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.
A dispersive wave equation using nonlocal elasticity
NASA Astrophysics Data System (ADS)
Challamel, Noël; Rakotomanana, Lalaonirina; Le Marrec, Loïc
2009-08-01
Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro- or nano-structures. This Note investigates a model of wave propagation in a nonlocal elastic material. We show that a dispersive wave equation is obtained from a nonlocal elastic constitutive law, based on a mixture of a local and a nonlocal strain. This model comprises both the classical gradient model and the Eringen's integral model. The dynamic properties of the model are discussed, and corroborate well some recent theoretical studies published to unify both static and dynamics gradient elasticity theories. Moreover, an excellent matching of the dispersive curve of the Born-Kármán model of lattice dynamics is obtained with such nonlocal model. To cite this article: N. Challamel et al., C. R. Mecanique 337 (2009).
Chaotic Orbits for Systems of Nonlocal Equations
NASA Astrophysics Data System (ADS)
Dipierro, Serena; Patrizi, Stefania; Valdinoci, Enrico
2016-07-01
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.
Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation
NASA Astrophysics Data System (ADS)
Jin, Yan; Jia, Man; Lou, Sen-Yue
2012-12-01
Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group invariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.
Symmetries and nonlocal conservation laws of the general magma equation
NASA Astrophysics Data System (ADS)
Khamitova, Raisa
2009-11-01
In this paper the general magma equation modelling a melt flow in the Earth's mantle is discussed. Applying the new theorem on nonlocal conservation laws [Ibragimov NH. A new conservation theorem. J Math Anal Appl 2007;333(1):311-28] and using the symmetries of the model equation nonlocal conservation laws are computed. In accordance with Ibragimov [Ibragimov NH. Quasi-self-adjoint differential equations. Preprint in Archives of ALGA, vol. 4, BTH, Karlskrona, Sweden: Alga Publications; 2007. p. 55-60, ISSN: 1652-4934] it is shown that the general magma equation is quasi-self-adjoint for arbitrary m and n and self-adjoint for n = -m. These important properties are used for deriving local conservation laws.
Solution of K-V envelope equations
Anderson, O.A.
1995-04-01
The envelope equations for a KV beam with space charge have been analyzed systematically by an e expansion followed by integrations. The focusing profile as a function of axial length is assumed to be symmetric but otherwise arbitrary. Given the bean current, emittance, and peak focusing field, we find the envelopes a(s) and b(s) and obtain , a{sub max}, {sigma}, and {sigma}{sub 0}. Explicit results are presented for various truncations of the expansion. The zeroth order results correspond to those from the well-known smooth approximation; the same convenient format is retained for the higher order cases. The first order results, involving single correction terms, give 3--10 times better accuracy and are good to {approximately}1% at {sigma}{sub 0} = 70{degree}. Third order gives a factor of 10--30 improvement over the smooth approximation and derived quantities accurate to {approximately}1% at {sigma}{sub 0} = 112 {degree}. The first order expressions are convenient design tools. They lend themselves to variable energy problems and have been applied to the design, construction, and testing of ESQ accelerators at LBL.
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.
Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation
NASA Astrophysics Data System (ADS)
Johnson, Mathew A.; Noble, Pascal; Rodrigues, L. Miguel; Zumbrun, Kevin
2013-02-01
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized modulation plus a localized ( L 1) perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist of a leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation.
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
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
Exact solutions of fractional Schroedinger-like equation with a nonlocal term
Jiang Xiaoyun; Xu Mingyu; Qi Haitao
2011-04-15
We study the time-space fractional Schroedinger equation with a nonlocal potential. By the method of Fourier transform and Laplace transform, the Green function, and hence the wave function, is expressed in terms of H-functions. Graphical analysis demonstrates that the influence of both the space-fractal parameter {alpha} and the nonlocal parameter {nu} on the fractional quantum system is strong. Indeed, the nonlocal potential may act similar to a fractional spatial derivative as well as fractional time derivative.
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.
Improved Envelope And Centroid Equations for High Current Beams
NASA Astrophysics Data System (ADS)
Genoni, Thomas C.; Hughes, Thomas P.
2002-04-01
The standard envelope equation for electron beams (e.g., Lee-Cooper), neglects self-field contributions from the beam rotation and the slope of the beam envelope. We have carried out an expansion which includes these effects to first order, resulting in a new equation for the beam edge radius. The change in beam kinetic energy due to spacecharge depression as the beam radius varies is also included. For the centroid equation, we have included the "self-steering" effect due to the curvature of the beam orbit. To leading order, there is a cancellation between the self-steering effect and the spacecharge depression of the beam energy, so that a more accurate centroid equation is obtained by using the undepressed value of the energy (i.e., the total beam energy) to calculate the orbit. We have implemented the envelope and centroid equations in the LAMDA code. The effect of the new terms will be illustrated with calculations for the DARHT accelerators at Los Alamos National Laboratory.
Improved Envelope and Centroid Equations for High Current Beams
NASA Astrophysics Data System (ADS)
Genoni, Thomas C.; Hughes, Thomas P.; Thoma, Carsten H.
2002-12-01
The standard envelope equation for charged particle beams (e.g., Lee-Cooper) neglects self-field contributions from the beam rotation and the slope of the beam envelope. We have carried out an expansion that includes these effects to first order, resulting in a new equation for the edge radius. The change in beam kinetic energy due to space-charge depression as the beam radius varies is also included. For the centroid equation, we have included the "self-steering" effect due to the curvature of the beam orbit. To leading order, there is a cancellation between the self-steering effect and the space-charge depression of the beam energy, so that a more accurate centroid equation is obtained by using the undepressed value of the energy (i.e., the total beam energy) to calculate the orbit. We have implemented the envelope and centroid equations in the Lamda code [1]. The effect of the new terms will be illustrated with calculations for the DARHT accelerators at the Los Alamos National Laboratory [2].
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
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.
Asymptotic reductions and solitons of nonlocal nonlinear Schrödinger equations
NASA Astrophysics Data System (ADS)
Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.
2016-05-01
Asymptotic reductions of a defocusing nonlocal nonlinear Schrödinger model in (3 + 1)-dimensions, in both Cartesian and cylindrical geometry, are presented. First, at an intermediate stage, a Boussinesq equation is derived, and then its far-field, in the form of a variety of Kadomtsev–Petviashvilli (KP) equations for right- and left-going waves, is found. KP models include versions of the KP-I and KP-II equations, in Cartesian and cylindrical geometry. Solitary waves solutions, planar or ring-shaped, and of dark or anti-dark type, are also predicted to occur. Their nature and stability is determined by a parameter defined by the physical parameters of the original nonlocal system. It is thus found that (dark) anti-dark solitary waves are only supported by a weak (strong) nonlocality, and are unstable (stable) in higher-dimensions. Our analytical predictions are corroborated by direct numerical simulations.
Interaction solutions for mKP equation with nonlocal symmetry reductions and CTE method
NASA Astrophysics Data System (ADS)
Ren, Bo
2015-06-01
The nonlocal symmetries for the modified Kadomtsev-Petviashvili (mKP) equation are obtained with the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent variables. The finite symmetry transformations and similarity reductions related with the nonlocal symmetries are computed. The multi-solitary wave solution and interaction solutions among a soliton and cnoidal waves of the mKP equation are presented. In the meantime, the consistent tanh expansion method is applied to the mKP equation. The explicit interaction solutions among a soliton and other types of nonlinear waves such as cnoidal periodic waves and multiple resonant soliton solutions are given.
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
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
Nonlocal Symmetry Reductions, CTE Method and Exact Solutions for Higher-Order KdV Equation
NASA Astrophysics Data System (ADS)
Ren, Bo; Liu, Xi-Zhong; Liu, Ping
2015-02-01
The nonlocal symmetries for the higher-order KdV equation are obtained with the truncated Painlevé method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing suitable prolonged systems. The finite symmetry transformations and similarity reductions for the prolonged systems are computed. Moreover, the consistent tanh expansion (CTE) method is applied to the higher-order KdV equation. These methods lead to some novel exact solutions of the higher-order KdV system.
Nonlocal growth equations-a test case for dynamic renormalization group analysis
NASA Astrophysics Data System (ADS)
Schwartz, Moshe; Katzav, Eytan
2003-12-01
In this paper we discuss nonlocal growth equations such as the generalization of the Kardar-Parisi-Zhang (KPZ) equation that includes long-range interactions, also known as the Nonlocal-Kardar-Parisi-Zhang (NKPZ) equation, and the nonlocal version of the molecular-beam-epitaxy (NMBE) equation. We show that the steady-state strong coupling solution for nonlocal models such as NKPZ and NMBE can be obtained exactly in one dimension for some special cases, using the Fokker-Planck form of these equations. The exact results we derive do not agree with previous results obtained by Dynamic Renormalization Group (DRG) analysis. This discrepancy is important because DRG is a common method used extensively to deal with nonlinear field equations. While difficulties with this method for d>1 has been realized in the past, it has been believed so far that DRG is still safe in one dimension. Our result shows differently. The reasons for the failure of DRG to recover the exact one-dimensional results are also discussed.
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.
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
NASA Astrophysics Data System (ADS)
Levchenko, E. A.; Shapovalov, A. V.; Trifonov, A. Yu
2016-07-01
In this paper we construct asymptotic solutions for the nonlocal multidimensional Fisher–Kolmogorov–Petrovskii–Piskunov equation in the class of functions concentrated on a one-dimensional manifold (curve) using a semiclassical approximation technique. We show that the construction of these solutions can be reduced to solving a similar problem for the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov in the class of functions concentrated at a point (zero-dimensional manifold) together with an additional operator condition. The general approach is exemplified by constructing a two-dimensional two-parametric solution, which describes quasi-steady-state patterns on a circumference.
Towards a gauge-equivalent magnetic structure of the nonlocal nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Gadzhimuradov, T. A.; Agalarov, A. M.
2016-06-01
It is shown that the nonlocal nonlinear Schrödinger equation recently proposed by Ablowitz and Musslimani [Phys. Rev. Lett. 110, 064105 (2013), 10.1103/PhysRevLett.110.064105] is gauge equivalent to the unconventional system of coupled Landau-Lifshitz equations. The first integrals of motion and one-soliton solution of an obtained model are given. The physical and geometrical aspects of model and their effect on expected metamagnetic structures are studied.
Nonlocal Symmetries, Explicit Solutions, and Wave Structures for the Korteweg-de Vries Equation
NASA Astrophysics Data System (ADS)
Ma, Zheng-Yi; Fei, Jin-Xi
2016-08-01
From the known Lax pair of the Korteweg-de Vries (KdV) equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the KdV equation with nonlocal symmetries by introducing two suitable auxiliary variables. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to the hyperbolic and Jacobi elliptic functions are derived. Figures show the physical interaction between the cnoidal waves and a solitary wave.
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.
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.
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
Positive or sign-changing solutions for a critical semilinear nonlocal equation
NASA Astrophysics Data System (ADS)
Long, Wei; Yang, Jing
2016-06-01
We consider the following critical semilinear nonlocal equation involving the fractional Laplacian (-Δ)su = K(|x|)|u|^{2^{*}s-2}u,quad in {R}^N, where {K(|x|)} is a positive radial function, {N > 2 + 2s, 0 < s < 1}, and {2^{*}s = 2N/N-2s}. Under some asymptotic assumptions on K( x) at an extreme point, we show that this problem has infinitely many nonradial positive or sign-changing solutions.
A Widder's Type Theorem for the Heat Equation with Nonlocal Diffusion
NASA Astrophysics Data System (ADS)
Barrios, Begoña; Peral, Ireneo; Soria, Fernando; Valdinoci, Enrico
2014-08-01
The main goal of this work is to prove that every non-negative strong solution u( x, t) to the problem can be written as where and This result shows uniqueness in the setting of non-negative solutions and extends some classical results for the heat equation by Widder in [
Global stability of travelling wave fronts for non-local diffusion equations with delay
NASA Astrophysics Data System (ADS)
Wang, X.; Lv, G.
2014-04-01
This paper is concerned with the global stability of travelling wave fronts for non-local diffusion equations with delay. We prove that the non-critical travelling wave fronts are globally exponentially stable under perturbations in some exponentially weighted L^\\infty-spaces. Moreover, we obtain the decay rates of \\sup_{x\\in{R}}\\vert u(x,t)-\\varphi(x+ct)\\vert using weighted energy estimates.
Monotone waves for non-monotone and non-local monostable reaction-diffusion equations
NASA Astrophysics Data System (ADS)
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2016-07-01
We propose a new approach for proving existence of monotone wavefronts in non-monotone and non-local monostable diffusive equations. This allows to extend recent results established for the particular case of equations with local delayed reaction. In addition, we demonstrate the uniqueness (modulo translations) of obtained monotone wavefront within the class of all monotone wavefronts (such a kind of conditional uniqueness was recently established for the non-local KPP-Fisher equation by Fang and Zhao). Moreover, we show that if delayed reaction is local then each monotone wavefront is unique (modulo translations) within the class of all non-constant traveling waves. Our approach is based on the construction of suitable fundamental solutions for linear integral-differential equations. We consider two alternative scenarios: in the first one, the fundamental solution is negative (typically holds for the Mackey-Glass diffusive equations) while in the second one, the fundamental solution is non-negative (typically holds for the KPP-Fisher diffusive equations).
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. PMID:26382386
Internal noise-driven generalized Langevin equation from a nonlocal continuum model
NASA Astrophysics Data System (ADS)
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)
Gan, Zaihui
2016-07-01
In this paper, we consider the standing waves and the global existence for two-dimensional nonlocal nonlinear Schrödinger equations. It is a coupled system which describes the spontaneous generation of a magnetic field in a cold plasma under the static limit. The main difficulty in the proofs lies in exploring the inner structure of the equations due to the fact that the nonlocal terms violate the inner scaling invariance, which may cause the non-zero energy for the ground state. For this reason, we first make a proper use of the inner structure of the equations to establish the existence of standing waves, and then we apply an energy scaling to obtain the instability of standing waves. Finally we show a sharp threshold for the global existence of solutions to the nonlocal nonlinear Schrödinger equations by a variational method, which depends again on the inner structure of the equations under consideration.
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. PMID:26577816
NASA Astrophysics Data System (ADS)
Tarhini, Rana
2015-12-01
In this paper, we study a nonlocal degenerate parabolic equation of order α + 2 for α ∈ (0, 2). The equation is a generalization of the one arising in the modeling of hydraulic fractures studied by Imbert and Mellet in 2011. Using the same approach, we prove the existence of solutions for this equation for 0 < α < 2 and for nonnegative initial data satisfying appropriate assumptions. The main difference is the compactness results due to different Sobolev embeddings. Furthermore, for α > 1, we construct a nonnegative solution for nonnegative initial data under weaker assumptions.
Nonlocal diffusion problems that approximate a parabolic equation with spatial dependence
NASA Astrophysics Data System (ADS)
Molino, Alexis; Rossi, Julio D.
2016-06-01
In this paper, we show that smooth solutions to the Dirichlet problem for the parabolic equation v_t(x,t)=sum_{i,j=1}N a_{ij}(x)partial2v(x,t)/partial{xipartial{x}j} + sum_{i =1}N bi(x)partial{v}(x,t)/partial{x_i} qquad x in Ω, with v( x, t) = g( x, t), {x in partial Ω,} can be approximated uniformly by solutions of nonlocal problems of the form ut^{\\varepsilon}(x,t)=int_{mathbb{R}n} K_{\\varepsilon}(x,y)(u^{\\varepsilon}(y,t)-u^{\\varepsilon}(x,t))dy, quad x in Ω, with {u^{\\varepsilon}(x,t)=g(x,t)}, {x notin Ω}, as {\\varepsilon to 0}, for an appropriate rescaled kernel {K_{\\varepsilon}}. In this way, we show that the usual local evolution problems with spatial dependence can be approximated by nonlocal ones. In the case of an equation in divergence form, we can obtain an approximation with symmetric kernels, that is, {K_{\\varepsilon}(x,y) = K_{\\varepsilon}(y,x)}.
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.
Lund, S M; Chilton, S H; Lee, E P
2006-01-17
A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing lattice of arbitrary complexity. Implementation of the method is straightforward. It is highly convergent and can be applied to all usual parameterizations of the matched envelope solutions. The method is applicable to all classes of linear focusing lattices without skew couplings, and also applies to parameters where the matched beam envelope is strongly unstable. Example applications are presented for periodic solenoidal and quadrupole focusing lattices. Convergence properties are summarized over a wide range of system parameters.
Analytic structure of two 1D-transport equations with nonlocal fluxes
NASA Astrophysics Data System (ADS)
Baker, Gregory R.; Li, Xiao; Morlet, Anne C.
We replace the flux term in Burger's equation by two simple alternates that contain contributions depending globally on the solution. In one case, the term is in the form of a hyperbolic equation where the characteristic speed is nonlocal, and in the other the term is in conservation form. In both cases, the nonanalytic is due to the presence of the Hilbert transform. The equations have a loose analogy to the motion of vortex sheets. In particular, they both form singularities in finite time in the absence of viscous effects. Our motivation then is to study the influence of viscosity. In one case, viscosity does not prevent singularity formation. In the other, we can prove solutions exist for all time, and determine the likely weak solution as viscosity vanishes. An interesting aspect of our work is that singularity formation can be viewed as the motion of singularities in the complex physical plane that reach the real axis in finite time. In one case, the singularity is a pole and causes the solution to blow up when it reaches the real axis. In the other, numerical solutions and an asymptotic analysis suggest that the weak solution contains a square root singularity that reaches the real axis in finite time, and then propagates along it. We hope our results will spur further interest in the role of singularities in the complex spatial plane in solutions to transport equations.
Global existence for a nonlocal and nonlinear Fokker-Planck equation
NASA Astrophysics Data System (ADS)
Dreyer, Wolfgang; Huth, Robert; Mielke, Alexander; Rehberg, Joachim; Winkler, Michael
2015-04-01
We consider a Fokker-Planck equation on a compact interval where, as a constraint, the first moment is a prescribed function of time. Eliminating the associated Lagrange multiplier, one obtains nonlinear and nonlocal terms. After establishing suitable local existence results, we use the relative entropy as an energy functional. However, the time-dependent constraint leads to a source term such that a delicate analysis is needed to show that the dissipation terms are strong enough to control the work done by the constraint. We obtain global existence of solutions as long as the prescribed first moment stays in the interior of an interval. If the prescribed moment converges to a constant value inside the interior of the interval, then the solution stabilises to the unique steady state.
NASA Astrophysics Data System (ADS)
Li, Wan-Tong; Wang, Jia-Bing; Zhang, Li
2016-08-01
This paper is concerned with the new types of entire solutions other than traveling wave solutions of nonlocal dispersal equations with monostable nonlinearity in space periodic habitats. We first establish the existence and properties of spatially periodic solutions connecting two steady states. Then new types of entire solutions are constructed by combining the rightward and leftward pulsating traveling fronts with different speeds and a spatially periodic solution. Finally, for a class of special heterogeneous reaction, we further establish the uniqueness of entire solutions and the continuous dependence of such an entire solution on parameters, such as wave speeds and the shifted variables. In other words, we build a five-dimensional manifold of solutions and the traveling wave solutions are on the boundary of the manifold.
Fast-varying envelope transient equation for supercontinuum generation
NASA Astrophysics Data System (ADS)
Huang, Jing
2016-01-01
The transient nonlinear Schrodinger equation in which the frequency is a function of time is established to describe the fast-varying field in the process of supercontinuum generation. It is solved with two methods and validated by comparing its simulation results with those of reported experiments. Based on the simulations of this extended equation, it is also demonstrated that the second-order differential of the field to longitude (z) can be ignored in the supercontinuum generation, and the additive item caused by the relationship between frequency and time will induce a homogeneous frequency shift.
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.
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
Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation
NASA Astrophysics Data System (ADS)
Sun, Linan; Shi, Junping; Wang, Yuwen
2013-08-01
In this paper, we consider a dynamical model of population biology which is of the classical Fisher type, but the competition interaction between individuals is nonlocal. The existence, uniqueness, and stability of the steady state solution of the nonlocal problem on a bounded interval with homogeneous Dirichlet boundary conditions are studied.
NASA Astrophysics Data System (ADS)
Feng, Xiaojing
2016-06-01
This paper focuses on the following Schrödinger-Poisson equations involving a fractional nonlocal operator -Δ u+u+φ u=f(x,u),&in {R}^3,(-Δ)^{α/2}φ=u^2,lim_{|x|to ∞}φ(x)=0,&in {R}^3, where {α in (1,2]}. Under certain assumptions, we obtain the existence of nontrivial solution of the above problem without compactness by using the methods of perturbation and the mountain pass theorem.
A pseudo-spectral method for a non-local KdV-Burgers equation posed on R
NASA Astrophysics Data System (ADS)
de la Hoz, Francisco; Cuesta, Carlota M.
2016-04-01
In this paper, we present a new pseudo-spectral method to solve the initial value problem associated to a non-local KdV-Burgers equation involving a Caputo-type fractional derivative. The basic idea is, using an algebraic map, to transform the whole real line into a bounded interval where we can apply a Fourier expansion. Special attention is given to the correct computation of the fractional derivative in this setting.
NASA Astrophysics Data System (ADS)
Alrachid, Houssam; Lelièvre, Tony; Talhouk, Raafat
2016-05-01
We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non-linear term is related to a conditional expectation, and is thus non-local. The proof uses tools from the theory of semigroups of linear operators for the local existence result, and an a priori estimate based on a supersolution for the global existence result.
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.
NASA Astrophysics Data System (ADS)
Ren, Bo
2016-08-01
The N = 1 supersymmetric mKdVB system is transformed to a coupled bosonic system by using the bosonization approach. By a singularity structure analysis, the bosonized supersymmetric mKdVB (BSmKdVB) equation admits the Painlevé property. Starting from the standard truncated Painlevé method, the nonlocal symmetry for the BSmKdVB equation is obtained. To solve the first Lie's principle related with the nonlocal symmetry, the nonlocal symmetry is localized to the Lie point symmetry by introducing multiple new fields. Thanks to localization processes, similarity reductions for the prolonged systems are studied by the Lie point symmetry method. The interaction solutions among solitons and other complicated waves including Painlevé II waves and periodic cnoidal waves are given through the reduction theorems. The soliton-cnoidal wave interaction solutions are explicitly given by using the mapping and deformation method. The concrete soliton-cnoidal interaction solutions are displayed both in analytical and graphical ways.
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
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.
NASA Astrophysics Data System (ADS)
Katzav, Eytan
2002-06-01
In this paper I discuss a generalization of the well-known Kardar-Parisi-Zhang (KPZ) equation that includes long-range interactions. This Non-local Kardar-Parisi-Zhang (NKPZ) equation has been suggested in the past to describe physical phenomena such as burning paper or deposition of colloids. I show that the steady state strong coupling solution for a subfamily of the NKPZ models can be solved exactly in one dimension, using the Fokker-Planck form of the equation, and yields a Gaussian distribution. This exact result does not agree with a previous result obtained by dynamic renormalization group (DRG) analysis. The reasons for this disagreement are not yet clear.
NASA Astrophysics Data System (ADS)
Hasik, Karel; Kopfová, Jana; Nábělková, Petra; Trofimchuk, Sergei
2016-04-01
We consider the nonlocal KPP-Fisher equation ut (t , x) =uxx (t , x) + u (t , x) (1 - (K * u) (t , x)) which describes the evolution of population density u (t , x) with respect to time t and location x. The non-locality is expressed in terms of the convolution of u (t , ṡ) with kernel K (ṡ) ≥ 0, ∫R K (s) ds = 1. The restrictions K (s), s ≥ 0, and K (s), s ≤ 0, are responsible for interactions of an individual with his left and right neighbors, respectively. We show that these two parts of K play quite different roles as for the existence and uniqueness of traveling fronts to the KPP-Fisher equation. In particular, if the left interaction is dominant, the uniqueness of fronts can be proved, while the dominance of the right interaction can induce the co-existence of monotone and oscillating fronts. We also present a short proof of the existence of traveling waves without assuming various technical restrictions usually imposed on K.
NASA Astrophysics Data System (ADS)
Herrmann, Michael; Niethammer, Barbara; Velázquez, Juan J. L.
2014-08-01
The hysteretic behavior of many-particle systems with non-convex free energy can be modeled by nonlocal Fokker-Planck equations that involve two small parameters and are driven by a time-dependent constraint. In this paper we consider the fast reaction regime related to Kramers-type phase transitions and show that the dynamics in the small-parameter limit can be described by a rate-independent evolution equation with hysteresis. For the proof we first derive mass-dissipation estimates by means of Muckenhoupt constants, formulate conditional stability estimates, and characterize the mass flux between the different phases in terms of moment estimates that encode large deviation results. Afterwards we combine all these partial results and establish the dynamical stability of localized peaks as well as sufficiently strong compactness results for the basic macroscopic quantities.
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)
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.
Stability of Planar Fronts for a Non-Local Phase Kinetics Equation with a Conservation Law in D ≤ 3
NASA Astrophysics Data System (ADS)
Carlen, Eric A.; Orlandi, Enza
2012-05-01
We consider, in a D-dimensional cylinder, a non-local evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider sub-critical temperatures, for which there are two local spatially homogeneous equilibria, and show a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibrium; i.e. the planar fronts: We show that an initial perturbation of a front that is sufficiently small in L2 norm, and sufficiently localized yields a solution that relaxes to another front, selected by a conservation law, in the L1 norm at an algebraic rate that we explicitly estimate. We also obtain rates for the relaxation in the L2 norm and the rate of decrease of the excess free energy.
Seismology of the solar envelope - Towards the calibration of the equation of state
NASA Astrophysics Data System (ADS)
Vorontsov, S. V.; Baturin, V. A.; Pamiatnykh, A. A.
1992-07-01
The solar p-mode frequencies represent a unique source of observational information about the physical properties of the solar interior, including the equation of state (EPS). The influence of possible uncertainties in the EOS on the frequencies is small, and mixed with a variety of possible uncertainties in solar structure and physics of the oscillations. This paper describes a technique aimed at separating the effects of the EOS in the information contained in the intermediate-degree data by extracting some functions, or 'tracers', sensitive to the EOS, and insensitive, as far as possible, to the irrelevant effects. The possibilities of the technology are examined by testing a variety of solar envelope models computed with four versions of EOS, in increasing degree of sophistication: (1) EOS of partially ionized ideal gas; (2) EOS with Debye-Hueckel electrostatic corrections; (3) EOS with short-range corrections to the Debye-Hueckel term, and (4) the most recent (Mihalas, et al.) MHD equation of state. By comparing the models with observational data, the effects of the electrostatic corrections are discussed, and first tentative conclusions on two more elaborate versions of the EOS are drawn.
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 Astrophysics Data System (ADS)
Morales-Casique, E.; Lezama-Campos, J. L.; Guadagnini, A.; Neuman, S. P.
2013-05-01
Modeling tracer transport in geologic porous media suffers from the corrupt characterization of the spatial distribution of hydrogeologic properties of the system and the incomplete knowledge of processes governing transport at multiple scales. Representations of transport dynamics based on a Fickian model of the kind considered in the advection-dispersion equation (ADE) fail to capture (a) the temporal variation associated with the rate of spreading of a tracer, and (b) the distribution of early and late arrival times which are often observed in field and/or laboratory scenarios and are considered as the signature of anomalous transport. Elsewhere we have presented exact stochastic moment equations to model tracer transport in randomly heterogeneous aquifers. We have also developed a closure scheme which enables one to provide numerical solutions of such moment equations at different orders of approximations. The resulting (ensemble) average and variance of concentration fields were found to display a good agreement against Monte Carlo - based simulation results for mildly heterogeneous (or well-conditioned strongly heterogeneous) media. Here we explore the ability of the moment equations approach to describe the distribution of early arrival times and late time tailing effects which can be observed in Monte-Carlo based breakthrough curves (BTCs) of the (ensemble) mean concentration. We show that BTCs of mean resident concentration calculated at a fixed space location through higher-order approximations of moment equations display long tailing features of the kind which is typically associated with anomalous transport behavior and are not represented by an ADE model with constant dispersive parameter, such as the zero-order approximation.
Multiple beam envelope equations for electron injectors using a bunch segmentation model
NASA Astrophysics Data System (ADS)
Mizuno, A.; Dewa, H.; Taniuchi, T.; Tomizawa, H.; Hanaki, H.; Hotta, E.
2012-06-01
A new semianalytical method of investigating the beam dynamics for electron injectors was developed. In this method, a short bunched electron beam is assumed to be an ensemble of several segmentation pieces in both the longitudinal and the transverse directions. The trajectory of each electron in the segmentation pieces is solved by the beam envelope equations while taking into account the space charge fields produced by all the pieces, the electromagnetic fields of an rf cavity, and the image charge fields at a cathode surface. The shape of the entire bunch is consequently calculated, and thus the emittances can be obtained from weighted mean values of the solutions for the obtained electron trajectories. The advantage of this method is its unique assumption for the beam parameters. We assume that each segmentation slice is not warped in the calculations. Although if the beam energy is low and the charge density is large, this condition is not satisfied, in practice, this condition is usually satisfied. We have performed beam dynamics calculations to obtain traces in free space and in the BNL-type rf gun cavity by comparing the analytical solutions with those obtained by simulation. In most cases, the emittances obtained by the simulation become closer to those obtained analytically with increasing the number of particles used in the simulation. Therefore, the analytically obtained emittances are expected to coincide with converged values obtained by the simulation. The applicable range of the analytical method for the BNL-type rf gun cavity is under 0.5 nC per bunch. This range is often used in recently built x-ray free electron laser facilities.
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. PMID:27368788
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.
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.
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. PMID:25974563
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.
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.
Stochastic averaging of energy envelope of Preisach hysteretic systems
NASA Astrophysics Data System (ADS)
Wang, Y.; Ying, Z. G.; Zhu, W. Q.
2009-04-01
A new stochastic averaging technique for analyzing the response of a single-degree-of-freedom Preisach hysteretic system with nonlocal memory under stationary Gaussian stochastic excitation is proposed. An equivalent nonhysteretic nonlinear system with amplitude-envelope-dependent damping and stiffness is firstly obtained from the given system by using the generalized harmonic balance technique. The relationship between the amplitude envelope and the energy envelope is then established, and the equivalent damping and stiffness coefficients are expressed as functions of the energy envelope. The available range of the yielding force of the system is extended and also the strong nonlinear stiffness of the system is incorporated so as to improve the response prediction. Finally, an averaged Itô stochastic differential equation for the energy envelope of the system as one-dimensional diffusion process is derived by using the stochastic averaging method of energy envelope, and the Fokker-Planck-Kolmogorov equation associated with the averaged Itô equation is solved to obtain stationary probability densities of the energy envelope and amplitude envelope. The approximate solutions are validated by using the Monte Carlo simulation.
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)
Hansson, Tobias; Leo, François; Erkintalo, Miro; Anthony, Jessienta; Coen, Stéphane; Ricciardi, Iolanda; De Rosa, Maurizio; Wabnitz, Stefan
2016-06-01
We numerically study, by means of the single envelope equation, the generation of optical frequency combs ranging from the visible to the mid-infrared spectral regions in resonators with quadratic and cubic nonlinearities. Phase-matched quadratic wave-mixing processes among the comb lines can be activated by low-power continuous wave pumping in the near infrared of a radially poled lithium niobate whispering gallery resonator (WGR). We examine both separate and co-existing intra-cavity doubly resonant second-harmonic generation and parametric oscillation processes, and find that modulation instabilities may lead to the formation of coupled comb arrays extending over multiple octaves. In the temporal domain, the frequency combs may correspond to pulse trains, or isolated pulses.
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.
Unstable nonlocal interface dynamics.
Nicoli, Matteo; Cuerno, Rodolfo; Castro, Mario
2009-06-26
Nonlocal effects occur in many nonequilibrium interfaces, due to diverse physical mechanisms like diffusive, ballistic, or anomalous transport, with examples from flame fronts to thin films. While dimensional analysis describes stable nonlocal interfaces, we show the morphologically unstable condition to be nontrivial. This is the case for a family of stochastic equations of experimental relevance, paradigmatically including the Michelson-Sivashinsky system. For a whole parameter range, the asymptotic dynamics is scale invariant with dimension-independent exponents reflecting a hidden Galilean symmetry. The usual Kardar-Parisi-Zhang nonlinearity, albeit irrelevant in that parameter range, plays a key role in this behavior. PMID:19659099
Turbulence transport with nonlocal interactions
Linn, R.R.; Clark, T.T.; Harlow, F.H.; Turner, L.
1998-03-01
This preliminary report describes a variety of issues in turbulence transport analysis with particular emphasis on closure procedures that are nonlocal in wave-number and/or physical space. Anomalous behavior of the transport equations for large scale parts of the turbulence spectrum are resolved by including the physical space nonlocal interactions. Direct and reverse cascade processes in wave-number space are given a much richer potential for realistic description by the nonlocal formulations. The discussion also describes issues, many still not resolved, regarding new classes of self-similar form functions.
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.
Hybrid nonlocality distillation
NASA Astrophysics Data System (ADS)
Wu, Keng-Shuo; Hsu, Li-Yi
2013-08-01
In this Letter, we introduce the notion of hybrid nonlocality distillation, in which different nonlocal boxes are exploited for nonlocality distillation. Here, we quantify the nonlocality using the violation degree of either the Clauser-Horne-Shimony-Holt inequality or the I3322 inequality. Our study shows that hybrid nonlocality distillation can outperform nonlocality distillation using copies of single nonlocal boxes. In particular, more nonlocality of undistillable boxes can be activated with the assistance of distillable boxes. Equivalently, distillable boxes can achieve more nonlocality with the assistance of undistillable boxes.
NASA Astrophysics Data System (ADS)
Carlen, E. A.; Carvalho, M. C.; Orlandi, E.
1999-06-01
This is the first of two papers devoted to the study of a nonlocal evolution equation that describes the evolution of the local magnetization in a continuum limit of an Ising spin system with Kawasaki dynamics and Kac potentials. We consider subcritical temperatures, for which there are two local equilibria, and begin the proof of a local nonlinear stability result for the minimum free energy profiles for the magnetization at the interface between regions of these two different local equilibria; i.e., the fronts. We shall show in the second paper that an initial perturbation v 0 of a front that is sufficiently small in L 2 norm, and sufficiently localized that ∫ x 2 v 0( x)2 dx<∞, yields a solution that relaxes to another front, selected by a conservation law, in the L 1 norm at an algebraic rate that we explicitly estimate. There we also obtain rates for the relaxation in the L 2 norm and the rate of decrease of the excess free energy. Here we prove a number of estimates essential for this result. Moreover, the estimates proved here suffice to establish the main result in an important special case.
NASA Astrophysics Data System (ADS)
Kumar, Praveen; Jang, Seogjoo
2013-04-01
The emission lineshape of the B850 band in the light harvesting complex 2 of purple bacteria is calculated by extending the approach of 2nd order time-nonlocal quantum master equation [S. Jang and R. J. Silbey, J. Chem. Phys. 118, 9312 (2003), 10.1063/1.1569239]. The initial condition for the emission process corresponds to the stationary excited state density where exciton states are entangled with the bath modes in equilibrium. This exciton-bath coupling, which is not diagonal in either site excitation or exciton basis, results in a new inhomogeneous term that is absent in the expression for the absorption lineshape. Careful treatment of all the 2nd order terms are made, and explicit expressions are derived for both full 2nd order lineshape expression and the one based on secular approximation that neglects off-diagonal components in the exciton basis. Numerical results are presented for a few representative cases of disorder and temperature. Comparison of emission line shape with the absorption line shape is also made. It is shown that the inhomogeneous term coming from the entanglement of the system and bath degrees of freedom makes significant contributions to the lineshape. It is also found that the perturbative nature of the theory can result in negative portion of lineshape in some situations, which can be removed significantly by inclusion of the inhomogeneous term and completely by using the secular approximation. Comparison of the emission and absorption lineshapes at different temperatures demonstrates the role of thermal population of different exciton states and exciton-phonon couplings.
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.
Quantum nonlocality does not exist.
Tipler, Frank J
2014-08-01
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
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.
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
Nonsmooth feedback controls of nonlocal dispersal models
NASA Astrophysics Data System (ADS)
Malaguti, Luisa; Rubbioni, Paola
2016-03-01
The paper deals with a nonlocal diffusion equation which is a model for biological invasion and disease spread. A nonsmooth feedback control term is included and the existence of controlled dynamics is proved, satisfying different kinds of nonlocal condition. Jump discontinuities appear in the process. The existence of optimal control strategies is also shown, under suitably regular control functionals. The investigation makes use of techniques of multivalued analysis and is based on the degree theory for condensing operators in Hilbert spaces.
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.
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.
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
Nonlocal magnetorotational instability
Mikhailovskii, A. B.; Erokhin, N. N.; Lominadze, J. G.; Galvao, R. M. O.; Churikov, A. P.; Kharshiladze, O. A.; Amador, C. H. S.
2008-05-15
An analytical theory of the nonlocal magnetorotational instability (MRI) is developed for the simplest astrophysical plasma model. It is assumed that the rotation frequency profile has a steplike character, so that there are two regions in which it has constant different values, separated by a narrow transition layer. The surface wave approach is employed to investigate the MRI in this configuration. It is shown that the main regularities of the nonlocal MRI are similar to those of the local instability and that driving the nonaxisymmetric MRI is less effective than the axisymmetric one, also for the case of the nonlocal instability. The existence of nonlocal instabilities in nonmagnetized plasma is predicted.
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.
NASA Astrophysics Data System (ADS)
Morales-Casique, E.; Briseño-Ruiz, J. V.; Hernández, A. F.; Herrera, G. S.; Escolero-Fuentes, O.
2014-12-01
We present a comparison of three stochastic approaches for estimating log hydraulic conductivity (Y) and predicting steady-state groundwater flow. Two of the approaches are based on the data assimilation technique known as ensemble Kalman filter (EnKF) and differ in the way prior statistical moment estimates (PSME) (required to build the Kalman gain matrix) are obtained. In the first approach, the Monte Carlo method is employed to compute PSME of the variables and parameters; we denote this approach by EnKFMC. In the second approach PSME are computed through the direct solution of approximate nonlocal (integrodifferential) equations that govern the spatial conditional ensemble means (statistical expectations) and covariances of hydraulic head (h) and fluxes; we denote this approach by EnKFME. The third approach consists of geostatistical stochastic inversion of the same nonlocal moment equations; we denote this approach by IME. In addition to testing the EnKFMC and EnKFME methods in the traditional manner that estimate Y over the entire grid, we propose novel corresponding algorithms that estimate Y at a few selected locations and then interpolate over all grid elements via kriging as done in the IME method. We tested these methods to estimate Y and h in steady-state groundwater flow in a synthetic two-dimensional domain with a well pumping at a constant rate, located at the center of the domain. In addition, to evaluate the performance of the estimation methods, we generated four unconditional different realizations that served as "true" fields. The results of our numerical experiments indicate that the three methods were effective in estimating h, reaching at least 80% of predictive coverage, although both EnKF were superior to the IME method. With respect to estimating Y, the three methods reached similar accuracy in terms of the mean absolute value error. Coupling the EnKF methods with kriging to estimate Y reduces to one fourth the CPU time required for data
Anisotropic charged core envelope star
NASA Astrophysics Data System (ADS)
Mafa Takisa, P.; Maharaj, S. D.
2016-08-01
We study a charged compact object with anisotropic pressures in a core envelope setting. The equation of state is quadratic in the core and linear in the envelope. There is smooth matching between the three regions: the core, envelope and the Reissner-Nordström exterior. We show that the presence of the electric field affects the masses, radii and compactification factors of stellar objects with values which are in agreement with previous studies. We investigate in particular the effect of electric field on the physical features of the pulsar PSR J1614-2230 in the core envelope model. The gravitational potentials and the matter variables are well behaved within the stellar object. We demonstrate that the radius of the core and the envelope can vary by changing the parameters in the speed of sound.
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 spectroscopy of Andreev bound states
NASA Astrophysics Data System (ADS)
Schindele, J.; Baumgartner, A.; Maurand, R.; Weiss, M.; Schönenberger, C.
2014-01-01
We experimentally investigate Andreev bound states (ABSs) in a carbon nanotube quantum dot (QD) connected to a superconducting Nb lead (S). A weakly coupled normal metal contact acts as a tunnel probe that measures the energy dispersion of the ABSs. Moreover, we study the response of the ABS to nonlocal transport processes, namely, Cooper pair splitting and elastic co-tunnelling, which are enabled by a second QD fabricated on the same nanotube on the opposite side of S. We find an appreciable nonlocal conductance with a rich structure, including a sign reversal at the ground-state transition from the ABS singlet to a degenerate magnetic doublet. We describe our device by a simple rate equation model that captures the key features of our observations and demonstrates that the sign of the nonlocal conductance is a measure for the charge distribution of the ABS, given by the respective Bogoliubov-de Gennes amplitudes u and v.
NASA Astrophysics Data System (ADS)
Millen, James
2016-04-01
George Musser's book Spooky Action at a Distance focuses on one of quantum physics' more challenging concepts, nonlocality, and its multitude of implications, particularly its assault on space itself.
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.
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. PMID:27152787
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.
COMMON ENVELOPE: ENTHALPY CONSIDERATION
Ivanova, N.; Chaichenets, S.
2011-04-20
In this Letter, we discuss a modification to the criterion for the common envelope (CE) event to result in envelope dispersion. We emphasize that the current energy criterion for the CE phase is not sufficient for an instability of the CE, nor for an ejection. However, in some cases, stellar envelopes undergo stationary mass outflows, which are likely to occur during the slow spiral-in stage of the CE event. We propose the condition for such outflows, in a manner similar to the currently standard {alpha}{sub CE}{lambda}-prescription but with an addition of P/{rho} term in the energy balance equation, accounting therefore for the enthalpy of the envelope rather than merely the gas internal energy. This produces a significant correction, which might help to dispense with an unphysically high value of energy efficiency parameter during the CE phase, currently required in the binary population synthesis studies to make the production of low-mass X-ray binaries with a black hole companion to match the observations.
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
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.
Linear delta-f simulations of nonlocal electron heat transport
Brunner, S.; Valeo, E.; Krommes, J.A.
2000-01-27
Nonlocal electron heat transport calculations are carried out by making use of some of the techniques developed previously for extending the delta f method to transport time scale simulations. By considering the relaxation of small amplitude temperature perturbations of a 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. 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.
Quantum networks reveal quantum nonlocality.
Cavalcanti, Daniel; Almeida, Mafalda L; Scarani, Valerio; Acín, Antonio
2011-01-01
The results of local measurements on some composite quantum systems cannot be reproduced classically. This impossibility, known as quantum nonlocality, represents a milestone in the foundations of quantum theory. Quantum nonlocality is also a valuable resource for information-processing tasks, for example, quantum communication, quantum key distribution, quantum state estimation or randomness extraction. Still, deciding whether a quantum state is nonlocal remains a challenging problem. Here, we introduce a novel approach to this question: we study the nonlocal properties of quantum states when distributed and measured in networks. We show, using our framework, how any one-way entanglement distillable state leads to nonlocal correlations and prove that quantum nonlocality is a non-additive resource, which can be activated. There exist states, local at the single-copy level, that become nonlocal when taking several copies of them. Our results imply that the nonlocality of quantum states strongly depends on the measurement context. PMID:21304513
A caveat on building nonlocal models of cosmology
Tsamis, N.C.; Woodard, R.P. E-mail: woodard@phys.ufl.edu
2014-09-01
Nonlocal models of cosmology might derive from graviton loop corrections to the effective field equations from the epoch of primordial inflation. Although the Schwinger-Keldysh formalism would automatically produce causal and conserved effective field equations, the models so far proposed have been purely phenomenological. Two techniques have been employed to generate causal and conserved field equations: either varying an invariant nonlocal effective action and then enforcing causality by the ad hoc replacement of any advanced Green's function with its retarded counterpart, or else introducing causal nonlocality into a general ansatz for the field equations and then enforcing conservation. We point out here that the two techniques access very different classes of models, and that neither one of them may represent what would actually arise from fundamental theory.
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.
Kummer solitons in strongly nonlocal nonlinear media
NASA Astrophysics Data System (ADS)
Zhong, Wei-Ping; Belić, Milivoj
2009-01-01
We solve the three-dimensional (3D) time-dependent strongly nonlocal nonlinear Schrödinger equation (NNSE) in spherical coordinates, with the help of Kummer's functions. We obtain analytical solitary solutions, which we term the Kummer solitons. We compare analytical solutions with the numerical solutions of NNSE. We discuss higher-order Kummer spatial solitons, which can exist in various forms, such as the 3D vortex solitons and the multipole solitons.
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…
Effects of nonlocal potentials on (p ,d ) transfer reactions
NASA Astrophysics Data System (ADS)
Ross, A.; Titus, L. J.; Nunes, F. M.; Mahzoon, M. H.; Dickhoff, W. H.; Charity, R. J.
2015-10-01
Background: Although local phenomenological optical potentials have been standardly used to interpret nuclear reactions, recent studies suggest the effects of nonlocality should not be neglected. Purpose: In this work we investigate the effects of nonlocality in (p ,d ) transfer reactions using nonlocal optical potentials. We compare results obtained with the dispersive optical model to those obtained using the Perey-Buck interaction. Method: We solve the scattering and bound-state equations for the nonlocal version of the dispersive optical model. Then, using the distorted-wave Born approximation, we calculate the transfer cross section for (p ,d ) on 40Ca at Ep=20 , 35, and 50 MeV. Results: The inclusion of nonlocality in the bound state has a larger effect than that in the scattering states. The overall effect on the transfer cross section is very significant. We found an increase due to nonlocality in the transfer cross section of ≈30 - 50 % when using the Perey-Buck interaction and of ≈15 - 50 % when using the dispersive optical potential. Conclusions: Although the details of the nonlocal interaction can change the magnitude of the effects, our study shows that qualitatively the results obtained using the dispersive optical potential and the Perey-Buck interaction are consistent, in both cases the transfer cross sections are significantly increased.
Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions
NASA Astrophysics Data System (ADS)
Ablowitz, Mark J.
2009-09-01
Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.
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.
Lévy flights and nonlocal quantum dynamics
NASA Astrophysics Data System (ADS)
Garbaczewski, Piotr; Stephanovich, Vladimir
2013-07-01
We develop a fully fledged theory of quantum dynamical patterns of behavior that are nonlocally induced. To this end we generalize the standard Laplacian-based framework of the Schrödinger picture quantum evolution to that employing nonlocal (pseudodifferential) operators. Special attention is paid to the Salpeter (here, m ⩾ 0) quasirelativistic equation and the evolution of various wave packets, in particular to their radial expansion in 3D. Foldy's synthesis of "covariant particle equations" is extended to encompass free Maxwell theory, which however is devoid of any "particle" content. Links with the photon wave mechanics are explored.
Superlinear nonlocal fractional problems with infinitely many solutions
NASA Astrophysics Data System (ADS)
Binlin, Zhang; Molica Bisci, Giovanni; Servadei, Raffaella
2015-07-01
In this paper we study the existence of infinitely many weak solutions for equations driven by nonlocal integrodifferential operators with homogeneous Dirichlet boundary conditions. A model for these operators is given by the fractional Laplacian where s ∈ (0, 1) is fixed. We consider different superlinear growth assumptions on the nonlinearity, starting from the well-known Ambrosetti-Rabinowitz condition. In this framework we obtain three different results about the existence of infinitely many weak solutions for the problem under consideration, by using the Fountain Theorem. All these theorems extend some classical results for semilinear Laplacian equations to the nonlocal fractional setting.
A theory of non-local linear drift wave transport
Moradi, S.; Anderson, J.; Weyssow, B.
2011-06-15
Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated through a Fokker-Planck equation with fractional velocity derivatives. A dispersion relation for density gradient driven linear drift modes is derived including the effects of the fractional velocity derivative in the Fokker-Planck equation. It is found that a small deviation (a few percent) from the Maxwellian distribution function alters the dispersion relation such that the growth rates are substantially increased and thereby may cause enhanced levels of transport.
Uncertainty-induced quantum nonlocality
NASA Astrophysics Data System (ADS)
Wu, Shao-xiong; Zhang, Jun; Yu, Chang-shui; Song, He-shan
2014-01-01
Based on the skew information, we present a quantity, uncertainty-induced quantum nonlocality (UIN) to measure the quantum correlation. It can be considered as the updated version of the original measurement-induced nonlocality (MIN) preserving the good computability but eliminating the non-contractivity problem. For 2×d-dimensional state, it is shown that UIN can be given by a closed form. In addition, we also investigate the maximal uncertainty-induced nonlocality.
Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions
NASA Astrophysics Data System (ADS)
Caflisch, Russel E.; Lombardo, Maria Carmela; Sammartino, Marco
2011-05-01
In this paper nonlocal boundary conditions for the Navier-Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69-82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier-Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.
On an Inviscid Model for Incompressible Two-Phase Flows with Nonlocal Interaction
NASA Astrophysics Data System (ADS)
Gal, Ciprian G.
2016-03-01
We consider a diffuse interface model which describes the motion of an ideal incompressible mixture of two immiscible fluids with nonlocal interaction in two-dimensional bounded domains. This model consists of the Euler equation coupled with a convective nonlocal Cahn-Hilliard equation. We establish the existence of globally defined weak solutions as well as well-posedness results for strong/classical solutions.
(1+2)-dimensional strongly nonlocal solitons
Ouyang Shigen; Guo Qi
2007-11-15
Approximate solutions of (1+2)-dimensional strongly nonlocal solitons (SNSs) are presented. It is shown that the power of a SNS in a nematic liquid crystal is in direct proportion to the second power of the degree of nonlocality, the power of a SNS in a nonlocal medium with a logarithmic nonlocal response is in inverse proportion to the second power of its beamwidth, and the power of a SNS in a nonlocal medium with an sth-power decay nonlocal response is in direct proportion to the (s+2)th power of the degree of nonlocality.
Ring dark and antidark solitons in nonlocal media.
Horikis, Theodoros P; Frantzeskakis, Dimitrios J
2016-02-01
Ring dark and antidark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable CW background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvili (aka Johnson's) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties. PMID:26907429
Phonons in nonlocal van der Waals density functional theory
NASA Astrophysics Data System (ADS)
Sabatini, Riccardo; Küçükbenli, Emine; Pham, Cong Huy; de Gironcoli, Stefano
2016-06-01
We extend the formulation of density functional perturbation theory to treat nonlocal density functionals, accounting for van der Waals interactions, in a rigorous and efficient way. We provide a general formalism, suitable for any functional in this family, and give specific equations for the most widely used ones. We then study the lattice dynamics of graphite, comparing several nonlocal functionals and the local density approximation, showing that our recent revision of the VV10 functional [R. Sabatini et al., Phys. Rev. B 87, 041108(R) (2013), 10.1103/PhysRevB.87.041108] gives the best comparison with experiments.
Bounds for nonlocality distillation protocols
Forster, Manuel
2011-06-15
Nonlocality can be quantified by the violation of a Bell inequality. Since this violation may be amplified by local operations, an alternative measure has been proposed--distillable nonlocality. The alternative measure is difficult to calculate exactly due to the double exponential growth of the parameter space. In this paper, we give a way to bound the distillable nonlocality of a resource by the solutions to a related optimization problem. Our upper bounds are exponentially easier to compute than the exact value and are shown to be meaningful in general and tight in some cases.
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.
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.
Effects of nonlocal heat transport on laser implosion
Mima, K.; Honda, M.; Miyamoto, S.; Kato, S.
1996-05-01
A numerical simulation code describing the spherically symmetric implosion hydrodynamics has been developed to investigate the nonlocal heat transport effects on stable high velocity implosion and fast ignition. In the implosion simulation code HIMICO, the Fokker Planck equation for electron transport is solved to describe the nonlocal effects. For high ablation pressure implosion with a pressure higher than 200 Mbar, the isentrope is found higher by a factor 2 in the nonlocal transport model than in the Spitzer Harm model. As for the fast ignition simulation, the neutron yield for the high density compression with 10 KJ laser increases to be 20 times by injecting an additional heating pulse of 10 KJ with 1 psec. {copyright} {ital 1996 American Institute of Physics.}
Nonlocal reactive transport with physical, chemical, and biological heterogeneity
NASA Astrophysics Data System (ADS)
Hu, Bill X.; Cushman, John H.; Deng, Fei-Wen
When a natural porous medium is viewed from an eulerian perspective, incomplete characterization of the hydraulic conductivity, chemical reactivity, and biological activity leads to nonlocal constitutive theories, irrespective of whether the medium has evolving heterogeneity with fluctuations over all scales. Within this framework a constitutive theory involving nonlocal dispersive and convective fluxes and nonlocal sources/sinks is developed for chemicals undergoing random linear nonequilibrium reactions and random equilibrium first-order decay in a random conductivity field. The resulting transport equations are solved exactly in Fourier-Laplace space and then numerically inverted to real space. Mean concentration contours and various spatial moments are presented graphically for several covariance structures. 1997 Published by Elsevier Science Ltd. All rights reserved
Highly nonlocal optical nonlinearities in atoms trapped near a waveguide
NASA Astrophysics Data System (ADS)
Shahmoon, Ephraim; Grisins, Pjotrs; Stimming, Hans Peter; Mazets, Igor; Kurizki, Gershon
2016-05-01
Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms can be tailored. When the atoms are in an electromagnetically-induced transparency configuration, the atomic interactions are translated to long-range interactions between photons and thus to highly nonlocal optical nonlinearities. We derive and analyze the governing nonlinear propagation equation, finding a roton-like excitation spectrum for light and the emergence of long-range order in its output intensity. These predictions open the door to studies of unexplored wave dynamics and many-body physics with highly-nonlocal interactions of optical fields in one dimension.
Nonlocal Transport Model for Two-Component Plasmas
NASA Astrophysics Data System (ADS)
Zheng, Zhen
My PhD thesis concerns nonlocal effects on the transport processes in two-component (electron and ion) plasmas. My objective is to construct a self-consistent nonlocal transport model that is applicable in fully-ionized homogeneous Maxwellian plasmas with small-amplitude perturbations for arbitrary particle collisionalities. The fundamental method starts with a rigorous solution of the full set of linearized Fokker-Planck kinetic equations with the Landau collision operators for two-component plasmas. Then a procedure is implemented for derivation of the linear fluid equations which are closed by the transport relations. Thereby a complete list of transport coefficients for each component is computed in the broad range of temporal and spatial scales. Some new transport coefficients are found from the nonlocal hydrodynamic formulation. Ion collisions are self-consistently included in all the calculations. The electric susceptibilities and dispersion relation can thus be derived from this linear nonlocal hydrodynamics for both isothermal and non-isothermal cases. With the aid of these formulations, some important plasma quantities are successfully calculated and some practical fitting formulae are proposed, i.e., the mode frequencies and damping rates of ion acoustic wave (IAW) and entropy wave (ENW). In addition, this linear nonlocal hydrodynamics has been applied to a derivation of the dynamic form factor S(k,w) that serves to describe and explain correctly the features of the frequency spectra observed in Thomson scattering experiments. The most significant accomplishment in my research work is a thorough investigation and a deep analysis of nonlocal ion effects on longitudinal low-frequency plasma fluctuations.
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.
(1 + 2)-Dimensional sub-strongly nonlocal spatial optical solitons: Perturbation method
NASA Astrophysics Data System (ADS)
Ren, Hongyan; Ouyang, Shigen; Guo, Qi; Wu, Lijun
2007-07-01
By extending the (1 + 1)-dimensional [(1 + 1)-D] perturbation method suggested by Ouyang et al. [S. Ouyang, Q. Guo, W. Hu, Phys. Rev. E. 74 (2006) 036622] to the (1 + 2)-D case, we obtain a fundamental soliton solution to the (1 + 2)-D nonlocal nonlinear Schrödinger equation (NNLSE) with a Gaussian-type response function for the sub-strongly nonlocal case. Numerical simulations show that the soliton solution obtained in this paper can describe the soliton states in both the sub-strongly nonlocal case and the strongly nonlocal case. It is found that the phase constant and the power of the (1 + 2)-D strongly nonlocal spatial optical soliton with a Gaussian-type response function are both in inverse proportion to the 4th power of its beam width.
a New Nonlocal Beam Theory with Thickness Stretching Effect for Nanobeams
NASA Astrophysics Data System (ADS)
Tounsi, Abdelouahed; Benguediab, Soumia; Houari, Mohammed Sid Ahmed; Semmah, Abdelwahed
2013-08-01
This paper presents a new nonlocal thickness-stretching sinusoidal shear deformation beam theory for the static and vibration of nanobeams. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and it accounts for both shear deformation and thickness stretching effects by a sinusoidal variation of all displacements through the thickness without using shear correction factor. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanobeam are derived using Hamilton's principle. The effects of nonlocal parameter, aspect ratio and the thickness stretching on the static and dynamic responses of the nanobeam are discussed. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the bending and dynamic behaviors of complex-nanobeam-system such as complex carbon nanotube system.
Aspects of nonlocality in quantum field theory, quantum gravity and cosmology
NASA Astrophysics Data System (ADS)
Barvinsky, A. O.
2015-01-01
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.
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.
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.
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 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
NASA Astrophysics Data System (ADS)
Ghosh, Sanjay; Chaudhury, Kunal N.
2016-03-01
We propose a simple and fast algorithm called PatchLift for computing distances between patches (contiguous block of samples) extracted from a given one-dimensional signal. PatchLift is based on the observation that the patch distances can be efficiently computed from a matrix that is derived from the one-dimensional signal using lifting; importantly, the number of operations required to compute the patch distances using this approach does not scale with the patch length. We next demonstrate how PatchLift can be used for patch-based denoising of images corrupted with Gaussian noise. In particular, we propose a separable formulation of the classical nonlocal means (NLM) algorithm that can be implemented using PatchLift. We demonstrate that the PatchLift-based implementation of separable NLM is a few orders faster than standard NLM and is competitive with existing fast implementations of NLM. Moreover, its denoising performance is shown to be consistently superior to that of NLM and some of its variants, both in terms of peak signal-to-noise ratio/structural similarity index and visual quality.
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. PMID:25893883
Towards LHC physics with nonlocal Standard Model
NASA Astrophysics Data System (ADS)
Biswas, Tirthabir; Okada, Nobuchika
2015-09-01
We take a few steps towards constructing a string-inspired nonlocal extension of the Standard Model. We start by illustrating how quantum loop calculations can be performed in nonlocal scalar field theory. In particular, we show the potential to address the hierarchy problem in the nonlocal framework. Next, we construct a nonlocal abelian gauge model and derive modifications of the gauge interaction vertex and field propagators. We apply the modifications to a toy version of the nonlocal Standard Model and investigate collider phenomenology. We find the lower bound on the scale of nonlocality from the 8 TeV LHC data to be 2.5-3 TeV.
NASA Astrophysics Data System (ADS)
Nicolaï, Ph.; Feugeas, J.-L.; Schurtz, G.
2006-06-01
We present a model of nonlocal transport for multidimensional radiation magneto hydrodynamic codes. In laser produced plasmas, it is now believed that the heat transfert can be strongly modified by the nonlocal nature of the electron conduction. Nevertheless other mechanisms as self generated magnetic fields may affect heat transport too. The model described in this work aims at extending the formula of G. Schurtz, Ph. Nicolaï and M. Busquet [1] to magnetized plasmas. A system of nonlocal equations is derived from kinetic equations with self-consistent electric and magnetic fields. These equations are analyzed and applied to a physical problem in order to demonstrate the main features of the model.
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 Measurements via Quantum Erasure
NASA Astrophysics Data System (ADS)
Brodutch, Aharon; Cohen, Eliahu
2016-02-01
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.
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. PMID:26943514
Alleviation of catastrophic quenching in solar dynamo model with nonlocal alpha-effect
NASA Astrophysics Data System (ADS)
Kitchatinov, L. L.; Olemskoy, S. V.
2011-06-01
The nonlocal alpha-effect of Babcock-Leighton type is not prone to the catastrophic quenching due to conservation of magnetic helicity. This is shown with a dynamo model, which jointly applies the nonlocal alpha-effect, the diamagnetic pumping, and dynamical equation for the magnetic alpha-effect. The same model shows catastrophic quenching when the alpha-effect is changed to its local formulation. The nonlocal model shows a preferred excitation of magnetic fields of dipolar symmetry, which oscillate with a period of about ten years and have a toroidal-to-polar fields ratio of about a thousand.
Localization of the SFT inspired nonlocal linear models and exact solutions
NASA Astrophysics Data System (ADS)
Vernov, S. Yu.
2011-05-01
A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function ℱ(□ g ), which has both simple and double roots. The way of localization of nonlocal Einstein equations is generalized on models with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and Bianchi I metrics are presented.
Closed sets of nonlocal correlations
Allcock, Jonathan; Linden, Noah; Brunner, Nicolas; Popescu, Sandu; Skrzypczyk, Paul; Vertesi, Tamas
2009-12-15
We present a fundamental concept - closed sets of correlations - for studying nonlocal correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum nonlocality is limited, and for finding constraints on physical theories beyond quantum mechanics.
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
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.
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.
Weakly nonlocal hydrodynamics and the origin of viscosity in the adhesion model
Ribeiro, A.L.B.; Peixoto de Faria, J.G.
2005-03-15
We use the weakly nonlocal hydrodynamics approach to obtain a dynamical equation for the peculiar velocity field in which the viscosity term is physically motivated. Based on some properties of the Ginzburg-Landau equation and the wave mechanics analog of hydrodynamics we find the nonlocal adhesion approximation taking into account the internal structures of the Zeldovich pancakes. If the internal structures correspond to significant mesoscopic fluctuations, viscosity is probably driven by a stochastic force and dynamics is given by the noisy Burgers equation.
Stereopsis from contrast envelopes.
Langley, K; Fleet, D J; Hibbard, P B
1999-07-01
We report two experiments concerning the site of the principal nonlinearity in second-order stereopsis. The first exploits the asymmetry in perceiving transparency with second-order stimuli found by Langley et al. (1998) (Proceedings of the Royal Society of London B, 265, 1837-1845) i.e. the product of a positive-valued contrast envelope and a mean-zero carrier grating can be seen transparently only when the disparities are consistent with the envelope appearing in front of the carrier. We measured the energy at the envelope frequencies that must be added in order to negate this asymmetry. We report that this amplitude can be predicted from the envelope sidebands and not from the magnitude of compressive pre-cortical nonlinearities measured by other researchers. In the second experiment, contrast threshold elevations were measured for the discrimination of envelope disparities following adaptation to sinusoidal gratings. It is reported that perception of the envelope's depth was affected most when the adapting grating was similar (in orientation and frequency) to the carrier, rather than to the contrast envelope. These results suggest that the principal nonlinearity in second-order stereopsis is cortical, occurring after orientation- and frequency-selective linear filtering. PMID:10367053
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.
On nonlocal electron heat conduction
Krasheninnikov, S.I. )
1993-01-01
An improvement of the Albritton nonlocal electron heat transport model is proposed for high-[ital Z] plasmas. The thermal decay of the temperature perturbation in a uniform plasma as calculated by this model is compared with that obtained by Fokker--Planck simulations. Complete agreement is found up to values [ital k][lambda][sub [ital e
Plastic failure of nonlocal beams.
Challamel, Noël; Lanos, Christophe; Casandjian, Charles
2008-08-01
This paper questions the mode of collapse of some simple softening nonlocal structural systems comprising the classical cantilever beam. Nanobeams can be concerned by such an elementary model. The homogeneous cantilever beam loaded by a concentrated force at its extremity is first considered as a structural paradigm. A nonlocal plasticity model is developed in order to control the localization process induced by microcracking phenomena. An implicit gradient plasticity model equivalent to a nonlocal integral plasticity model is used in this paper. It is shown that the regularized problem is well posed. Closed-form solutions of the elastoplastic deflection are finally derived. The length of the plastic zone grows during the softening process until an asymptotic limited value, which depends on the characteristic length of the material. Scale effects are clearly obtained for these static bending tests. Other structural cases are also presented, including the simply supported beam under uniform transverse loading. It is concluded that the mode of collapse is firmly a nonlocal phenomenon. PMID:18850959
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…
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.
NASA Technical Reports Server (NTRS)
Burlaga, L. F.
1971-01-01
Processes which occur within the region between approximately 2 solar radii and 25 solar radii, which is called the solar envelope and the effect on the solar wind as seen at 1 AU are discussed. In the envelope the wind speed becomes supersonic and super-Alfvenic, the magnetic energy density is larger than the flow energy density, and the magnetic energy density is much larger than the thermal energy density. Large azimuthal gradients in the bulk speed are expected in the envelope, but the stream interactions near the outer edge of the envelope are probably relatively small. Cosmic ray observations suggest the presence of hydromagnetic waves in the envelope. The collisionless damping of such waves could heat protons out to approximately 25 solar radii and thereby cause an increase in V and T sub p consistent with the observed T sub p -V relation. A mechanism which couples protons and electrons would also heat and accelerate the wind. Alfven waves can accelerate the wind in the envelope without necessarily causing heating of protons; the Lorentz force might have a similar effect.
Quadrature rules for finite element approximations of 1D nonlocal problems
NASA Astrophysics Data System (ADS)
Zhang, Xiaoping; Gunzburger, Max; Ju, Lili
2016-04-01
It is well known that calculations of the entries of the stiffness matrix in the finite element approximations of nonlocal diffusion and mechanics models are often very time-consuming due to the double integration process over the domain and the singularities of the nonlocal kernel functions. In this paper, we propose some effective and accurate quadrature rules for computing these double integrals for one-dimensional nonlocal problems; in particular, for problems with highly singular kernels, the corresponding inner integrals can be first evaluated exactly in our method, and the outer one then will be approximated by some popular quadrature rules. With these quadrature rules, the assembly of the stiffness matrix in the finite element method for the nonlocal problems becomes similar to that for the classical partial differential equations and is thus quite efficient.
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.; 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,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
Influence of nonlocal damping on the field-driven domain wall motion
NASA Astrophysics Data System (ADS)
Yuan, H. Y.; Yuan, Zhe; Xia, Ke; Wang, X. R.
2016-08-01
We derive a general expression of nonlocal damping in noncollinear magnetization due to the nonuniform spin current pumped by precessional magnetization and incorporate it into a generalized Thiele equation to study its effects on the dynamics of the transverse and vortex domain walls (DWs) in ferromagnetic nanowires. We demonstrate that the transverse component of nonlocal damping slows down the field-driven DW propagation and increases the Walker breakdown field, whereas it is neglected in many previous works in literature. The experimentally measured DW mobility variation with the damping tuned by doping with heavy rare-earth elements that had discrepancy from micromagnetic simulation is now well understood with the nonlocal damping. Our results suggest that the nonlocal damping should be properly included as a prerequisite for quantitative studies of current-induced torques in noncollinear magnetization.
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.
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
Optimal protocols for nonlocality distillation
Hoeyer, Peter; Rashid, Jibran
2010-10-15
Forster et al. recently showed that weak nonlocality can be amplified by giving the first protocol that distills a class of nonlocal boxes (NLBs) [Phys. Rev. Lett. 102, 120401 (2009)] We first show that their protocol is optimal among all nonadaptive protocols. We next consider adaptive protocols. We show that the depth-2 protocol of Allcock et al. [Phys. Rev. A 80, 062107 (2009)] performs better than previously known adaptive depth-2 protocols for all symmetric NLBs. We present a depth-3 protocol that extends the known region of distillable NLBs. We give examples of NLBs for which each of the Forster et al., the Allcock et al., and our protocols perform best. The understanding we develop is that there is no single optimal protocol for NLB distillation. The choice of which protocol to use depends on the noise parameters for the NLB.
Randomness versus nonlocality and entanglement.
Acín, Antonio; Massar, Serge; Pironio, Stefano
2012-03-01
The outcomes obtained in Bell tests involving two-outcome measurements on two subsystems can, in principle, generate up to 2 bits of randomness. However, the maximal violation of the Clauser-Horne-Shimony-Holt inequality guarantees the generation of only 1.23 bits of randomness. We prove here that quantum correlations with arbitrarily little nonlocality and states with arbitrarily little entanglement can be used to certify that close to the maximum of 2 bits of randomness are produced. Our results show that nonlocality, entanglement, and randomness are inequivalent quantities. They also imply that device-independent quantum key distribution with an optimal key generation rate is possible by using almost-local correlations and that device-independent randomness generation with an optimal rate is possible with almost-local correlations and with almost-unentangled states. PMID:22463395
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. PMID:25635538
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.
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. PMID:21405447
NASA Astrophysics Data System (ADS)
Narendar, S.; Gopalakrishnan, S.
2010-11-01
This paper presents the strong nonlocal scale effect on the flexural wave propagation in a monolayer graphene sheet. The graphene is modeled as an isotropic plate of one atom thick. Nonlocal governing equation of motion is derived and wave propagation analysis is performed using spectral analysis. The present analysis shows that the flexural wave dispersion in graphene obtained by local and nonlocal elasticity theories is quite different. The nonlocal elasticity calculation shows that the wavenumber escapes to infinite at certain frequency and the corresponding wave velocity tends to zero at that frequency indicating localization and stationary behavior. This behavior is captured in the spectrum and dispersion curves. The cut-off frequency of flexural wave not only depend on the axial wavenumber but also on the nonlocal scaling parameter. The effect of axial wavenumber on the wave behavior in graphene is also discussed in the present manuscript.
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.
Serendipitous discoveries in nonlocal gravity theory
NASA Astrophysics Data System (ADS)
Barvinsky, A. O.
2012-05-01
We present a class of generally covariant nonlocal gravity models which have a flat-space general relativistic limit and also possess a stable de Sitter or anti-de Sitter (AdS) background with an arbitrary value of its cosmological constant. The nonlocal action of the theory is formulated in the Euclidean signature spacetime and is understood as an approximation to the quantum effective action (generating functional of one-particle irreducible diagrams) originating from fundamental quantum gravity theory. Using the known relation between the Schwinger-Keldysh technique for quantum expectation values and the Euclidean quantum field theory we derive from this action the causal effective equations of motion for mean value of the metric field in the physical Lorentzian-signature spacetime. Thus we show that the (A)dS background of the theory carries as free propagating modes massless gravitons having two polarizations identical to those of the Einstein theory with a cosmological term. The on-shell action of the theory is vanishing both for the flat-space and (A)dS backgrounds which play the role of stable vacua underlying, respectively, the ultraviolet and infrared phases of the theory. We also obtain linearized gravitational potentials of compact matter sources and show that in the infrared (A)dS phase their effective gravitational coupling Geff can be essentially different from the Newton gravitational constant GN of the short-distance general relativistic phase. When Geff≫GN the (A)dS phase can be regarded as a strongly coupled infrared modification of Einstein theory not only describing the dark energy mechanism of cosmic acceleration but also simulating the dark matter phenomenon by enhanced gravitational attraction at long distances.
Evidence for Nonlocal Electrodynamics in Planar Josephson Junctions
NASA Astrophysics Data System (ADS)
Boris, A. A.; Rydh, A.; Golod, T.; Motzkau, H.; Klushin, A. M.; Krasnov, V. M.
2013-09-01
We study the temperature dependence of the critical current modulation Ic(H) for two types of planar Josephson junctions: a low-Tc Nb/CuNi/Nb and a high-Tc YBa2Cu3O7-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 Ic(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.
Explaination of nonlocal granular fluidity in terms of microscopic fluctuations
NASA Astrophysics Data System (ADS)
Zhang, Qiong; Kamrin, Ken
A recently proposed granular constitutive law has shown capability to predict nonlocal granular rheology using a variable denoted ``granular fluidity''. This work is aimed at finding the microscopic physical meaning of fluidity in terms of fluctuations such as fluctuation of normalized shear stress and fluctuation of velocity. We try to predict the fluidity as a function of the fluctuation of normalized shear stress, and also test Eyring equation and kinetic theory based on the theoretical prediction proposed in other work. We find a consistent definition for the fluidity to be proportional to the product of the velocity fluctuations and some function of packing fraction divided by the average diameter of the grains. This definition shows predictive ability in multiple geometries for which flow behavior is nonlocal. It is notable that the fluidity is well-defined as a function of kinematic state variables, as one would hope for a quantity of this nature.
Beam envelope calculations in general linear coupled lattices
NASA Astrophysics Data System (ADS)
Chung, Moses; Qin, Hong; Groening, Lars; Davidson, Ronald C.; Xiao, Chen
2015-01-01
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.
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.
Nonlocality in quantum theory understood in terms of Einstein's nonlinear field approach
NASA Astrophysics Data System (ADS)
Bohm, D.; Hiley, B. J.
1981-08-01
We discuss Einstein's ideas on the need for a theory that is both objective and local and also his suggestion for realizing such a theory through nonlinear field equations. We go on to analyze the nonlocality implied by the quantum theory, especially in terms of the experiment of Einstein, Podolsky, and Rosen. We then suggest an objective local field model along Einstein's lines, which might explain quantum nonlocality as a coordination of the properties of pulse-like solutions of the nonlinear equations that would represent particles. Finally, we discuss the implications of our model for Bell's inequality.
Cosmological perturbations in SFT inspired non-local scalar field models
NASA Astrophysics Data System (ADS)
Koshelev, Alexey S.; Vernov, Sergey Yu.
2012-10-01
We study cosmological perturbations in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field and explicitly prove that for the free field it is identical to a system of local cosmological perturbation equations in a particular model with multiple (maybe infinitely many) local free scalar fields. We also show that vector and tensor perturbations are absent in this set-up.
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.
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.
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.
Robustness of multiparty nonlocality to local decoherence
NASA Astrophysics Data System (ADS)
Jang, Sung Soon; Cheong, Yong Wook; Kim, Jaewan; Lee, Hai-Woong
2006-12-01
We investigate the robustness of multiparty nonlocality under local decoherence, acting independently and equally on each subsystem. To be specific, we consider an N -qubit Greenberger-Horne-Zeilinger (GHZ) state under a depolarization, dephasing, or dissipation channel, and examine nonlocality by testing violation of the Mermin-Klyshko inequality, which is one of Bell’s inequalities for multiqubit systems. The results show that the robustness of nonlocality increases with the number of qubits, and that the nonlocality of an N -qubit GHZ state with even N is extremely persistent against dephasing.
Targeting Nuclear Envelope Repair.
2016-06-01
Migrating cancer cells undergo repeated rupture of the protective nuclear envelope as they squeeze through small spaces in the surrounding tissue, compromising genomic integrity. Inhibiting both general DNA repair and the mechanism that seals these tears may enhance cell death and curb metastasis. PMID:27130435
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.
Nonlocal plate model for free vibrations of single-layered graphene sheets
NASA Astrophysics Data System (ADS)
Ansari, R.; Sahmani, S.; Arash, B.
2010-11-01
Vibration analysis of single-layered graphene sheets (SLGSs) is investigated using nonlocal continuum plate model. To this end, Eringens's nonlocal elasticity equations are incorporated into the classical Mindlin plate theory for vibrations of rectangular nanoplates. In contrast to the classical model, the nonlocal model developed in this study has the capability to evaluate the natural frequencies of the graphene sheets with considering the size-effects on the vibrational characteristics of them. Solutions for frequencies of the free vibration of simply-supported and clamped SLGSs are computed using generalized differential quadrature (GDQ) method. Then, molecular dynamics (MD) simulations for the free vibration of various SLGSs with different values of side length and chirality are employed, the results of which are matched with the nonlocal model ones to derive the appropriate values of the nonlocal parameter relevant to each boundary condition. It is found that the value of the nonlocal parameter is independent of the magnitude of the geometrical variables of the system.
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.
More nonlocality with less entanglement
Vidick, Thomas; Wehner, Stephanie
2011-05-15
Recent numerical investigations [K. Pal and T. Vertesi, Phys. Rev. A 82, 022116 (2010)] suggest that the I3322 inequality, arguably the simplest extremal Bell inequality after the CHSH inequality, has a very rich structure in terms of the entangled states and measurements that maximally violate it. Here we show that for this inequality the maximally entangled state of any dimension achieves the same violation than just a single EPR pair. In contrast, stronger violations can be achieved using higher dimensional states which are less entangled. This shows that the maximally entangled state is not the most nonlocal resource, even when one restricts attention to the most simple extremal Bell inequalities.
NASA Technical Reports Server (NTRS)
1983-01-01
STS-8 postal Stamp envelope with Challenger insignia, USA eagle stamp, 25th NASA anniversary stamp. The envelope is stamped with various postmarks, one saying Kennedy Space Center, Fl., another saying 'Returned to earth, Edwards AFB, CA'.
Nonlocal Closures for Plasma Fluid Simulations
NASA Astrophysics Data System (ADS)
Held, Eric
2003-10-01
Theoretical tools applied to lab and astrophysical plasmas tend toward two extremes: kinetic models rife with physics but operating for short times and fluid models employing simplified closure relations but operating for long times. Until computers are fast enough to calculate kinetic physics over resistive times, efforts to extend plasma fluid models to handle a wider range of physics are critical. In this work, we generalize the program of fluid closure to capture kinetic effects in nonlocal, integral forms for higher-order fluid moments. These closures embody collisional, particle-trapping and Landau physics by integrating the fluid drives and closure moments along characteristics of the distribution function, F. The inversion of an operator that includes these physical effects begins with an expansion in eigenfunctions of the collision operator. Next, the characteristics of F are identified by diagonalizing the resultant system of hyperbolic equations. Integrating and taking the closure moments of F results in coupled Volterra equations involving the fluid drives and closures. It is shown that the collisional and nearly collisionless limits of these integral equations match onto previous expressions. In addition to significantly advancing the realism of previous fluid closures, integration along comparatively few ( ˜ 100)characteristics represents a significant reduction in work compared to kinetic treatments that follow millions of particles. These characteristics uncover the essential velocity-space dependence of F and hence render this closure scheme suitable for simulation of long time scale behavior. As a specific example, we conclude this talk by discussing the incorporation of these closures in plasma fluid simulations of neoclassical tearing modes in ITER-relevant discharges.
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.
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.
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. PMID:23787690
Virial Theorem in Nonlocal Newtonian Gravity
NASA Astrophysics Data System (ADS)
Mashhoon, Bahram
2016-05-01
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.
NASA Astrophysics Data System (ADS)
Fathi, Reza; Lotfan, Saeed
2016-05-01
Nowadays investigating the vibration behavior of carbon nanotubes (CNTs) has drawn considerable attention due to the superior mechanical properties of the CNTs. One of the powerful theoretical methods to study the vibration behavior of CNTs is implementing the nonlocal theory. Most of studies on the vibration behavior of CNTs have assumed a fixed value for small scale parameter for all vibration modes, however, this value is mode-dependent. Therefore, in this paper, the small scale parameter is calibrated for a single-walled carbon nanotube (SWCNT) with respect to each vibration mode. For this propose, the governing equation of motion based on the nonlocal beam theory is extracted by applying the Hamilton's principle. Then, by using the power series method, an eigenvalue problem is defined to derive the calibrated value of small scale constant and nonlocal mode shapes of the CNT. By using the expansion theory, the equation of motion is discretized, and the effect of nonlocality on the modal parameters and stability of the CNT under compressive force is investigated. Finally, the possibility of estimating nonlocal parameter based on simulated frequency domain response of the system by using modal analysis methods is studied. The results show that the calibration of small scale constant is important and the critical axial force is highly sensitive to this value.
Stability and bifurcations in a nonlocal delayed reaction-diffusion population model
NASA Astrophysics Data System (ADS)
Chen, Shanshan; Yu, Jianshe
2016-01-01
A nonlocal delayed reaction-diffusion equation with Dirichlet boundary condition is considered in this paper. It is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium. The stability/instability of the bifurcated positive equilibrium and associated Hopf bifurcation are investigated, providing us with a complete picture of the dynamics.
Nonlocal contour dynamics model for chemical front motion
NASA Astrophysics Data System (ADS)
Petrich, Dean M.; Goldstein, Raymond E.
1994-02-01
Pattern formation exhibited by a two-dimensional reaction-diffusion system in the fast inhibitor limit is considered for the point of view of interface motion. A dissipative nonlocal equation of motion for the boundary between high and low concentrations of the slow species is derived heuristically. Under these dynamics, a compact domain of high concentration may develop into a space-filling labyrinthine structure in which nearby fronts repel. Similar patterns have been observed recently by Lee, McCormick, Ouyang, and Swinney in a reacting chemical system.
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.
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.
Can EPR non-locality be geometrical?
Ne`eman, Y. |; Botero, A.
1995-10-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3.
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. PMID:27532045
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
All entangled quantum states are nonlocal.
Buscemi, Francesco
2012-05-18
Departing from the usual paradigm of local operations and classical communication adopted in entanglement theory, we study here the interconversion of quantum states by means of local operations and shared randomness. A set of necessary and sufficient conditions for the existence of such a transformation between two given quantum states is given in terms of the payoff they yield in a suitable class of nonlocal games. It is shown that, as a consequence of our result, such a class of nonlocal games is able to witness quantum entanglement, however weak, and reveal nonlocality in any entangled quantum state. An example illustrating this fact is provided. PMID:23003127
Nonlocality of the Aharonov-Bohm effect
NASA Astrophysics Data System (ADS)
Aharonov, Yakir; Cohen, Eliahu; Rohrlich, Daniel
2016-04-01
Although the Aharonov-Bohm and related effects are familiar in solid-state and high-energy physics, the nonlocality of these effects has been questioned. Here we show that the Aharonov-Bohm effect has two very different aspects. One aspect is instantaneous and nonlocal; the other aspect, which depends on entanglement, unfolds continuously over time. While local, gauge-invariant variables may occasionally suffice for explaining the continuous aspect, we argue that they cannot explain the instantaneous aspect. Thus the Aharonov-Bohm effect is, in general, nonlocal.
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.
Non-local ocean mixing model and a new plume model for deep convection
NASA Astrophysics Data System (ADS)
Canuto, V. M.; Cheng, Y.; Howard, A. M.
Turbulent fluxes can be represented by a diffusivity tensor, the symmetric part of which describes " turbulent diffusion" while the anti-symmetric part describes " advection". Diffusion is a local process in the sense that it depends only on the local gradients of the mean fields while advection is non-local for it is represented by an integral over all length scales (all eddies) that can "fit" from say the bottom of the physical domain to the z where the fluxes are computed. In the ocean, there are two main regimes where non-local transport is important. One regime is where storms release a sudden burst of mechanical energy to the ocean surface that is then transported downward by energetic eddies that deepen the mixed layer. Even relatively simple non-local models yield results considerably more realistic than those of local models. The second regime is deep convection (DC) caused by loss of surface buoyancy, the description of which is required for a reliable assessment of water masses formation. At present, there is no reliable model for either of these non-local regimes individually or much less a formalism capable of accounting for both regimes simultaneously. The goal of this paper is to present a formalism that provides the expressions for the non-local fluxes for momentum, heat and salinity encompassing both cases. Since the resulting number of dynamic equations involves is however large, we work out two sub-models, one when only shear must be treated non-locally (e.g., when storms release mechanical energy) and one when only buoyancy is to be treated non-locally (the DC case). We employ the Reynolds Stress formalism in which non-locality is represented by the third-order moments which in turn depend on the fourth-order moments for which we employ a new model that has been tested against LES data, aircraft data and a full PBL simulation. For the DC case, we rewrite the non-local model in terms of Plumes since thus far the only non-local model used to treat
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.
Discontinuous envelope function in semiconductor heterostructures
NASA Astrophysics Data System (ADS)
Drouhin, Henri-Jean; Bottegoni, Federico; Nguyen, T. L. Hoai; Wegrowe, Jean-Eric; Fishman, Guy
2013-09-01
Based on a proper definition of the current operators for non-quadratic Hamiltonians, we derive the expression for the transport current which involves the derivative of the imaginary part of the free-electron current, highlighting peculiarities of the extra terms. The expression of the probability current, when Spin-Orbit Interaction (SOI) is taken into account, requires a reformulation of the boudary conditions. This is especially important for tunnel heterojunctions made of non-centrosymmetric semiconductors. Therefore, we consider a model case: tunneling of conduction electrons through a [110]-oriented GaAs barrier. The new boundary conditions are reduced to two set of equations: the first one expresses the discontinuity of the envelope function at the interface while the other one expresses the discontinuity of the derivative of the envelope function.
NASA Astrophysics Data System (ADS)
Shafiei, Navvab; Kazemi, Mohammad; Ghadiri, Majid
2016-08-01
This study is concerned with the small-scale effect on the nonlinear flapwise bending vibration of rotating cantilever and propped cantilever nanobeams. Euler-Bernoulli beam theory is used to model the nanobeam with nonlinearity. Nonlinear strain-displacement relations are employed to account for geometric nonlinearity of the system. The axial forces are modeled as the true spatial and thermal variations due to the rotation. Hamilton's principle is used to derive the nonlinear governing equation and nonlocal nonlinear boundary conditions based on Eringen's nonlocal elasticity theory. Finally, the differential quadrature method is used in conjunction with the direct iterative method to derive the nonlinear vibration frequencies of the nanobeam. The effects of the angular velocity, nonlocal small-scale parameter, temperature change and nonlinear amplitude on nonlinear vibration of the rotary nanobeam are discussed. The results of this work can be used in nanosensors, nanomotors, nanoturbines and NEMS applications.
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.
NASA Astrophysics Data System (ADS)
Arash, B.; Ansari, R.
2010-06-01
Based upon a nonlocal shell model accounting for the small-scale effects, the vibration characteristics of single-walled carbon nanotubes (SWCNTs) with different boundary conditions subjected to initial strain are studied in this paper. The set of governing equations of motion is numerically solved by a method that emerged from incorporating the radial point interpolation approximation within the framework of the generalized differential quadrature method. The effectiveness of the present nonlocal shell model is assessed by the molecular dynamics simulations as a benchmark of good accuracy. Accordingly, nonlocal parameters for clamped and cantilever SWCNTs with thicknesses of 0.066 and 0.34 nm are proposed due to the uncertainty that exists in defining nanotube wall thickness. The simulation results show that the resonant frequencies of SWCNTs are very sensitive to the initial strain, although small.
NASA Astrophysics Data System (ADS)
Zenkour, Ashraf M.
2016-05-01
The transient thermal analysis of a single-layered graphene sheet (SLGS) embedded in viscoelastic medium is presented by using the nonlocal elasticity theory. The elastic medium, which characterized by the linear Winkler's modulus and Pasternak's (shear) foundation modulus, is changed to a viscoelastic one by including the viscous damping term. The governing dynamical equation is obtained and solved for simply-supported SLGSs. Firstly; the effect of the nonlocal parameter is discussed carefully for the vibration and bending problems. Secondly, the effects of other parameter like aspect ratio, thickness-to-length ratio, Winkler-Pasternak's foundation, viscous damping coefficient on bending field quantities of the SLGSs are investigated in detail. The present results are compared with the corresponding available in the literature. Additional results for thermal local and nonlocal deflections and stresses are presented to investigate the thermal visco-Pasternak's parameters for future comparisons.
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.
NASA Astrophysics Data System (ADS)
Ebrahimi, Farzad; Barati, Mohammad Reza
2016-09-01
In this article, combined effect of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is investigated by developing various refined beam theories which capture shear deformation influences needless of any shear correction factor. The material properties of FG nanobeam are temperature dependent and change gradually along the thickness through the power-law model. Size-dependent description of the nanobeam is performed applying nonlocal elasticity theory of Eringen. Nonlocal governing equations of embedded FG nanobeam in hygro-thermal environment obtained from Hamilton's principle are solved analytically. To verify the validity of the developed theories, the results of the present work are compared with those available in the literature. The effects of various hygro-thermal loadings, elastic foundation, gradient index, nonlocal parameter, and slenderness ratio on the vibrational behavior of FG nanobeams modeled via various beam theories are explored.
Nonlocal ordinary magnetoresistance in indium arsenide
NASA Astrophysics Data System (ADS)
Liu, Pan.; Yuan, Zhonghui.; Wu, Hao.; Ali, S. S.; Wan, Caihua.; Ban, Shiliang.
2015-07-01
Deflection of carriers by Lorentz force results in an ordinary magnetoresistance (OMR) of (μB)2 at low field. Here we demonstrate that the OMR in high mobility semiconductor InAs could be enhanced by measurement geometry where two probes of voltmeter were both placed on one outer side of two probes of current source. The nonlocal OMR was 3.6 times as large as the local one, reaching 1.8×104% at 5 T. The slope of the linear field dependence of the nonlocal OMR was improved from 12.6 T-1 to 45.3 T-1. The improvement was ascribed to polarity-conserved charges accumulating on boundaries in nonlocal region due to Hall effect. This InAs device with nonlocal geometry could be competitive in B-sensors due to its high OMR ratio, linear field dependence and simple structure.
Nonlocal transport of passive scalars in turbulent penetrative convection
Miesch; Brandenburg; Zweibel
2000-01-01
We present a Green's function approach for quantifying the transport of a passive scalar (tracer) field in three-dimensional simulations of turbulent convection. Nonlocal, nondiffusive behavior is described by a transilient matrix (the discretized Green's function), whose elements contain the fractional tracer concentrations moving from one subvolume to another as a function of time. The approach was originally developed for and applied to geophysical flows, but here we extend the formalism and apply it in an astrophysical context to three-dimensional simulations of turbulent compressible convection with overshoot into convectively stable bounding regions. We introduce a novel technique to compute this matrix in a single simulation by advecting labeled particles rather than solving the passive scalar equation for a large number of different initial conditions. The transilient matrices thus computed are used as a diagnostic tool to quantitatively describe nonlocal transport via matrix moments and transport coefficients in a generalized, multiorder diffusion equation. Results indicate that transport in both the vertical and horizontal directions is strongly influenced by the presence of coherent velocity structures, generally resembling ballistic advection more than diffusion. The transport of a small fraction of tracer particles deep into the underlying stable region is reasonably efficient, a result which has possible implications for the problem of light-element depletion in late-type stars. PMID:11046285
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.
Structure of quantum and broadcasting nonlocal correlations
NASA Astrophysics Data System (ADS)
Saha, Debashis; Pawłowski, Marcin
2015-12-01
The multipartite setting offers much more complexity of nonlocality than the bipartite one. We analyze the structure of tripartite nonlocal correlations by proposing inequalities satisfied by each of type bilocal, broadcasting, and quantum but violated by the other two. One of the inequalities satisfied by broadcasting correlations is generalized for multipartite systems. The study of its quantum mechanical violation reveals that Greenberger-Horne-Zeilinger-like states exhibit new, powerful correlations.
Nonlocality with ultracold atoms in a lattice
NASA Astrophysics Data System (ADS)
Pelisson, Sophie; Pezzè, Luca; Smerzi, Augusto
2016-02-01
We study the creation of nonlocal states with ultracold atoms trapped in an optical lattice. We show that these states violate Bell inequality by measuring one- and two-body correlations. Our scheme only requires beam-splitting operations and global phase shifts, and can be realized within the current technology, employing single-site addressing. This proposal paves the way to study multipartite nonlocality and entanglement in ultracold-atomic systems.
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.
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.
Nonlocalized receptivity of boundary layers to three-dimensional disturbances
NASA Astrophysics Data System (ADS)
Crouch, J. D.; Bertolotti, F. P.
1992-01-01
The nonlocalized receptivity of the Blasius boundary layer over a wavy surface is analyzed using two different approaches. First, a mode-interaction theory is employed to unveil basic mechanisms and to explore the interplay between different components of the disturbance field. The second approach is derived from the parabolized stability equations. These nonlinear equations incorporate the effects of the stream-wise divergence of the boundary layer. The analysis provides results for three-dimensional disturbances and also considers nonparallel effects. Results for two-dimensional disturbances demonstrate that nonparallel effects are negligible and substantiates the mechanism described by the mode-interaction theory. Nonparallel effects become significant with increasing three-dimensionality. Receptivity amplitudes are shown to be large over a broad range of surface wave numbers. When operative, this mechanism is likely to dominate the boundary-layer receptivity.
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)
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.
Nonlocality of orthogonal product states
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Chao; Gao, Fei; Qin, Su-Juan; Yang, Ying-Hui; Wen, Qiao-Yan
2015-07-01
In this paper, we mainly study the local indistinguishability of mutually orthogonal product basis quantum states in d ⊗d . In 3 ⊗3 , Bennett et al. [ Phys. Rev. A 59, 1070 (1999), 10.1103/PhysRevA.59.1070] presented nine orthogonal product basis quantum states which cannot be distinguished by local operations and classical communication (LOCC). In the work by Zhang et al. [Z.-C. Zhang et al., Phys. Rev. A 90, 022313 (2014), 10.1103/PhysRevA.90.022313], this result was generalized in d ⊗d , where d is odd. In this paper, we aim to construct locally indistinguishable orthogonal product basis quantum states in d ⊗d . For the general d ⊗d (d >2 ) quantum system, we first construct 4 d -4 orthogonal product states, and prove these states are locally indistinguishable using a very simple but quite effective method. Then, based on these states, we construct some classes of locally indistinguishable orthogonal product basis quantum states (OPBS) in d ⊗d (d >2 ) . Finally, we construct some LOCC indistinguishable OPBS in multipartite quantum systems. All of the above results demonstrate the phenomenon of nonlocality without entanglement.
Dark matter from spacetime nonlocality
NASA Astrophysics Data System (ADS)
Saravani, Mehdi; Aslanbeigi, Siavash
2015-11-01
We propose that dark matter is not yet another new particle in nature, but that it is a remnant of quantum gravitational effects on known fields. We arrive at this possibility in an indirect and surprising manner: by considering retarded, nonlocal, and Lorentzian evolution for quantum fields. This is inspired by recent developments in causal set theory, where such an evolution shows up as the continuum limit of scalar field propagation on a background causal set. Concretely, we study the quantum theory of a massless scalar field whose evolution is given not by the the d'Alembertian □, but by an operator □˜ which is Lorentz invariant, reduces to □ at low energies, and defines an explicitly retarded evolution: (□˜ϕ )(x ) only depends on ϕ (y ), where y is in the causal past of x . This modification results in the existence of a continuum of massive particles, in addition to the usual massless ones, in the free theory. When interactions are introduced, these massive or off-shell quanta can be produced by the scattering of massless particles, but once produced, they no longer interact, which makes them a natural candidate for dark matter.
Nonlocality in deuteron stripping reactions.
Timofeyuk, N K; Johnson, R C
2013-03-15
We propose a new method for the analysis of deuteron stripping reactions, A(d,p)B, in which the nonlocality of nucleon-nucleus interactions and three-body degrees of freedom are accounted for in a consistent way. The model deals with equivalent local nucleon potentials taken at an energy shifted by ∼40 MeV from the "E(d)/2" value frequently used in the analysis of experimental data, where E(d) is the incident deuteron energy. The "E(d)/2" rule lies at the heart of all three-body analyses of (d, p) reactions performed so far with the aim of obtaining nuclear structure properties such as spectroscopic factors and asymptotic normalization coefficients that are crucial for our understanding of nuclear shell evolution in neutron- and proton-rich regions of the nuclear periodic table and for predicting the cross sections of stellar reactions. The large predicted shift arises from the large relative kinetic energy of the neutron and proton in the incident deuteron in those components of the n+p+A wave function that dominate the (d, p) reaction amplitude. The large shift reduces the effective d-A potentials and leads to a change in predicted (d, p) cross sections, thus affecting the interpretation of these reactions in terms of nuclear structure. PMID:25166525
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.
On the fractional generalization of Eringenʼs nonlocal elasticity for wave propagation
NASA Astrophysics Data System (ADS)
Challamel, Noël; Zorica, Dušan; Atanacković, Teodor M.; Spasić, Dragan T.
2013-03-01
A fractional nonlocal elasticity model is presented in this Note. This model can be understood as a possible generalization of Eringen's nonlocal elastic model, with a free non-integer derivative in the stress-strain fractional order differential equation. This model only contains a single length scale and the fractional derivative order as parameters. The kernel of this integral-based nonlocal model is explicitly given for various fractional derivative orders. The dynamical properties of this new model are investigated for a one-dimensional problem. It is possible to obtain an analytical dispersive equation for the axial wave problem, which is parameterized by the fractional derivative order. The fractional derivative order of this generalized fractional Eringen's law is then calibrated with the dispersive wave properties of the Born-Kármán model of lattice dynamics and appears to be greater than the one of the usual Eringen's model. An excellent matching of the dispersive curve of the Born-Kármán model of lattice dynamics is obtained with such generalized integral-based nonlocal model.
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.
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.
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. PMID:25955039
Tounsi, Abdeloauhed; Heireche, Houari; Benzair, Abdelnour; Mechab, Ismail
2009-11-01
Most recently, Lee and Chang (2009 J. Phys.: Condens. Matter 21 115302) combined nonlocal theory and Euler-Bernoulli beam theory in the study of the vibration of the fluid-conveying double-walled carbon nanotube. In this recent published work, the importance of using nonlocal stress tensors consistently has been overlooked, and some ensuring relations were still presented based on the local stress components. Therefore, the governing equations and applied forces obtained in this manner are either inconsistent or incomplete. In this comment, the consistent governing equations for modelling free transverse vibration of the fluid-conveying double-walled carbon nanotube using the nonlocal Euler-Bernoulli beam model are derived. PMID:21832479
Nonlocal Drag of Magnons in a Ferromagnetic Bilayer.
Liu, Tianyu; Vignale, G; Flatté, Michael E
2016-06-10
Quantized spin waves, or magnons, in a magnetic insulator are assumed to interact weakly with the surroundings, and to flow with little dissipation or drag, producing exceptionally long diffusion lengths and relaxation times. In analogy to Coulomb drag in bilayer two-dimensional electron gases, in which the contribution of the Coulomb interaction to the electric resistivity is studied by measuring the interlayer resistivity (transresistivity), we predict a nonlocal drag of magnons in a ferromagnetic bilayer structure based on semiclassical Boltzmann equations. Nonlocal magnon drag depends on magnetic dipolar interactions between the layers and manifests in the magnon current transresistivity and the magnon thermal transresistivity, whereby a magnon current in one layer induces a chemical potential gradient and/or a temperature gradient in the other layer. The largest drag effect occurs when the magnon current flows parallel to the magnetization; however, for oblique magnon currents a large transverse current of magnons emerges. We examine the effect for practical parameters, and find that the predicted induced temperature gradient is readily observable. PMID:27341254
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. PMID:27300886
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.
Nonlocal Drag of Magnons in a Ferromagnetic Bilayer
NASA Astrophysics Data System (ADS)
Liu, Tianyu; Vignale, G.; Flatté, Michael E.
2016-06-01
Quantized spin waves, or magnons, in a magnetic insulator are assumed to interact weakly with the surroundings, and to flow with little dissipation or drag, producing exceptionally long diffusion lengths and relaxation times. In analogy to Coulomb drag in bilayer two-dimensional electron gases, in which the contribution of the Coulomb interaction to the electric resistivity is studied by measuring the interlayer resistivity (transresistivity), we predict a nonlocal drag of magnons in a ferromagnetic bilayer structure based on semiclassical Boltzmann equations. Nonlocal magnon drag depends on magnetic dipolar interactions between the layers and manifests in the magnon current transresistivity and the magnon thermal transresistivity, whereby a magnon current in one layer induces a chemical potential gradient and/or a temperature gradient in the other layer. The largest drag effect occurs when the magnon current flows parallel to the magnetization; however, for oblique magnon currents a large transverse current of magnons emerges. We examine the effect for practical parameters, and find that the predicted induced temperature gradient is readily observable.
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.
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.
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.
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. PMID:27583683
Nonlocal formulation of spin Coulomb drag
NASA Astrophysics Data System (ADS)
D'Amico, I.; Ullrich, C. A.
2013-10-01
The spin Coulomb drag (SCD) effect occurs in materials and devices where charged carriers with different spins exchange momentum via Coulomb scattering. This causes frictional forces between spin-dependent currents that lead to intrinsic dissipation, which may limit spintronics applications. A nonlocal formulation of SCD is developed which is valid for strongly inhomogeneous systems such as nanoscale spintronics devices. This nonlocal formulation of SCD is successfully applied to linewidths of intersubband spin plasmons in semiconductor quantum wells, where experiments have shown that the local approximation fails.