models. To address the issue this letter examines the circumferential nonlocal effect (CNE) on the buckling and vibration of the NTs. Here the CNE is characterized by the difference between the nonlocal beam model considering the axial nonlocal effect only and the nonlocal shell model with both axial and circumferential nonlocal effects. The aspect ratio and radius-dependence of the CNE are calculated for the singlewall carbon NTs selected as a typical example. The results show that the CNE is substantial for the buckling and vibration of the NTs with small radius (e.g., <1 nm) and aspect ratio (e.g., <15). It however decreases with the rising radius and the aspect ratio, and turns out to be small for relatively wide and long NTs. The nonlocal beam theories thus may overestimate the buckling load and vibration frequency for the thin and short NTs.
The uncertainty principle determines the nonlocality of quantum mechanics.
Oppenheim, Jonathan; Wehner, Stephanie
2010-11-19
Two central concepts of quantum mechanics are Heisenberg's uncertainty principle and a subtle form of nonlocality that Einstein famously called "spooky action at a distance." These two fundamental features have thus far been distinct concepts. We show that they are inextricably and quantitatively linked: Quantum mechanics cannot be more nonlocal with measurements that respect the uncertainty principle. In fact, the link between uncertainty and nonlocality holds for all physical theories. More specifically, the degree of nonlocality of any theory is determined by two factors: the strength of the uncertainty principle and the strength of a property called "steering," which determines which states can be prepared at one location given a measurement at another.
Nonlocal optical properties in periodic lattice of graphene layers.
Chern, Ruey-Lin; Han, Dezhuan
2014-02-24
Based on the effective medium model, nonlocal optical properties in periodic lattice of graphene layers with the period much less than the wavelength are investigated. Strong nonlocal effects are found in a broad frequency range for TM polarization, where the effective permittivity tensor exhibits the Lorentzian resonance. The resonance frequency varies with the wave vector and coincides well with the polaritonic mode. Nonlocal features are manifest on the emergence of additional wave and the occurrence of negative refraction. By examining the characters of the eigenmode, the nonlocal optical properties are attributed to the excitation of plasmons on the graphene surfaces.
Enhanced soliton interactions by inhomogeneous nonlocality and nonlinearity
Ye, Fangwei; Kartashov, Yaroslav V.; Torner, Lluis
2007-09-15
We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a strongly nonlocal nonlinear response. We reveal that the variation of the nonlocality and nonlinearity along the propagation direction can substantially enhance or weaken the interaction between out-of-phase solitons. This phenomenon manifests itself as a slowdown or acceleration of the soliton collision dynamics in one-dimensional geometries or of the soliton spiraling rate in bulk media. Therefore, one finds that by engineering the nonlocality and nonlinearity variation rate one can control the output soliton location.
Nonlocality without inequality for spin-s systems
Kunkri, Samir; Choudhary, Sujit K.
2005-08-15
We critically review earlier works on Hardy's nonlocality argument for two spin-s systems and show that solutions previously found in this regard were restricted due to imposition of some conditions which have no role in the argument of nonlocality. We provide a compact form of the nonlocality condition for two spin-s particles, and we also extend it to n number of spin-s particles. Finally we apply a more general kind of nonlocality argument, still without an inequality, to higher-spin systems.
Survey on nonlocal games and operator space theory
NASA Astrophysics Data System (ADS)
Palazuelos, Carlos; Vidick, Thomas
2016-01-01
This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.
Heuristic theory of nonlocally broken gyro-Bohm scaling
Waltz, R.E.; Candy, J.
2005-07-15
Global gyrokinetic simulations of ion temperature gradient turbulent transport with piecewise-flat profiles are given to illustrate the breaking of gyro-Bohm scaling by a nonlocal mechanism. The nonlocal drainage of the turbulence from unstable regions spreading into stable (or less unstable) regions breaks the gyro-Bohm scaling toward Bohm in unstable regions and toward super-gyro-Bohm in stable (or less unstable) regions. A heuristic model for this nonlocal process is formulated in terms of a nonlocal growth rate resulting from a locally weighted radial average of the local linear ballooning mode growth rate. A nonlocality length L measured in ion gyroradii provides the exponential scale for the local weighting. The nonlocal growth rate can be incorporated into a local gyro-Bohm-scaled transport model in place of the local growth rate. The resulting nonlocal transport model will provide some transport in stable regions. A heuristic theory of this nonlocal transport mechanism based on the partial formation of global modes in toroidal geometry is detailed. The theory argues that the nonlocality length L increases with relative gyroradius and decreases with the linear growth rate.
Nonlocal effects on dynamic damage accumulation in brittle solids
Chen, E.P.
1995-12-01
This paper presents a nonlocal analysis of the dynamic damage accumulation processes in brittle solids. A nonlocal formulation of a microcrack based continuum damage model is developed and implemented into a transient dynamic finite element computer code. The code is then applied to the study of the damage accumulation process in a concrete plate with a central hole and subjected to the action of a step tensile pulse applied at opposite edges of the plate. Several finite element discretizations are used to examine the mesh size effect. Comparisons between calculated results based on local and nonlocal formulations are made and nonlocal effects are discussed.
Knobles, D P; Sagers, J D
2011-11-01
In an acoustic waveguide spatial inhomogeneities couple the forward and backward propagating modal amplitudes. To address the nature of such coupling the integral equation for the range-dependent modal amplitudes is decomposed into components that satisfy the asymptotic boundary conditions of the free Green's function operator. An equivalent set of equations is obtained by eliminating the components that become the asymptotically backward propagating channels to leave a set of integral equations that describe only the components that become asymptotically the forward propagating channels. The elimination of the components that become asymptotically the backward propagating channels is done at the expense of introducing a nonlocal effective coupling operator. The nonlocal operator contains all the effects of the asymptotically backward propagating field on the asymptotically forward propagating field. An expansion of the effective coupling operator allows an investigation of the importance of the coupling and provides a systematic approach to add correction terms to the forward only equation. Idealistic underwater waveguides with various degrees of inhomogeneities are used to illustrate the main features of the convergence characteristics for the expansion.
The equation of state for stellar envelopes. III - Thermodynamic quantities
NASA Technical Reports Server (NTRS)
Daeppen, Werner; Mihalas, Dimitri; Hummer, D. G.; Mihalas, Barbara Weibel
1988-01-01
A method is described for deriving general expressions for all thermodynamic quantities of interest of a partially ionized multicomponent gas in terms of derivatives of the free energy. Explicit analytical formulas for all derivatives required in the evaluation of these quantities are given. Representative results for a hydrogen-helium mixture are shown.
Non-local Second Order Closure Scheme for Boundary Layer Turbulence and Convection
NASA Astrophysics Data System (ADS)
Meyer, Bettina; Schneider, Tapio
2017-04-01
There has been scientific consensus that the uncertainty in the cloud feedback remains the largest source of uncertainty in the prediction of climate parameters like climate sensitivity. To narrow down this uncertainty, not only a better physical understanding of cloud and boundary layer processes is required, but specifically the representation of boundary layer processes in models has to be improved. General climate models use separate parameterisation schemes to model the different boundary layer processes like small-scale turbulence, shallow and deep convection. Small scale turbulence is usually modelled by local diffusive parameterisation schemes, which truncate the hierarchy of moment equations at first order and use second-order equations only to estimate closure parameters. In contrast, the representation of convection requires higher order statistical moments to capture their more complex structure, such as narrow updrafts in a quasi-steady environment. Truncations of moment equations at second order may lead to more accurate parameterizations. At the same time, they offer an opportunity to take spatially correlated structures (e.g., plumes) into account, which are known to be important for convective dynamics. In this project, we study the potential and limits of local and non-local second order closure schemes. A truncation of the momentum equations at second order represents the same dynamics as a quasi-linear version of the equations of motion. We study the three-dimensional quasi-linear dynamics in dry and moist convection by implementing it in a LES model (PyCLES) and compare it to a fully non-linear LES. In the quasi-linear LES, interactions among turbulent eddies are suppressed but nonlinear eddy—mean flow interactions are retained, as they are in the second order closure. In physical terms, suppressing eddy—eddy interactions amounts to suppressing, e.g., interactions among convective plumes, while retaining interactions between plumes and the
Symmetry algebras of linear differential equations
NASA Astrophysics Data System (ADS)
Shapovalov, A. V.; Shirokov, I. V.
1992-07-01
The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.
Li, Xian-Fang; Tang, Guo-Jin; Shen, Zhi-Bin; Lee, Kang Yong
2015-01-01
Free vibration and mass detection of carbon nanotube-based sensors are studied in this paper. Since the mechanical properties of carbon nanotubes possess a size effect, the nonlocal beam model is used to characterize flexural vibration of nanosensors carrying a concentrated nanoparticle, where the size effect is reflected by a nonlocal parameter. For nanocantilever or bridged sensor, frequency equations are derived when a nanoparticle is carried at the free end or the middle, respectively. Exact resonance frequencies are numerically determined for clamped-free, simply-supported, and clamped-clamped resonators. Alternative approximations of fundamental frequency are given in closed form within the relative error less than 0.4%, 0.6%, and 1.4% for cantilever, simply-supported, and bridged sensors, respectively. Mass identification formulae are derived in terms of the frequency shift. Identified masses via the present approach coincide with those using the molecular mechanics approach and reach as low as 10(-24)kg. The obtained results indicate that the nonlocal effect decreases the resonance frequency except for the fundamental frequency of nanocantilever sensor. These results are helpful to the design of micro/nanomechanical zeptogram-scale biosensor.
Modulational instability in nonlocal Kerr media with a sine-oscillatory response
NASA Astrophysics Data System (ADS)
Wang, Zhuo; Guo, Qi; Hong, Weiyi; Hu, Wei
2017-07-01
We discuss modulational instability (MI) in nonlocal optical Kerr media with a sine-oscillatory response which can model nematic liquid crystals with negative dielectric anisotropy. In the framework of nonlocal nonlinear Schrödinger equation, MI in this type of media is found to have two unique properties different from those in other media discussed previously. First, MI exists both when the Kerr coefficient is positive and when it is negative. Second, the maximum gain points of MI do not shift with light intensity. We also explore the physical mechanism behind MI in local and nonlocal optical Kerr media by utilizing the theory of four-wave mixing. Through introducing a phase mismatch term (Δk) and a growth factor (γ), we deduce that the necessary and sufficient condition for MI to occur is that the phase mismatching during the four-wave-mixing process should be small enough such that | Δk | < 2 | γ | . Based on this condition, we can uniformly and consistently explain the results of MI in optical Kerr media obtained in the current work as well as those presented in previous work by others.
Non-local magnetoelectric effects via Coulomb interaction in TI-FMI heterostructures
NASA Astrophysics Data System (ADS)
Rex, Stefan; Nogueira, Flavio S.; Sudbø, Asle
Magnetic order on the surface of a 3 D topological insulator (TI) has been predicted to evoke a topological magnetoelectric effect (TME) by the breaking of time-reversal invariance. In the TME, an electric field leads to a magnetic polarization in the same direction as the field and vice versa. Here, we consider heterostructures of TI and ferromagnetic insulator (FMI) layers. We show that in the presence of long-range Coulomb interactions the magnetization couples non-locally to the fluctuating electric field (non-local TME) by performing a field-theoretic calculation of the vacuum polarization. In addition, we obtain a Landau-Lifshitz equation for the magnetization dynamics, and find that charged magnetic textures lead to a net magnetization even at a large distance. Such textures can be induced by an external electric field with nonzero in-plane divergence. We apply this effect to a FMI-TI-FMI trilayer heterostructure with two parallel interfaces being well-separated by the bulk TI, where we propose to non-locally control the magnetic texture at one interface by proper gating of the other interface. A preprint can be found at arXiv:1510.04285 Supported by the Norwegian Research Council, Grants 205591/V20 and 216700/F20, and the Collaborative Research Center SFB 1143 ''Correlated Magnetism: From Frustration to Topology''.
Spin-Hall Non-Local Transport Mediated by a Magnetic Insulator
NASA Astrophysics Data System (ADS)
Ramezani Masir, Massoud; Chen, Hua; Sodemann, Inti; MacDonald, Allan. H.
Magnetic systems with easy-plane order support dissipationless spin supercurrents that can lead to non-local coupling between electrically separated conductors. Recently the electrical properties of a system containing two magnetic multilayer stacks with perpendicular magnetic anisotropy electrodes and a shared easy-plane magnetic layer have been discussed. In this research we discuss a closely related system in which the two conducting channels that are coupled by the easy-plane magnetic layer are co-planar thin film metals with large spin Hall effects. We theoretically explained the non-local relationship between the current-voltage relationships of two thin film metallic conductors. Coupling occurs because both conductors inject spins into the magnetic insulator and because this information is communicated between conductors via exchange interactions within the magnetic system. We investigate the non-local transport properties of the system in the macrospin and long thin nanomagnet limits, deriving conditions for the critical currents and using solutions to the Landau-Liftshitz-Gilbert equation to characterize the dynamic steady state case. This work was supported by as part of SHINES, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # SC0012670.
Advanced tests of nonlocality with entangled photons
NASA Astrophysics Data System (ADS)
Christensen, Bradley G.
In 1935, Einstein, Podolsky, and Rosen questioned whether quantum mechanics can be complete, as it seemingly does not adhere to a natural view of reality: local realism, which is the notion that an event can only be influenced by events in the past lightcone, and can only influence events in the future lightcone. This question sparked a philosophical debate that lasted for three decades, until John Bell demonstrated that not only are quantum mechanics and local realism philosophically incompatible, but they predict different statistical results for an appropriate set of measurements on entangled particles, which changed the debate to a scientific discussion. Since then, Bell inequality violations have occurred in a plethora of systems, hinting that local realism is indeed wrong. However, every experiment had imperfections that complicated the interpretation -- the experiments had so-called "loopholes" which allowed local realism to persist. In this manuscript, we present our work in using optimized sources of entangled photons to perform the long-sought loophole-free Bell test. This landmark experiment invalidates local realism to the best that science will allow. Beyond answering questions on reality, these Bell tests have a important application in generating provably-secure private random numbers, which then can be used as a seed for cryptographic applications. Not only do we demonstrate that nonlocality must exist, but we begin an experimental exploration in an attempt to understand and quantify this nonlocality. We do so by considering all theories that obey no-signaling (or relativistic causality). In our experiments, we observe the counter-intuitive feature of measuring more nonlocality with less entangled states. We also place a bound on the predictive power of any theory that obeys relativistic causality. And finally, we are able to measure quantum correlations only attainable through complex qubits. This work merely begins to probe the quantum boundary
Modeling of heat and mass transfer in lateritic building envelopes
NASA Astrophysics Data System (ADS)
Meukam, Pierre; Noumowe, Albert
2005-12-01
The aim of the present work is to investigate the behavior of building envelopes made of local lateritic soil bricks subjected to different climatic conditions. The building envelopes studied in this work consist of lateritic soil bricks with incorporation of natural pozzolan or sawdust in order to obtain small thermal conductivity and low-density materials. In order to describe coupled heat and moisture transfer in wet porous materials, the coupled equations were solved by the introduction of diffusion coefficients. A numerical model HMtrans, developed for prediction of heat and moisture transfer in multi-layered building components, was used to simulate the temperature, water content and relative humidity profiles within the building envelopes. The results allow the prediction of the duration of the exposed building walls to the local weather conditions. They show that the durability of building envelopes made of lateritic soil bricks with incorporation of natural pozzolan or sawdust is not strongly affected by the climatic conditions in tropical and equatorial areas.
On the conservation laws of Derrida-Lebowitz-Speer-Spohn equation
NASA Astrophysics Data System (ADS)
San, Sait; Yaşar, Emrullah
2015-05-01
In this study, the nonlocal conservation theorem and multiplier approach are performed on the 1 + 1 dimensional Derrida-Lebowitz-Speer-Spohn (DLSS) equation which arises in quantum semi conductor theory. We obtain local conservation laws by using the both methods. Furthermore by utilizing the relationship between conservation laws and Lie point symmetries, the DLSS equation is reduced to third order ordinary differential equation.
Lp-bounds for quasi-geostrophic equations via functional analysis
NASA Astrophysics Data System (ADS)
de la Llave, Rafael; Valdinoci, Enrico
2011-08-01
We give a proof of Lp-bounds for the quasi-geostrophic equation and other non-local equations. The proof uses mainly tools from functional analysis, notably the product formulas (also known as "operator splitting methods") and the Bochner-Pollard subordination identities, hence it could be applicable to other equations.
Relativistic three-partite non-locality
NASA Astrophysics Data System (ADS)
Moradpour, Hooman; Montakhab, Afshin
2016-05-01
Bell-like inequalities have been used in order to distinguish non-local quantum pure states by various authors. The behavior of such inequalities under Lorentz transformation (LT) has been a source of debate and controversies in the past. In this paper, we consider the two most commonly studied three-particle pure states, that of W and Greenberger-Horne-Zeilinger (GHZ) states which exhibit distinctly different types of entanglement. We discuss the various types of three-particle inequalities used in previous studies and point to their corresponding shortcomings and strengths. Our main result is that if one uses Czachor’s relativistic spin operator and Svetlichny’s inequality as the main measure of non-locality and uses the same angles in the rest frame (S) as well as the moving frame (S‧), then maximally violated inequality in S will decrease in the moving frame, and will eventually lead to lack of non-locality (i.e. satisfaction of inequality) in the v→c limit. This is shown for both the GHZ and W states and in two different configurations which are commonly studied (Cases 1 and 2). Our results are in line with a more familiar case of two particle case. We also show that the satisfaction of Svetlichny’s inequality in the v→c limit is independent of initial particles’ velocity. Our study shows that whenever we use Czachor’s relativistic spin operator, results draws a clear picture of three-particle non-locality making its general properties consistent with previous studies on two-particle systems regardless of the W state or the GHZ state is involved. Throughout the paper, we also address the results of using Pauli’s operator in investigating the behavior of |Sv| under LT for both of the GHZ and W states and two cases (Cases 1 and 2). Our investigation shows that the violation of |Sv| in moving frame depends on the particle’s energy in the lab frame, which is in agreement with some previous works on two and three-particle systems. Our work may
Some loopholes to save quantum nonlocality
NASA Astrophysics Data System (ADS)
Accardi, Luigi
2005-02-01
The EPR-chameleon experiment has closed a long standing debate between the supporters of quantum nonlocality and the thesis of quantum probability according to which the essence of the quantum pecularity is non Kolmogorovianity rather than non locality. The theory of adaptive systems (symbolized by the chameleon effect) provides a natural intuition for the emergence of non-Kolmogorovian statistics from classical deterministic dynamical systems. These developments are quickly reviewed and in conclusion some comments are introduced on recent attempts to "reconstruct history" on the lines described by Orwell in "1984".
Spectral tunneling of lattice nonlocal solitons
Kartashov, Yaroslav V.; Torner, Lluis; Vysloukh, Victor A.
2010-07-15
We address spectral tunneling of walking spatial solitons in photorefractive media with nonlocal diffusion component of the nonlinear response and an imprinted shallow optical lattice. In contrast to materials with local nonlinearities, where solitons traveling across the lattice close to the Bragg angle suffer large radiative losses, in photorefractive media with diffusion nonlinearity resulting in self-bending, solitons survive when their propagation angle approaches and even exceeds the Bragg angle. In the spatial frequency domain this effect can be considered as tunneling through the band of spatial frequencies centered around the Bragg frequency where the spatial group velocity dispersion is positive.
Safeguards Envelope Progress FY08
Robert Bean; Richard Metcalf; Aaron Bevill
2008-09-01
The Safeguards Envelope Project met its milestones by creating a rudimentary safeguards envelope, proving the value of the approach on a small scale, and determining the most appropriate path forward. The Idaho Chemical Processing Plant’s large cache of reprocessing process monitoring data, dubbed UBER Data, was recovered and used in the analysis. A probabilistic Z test was used on a Markov Monte Carlo simulation of expected diversion data when compared with normal operating data. The data regarding a fully transient event in a tank was used to create a simple requirement, representative of a safeguards envelope, whose impact was a decrease in operating efficiency by 1.3% but an increase in material balance period of 26%. This approach is operator, state, and international safeguards friendly and should be applied to future reprocessing plants. Future requirements include tank-to-tank correlations in reprocessing facilities, detailed operations impact studies, simulation inclusion, automated optimization, advanced statistics analysis, and multi-attribute utility analysis.
Heat recovery in building envelopes
Walker, Iain S.; Sherman, Max H.
2003-08-01
Infiltration has traditionally been assumed to contribute to the energy load of a building by an amount equal to the product of the infiltration flow rate and the enthalpy difference between inside and outside. Some studies have indicated that application of such a simple formula may produce an unreasonably high contribution because of heat recovery within the building envelope. The major objective of this study was to provide an improved prediction of the energy load due to infiltration by introducing a correction factor that multiplies the expression for the conventional load. This paper discusses simplified analytical modeling and CFD simulations that examine infiltration heat recovery (IHR) in an attempt to quantify the magnitude of this effect for typical building envelopes. For comparison, we will also briefly examine the results of some full-scale field measurements of IHR based on infiltration rates and energy use in real buildings. The results of this work showed that for houses with insulated walls the heat recovery is negligible due to the small fraction of the envelope that participates in heat exchange with the infiltrating air. However; there is the potential for IHR to have a significant effect for higher participation dynamic walls/ceilings or uninsulated walls. This result implies that the existing methods for evaluating infiltration related building loads provide adequate results for typical buildings.