Nonlocal continuum-based modeling of breathing mode of nanowires including surface stress and surface inertia effects

International Nuclear Information System (INIS)

Ghavanloo, Esmaeal; Fazelzadeh, S. Ahmad; Rafii-Tabar, Hashem

2014-01-01

Nonlocal and surface effects significantly influence the mechanical response of nanomaterials and nanostructures. In this work, the breathing mode of a circular nanowire is studied on the basis of the nonlocal continuum model. Both the surface elastic properties and surface inertia effect are included. Nanowires can be modeled as long cylindrical solid objects. The classical model is reformulated using the nonlocal differential constitutive relations of Eringen and Gurtin–Murdoch surface continuum elasticity formalism. A new frequency equation for the breathing mode of nanowires, including small scale effect, surface stress and surface inertia is presented by employing the Bessel functions. Numerical results are computed, and are compared to confirm the validity and accuracy of the proposed method. Furthermore, the model is used to elucidate the effect of nonlocal parameter, the surface stress, the surface inertia and the nanowire orientation on the breathing mode of several types of nanowires with size ranging from 0.5 to 4 nm. Our results reveal that the combined surface and small scale effects are significant for nanowires with diameter smaller than 4 nm.

Nonlocal continuum-based modeling of breathing mode of nanowires including surface stress and surface inertia effects

Energy Technology Data Exchange (ETDEWEB)

Ghavanloo, Esmaeal, E-mail: ghavanloo@shirazu.ac.ir [School of Mechanical Engineering, Shiraz University, Shiraz 71963-16548 (Iran, Islamic Republic of); Fazelzadeh, S. Ahmad [School of Mechanical Engineering, Shiraz University, Shiraz 71963-16548 (Iran, Islamic Republic of); Rafii-Tabar, Hashem [Department of Medical Physics and Biomedical Engineering, Research Center for Medical Nanotechnology and Tissue Engineering, Shahid Beheshti University of Medical Sciences, Evin, Tehran (Iran, Islamic Republic of); Computational Physical Sciences Research Laboratory, School of Nano-Science, Institute for Research in Fundamental Sciences (IPM), Tehran (Iran, Islamic Republic of)

2014-05-01

Nonlocal and surface effects significantly influence the mechanical response of nanomaterials and nanostructures. In this work, the breathing mode of a circular nanowire is studied on the basis of the nonlocal continuum model. Both the surface elastic properties and surface inertia effect are included. Nanowires can be modeled as long cylindrical solid objects. The classical model is reformulated using the nonlocal differential constitutive relations of Eringen and Gurtin–Murdoch surface continuum elasticity formalism. A new frequency equation for the breathing mode of nanowires, including small scale effect, surface stress and surface inertia is presented by employing the Bessel functions. Numerical results are computed, and are compared to confirm the validity and accuracy of the proposed method. Furthermore, the model is used to elucidate the effect of nonlocal parameter, the surface stress, the surface inertia and the nanowire orientation on the breathing mode of several types of nanowires with size ranging from 0.5 to 4 nm. Our results reveal that the combined surface and small scale effects are significant for nanowires with diameter smaller than 4 nm.

Nonlocal gauge theories

International Nuclear Information System (INIS)

Partovi, M.H.

1982-01-01

From a generalization of the covariant derivative, nonlocal gauge theories are developed. These theories enjoy local gauge invariance and associated Ward identities, a corresponding locally conserved current, and a locally conserved energy-momentum tensor, with the Ward identities implying the masslessness of the gauge field as in local theories. Their ultraviolet behavior allows the presence as well as the absence of the Adler-Bell-Jackiw anomaly, the latter in analogy with lattice theories

Vibration analysis of orthotropic circular and elliptical nano-plates embedded in elastic medium based on nonlocal Mindlin plate theory and using Galerkin method

International Nuclear Information System (INIS)

Anjomshoa, Amin; Tahani, Masoud

2016-01-01

In the present study a continuum model based on the nonlocal elasticity theory is developed for free vibration analysis of embedded ortho tropic thick circular and elliptical nano-plates rested on an elastic foundation. The elastic foundation is considered to behave like a Pasternak type of foundations. Governing equations for vibrating nano-plate are derived according to the Mindlin plate theory in which the effects of shear deformations of nano-plate are also included. The Galerkin method is then employed to obtain the size dependent natural frequencies of nano-plate. The solution procedure considers the entire nano-plate as a single super-continuum element. Effect of nonlocal parameter, lengths of nano-plate, aspect ratio, mode number, material properties, thickness and foundation on circular frequencies are investigated. It is seen that the nonlocal frequencies of the nano-plate are smaller in comparison to those from the classical theory and this is more pronounced for small lengths and higher vibration modes. It is also found that as the aspect ratio increases or the nanoplate becomes more elliptical, the small scale effect on natural frequencies increases. Further, it is observed that the elastic foundation decreases the influence of nonlocal parameter on the results. Since the effect of shear deformations plays an important role in vibration analysis and design of nano-plates, by predicting smaller values for fundamental frequencies, the study of these nano-structures using thick plate theories such as Mindlin plate theory is essential.

Nonlocal quantum field theory

International Nuclear Information System (INIS)

Efimov, G.V.

1976-01-01

The basic ideas for creating the theory of nonlocal interactions of a scalar one-component field are presented. Lagrangian describing a non-interacting field is the ordinary one so that non-interacting particles are described by standard methods of the Fock space. Form factors introduced have been chosen from a class of analytic functionals and quantized. Conditions of microcausality have been considered in detail. The convergence of all integrals corresponding to the arbitrary Feynman diagrams in spinor electrodynamics is guaranteed in the frame of the rules formulated. It is noted in conclusion that the spinor electrodynamics with nonlocal interaction contains no ultraviolet divergencies and satisfies all the requirements of the quantum field theory; in this sense it is mathematically more consistent than its local version

Thermal effects on the stability of circular graphene sheets via nonlocal continuum mechanics

Directory of Open Access Journals (Sweden)

Saeid Reza Asemi

Full Text Available Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. Different non-classical theories have been used for modeling of such nano-sized systems to take account of the effect of small length scale. Among all size-dependent theories, the nonlocal elasticity theory has been commonly used to examine the stability of nano-sized structures. Some research works have been reported about the mechanical behavior of rectangular nanoplates with the consideration of thermal effects. However, in comparison with the rectangular graphene sheets, research works about the nanoplates of circular shape are very limited, especially for the buckling properties with thermal effects. Hence, in this paper, an axisymmetric buckling analysis of circular single-layered graphene sheets (SLGS is presented by decoupling the nonlocal equations of Eringen theory. Constitutive relations are modified to describe the nonlocal effects. The governing equations are derived using equilibrium equations of the circular plate in polar coordinates. Numerical solutions for buckling loads are computed using Galerkin method. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate, radius-to-thickness ratio, temperature change and mode numbers are investigated.

Mermin Non-Locality in Abstract Process Theories

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Stefano Gogioso

2015-11-01

Full Text Available The study of non-locality is fundamental to the understanding of quantum mechanics. The past 50 years have seen a number of non-locality proofs, but its fundamental building blocks, and the exact role it plays in quantum protocols, has remained elusive. In this paper, we focus on a particular flavour of non-locality, generalising Mermin's argument on the GHZ state. Using strongly complementary observables, we provide necessary and sufficient conditions for Mermin non-locality in abstract process theories. We show that the existence of more phases than classical points (aka eigenstates is not sufficient, and that the key to Mermin non-locality lies in the presence of certain algebraically non-trivial phases. This allows us to show that fRel, a favourite toy model for categorical quantum mechanics, is Mermin local. We show Mermin non-locality to be the key resource ensuring the device-independent security of the HBB CQ (N,N family of Quantum Secret Sharing protocols. Finally, we challenge the unspoken assumption that the measurements involved in Mermin-type scenarios should be complementary (like the pair X,Y, opening the doors to a much wider class of potential experimental setups than currently employed. In short, we give conditions for Mermin non-locality tests on any number of systems, where each party has an arbitrary number of measurement choices, where each measurement has an arbitrary number of outcomes and further, that works in any abstract process theory.

Accurate nonlocal theory for cascaded quadratic soliton compression

DEFF Research Database (Denmark)

Bache, Morten; Bang, Ole; Moses, Jeffrey

2007-01-01

We study soliton compression in bulk quadratic nonlinear materials at 800 nm, where group-velocity mismatch dominates. We develop a nonlocal theory showing that efficient compression depends strongly on characteristic nonlocal time scales related to pulse dispersion....

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅵ)-CONSERVATION LAWS OF MASS AND INERTIA

Institute of Scientific and Technical Information of China (English)

戴安民

2003-01-01

The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented. Combining these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum and energy may be obtained by the usual localization.

Perturbative matching of continuum and lattice quasi-distributions

Directory of Open Access Journals (Sweden)

Ishikawa Tomomi

2018-01-01

Full Text Available Matching of the quasi parton distribution functions between continuum and lattice is addressed using lattice perturbation theory specifically withWilson-type fermions. The matching is done for nonlocal quark bilinear operators with a straightWilson line in a spatial direction. We also investigate operator mixing in the renormalization and possible O(a operators for the nonlocal operators based on a symmetry argument on lattice.

Nonlocal microscopic theory of quantum friction between parallel metallic slabs

International Nuclear Information System (INIS)

Despoja, Vito; Echenique, Pedro M.; Sunjic, Marijan

2011-01-01

We present a new derivation of the friction force between two metallic slabs moving with constant relative parallel velocity, based on T=0 quantum-field theory formalism. By including a fully nonlocal description of dynamically screened electron fluctuations in the slab, and avoiding the usual matching-condition procedure, we generalize previous expressions for the friction force, to which our results reduce in the local limit. Analyzing the friction force calculated in the two local models and in the nonlocal theory, we show that for physically relevant velocities local theories using the plasmon and Drude models of dielectric response are inappropriate to describe friction, which is due to excitation of low-energy electron-hole pairs, which are properly included in nonlocal theory. We also show that inclusion of dissipation in the nonlocal electronic response has negligible influence on friction.

A generalized non-local optical response theory for plasmonic nanostructures

DEFF Research Database (Denmark)

Mortensen, N. Asger; Raza, Søren; Wubs, Martijn

2014-01-01

for their description. Here instead we present a comparatively simple semiclassical generalized non-local optical response theory that unifies quantum pressure convection effects and induced charge diffusion kinetics, with a concomitant complex-valued generalized non-local optical response parameter. Our theory...

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

International Nuclear Information System (INIS)

Sahmani, S.; Ansari, R.

2011-01-01

Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen's equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions analysis

Nonlocal beam models for buckling of nanobeams using state-space method regarding different boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Sahmani, S.; Ansari, R. [University of Guilan, Rasht (Iran, Islamic Republic of)

2011-09-15

Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen's equations of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary conditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analysis of nanobeams relevant to each type of nonlocal beam model and boundary conditions analysis.

Survey on nonlocal games and operator space theory

Energy Technology Data Exchange (ETDEWEB)

Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es [Instituto de Ciencias Matemáticas (ICMAT), Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Madrid (Spain); Vidick, Thomas, E-mail: vidick@cms.caltech.edu [Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California 91125 (United States)

2016-01-15

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.

Survey on nonlocal games and operator space theory

International Nuclear Information System (INIS)

Palazuelos, Carlos; Vidick, Thomas

2016-01-01

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states

Formal framework for a nonlocal generalization of Einstein's theory of gravitation

International Nuclear Information System (INIS)

Hehl, Friedrich W.; Mashhoon, Bahram

2009-01-01

The analogy between electrodynamics and the translational gauge theory of gravity is employed in this paper to develop an ansatz for a nonlocal generalization of Einstein's theory of gravitation. Working in the linear approximation, we show that the resulting nonlocal theory is equivalent to general relativity with 'dark matter'. The nature of the predicted dark matter, which is the manifestation of the nonlocal character of gravity in our model, is briefly discussed. It is demonstrated that this approach can provide a basis for the Tohline-Kuhn treatment of the astrophysical evidence for dark matter.

The status and prospects of quantum non-local field theory

International Nuclear Information System (INIS)

Cornish, N.J.; Melbourne Univ., Parkville

1991-01-01

A critical review of the physical constraints on the form the non-locality can take is presented. The conclusion of this review is that non-locality must be restricted to interactions with the vacuum sea of virtual particles. A successful formulation of such a theory, Quantum Nonlocal Field Theory (QNFT), is applied to scalar electrodynamics and serves to illustrate how gauge invariance and manifest finiteness can be achieved. The importance of the infinite dimensional symmetry groups that occur in QNFT are discussed as an alternative to supersymmetry, the ability to generate masses by breaking the non-local symmetry with a non-invariant functional measure is given a critical assessment. To demonstrate some of the many novel applications QNFT may make possible, three disparate examples are mooted, the existence of electroweak monopoles, an mechanism for CP violation and the formulation of a finite perturbative theory of Quantum Gravity. 21 refs., ills

Nonlocal gravity

CERN Document Server

Mashhoon, Bahram

2017-01-01

Relativity theory is based on a postulate of locality, which means that the past history of the observer is not directly taken into account. This book argues that the past history should be taken into account. In this way, nonlocality---in the sense of history dependence---is introduced into relativity theory. The deep connection between inertia and gravitation suggests that gravity could be nonlocal, and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein's theory of gravitation has recently been developed. A significant consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. According to nonlocal gravity theory, what astronomers attribute to dark matter should instead be due to the nonlocality of gravitation. Nonlocality dominates on the scale of galaxies and beyond. Memory fades with time; therefore, the nonlocal aspect of gravity becomes wea...

A model of the extended electron and its nonlocal electromagnetic interaction: Gauge invariance of the nonlocal theory

International Nuclear Information System (INIS)

Namsrai, Kh.; Nyamtseren, N.

1994-09-01

A model of the extended electron is constructed by using definition of the d-operation. Gauge invariance of the nonlocal theory is proved. We use the Efimov approach to describe the nonlocal interaction of quantized fields. (author). 4 refs

Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load

Science.gov (United States)

Hérisson, Benjamin; Challamel, Noël; Picandet, Vincent; Perrot, Arnaud

2016-09-01

The static behavior of the Fermi-Pasta-Ulam (FPU) axial chain under distributed loading is examined. The FPU system examined in the paper is a nonlinear elastic lattice with linear and quadratic spring interaction. A dimensionless parameter controls the possible loss of convexity of the associated quadratic and cubic energy. Exact analytical solutions based on Hurwitz zeta functions are developed in presence of linear static loading. It is shown that this nonlinear lattice possesses scale effects and possible localization properties in the absence of energy convexity. A continuous approach is then developed to capture the main phenomena observed regarding the discrete axial problem. The associated continuum is built from a continualization procedure that is mainly based on the asymptotic expansion of the difference operators involved in the lattice problem. This associated continuum is an enriched gradient-based or nonlocal axial medium. A Taylor-based and a rational differential method are both considered in the continualization procedures to approximate the FPU lattice response. The Padé approximant used in the continualization procedure fits the response of the discrete system efficiently, even in the vicinity of the limit load when the non-convex FPU energy is examined. It is concluded that the FPU lattice system behaves as a nonlocal axial system in dynamic but also static loading.

Non-local coupled-channels optical calculation of electron scattering by atomic hydrogen at 54.42 eV

International Nuclear Information System (INIS)

Ratnavelu, K.; McCarthy, I.E.

1990-01-01

The present study incorporates the non-local optical potentials for the continuum within the coupled-channels optical framework to study electron scattering from atomic hydrogen at 54.42 eV. Nine-state coupled-channels calculations with non-local and local continuum optical potentials were performed. The results for differential, total and ionization cross sections as well as the 2p angular correlation parameters λ and R are comparable with other non-perturbative calculations. There are still discrepancies between theory and experiment, particularly for λ and R at larger angles. (author)

Non-local currents in 2D QFT: an alternative To - the quantum inverse scattering method

International Nuclear Information System (INIS)

Bernard, D.; Leclair, A.; Cornell Univ., Ithaca, NY

1990-01-01

The formalism based on non-local charges that we propose provides an alternative to the quantum inverse scattering method for solving integrable quantum field theories in 2D. The content of the paper is: 1. Introduction: historical background. 2. The NLC approach to 2D QFT: a summary. 3 Exchange algebras and on-shell conservation laws: why non-local charges are useful. 4. The lattice construction: the geometrical origin of non-local conserved currents. 5. The continuum construction: how to deal with non-local conserved currents. 6. Examples: Yangian and quantum group currents. 7 Conclusions: open problems. 22 refs., 4 figs

Canonical approach to constructing constants of motion for nonlocal field theories

International Nuclear Information System (INIS)

Garczynski, W.; Stelmach, J.

1984-01-01

A general method of derivation of conservation laws for non-local field theories is presented. Differences in comparison with a local case are stressed. Two kinds of Lagrangians appearing in a non-local theory are examined. Canonical choice of constants of motion is made corresponding to the transformations from the conformal and gauge groups. 11 refs. (author)

Non-local charges in local quantum field theory

International Nuclear Information System (INIS)

Buchholz, D.; Lopuszanski, J.T.; Rabsztyn, S.

1985-05-01

Non-local charges are studied in the general setting of local quantum field theory. It is shown, that these charges can be represented as polynomials in the incoming respectively outgoing fields with coefficients (kernels) which are subject to specific constraints. For the restricted class of models of a scalar, massive, self interacting particle in four dimensions, a more detailed analysis shows that all non-local charges of the generic type (genus 2) are products of generators of the Poincare group. This analysis, which is based on the macroscopic causality properties of the S-matrix, seems to indicate that less trivial examples of non-local charges can only exist in two dimensions. (orig.)

A nonlocal continuum model for the biaxial buckling analysis of composite nanoplates with shape memory alloy nanowires

Science.gov (United States)

Farajpour, M. R.; Shahidi, A. R.; Farajpour, A.

2018-03-01

In this study, the buckling behavior of a three-layered composite nanoplate reinforced with shape memory alloy (SMA) nanowires is examined. Whereas the upper and lower layers are reinforced with typical nanowires, SMA nanoscale wires are used to strengthen the middle layer of the system. The composite nanoplate is assumed to be under the action of biaxial compressive loading. A scale-dependent mathematical model is presented with the consideration of size effects within the context of the Eringen’s nonlocal continuum mechanics. Using the one-dimensional Brinson’s theory and the Kirchhoff theory of plates, the governing partial differential equations of SMA nanowire-reinforced hybrid nanoplates are derived. Both lateral and longitudinal deflections are taken into consideration in the theoretical formulation and method of solution. In order to reduce the governing differential equations to their corresponding algebraic equations, a discretization approach based on the differential quadrature method is employed. The critical buckling loads of the hybrid nanosystem with various boundary conditions are obtained with the use of a standard eigenvalue solver. It is found that the stability response of SMA composite nanoplates is strongly sensitive to the small scale effect.

Continuum regularized Yang-Mills theory

International Nuclear Information System (INIS)

Sadun, L.A.

1987-01-01

Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions

Non-local deformation of a supersymmetric field theory

Energy Technology Data Exchange (ETDEWEB)

Zhao, Qin [National University of Singapore, Department of Physics, Singapore (Singapore); Faizal, Mir [University of Lethbridge, Department of Physics and Astronomy, Lethbridge (Canada); University of British Columbia - Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); Shah, Mushtaq B.; Ganai, Prince A. [National Institute of Technology, Department of Physics, Srinagar, Kashmir (India); Bhat, Anha [National Institute of Technology, Department of Metallurgical and Materials Engineering, Srinagar (India); Zaz, Zaid [University of Kashmir, Department of Electronics and Communication Engineering, Srinagar, Kashmir (India); Masood, Syed; Raza, Jamil; Irfan, Raja Muhammad [International Islamic University, Department of Physics, Islamabad (Pakistan)

2017-09-15

In this paper, we will analyze a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling. It will be observed that this deformed supersymmetric field theory contains non-local fractional derivative terms. In order to construct such a deformed N = 1 supersymmetric theory, a harmonic extension of functions will be used. However, the supersymmetry will only be preserved for a free theory and will be broken by the inclusion of interaction terms. (orig.)

A nonlocal species concentration theory for diffusion and phase changes in electrode particles of lithium ion batteries

Science.gov (United States)

Zhang, Tao; Kamlah, Marc

2018-01-01

A nonlocal species concentration theory for diffusion and phase changes is introduced from a nonlocal free energy density. It can be applied, say, to electrode materials of lithium ion batteries. This theory incorporates two second-order partial differential equations involving second-order spatial derivatives of species concentration and an additional variable called nonlocal species concentration. Nonlocal species concentration theory can be interpreted as an extension of the Cahn-Hilliard theory. In principle, nonlocal effects beyond an infinitesimal neighborhood are taken into account. In this theory, the nonlocal free energy density is split into the penalty energy density and the variance energy density. The thickness of the interface between two phases in phase segregated states of a material is controlled by a normalized penalty energy coefficient and a characteristic interface length scale. We implemented the theory in COMSOL Multiphysics^{circledR } for a spherically symmetric boundary value problem of lithium insertion into a Li_xMn_2O_4 cathode material particle of a lithium ion battery. The two above-mentioned material parameters controlling the interface are determined for Li_xMn_2O_4 , and the interface evolution is studied. Comparison to the Cahn-Hilliard theory shows that nonlocal species concentration theory is superior when simulating problems where the dimensions of the microstructure such as phase boundaries are of the same order of magnitude as the problem size. This is typically the case in nanosized particles of phase-separating electrode materials. For example, the nonlocality of nonlocal species concentration theory turns out to make the interface of the local concentration field thinner than in Cahn-Hilliard theory.

Nonlocal modification and quantum optical generalization of effective-medium theory for metamaterials

DEFF Research Database (Denmark)

Wubs, Martijn; Yan, Wei; Amooghorban, Ehsan

2013-01-01

A well-known challenge for fabricating metamaterials is to make unit cells significantly smaller than the operating wavelength of light, so one can be sure that effective-medium theories apply. But do they apply? Here we show that nonlocal response in the metal constituents of the metamaterial...... leads to modified effective parameters for strongly subwavelength unit cells. For infinite hyperbolic metamaterials, nonlocal response gives a very large finite upper bound to the optical density of states that otherwise would diverge. Moreover, for finite hyperbolic metamaterials we show that nonlocal...... response affects their operation as superlenses, and interestingly that sometimes nonlocal theory predicts the better imaging. Finally, we discuss how to describe metamaterials effectively in quantum optics. Media with loss or gain have associated quantum noise, and the question is whether the effective...

Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology

CERN Document Server

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 and the nonperturbative method based on the late time asymptotics of the heat kernel. 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 stage of cosmological evolution at an arbitrary value of $\\varLambda$ -- a model of dark energy with its scale played by the dynamical variable that can be fixed by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of gravity theory mediated by a scala...

Multiple-Trace Operators and Non-Local String Theories

International Nuclear Information System (INIS)

Silverstein, Eva M.

2001-01-01

We propose that a novel deformation of string perturbation theory, involving non-local interactions between strings, is required to describe the gravity duals of field theories deformed by multiple-trace operators. The new perturbative expansion involves a new parameter, which is neither the string coupling nor the coefficient of a vertex operator on the worldsheet. We explore some of the properties of this deformation, focusing on a special case where the deformation in the field theory is exactly marginal

Nonlocal theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Directory of Open Access Journals (Sweden)

Zozulya V.V.

2017-09-01

Full Text Available New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

Theory of Nonlocal Point Transformations in General Relativity

Directory of Open Access Journals (Sweden)

Massimo Tessarotto

2016-01-01

Full Text Available A discussion of the functional setting customarily adopted in General Relativity (GR is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs. While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern (1 a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory; (2 the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times; (3 the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and (4 the diagonalization of nondiagonal metric tensors.

Geometric continuum regularization of quantum field theory

International Nuclear Information System (INIS)

Halpern, M.B.

1989-01-01

An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs

A space-jump derivation for non-local models of cell-cell adhesion and non-local chemotaxis.

Science.gov (United States)

Buttenschön, Andreas; Hillen, Thomas; Gerisch, Alf; Painter, Kevin J

2018-01-01

Cellular adhesion provides one of the fundamental forms of biological interaction between cells and their surroundings, yet the continuum modelling of cellular adhesion has remained mathematically challenging. In 2006, Armstrong et al. proposed a mathematical model in the form of an integro-partial differential equation. Although successful in applications, a derivation from an underlying stochastic random walk has remained elusive. In this work we develop a framework by which non-local models can be derived from a space-jump process. We show how the notions of motility and a cell polarization vector can be naturally included. With this derivation we are able to include microscopic biological properties into the model. We show that particular choices yield the original Armstrong model, while others lead to more general models, including a doubly non-local adhesion model and non-local chemotaxis models. Finally, we use random walk simulations to confirm that the corresponding continuum model represents the mean field behaviour of the stochastic random walk.

Quantum nonlocal theory of topological Fermi arc plasmons in Weyl semimetals

Science.gov (United States)

Andolina, Gian Marcello; Pellegrino, Francesco M. D.; Koppens, Frank H. L.; Polini, Marco

2018-03-01

The surface of a Weyl semimetal (WSM) displays Fermi arcs, i.e., disjoint segments of a two-dimensional Fermi contour. We present a quantum-mechanical nonlocal theory of chiral Fermi arc plasmons in WSMs with broken time-reversal symmetry. These are collective excitations constructed from topological Fermi arc and bulk electron states and arising from electron-electron interactions, which are treated in the realm of the random phase approximation. Our theory includes quantum effects associated with the penetration of the Fermi arc surface states into the bulk and dissipation, which is intrinsically nonlocal in nature and arises from decay processes mainly involving bulk electron-hole pair excitations.

Nonlocal quantum field theory and stochastic quantum mechanics

International Nuclear Information System (INIS)

Namsrai, K.

1986-01-01

This volume presents a systematic development of the implications to both quantum mechanics and quantum field theory of the hypothesis of a stochastic structure of space-time. Some applications to elementary particle physics are also considered. Part 1 is concerned with nonlocal quantum field theory and, among other topics, deals with quantized fields, electromagnetic and weak processes, the Schroedinger equation, and functional methods and their applications. Part 2 presents an introduction to stochastic mechanics and many specific problems of interest are discussed. (Auth.)

To the non-local theory of cold nuclear fusion.

Science.gov (United States)

Alexeev, Boris V

2014-10-01

In this paper, we revisit the cold fusion (CF) phenomenon using the generalized Bolzmann kinetics theory which can represent the non-local physics of this CF phenomenon. This approach can identify the conditions when the CF can take place as the soliton creation under the influence of the intensive sound waves. The vast mathematical modelling leads to affirmation that all parts of soliton move with the same velocity and with the small internal change of the pressure. The zone of the high density is shaped on the soliton's front. It means that the regime of the 'acoustic CF' could be realized from the position of the non-local hydrodynamics.

Fractional Quantum Field Theory: From Lattice to Continuum

Directory of Open Access Journals (Sweden)

Vasily E. Tarasov

2014-01-01

Full Text Available An approach to formulate fractional field theories on unbounded lattice space-time is suggested. A fractional-order analog of the lattice quantum field theories is considered. Lattice analogs of the fractional-order 4-dimensional differential operators are proposed. We prove that continuum limit of the suggested lattice field theory gives a fractional field theory for the continuum 4-dimensional space-time. The fractional field equations, which are derived from equations for lattice space-time with long-range properties of power-law type, contain the Riesz type derivatives on noninteger orders with respect to space-time coordinates.

Continuum gauge theories

International Nuclear Information System (INIS)

Stora, R.

1976-09-01

The mathematics of gauge fields and some related concepts are discussed: some corrections on the principal fiber bundles emphasize the idea that the present formulation of continuum theories is incomplete. The main ingredients used through the construction of the renormalized perturbation series are then described: the Faddeev Popov argument, and the Faddeev Popov Lagrangian; the Slavnov symmetry and the nature of the Faddeev Popov ghost fields; the Slavnov identity, with an obstruction: the Adler Bardeen anomaly, and its generalization to the local cohomology of the gauge Lie algebra. Some smooth classical configurations of gauge fields which ought to play a prominent role in the evaluation of the functional integral describing the theory are also reviewed

Constraining generalized non-local cosmology from Noether symmetries.

Science.gov (United States)

Bahamonde, Sebastian; Capozziello, Salvatore; Dialektopoulos, Konstantinos F

2017-01-01

We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory.

Continuum theory for nanotube piezoelectricity.

Science.gov (United States)

Michalski, P J; Sai, Na; Mele, E J

2005-09-09

We develop and solve a continuum theory for the piezoelectric response of one-dimensional nanotubes and nanowires, and apply the theory to study electromechanical effects in boron-nitride nanotubes. We find that the polarization of a nanotube depends on its aspect ratio, and a dimensionless constant specifying the ratio of the strengths of the elastic and electrostatic interactions. The solutions of the model as these two parameters are varied are discussed. The theory is applied to estimate the electric potential induced along the length of a boron-nitride nanotube in response to a uniaxial stress.

Constraining generalized non-local cosmology from Noether symmetries

Energy Technology Data Exchange (ETDEWEB)

Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Capozziello, Salvatore [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Gran Sasso Science Institute, L' Aquila (Italy); Complesso di Monte Sant' Angelo, Naples (Italy); INFN Sezione di Napoli, Naples (Italy); Dialektopoulos, Konstantinos F. [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Complesso di Monte Sant' Angelo, Naples (Italy); INFN Sezione di Napoli, Naples (Italy)

2017-11-15

We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory. (orig.)

Quantum Nonlocality and Reality

Science.gov (United States)

Bell, Mary; Gao, Shan

2016-09-01

Preface; Part I. John Stewart Bell: The Physicist: 1. John Bell: the Irish connection Andrew Whitaker; 2. Recollections of John Bell Michael Nauenberg; 3. John Bell: recollections of a great scientist and a great man Gian-Carlo Ghirardi; Part II. Bell's Theorem: 4. What did Bell really prove? Jean Bricmont; 5. The assumptions of Bell's proof Roderich Tumulka; 6. Bell on Bell's theorem: the changing face of nonlocality Harvey R. Brown and Christopher G. Timpson; 7. Experimental tests of Bell inequalities Marco Genovese; 8. Bell's theorem without inequalities: on the inception and scope of the GHZ theorem Olival Freire, Jr and Osvaldo Pessoa, Jr; 9. Strengthening Bell's theorem: removing the hidden-variable assumption Henry P. Stapp; Part III. Nonlocality: Illusions or Reality?: 10. Is any theory compatible with the quantum predictions necessarily nonlocal? Bernard d'Espagnat; 11. Local causality, probability and explanation Richard A. Healey; 12. Bell inequality and many-worlds interpretation Lev Vaidman; 13. Quantum solipsism and non-locality Travis Norsen; 14. Lessons of Bell's theorem: nonlocality, yes; action at a distance, not necessarily Wayne C. Myrvold; 15. Bell non-locality, Hardy's paradox and hyperplane dependence Gordon N. Fleming; 16. Some thoughts on quantum nonlocality and its apparent incompatibility with relativity Shan Gao; 17. A reasonable thing that just might work Daniel Rohrlich; 18. Weak values and quantum nonlocality Yakir Aharonov and Eliahu Cohen; Part IV. Nonlocal Realistic Theories: 19. Local beables and the foundations of physics Tim Maudlin; 20. John Bell's varying interpretations of quantum mechanics: memories and comments H. Dieter Zeh; 21. Some personal reflections on quantum non-locality and the contributions of John Bell Basil J. Hiley; 22. Bell on Bohm Sheldon Goldstein; 23. Interactions and inequality Philip Pearle; 24. Gravitation and the noise needed in objective reduction models Stephen L. Adler; 25. Towards an objective

Nonlocality in Bohmian mechanics

Science.gov (United States)

Ghafar, Zati Amalina binti Mohd Abdul; Radiman, Shahidan bin; Siong, Ch'ng Han

2018-04-01

The Einstein-Podolsky-Rosen (EPR) paradox demonstrates that entangled particles can interact in such a way that it is possible to measure both their position and momentum instantaneously. The position or momentum of one particle can be determined by measuring another identical particle that exists in another space. This instantaneous action is actually called nonlocality. The nonlocality has been proved by Bell's theorem that states that all quantum theories must be nonlocal. The Bell's theorem gives a strong support to the hidden variable theory, i.e. Bohmian mechanics. Using nonlocality, we present that the velocity field of one particle can be obtained by measuring the velocity of other particles. The trajectory of these particles is perhaps surrealistic trajectory due to the nonlocality.

Free vibration analysis of a multiple rotating nano-beams system based on the Eringen nonlocal elasticity theory

Energy Technology Data Exchange (ETDEWEB)

Ghafarian, M.; Ariaei, A., E-mail: ariaei@eng.ui.ac.ir [Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan (Iran, Islamic Republic of)

2016-08-07

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique to solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.

Nonlocal hidden variables and nonlocal gauge theories

International Nuclear Information System (INIS)

Boiteux, M.

1984-01-01

A possible unification of classical fundamental interactions together with quantum interactions is proposed, based on an extension of the concept of local gauge invariance to a nonlocal gauge invariance. As an example this new concept is developed for the particular case of the electromagnetic field. (Auth.)

Bending analysis of embedded nanoplates based on the integral formulation of Eringen's nonlocal theory using the finite element method

Science.gov (United States)

Ansari, R.; Torabi, J.; Norouzzadeh, A.

2018-04-01

Due to the capability of Eringen's nonlocal elasticity theory to capture the small length scale effect, it is widely used to study the mechanical behaviors of nanostructures. Previous studies have indicated that in some cases, the differential form of this theory cannot correctly predict the behavior of structure, and the integral form should be employed to avoid obtaining inconsistent results. The present study deals with the bending analysis of nanoplates resting on elastic foundation based on the integral formulation of Eringen's nonlocal theory. Since the formulation is presented in a general form, arbitrary kernel functions can be used. The first order shear deformation plate theory is considered to model the nanoplates, and the governing equations for both integral and differential forms are presented. Finally, the finite element method is applied to solve the problem. Selected results are given to investigate the effects of elastic foundation and to compare the predictions of integral nonlocal model with those of its differential nonlocal and local counterparts. It is found that by the use of proposed integral formulation of Eringen's nonlocal model, the paradox observed for the cantilever nanoplate is resolved.

Comparative Assessment of Nonlocal Continuum Solvent Models Exhibiting Overscreening

Directory of Open Access Journals (Sweden)

Ren Baihua

2017-01-01

Full Text Available Nonlocal continua have been proposed to offer a more realistic model for the electrostatic response of solutions such as the electrolyte solvents prominent in biology and electrochemistry. In this work, we review three nonlocal models based on the Landau-Ginzburg framework which have been proposed but not directly compared previously, due to different expressions of the nonlocal constitutive relationship. To understand the relationships between these models and the underlying physical insights from which they are derive, we situate these models into a single, unified Landau-Ginzburg framework. One of the models offers the capacity to interpret how temperature changes affect dielectric response, and we note that the variations with temperature are qualitatively reasonable even though predictions at ambient temperatures are not quantitatively in agreement with experiment. Two of these models correctly reproduce overscreening (oscillations between positive and negative polarization charge densities, and we observe small differences between them when we simulate the potential between parallel plates held at constant potential. These computations require reformulating the two models as coupled systems of local partial differential equations (PDEs, and we use spectral methods to discretize both problems. We propose further assessments to discriminate between the models, particularly in regards to establishing boundary conditions and comparing to explicit-solvent molecular dynamics simulations.

Nonlocal effects on dynamic damage accumulation in brittle solids

Energy Technology Data Exchange (ETDEWEB)

Chen, E.P.

1995-12-01

This paper presents a nonlocal analysis of the dynamic damage accumulation processes in brittle solids. A nonlocal formulation of a microcrack based continuum damage model is developed and implemented into a transient dynamic finite element computer code. The code is then applied to the study of the damage accumulation process in a concrete plate with a central hole and subjected to the action of a step tensile pulse applied at opposite edges of the plate. Several finite element discretizations are used to examine the mesh size effect. Comparisons between calculated results based on local and nonlocal formulations are made and nonlocal effects are discussed.

Towards an improved continuum theory for phase transformations

International Nuclear Information System (INIS)

Tijssens, M.G.A.; James, R.D.

2003-01-01

We develop a continuum theory for martensitic phase transformations in which explicit use is made of atomistic calculations based on density functional theory. Following the work of Rabe and coworkers, branches of the phonon-dispersion relation with imaginary frequencies are selected to construct a localized basis tailored to the symmetry of the crystal lattice. This so-called Wannier basis helps to construct an effective Hamiltonian of a particularly simple form. We extend the methodology by incorporating finite deformations and passing the effective Hamiltonian fully to continuum level. The developments so far are implemented on the shape memory material NiTi

A Morphing framework to couple non-local and local anisotropic continua

KAUST Repository

Azdoud, Yan

2013-05-01

In this article, we develop a method to couple anisotropic local continua with anisotropic non-local continua with central long-range forces. First, we describe anisotropic non-local models based on spherical harmonic descriptions. We then derive compatible classic continuum models. Finally, we apply the morphing method to these anisotropic non-local models and present three-dimensional numerical examples to validate the efficiency of the technique. © 2013 Elsevier Ltd. All rights reserved.

Vibration of nonuniform carbon nanotube with attached mass via nonlocal Timoshenko beam theory

International Nuclear Information System (INIS)

Tang, Hai Li; Shen, Zhi Bin; Li, Dao Kui

2014-01-01

This paper studies the vibrational behavior of nonuniform single-walled carbon nanotube (SWCNT) carrying a nanoparticle. A nonuniform cantilever beam with a concentrated mass at the free end is analyzed according to the nonlocal Timoshenko beam theory. A governing equation of a nonuniform SWCNT with attached mass is established. The transfer function method incorporating with the perturbation method is utilized to obtain the resonant frequencies of a vibrating nonlocal cantilever-mass system. The effects of the nonlocal parameter, taper ratio and attached mass on the natural frequencies and frequency shifts are discussed. Obtained results indicate that the sensitivity of the frequency shifts on the attached mass increases when the length-to-diameter ratio decreases. Tapered SWCNT possesses higher fundamental frequencies if the taper ratio becomes larger.

An advanced kinetic theory for morphing continuum with inner structures

Science.gov (United States)

Chen, James

2017-12-01

Advanced kinetic theory with the Boltzmann-Curtiss equation provides a promising tool for polyatomic gas flows, especially for fluid flows containing inner structures, such as turbulence, polyatomic gas flows and others. Although a Hamiltonian-based distribution function was proposed for diatomic gas flow, a general distribution function for the generalized Boltzmann-Curtiss equations and polyatomic gas flow is still out of reach. With assistance from Boltzmann's entropy principle, a generalized Boltzmann-Curtiss distribution for polyatomic gas flow is introduced. The corresponding governing equations at equilibrium state are derived and compared with Eringen's morphing (micropolar) continuum theory derived under the framework of rational continuum thermomechanics. Although rational continuum thermomechanics has the advantages of mathematical rigor and simplicity, the presented statistical kinetic theory approach provides a clear physical picture for what the governing equations represent.

Formulation analysis and computation of an optimization-based local-to-nonlocal coupling method.

Energy Technology Data Exchange (ETDEWEB)

D' Elia, Marta [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Bochev, Pavel Blagoveston [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research

2017-01-01

In this paper, we present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into 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 local and nonlocal problem domains, and the virtual controls are the nonlocal volume constraint and the local boundary condition. We present the method in the context of Local-to-Nonlocal di usion coupling. Numerical examples illustrate the theoretical properties of the approach.

SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

Energy Technology Data Exchange (ETDEWEB)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-09-01

This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

Virial Theorem in Nonlocal Newtonian Gravity

Directory of Open Access Journals (Sweden)

Bahram Mashhoon

2016-05-01

Full Text Available 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 D 0 —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 f D M times a universal length that is the basic nonlocality length scale λ 0 ≈ 3 ± 2 kpc.

Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes

Energy Technology Data Exchange (ETDEWEB)

Mehralian, Fahimeh [Mechanical Engineering Department, Shahrekord University, Shahrekord (Iran, Islamic Republic of); Tadi Beni, Yaghoub, E-mail: tadi@eng.sku.ac.ir [Faculty of Engineering, Shahrekord University, Shahrekord (Iran, Islamic Republic of); Karimi Zeverdejani, Mehran [Mechanical Engineering Department, Shahrekord University, Shahrekord (Iran, Islamic Republic of)

2017-06-01

Featured by two small length scale parameters, nonlocal strain gradient theory is utilized to investigate the free vibration of nanotubes. A new size-dependent shell model formulation is developed by using the first order shear deformation theory. The governing equations and boundary conditions are obtained using Hamilton's principle and solved for simply supported boundary condition. As main purpose of this study, since the values of two small length scale parameters are still unknown, they are calibrated by the means of molecular dynamics simulations (MDs). Then, the influences of different parameters such as nonlocal parameter, scale factor, length and thickness on vibration characteristics of nanotubes are studied. It is also shown that increase in thickness and decrease in length parameters intensify the effect of nonlocal parameter and scale factor.

Rationale for switching to nonlocal functionals in density functional theory.

Science.gov (United States)

Lazić, P; Atodiresei, N; Caciuc, V; Brako, R; Gumhalter, B; Blügel, S

2012-10-24

Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.

Rationale for switching to nonlocal functionals in density functional theory

International Nuclear Information System (INIS)

Lazić, P; Atodiresei, N; Caciuc, V; Blügel, S; Brako, R; Gumhalter, B

2012-01-01

Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.

Continuum robots and underactuated grasping

Directory of Open Access Journals (Sweden)

N. Giri

2011-02-01

Full Text Available We discuss the capabilities of continuum (continuous backbone robot structures in the performance of under-actuated grasping. Continuum robots offer the potential of robust grasps over a wide variety of object classes, due to their ability to adapt their shape to interact with the environment via non-local continuum contact conditions. Furthermore, this capability can be achieved with simple, low degree of freedom hardware. However, there are practical issues which currently limit the application of continuum robots to grasping. We discuss these issues and illustrate via an experimental continuum grasping case study.

This paper was presented at the IFToMM/ASME International Workshop on Underactuated Grasping (UG2010, 19 August 2010, Montréal, Canada.

Nonlocal String Theories on AdS3 x S3 and Stable Non-Supersymmetric Backgrounds

International Nuclear Information System (INIS)

Silverstein, Eva M

2002-01-01

We exhibit a simple class of exactly marginal ''double-trace'' deformations of two dimensional CFTs which have AdS 3 duals, in which the deformation is given by a product of left and right-moving U(1) currents. In this special case the deformation on AdS 3 is generated by a local boundary term in three dimensions, which changes the physics also in the bulk via bulk-boundary propagators. However, the deformation is non-local in six dimensions and on the string worldsheet, like generic non-local string theories (NLSTs). Due to the simplicity of the deformation we can explicitly make computations in the non-local string theory and compare them to CFT computations, and we obtain precise agreement. We discuss the effect of the deformation on closed strings and on D-branes. The examples we analyze include a supersymmetry-breaking but exactly marginal ''double-trace'' deformation, which is dual to a string theory in which no destabilizing tadpoles are generated for moduli nonperturbatively in all couplings, despite the absence of supersymmetry. We explain how this cancellation works on the gravity side in string perturbation theory, and also non-perturbatively at leading order in the deformation parameter. We also discuss possible flat space limits of our construction

Strong Local-Nonlocal Coupling for Integrated Fracture Modeling

Energy Technology Data Exchange (ETDEWEB)

Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Silling, Stewart A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mitchell, John A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Seleson, Pablo D. [Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Parks, Michael L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Burnett, Damon J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Ostien, Jakob [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Gunzburger, Max [Florida State Univ., Tallahassee, FL (United States)

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

Nonlocal stochastic mixing-length theory and the velocity profile in the turbulent boundary layer

NARCIS (Netherlands)

Dekker, H.; Leeuw, G. de; Maassen van den Brink, A.

1995-01-01

Turbulence mixing by finite size eddies will be treated by means of a novel formulation of nonlocal K-theory, involving sample paths and a stochastic closure hypothesis, which implies a well defined recipe for the calculation of sampling and transition rates. The connection with the general theory

Morphing continuum theory for turbulence: Theory, computation, and visualization

Science.gov (United States)

Chen, James

2017-10-01

A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the Coleman-Noll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second-order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCT-based direct numerical simulation (DNS) provides a better prediction than Navier-Stokes (NS)-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based Q criterion, the MCT-based Q criterion is objective without the limitation of Galilean invariance.

Nonlocal gravity simulates dark matter

OpenAIRE

Hehl, Friedrich W.; Mashhoon, Bahram

2009-01-01

A nonlocal generalization of Einstein's theory of gravitation is constructed within the framework of the translational gauge theory of gravity. In the linear approximation, the nonlocal theory can be interpreted as linearized general relativity but in the presence of "dark matter" that can be simply expressed as an integral transform of matter. It is shown that this approach can accommodate the Tohline-Kuhn treatment of the astrophysical evidence for dark matter.

Antieigenvalue analysis for continuum mechanics, economics, and number theory

Directory of Open Access Journals (Sweden)

Gustafson Karl

2016-01-01

Full Text Available My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly my matrix maximum turning angle of the stress tensor of the material. The important Sharpe ratio of the Capital Asset Pricing Model is now seen in terms of my antieigenvalue theory. Euclid’s Formula for Pythagorean triples becomes a special case of my operator trigonometry.

Nonlocal astrophysics dark matter, dark energy and physical vacuum

CERN Document Server

Alexeev, Boris V

2017-01-01

Non-Local Astrophysics: Dark Matter, Dark Energy and Physical Vacuum highlights the most significant features of non-local theory, a highly effective tool for solving many physical problems in areas where classical local theory runs into difficulties. The book provides the fundamental science behind new non-local astrophysics, discussing non-local kinetic and generalized hydrodynamic equations, non-local parameters in several physical systems, dark matter, dark energy, black holes and gravitational waves. Devoted to the solution of astrophysical problems from the position of non-local physics Provides a solution for dark matter and dark energy Discusses cosmological aspects of the theory of non-local physics Includes a solution for the problem of the Hubble Universe expansion, and of the dependence of the orbital velocity from the center of gravity

Multipartite nonlocality distillation

International Nuclear Information System (INIS)

Hsu, Li-Yi; Wu, Keng-Shuo

2010-01-01

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.

Electrovacuum solutions in nonlocal gravity

Science.gov (United States)

Fernandes, Karan; Mitra, Arpita

2018-05-01

We consider the coupling of the electromagnetic field to a nonlocal gravity theory comprising of the Einstein-Hilbert action in addition to a nonlocal R □-2R term associated with a mass scale m . We demonstrate that in the case of the minimally coupled electromagnetic field, real corrections about the Reissner-Nordström background only exist between the inner Cauchy horizon and the event horizon of the black hole. This motivates us to consider the modified coupling of electromagnetism to this theory via the Kaluza ansatz. The Kaluza reduction introduces nonlocal terms involving the electromagnetic field to the pure gravitational nonlocal theory. An iterative approach is provided to perturbatively solve the equations of motion to arbitrary order in m2 about any known solution of general relativity. We derive the first-order corrections and demonstrate that the higher order corrections are real and perturbative about the external background of a Reissner-Nordström black hole. We also discuss how the Kaluza reduced action, through the inclusion of nonlocal electromagnetic fields, could also be relevant in quantum effects on curved backgrounds with horizons.

Nonlocal effects in nonisothermal hydrodynamics from the perspective of beyond-equilibrium thermodynamics.

Science.gov (United States)

Hütter, Markus; Brader, Joseph M

2009-06-07

We examine the origins of nonlocality in a nonisothermal hydrodynamic formulation of a one-component fluid of particles that exhibit long-range correlations, e.g., due to a spherically symmetric, long-range interaction potential. In order to furnish the continuum modeling with physical understanding of the microscopic interactions and dynamics, we make use of systematic coarse graining from the microscopic to the continuum level. We thus arrive at a thermodynamically admissible and closed set of evolution equations for the densities of momentum, mass, and internal energy. From the consideration of an illustrative special case, the following main conclusions emerge. There are two different source terms in the momentum balance. The first is a body force, which in special circumstances can be related to the functional derivative of a nonlocal Helmholtz free energy density with respect to the mass density. The second source term is proportional to the temperature gradient, multiplied by the nonlocal entropy density. These two source terms combine into a pressure gradient only in the absence of long-range effects. In the irreversible contributions to the time evolution, the nonlocal contributions arise since the self-correlations of the stress tensor and heat flux, respectively, are nonlocal as a result of the microscopic nonlocal correlations. Finally, we point out specific points that warrant further discussions.

Nonlocal analysis of the excitation of the geodesic acoustic mode by drift waves

DEFF Research Database (Denmark)

Guzdar, P.N.; Kleva, R.G.; Chakrabarti, N.

2009-01-01

The geodesic acoustic modes (GAMs) are typically observed in the edge region of toroidal plasmas. Drift waves have been identified as a possible cause of excitation of GAMs by a resonant three wave parametric process. A nonlocal theory of excitation of these modes in inhomogeneous plasmas typical...... of the edge region of tokamaks is presented in this paper. The continuum GAM modes with coupling to the drift waves can create discrete "global" unstable eigenmodes localized in the edge "pedestal" region of the plasma. Multiple resonantly driven unstable radial eigenmodes can coexist on the edge pedestal....

Development an efficient calibrated nonlocal plate model for nonlinear axial instability of zirconia nanosheets using molecular dynamics simulation.

Science.gov (United States)

Sahmani, S; Fattahi, A M

2017-08-01

New ceramic materials containing nanoscaled crystalline phases create a main object of scientific interest due to their attractive advantages such as biocompatibility. Zirconia as a transparent glass ceramic is one of the most useful binary oxides in a wide range of applications. In the present study, a new size-dependent plate model is constructed to predict the nonlinear axial instability characteristics of zirconia nanosheets under axial compressive load. To accomplish this end, the nonlocal continuum elasticity of Eringen is incorporated to a refined exponential shear deformation plate theory. A perturbation-based solving process is put to use to derive explicit expressions for nonlocal equilibrium paths of axial-loaded nanosheets. After that, some molecular dynamics (MD) simulations are performed for axial instability response of square zirconia nanosheets with different side lengths, the results of which are matched with those of the developed nonlocal plate model to capture the proper value of nonlocal parameter. It is demonstrated that the calibrated nonlocal plate model with nonlocal parameter equal to 0.37nm has a very good capability to predict the axial instability characteristics of zirconia nanosheets, the accuracy of which is comparable with that of MD simulation. Copyright © 2017 Elsevier Inc. All rights reserved.

Some topics in continuum theory of liquid crystals

Energy Technology Data Exchange (ETDEWEB)

Anderson, Claire

2000-07-01

Since advancements by Ericksen and Leslie in the 1960's, interest in the continuum theory for liquid crystals has escalated. In this thesis, we present the well established continuum theory for nematics, and apply it to the simple Tsvetkov experiment. This analysis is further extended by studying a similar geometric setup which allows additional degrees of freedom. Steady state solutions are studied, and stable/unstable solutions discussed. The bulk of this thesis however, is concerned with the smectic continuum theory. The theory presented allows variable layer spacing, and hence goes beyond the scope of that proposed by Leslie, Stewart and Nakagawa in 1991. With this theory, we initially study a sample of SmA liquid crystal in the bookshelf geometry between two parallel plates, and subject to a strongly anchored pretilt at the boundaries. Weakly anchored solutions are also briefly discussed at the end of this chapter. This work is extended by considering the same problem with a SmC sample, and the distinct differences between the SmA and SmC solutions are highlighted. Symmetric chevron solutions of C1 and C2 type are discussed fully, and energy considerations are made to find the physically realistic configurations. Again, the last part of this chapter is dedicated to solutions subject to weak anchoring. Finally, we take a brief look at Freedericksz transitions when a magnetic field is applied across a cell containing a SmA sample in the bookshelf geometry. The Freedericksz thresholds for two possible deformations are obtained by linearising the appropriate equation, and solving the resulting eigenvalue problem. Numerical calculations finally show where the transitions occur, and confirm the accuracy of the threshold values obtained analytically. (author)

Some topics in continuum theory of liquid crystals

International Nuclear Information System (INIS)

Anderson, Claire

2000-01-01

Since advancements by Ericksen and Leslie in the 1960's, interest in the continuum theory for liquid crystals has escalated. In this thesis, we present the well established continuum theory for nematics, and apply it to the simple Tsvetkov experiment. This analysis is further extended by studying a similar geometric setup which allows additional degrees of freedom. Steady state solutions are studied, and stable/unstable solutions discussed. The bulk of this thesis however, is concerned with the smectic continuum theory. The theory presented allows variable layer spacing, and hence goes beyond the scope of that proposed by Leslie, Stewart and Nakagawa in 1991. With this theory, we initially study a sample of SmA liquid crystal in the bookshelf geometry between two parallel plates, and subject to a strongly anchored pretilt at the boundaries. Weakly anchored solutions are also briefly discussed at the end of this chapter. This work is extended by considering the same problem with a SmC sample, and the distinct differences between the SmA and SmC solutions are highlighted. Symmetric chevron solutions of C1 and C2 type are discussed fully, and energy considerations are made to find the physically realistic configurations. Again, the last part of this chapter is dedicated to solutions subject to weak anchoring. Finally, we take a brief look at Freedericksz transitions when a magnetic field is applied across a cell containing a SmA sample in the bookshelf geometry. The Freedericksz thresholds for two possible deformations are obtained by linearising the appropriate equation, and solving the resulting eigenvalue problem. Numerical calculations finally show where the transitions occur, and confirm the accuracy of the threshold values obtained analytically. (author)

Intuitive understanding of nonlocality as implied by quantum theory

International Nuclear Information System (INIS)

Bohm, D.G.; Hiley, B.J.

1975-01-01

The fact is brought out that the essential new quality implied by the quantum theory is nonlocality; i.e., that a system cannot be analyzed into parts whose basic properties do not depend on the state of the whole system. This is done in terms of the causal interpretation of the quantum theory, proposed by one of us (D.B.) in 2952, involving the introduction of the ''quantum potential.'' It is shown that this approach implies a new universal type of description, in which the standard or canonical form is always supersystem-system-subsystem; and this leads to the radically new notion of unbroken wholeness of the entire universe. Finally, some of the implications of extending these notions to the relativity domain, and in so doing, a novel concept of time, in terms of which relativity and quantum theory may eventually be brought together, is indicated

Generating functional and large N limit of nonlocal 2D generalized Yang-Mills theories (nlgYM2's)

International Nuclear Information System (INIS)

Saaidi, K.; Sajadi, H.M.

2001-01-01

Using the path integral method, we calculate the partition function and the generating functional (of the field strengths) on nonlocal generalized 2D Yang-Mills theories (nlgYM 2 's), which are nonlocal in the auxiliary field. This has been considered before by Saaidi and Khorrami. Our calculations are done for general surfaces. We find a general expression for the free energy of W(φ) =φ 2k in nlgYM 2 theories at the strong coupling phase (SCP) regime (A > A c ) for large groups. In the specific φ 4 model, we show that the theory has a third order phase transition. (orig.)

Can EPR non-locality be geometrical?

International Nuclear Information System (INIS)

Ne'eman, Y.

1995-01-01

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

Local observables in non-Abelian gauge theories

International Nuclear Information System (INIS)

Sharatchandra, H.S.

1981-09-01

Labelling of the physical states of a non-Abelian gauge theory on a lattice in terms of local observables in considered. The labelling is in terms of local color electric field observables and (separately) local color magnetic field observables. Matter field is also included. The non-local variables required when space is multiply-connected, are specified. Non-Abelian version of the Stokes' theorem is considered. Relevance to the continuum theory is discussed in detail. (orig.)

Hyperbolic metamaterial lens with hydrodynamic nonlocal response

DEFF Research Database (Denmark)

Yan, Wei; Mortensen, N. Asger; Wubs, Martijn

2013-01-01

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...

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Science.gov (United States)

Rohringer, G.; Hafermann, H.; Toschi, A.; Katanin, A. A.; Antipov, A. E.; Katsnelson, M. I.; Lichtenstein, A. I.; Rubtsov, A. N.; Held, K.

2018-04-01

Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge, magnetic, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved, mainly for model Hamiltonians, and an outline is given of future prospects for realistic material calculations.

Continuum limit and improved action in lattice theories. Pt. 1

International Nuclear Information System (INIS)

Symanzik, K.

1983-03-01

Corrections to continuum theory results stemming from finite lattice-spacing can be diminished systematically by use of lattice actions that include also suitable irrelevant terms. We describe in detail the principles of such constructions at the example of PHI 4 theory. (orig.)

Quantum Noether identities for non-local transformations in higher-order derivatives theories

International Nuclear Information System (INIS)

Li, Z.P.; Long, Z.W.

2003-01-01

Based on the phase-space generating functional of the Green function for a system with a regular/singular higher-order Lagrangian, the quantum canonical Noether identities (NIs) under a local and non-local transformation in phase space have been deduced, respectively. For a singular higher-order Lagrangian, one must use an effective canonical action I eff P in quantum canonical NIs instead of the classical I P in classical canonical NIs. The quantum NIs under a local and non-local transformation in configuration space for a gauge-invariant system with a higher-order Lagrangian have also been derived. The above results hold true whether or not the Jacobian of the transformation is equal to unity or not. It has been pointed out that in certain cases the quantum NIs may be converted to conservation laws at the quantum level. This algorithm to derive the quantum conservation laws is significantly different from the quantum first Noether theorem. The applications of our formulation to the Yang-Mills fields and non-Abelian Chern-Simons (CS) theories with higher-order derivatives are given, and the conserved quantities at the quantum level for local and non-local transformations are found, respectively. (orig.)

Local versus nonlocal information in quantum-information theory: Formalism and phenomena

International Nuclear Information System (INIS)

Horodecki, Michal; Horodecki, Ryszard; Synak-Radtke, Barbara; Horodecki, Pawel; Oppenheim, Jonathan; Sen, Aditi; Sen, Ujjwal

2005-01-01

In spite of many results in quantum information theory, the complex nature of compound systems is far from clear. In general the information is a mixture of local and nonlocal ('quantum') information. It is important from both pragmatic and theoretical points of view to know the relationships between the two components. To make this point more clear, we develop and investigate the quantum-information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm in detail, we show that the upper bound for the deficit is given by the relative entropy distance to so-called pseudoclassically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal - i.e., has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other nonlocal phenomena which can be found using the paradigm of local information. For example, we prove the existence of a form of nonlocality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal. We also show that there do not exist states for which the deficit is strictly equal to the whole informational content (bound local information). We discuss the relation of the paradigm with measures of classical correlations introduced earlier. It is also proved that in the one-way scenario, the deficit is additive for Bell diagonal states. We then discuss complementary features of

Complete mechanical behavior analysis of FG Nano Beam under non-uniform loading using non-local theory

Science.gov (United States)

Ghaffari, I.; Parhizkar Yaghoobi, M.; Ghannad, M.

2018-01-01

The purpose of this study is to offer a complete solution to analyze the mechanical behavior (bending, buckling and vibration) of Nano-beam under non-uniform loading. Furthermore, the effects of size (nonlocal parameters), non-homogeneity constants, and different boundary conditions are investigated by using this method. The exact solution presented here reduces costs incurred by experiments. In this research, the displacement field obeys the kinematics of the Euler-Bernoulli beam theory and non-local elasticity theory has been used. The governing equations and general boundary conditions are derived for a beam by using energy method. The presented solution enables us to analyze any kind of loading profile and boundary conditions with no limitations. Furthermore, this solution, unlike previous studies, is not a series-solution; hence, there is no limitation prior to existing with the series-solution, nor does it need to check convergence. Based on the developed analytical solution, the influence of size, non-homogeneity and non-uniform loads on bending, buckling and vibration behaviors is discussed. Also, the obtained result is highly accurate and in good agreement with previous research. In theoretical method, the allowable range for non-local parameters can be determined so as to make a major contribution to the reduction of the cost of experiments determining the value of non-local parameters.

Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid.

Science.gov (United States)

Sahin, Buyukdagli; Ralf, Blossey

2014-07-16

We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.

Nonlocal and nonlinear dispersion in a nonlinear Schrodinger-type equation: exotic solitons and short-wavelength instabilities

DEFF Research Database (Denmark)

Oster, Michael; Gaididei, Yuri B.; Johansson, Magnus

2004-01-01

We study the continuum limit of a nonlinear Schrodinger lattice model with both on-site and inter-site nonlinearities, describing weakly coupled optical waveguides or Bose-Einstein condensates. The resulting continuum nonlinear Schrodinger-type equation includes both nonlocal and nonlinear...

Universality and the approach to the continuum limit in lattice gauge theory

CERN Document Server

De Divitiis, G M; Guagnelli, M; Lüscher, Martin; Petronzio, Roberto; Sommer, Rainer; Weisz, P; Wolff, U; de Divitiis, G; Frezzotti, R; Guagnelli, M; Luescher, M; Petronzio, R; Sommer, R; Weisz, P; Wolff, U

1995-01-01

The universality of the continuum limit and the applicability of renormalized perturbation theory are tested in the SU(2) lattice gauge theory by computing two different non-perturbatively defined running couplings over a large range of energies. The lattice data (which were generated on the powerful APE computers at Rome II and DESY) are extrapolated to the continuum limit by simulating sequences of lattices with decreasing spacings. Our results confirm the expected universality at all energies to a precision of a few percent. We find, however, that perturbation theory must be used with care when matching different renormalized couplings at high energies.

Hyperbolic metamaterial lens with hydrodynamic nonlocal response.

Science.gov (United States)

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.

Thermoelastic Damping in FGM Nano-Electromechanical System in Axial Vibration Based on Eringen Nonlocal Theory

Science.gov (United States)

Rahimi, Z.; Rashahmadi, S.

2017-11-01

The thermo-elastic damping is a dominant source of internal damping in micro-electromechanical systems (MEMS) and nano-electromechanical systems (NEMS). The internal damping cannot neither be controlled nor minimized unless either mechanical or geometrical properties are changed. Therefore, a novel FGMNEM system with a controllable thermo-elastic damping of axial vibration based on Eringen nonlocal theory is considered. The effects of different parameter like the gradient index, nonlocal parameter, length of nanobeam and ambient temperature on the thermo-elastic damping quality factor are presented. It is shown that the thermo-elastic damping can be controlled by changing different parameter.

Towards LHC physics with nonlocal Standard Model

Energy Technology Data Exchange (ETDEWEB)

Biswas, Tirthabir, E-mail: tbiswas@loyno.edu [Department of Physics, Loyola University, 6363 St. Charles Avenue, Box 92, New Orleans, LA 70118 (United States); Okada, Nobuchika, E-mail: okadan@ua.edu [Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487-0324 (United States)

2015-09-15

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.

Closed sets of nonlocal correlations

International Nuclear Information System (INIS)

Allcock, Jonathan; Linden, Noah; Brunner, Nicolas; Popescu, Sandu; Skrzypczyk, Paul; Vertesi, Tamas

2009-01-01

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.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method

Energy Technology Data Exchange (ETDEWEB)

Wang, Yu; Wang, Yi-Ze [School of Astronautics, Harbin Institute of Technology, P. O. Box 137, Harbin 150001 (China); Li, Feng-Ming, E-mail: fmli@bjut.edu.cn [School of Astronautics, Harbin Institute of Technology, P. O. Box 137, Harbin 150001 (China); College of Mechanical Engineering, Beijing University of Technology, Beijing 100124 (China)

2015-06-15

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method.

Science.gov (United States)

Wang, Yu; Li, Feng-Ming; Wang, Yi-Ze

2015-06-01

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.

Nonlocal Galileons and self-acceleration

Energy Technology Data Exchange (ETDEWEB)

Gabadadze, Gregory; Yu, Siqing, E-mail: sy1430@nyu.edu

2017-05-10

A certain class of nonlocal theories eliminates an arbitrary cosmological constant (CC) from a universe that can be perceived as our world. Dark energy then cannot be explained by a CC; it could however be due to massive gravity. We calculate the new corrections, which originate from the nonlocal terms that eliminate the CC, to the decoupling limit Lagrangian of massive gravity. The new nonlocal terms also have internal field space Galilean symmetry and are referred here as “nonlocal Galileons.” We then study a self-accelerated solution and show that the new nonlocal terms change the perturbative stability analysis. In particular, small fluctuations are now stable and non-superluminal for some simple parameter choices, whereas for the same choices the pure massive gravity fluctuations are unstable. We also study stable spherically symmetric solutions on this background.

On the physical origin for the geometric theory of continuum mechanics

International Nuclear Information System (INIS)

Guenther, H.

1984-01-01

It is explained, that the basic notion for a geometric picture of the continuum mechanics is a four dimensional material manifold. The four dimensional mechanical affinity is then the unified field for any defect distribution in the general time dependent case. The minimal number of geometric relations being valid for any continuum is formulated as a set of pure affine relations. The state variables of the theory are additional tensor fields as e.g. deformation defining a metric. A material with a well defined deformation has a Newton-Cartan structure. Only if defects are included into the dynamical determination by additional equilibrium conditions, the theory has a pseudo relativistic structure. (author)

Static and dynamic continuum theory liquid crystals a mathematical introduction

CERN Document Server

Stewart, Iain W

2004-01-01

Providing a rigorous, clear and accessible text for graduate students regardless of scientific background, this text introduces the basic continuum theory for nematic liquid crystals in equilibria, and details its various simple applications.

Gauging Non-local Quark Models

International Nuclear Information System (INIS)

Broniowski, W.

1999-09-01

The gauge effective quark model with non-local interactions is considered. It is shown how this approach regularize the theory in such a way that the anomalies are preserved and charges are properly quantized. With non-local interactions the effective action is finite to all orders in the loop expansion and there is no need to introduce the quark momentum cut-off parameter

IUTAM-Symposium on The Generalized Cosserat Continuum and the Continuum Theory of Dislocations with Applications

CERN Document Server

1968-01-01

5 The symposium was held in Freudenstadt from 28\\h to 31 \\ ofAugust st nd 1967 and in Stuttgart from 1 to 2 of September 1967. The proposal to hold this symposium originated with the German Society of Applied Mathematics and Mechanics (GAMM) late in 1964 and was examined by a committee of IUTAM especially appointed for this purpose. The basis of this examination was a report in which the present situation in the field and the possible aims of the symposium were surveyed. Briefly, the aims of the symposium were stated to be 1. the unification of the various approaches developed in recent years with the aim of penetrating into the microscopic world of matter by means of continuum theories; 2. the bridging of the gap between microscopic (or atomic) research on mechanics on one hand, and the phenomenological (or continuum mechanical) approach on the other hand; 3. the physical interpretation and the relation to actual material behaviour of the quantities and laws introduced into the new theories, together with ap...

Nonlocal effects in nonisothermal hydrodynamics from the perspective of beyond-equilibrium thermodynamics

OpenAIRE

Hütter, Markus; Brader, Joseph M.

2009-01-01

We examine the origins of nonlocality in a nonisothermal hydrodynamic formulation of a one-component fluid of particles that exhibit long-range correlations, e.g., due to a spherically symmetric, long-range interaction potential. In order to furnish the continuum modeling with physical understanding of the microscopic interactions and dynamics, we make use of systematic coarse graining from the microscopic to the continuum level. We thus arrive at a thermodynamically admissible and closed set...

Constraints and Hamiltonian in light-front quantized field theory

International Nuclear Information System (INIS)

Srivastava, P.P.

1993-01-01

Self-consistent hamiltonian formulation of scalar theory on the null plane is constructed and quantized following the Dirac procedure. The theory contains also constraint equations which would give, if solved, to a nonlocal Hamiltonian. In contrast to the equal-time formulation we obtain a different description of the spontaneous symmetry breaking in the continuum and the symmetry generators are found to annihilate the light-front vacuum. Two examples are given where the procedure cannot be applied self-consistently. The corresponding theories are known to be ill-defined from the equal-time quantization. (author)

Variational continuum multiphase poroelasticity theory and applications

CERN Document Server

Serpieri, Roberto

2017-01-01

This book collects the theoretical derivation of a recently presented general variational macroscopic continuum theory of multiphase poroelasticity (VMTPM), together with its applications to consolidation and stress partitioning problems of interest in several applicative engineering contexts, such as in geomechanics and biomechanics. The theory is derived based on a purely-variational deduction, rooted in the least-Action principle, by considering a minimal set of kinematic descriptors. The treatment herein considered keeps a specific focus on the derivation of most general medium-independent governing equations. It is shown that VMTPM recovers paradigms of consolidated use in multiphase poroelasticity such as Terzaghi's stress partitioning principle and Biot's equations for wave propagation. In particular, the variational treatment permits the derivation of a general medium-independent stress partitioning law, and the proposed variational theory predicts that the external stress, the fluid pressure, and the...

Effect of the nonlocal exchange on the performance of the orbital-dependent correlation functionals from second-order perturbation theory.

Science.gov (United States)

Schweigert, Igor V; Bartlett, Rodney J

2008-09-28

Adding a fraction of the nonlocal exchange operator to the local orbital-dependent exchange potential improves the many-body perturbation expansion based on the Kohn-Sham determinant. The effect of such a hybrid scheme on the performance of the orbital-dependent correlation functional from the second-order perturbation theory (PT2H) is investigated numerically. A small fraction of the nonlocal exchange is often sufficient to ensure the existence of the self-consistent solution for the PT2H potential. In the He and Be atoms, including 37% of the nonlocal exchange leads to the correlation energies and electronic densities that are very close to the exact ones. In molecules, varying the fraction of the nonlocal exchange may result in the PT2H energy closely reproducing the CCSD(T) value; however such a fraction depends on the system and does not always result in an accurate electronic density. We also numerically verify that the "semicanonical" perturbation series includes most of the beneficial effects of the nonlocal exchange without sacrificing the locality of the exchange potential.

Multiscaling for systems with a broad continuum of characteristic lengths and times: Structural transitions in nanocomposites.

Science.gov (United States)

Pankavich, S; Ortoleva, P

2010-06-01

The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time variables and of order parameters (OPs) specifying major features of the system. We adopt this perspective as a natural extension of the commonly used discrete set of time scales and OPs which is practical when only a few, widely separated scales exist. The existence of a gap in the spectrum of time scales for such a system (under quasiequilibrium conditions) is used to introduce a continuous scaling and perform a multiscale analysis of the Liouville equation. A functional-differential Smoluchowski equation is derived for the stochastic dynamics of the continuum of Fourier component OPs. A continuum of spatially nonlocal Langevin equations for the OPs is also derived. The theory is demonstrated via the analysis of structural transitions in a composite material, as occurs for viral capsids and molecular circuits.

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

Directory of Open Access Journals (Sweden)

Iman Eshraghi

2016-09-01

Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

Local models and hidden nonlocality in Quantum Theory

OpenAIRE

Guerini, Leonardo

2014-01-01

This Master's thesis has two central subjects: the simulation of correlations generated by local measurements on entangled quantum states by local hidden-variables models and the revelation of hidden nonlocality. We present and detail the Werner's local model and the hidden nonlocality of some Werner states of dimension $d\\geq5$, the Gisin-Degorre's local model for a Werner state of dimension $d=2$ and the local model of Hirsch et al. for mixtures of the singlet state and noise, all of them f...

New numerical methods for quantum field theories on the continuum

Energy Technology Data Exchange (ETDEWEB)

Emirdag, P.; Easter, R.; Guralnik, G.S.; Hahn, S.C

2000-03-01

The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to increase the accuracy and speed of calculations, and takes full advantage of symmetries of the theory. The application of this method to the non-linear {sigma} model is outlined.

Dynamic analysis of isotropic nanoplates subjected to moving load using state-space method based on nonlocal second order plate theory

Energy Technology Data Exchange (ETDEWEB)

Nami, Mohammad Rahim [Shiraz University, Shiraz, Iran (Iran, Islamic Republic of); Janghorban, Maziar [Islamic Azad University, Marvdash (Iran, Islamic Republic of)

2015-06-15

In this work, dynamic analysis of rectangular nanoplates subjected to moving load is presented. In order to derive the governing equations of motion, second order plate theory is used. To capture the small scale effects, the nonlocal elasticity theory is adopted. It is assumed that the nanoplate is subjected to a moving concentrated load with the constant velocity V in the x direction. To solve the governing equations, state-space method is used to find the deflections of rectangular nanoplate under moving load. The results obtained here reveal that the nonlocality has significant effect on the deflection of rectangular nanoplate subjected to moving load.

Nonlocal N=1 supersymmetry

Energy Technology Data Exchange (ETDEWEB)

Kimura, Tetsuji [Research and Education Center for Natural Sciences, Keio University,Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521 (Japan); Department of Physics, Tokyo Institute of Technology,Tokyo 152-8551 (Japan); Mazumdar, Anupam [Consortium for Fundamental Physics, Physics Department, Lancaster University,Lancaster LA1 4YB (United Kingdom); Kapteyn Astronomical Institute, University of Groningen,9700 AV Groningen (Netherlands); Noumi, Toshifumi [Institute for Advanced Study, Hong Kong University of Science and Technology,Clear Water Bay (Hong Kong); Department of Physics, Kobe University,Kobe 657-8501 (Japan); Yamaguchi, Masahide [Department of Physics, Tokyo Institute of Technology,Tokyo 152-8551 (Japan)

2016-10-05

We construct N=1 supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of Kähler potential and superpotential up to quadratic order. We derive the condition in which an auxiliary field remains non-dynamical, and the dynamical scalars and fermions are free from the ghost degrees of freedom. We also investigate the nonlocal effects on the supersymmetry breaking and find that supertrace (mass) formula is significantly modified even at the tree level.

Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory

International Nuclear Information System (INIS)

Wang, C M; Zhang, Y Y; Ramesh, Sai Sudha; Kitipornchai, S

2006-01-01

This paper is concerned with the elastic buckling analysis of micro- and nano-rods/tubes based on Eringen's nonlocal elasticity theory and the Timoshenko beam theory. In the former theory, the small scale effect is taken into consideration while the effect of transverse shear deformation is accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. Explicit expressions for the critical buckling loads are derived for axially loaded rods/tubes with various end conditions. These expressions account for a better representation of the buckling behaviour of micro- and nano-rods/tubes where small scale effect and transverse shear deformation effect are significant. By comparing it with the classical beam theories, the sensitivity of the small scale effect on the buckling loads may be observed

Nonlocal effects in nonisothermal hydrodynamics from the perspective of beyond-equilibrium thermodynamics

NARCIS (Netherlands)

Hütter, M.; Brader, J.M.

2009-01-01

We examine the origins of nonlocality in a nonisothermal hydrodynamic formulation of a one-component fluid of particles that exhibit long-range correlations, e.g., due to a spherically symmetric, long-range interaction potential. In order to furnish the continuum modeling with physical understanding

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Large-N limit of the non-local 2D Yang-Mills and generalized Yang-Mills theories on a cylinder

Energy Technology Data Exchange (ETDEWEB)

Saaidi, K. [Department of Physics, Tehran University (Iran); Khorrami, M. [Institute for Advanced Studies in Basic Sciences, Zanjan (Iran)

2002-04-01

The large-group behavior of the non-local YM{sub 2}'s and gYM{sub 2}'s on a cylinder or a disk is investigated. It is shown that this behavior is similar to that of the corresponding local theory, but with the area of the cylinder replaced by an effective area depending on the dominant representation. The critical areas for non-local YM{sub 2}'s on a cylinder with some special boundary conditions are also obtained. (orig.)

Evidence against the continuum structure underlying motivation measures derived from self-determination theory.

Science.gov (United States)

Chemolli, Emanuela; Gagné, Marylène

2014-06-01

Self-determination theory (SDT) proposes a multidimensional conceptualization of motivation in which the different regulations are said to fall along a continuum of self-determination. The continuum has been used as a basis for using a relative autonomy index as a means to create motivational scores. Rasch analysis was used to verify the continuum structure of the Multidimensional Work Motivation Scale and of the Academic Motivation Scale. We discuss the concept of continuum against SDT's conceptualization of motivation and argue against the use of the relative autonomy index on the grounds that evidence for a continuum structure underlying the regulations is weak and because the index is statistically problematic. We suggest exploiting the full richness of SDT's multidimensional conceptualization of motivation through the use of alternative scoring methods when investigating motivational dynamics across life domains.

Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review

Directory of Open Access Journals (Sweden)

Zhi Yan

2017-01-01

Full Text Available Piezoelectric nanomaterials (PNs are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.

Modified Continuum Mechanics Modeling on Size-Dependent Properties of Piezoelectric Nanomaterials: A Review.

Science.gov (United States)

Yan, Zhi; Jiang, Liying

2017-01-26

Piezoelectric nanomaterials (PNs) are attractive for applications including sensing, actuating, energy harvesting, among others in nano-electro-mechanical-systems (NEMS) because of their excellent electromechanical coupling, mechanical and physical properties. However, the properties of PNs do not coincide with their bulk counterparts and depend on the particular size. A large amount of efforts have been devoted to studying the size-dependent properties of PNs by using experimental characterization, atomistic simulation and continuum mechanics modeling with the consideration of the scale features of the nanomaterials. This paper reviews the recent progresses and achievements in the research on the continuum mechanics modeling of the size-dependent mechanical and physical properties of PNs. We start from the fundamentals of the modified continuum mechanics models for PNs, including the theories of surface piezoelectricity, flexoelectricity and non-local piezoelectricity, with the introduction of the modified piezoelectric beam and plate models particularly for nanostructured piezoelectric materials with certain configurations. Then, we give a review on the investigation of the size-dependent properties of PNs by using the modified continuum mechanics models, such as the electromechanical coupling, bending, vibration, buckling, wave propagation and dynamic characteristics. Finally, analytical modeling and analysis of nanoscale actuators and energy harvesters based on piezoelectric nanostructures are presented.

SOUND-SPEED INVERSION OF THE SUN USING A NONLOCAL STATISTICAL CONVECTION THEORY

International Nuclear Information System (INIS)

Zhang Chunguang; Deng Licai; Xiong Darun; Christensen-Dalsgaard, Jørgen

2012-01-01

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.

The Green’s functions for peridynamic non-local diffusion

Science.gov (United States)

Wang, L. J.; Xu, J. F.

2016-01-01

In this work, we develop the Green’s function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green’s functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green’s functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems. PMID:27713658

Universal Exciton Size in Organic Polymers is Determined by Nonlocal Orbital Exchange in Time-Dependent Density Functional Theory.

Science.gov (United States)

Mewes, Stefanie A; Plasser, Felix; Dreuw, Andreas

2017-03-16

The exciton size of the lowest singlet excited state in a diverse set of organic π-conjugated polymers is studied and found to be a universal, system-independent quantity of approximately 7 Å in the single-chain picture. With time-dependent density functional theory (TDDFT), its value as well as the overall description of the exciton is almost exclusively governed by the amount of nonlocal orbital exchange. This is traced back to the lack of the Coulomb attraction between the electron and hole quasiparticles in pure TDDFT, which is reintroduced only with the admixture of nonlocal orbital exchange.

Non-local correlations within dynamical mean field theory

Energy Technology Data Exchange (ETDEWEB)

Li, Gang

2009-03-15

The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)

Non-local correlations within dynamical mean field theory

International Nuclear Information System (INIS)

Li, Gang

2009-03-01

The contributions from the non-local fluctuations to the dynamical mean field theory (DMFT) were studied using the recently proposed dual fermion approach. Straight forward cluster extensions of DMFT need the solution of a small cluster, where all the short-range correlations are fully taken into account. All the correlations beyond the cluster scope are treated in the mean-field level. In the dual fermion method, only a single impurity problem needs to be solved. Both the short and long-range correlations could be considered on equal footing in this method. The weak-coupling nature of the dual fermion ensures the validity of the finite order diagram expansion. The one and two particle Green's functions calculated from the dual fermion approach agree well with the Quantum Monte Carlo solutions, and the computation time is considerably less than with the latter method. The access of the long-range order allows us to investigate the collective behavior of the electron system, e.g. spin wave excitations. (orig.)

Extreme nonlocality with one photon

Energy Technology Data Exchange (ETDEWEB)

Heaney, Libby; Vedral, Vlatko [Department of Physics, University of Oxford, Clarendon Laboratory, Oxford, OX1 3PU (United Kingdom); Cabello, Adan [Departamento de Fisica Aplicada II, Universidad de Sevilla, E-41012 Sevilla (Spain); Santos, Marcelo Franca, E-mail: l.heaney1@physics.ox.ac.uk, E-mail: adan@us.es [Departamento de Fisica, Universidade Federal de Minas Gerais, Belo Horizonte, Caixa Postal 702, 30123-970, MG (Brazil)

2011-05-15

Quantum nonlocality is typically assigned to systems of two or more well-separated particles, but nonlocality can also exist in systems consisting of just a single particle when one considers the subsystems to be distant spatial field modes. Single particle nonlocality has been confirmed experimentally via a bipartite Bell inequality. In this paper, we introduce an N-party Hardy-like proof of the impossibility of local elements of reality and a Bell inequality for local realistic theories in the case of a single particle superposed symmetrically over N spatial field modes (i.e. N qubit W state). We show that, in the limit of large N, the Hardy-like proof effectively becomes an all-versus-nothing (or Greenberger-Horne-Zeilinger (GHZ)-like) proof, and the quantum-classical gap of the Bell inequality tends to be the same as that in a three-particle GHZ experiment. We describe how to test the nonlocality in realistic systems.

Bell inequality, nonlocality and analyticity

International Nuclear Information System (INIS)

Socolovsky, M.

2003-01-01

The Bell and the Clauser-Horne-Shimony-Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein-Podolsky-Rosen-Bohm experiments for spin ((1)/(2)) particles and photons, in both the deterministic and stochastic cases. Therefore, the theoretical and experimental violation of the inequalities by quantum mechanics excludes all hidden variables theories with that kind of nonlocality. In particular, real analyticity leads to negative definite correlations, in contradiction with quantum mechanics

Bell inequality, nonlocality and analyticity

Energy Technology Data Exchange (ETDEWEB)

Socolovsky, M

2003-09-15

The Bell and the Clauser-Horne-Shimony-Holt inequalities are shown to hold for both the cases of complex and real analytic nonlocality in the setting parameters of Einstein-Podolsky-Rosen-Bohm experiments for spin ((1)/(2)) particles and photons, in both the deterministic and stochastic cases. Therefore, the theoretical and experimental violation of the inequalities by quantum mechanics excludes all hidden variables theories with that kind of nonlocality. In particular, real analyticity leads to negative definite correlations, in contradiction with quantum mechanics.

Fully discrete Galerkin schemes for the nonlinear and nonlocal Hartree equation

Directory of Open Access Journals (Sweden)

Walter H. Aschbacher

2009-01-01

Full Text Available We study the time dependent Hartree equation in the continuum, the semidiscrete, and the fully discrete setting. We prove existence-uniqueness, regularity, and approximation properties for the respective schemes, and set the stage for a controlled numerical computation of delicate nonlinear and nonlocal features of the Hartree dynamics in various physical applications.

Testing the non-locality of quantum theory in two-kaon systems

Energy Technology Data Exchange (ETDEWEB)

Eberhard, P.H. (California Univ., Berkeley (United States). Lawrence Berkeley Lab.)

1993-06-07

An idea for testing the non-local character of quantum theory in systems made of two neutral kaons is suggested. Such tests require detecting two long-lived or two short-lived neutral kaons in coincidence, when copper slabs are either interposed on or removed from their paths. They may be performed at an asymmetric [Phi][sup 0]-factory. They could answer some questions raised by the EPR paradox and Bell's inequalities. If such tests are performed and if predictions of quantum mechanics and standard theory of kaon regeneration are verified experimentally, all descriptions of the relevant phenomena in terms of local interactions will be ruled out in principle with the exception of very peculiar ones, which imply the existence of hidden variables, of different kinds of kaons corresponding to different values of the hidden variables, and, for some of these kaons, of regeneration probabilities enhanced by a factor of the order of 400 or more over the average. Of course, the experiment may also reveal a break down of quantum theory. (orig.)

On the origin of nonlocal damping in plasmonic monomers and dimers

DEFF Research Database (Denmark)

Tserkezis, Christos; Yan, Wei; Hsieh, Wenting

2017-01-01

The origin and importance of nonlocal damping is discussed through simulations with the generalized nonlocal optical response (GNOR) theory, in conjunction with time-dependent density functional theory (TDDFT) calculations and equivalent circuit modeling, for some of the most typical plasmonic...... architectures: metal–dielectric interfaces, metal–dielectric–metal gaps, spherical nanoparticles and nanoparticle dimers. It is shown that diffusive damping, as introduced by the convective–diffusive GNOR theory, describes well the enhanced losses and plasmon broadening predicted by ab initio...... the interface. Diffusive nonlocal theories provide therefore an efficient means to tackle plasmon damping when electron tunneling can be safely disregarded, without the need to resort to more accurate, but time-consuming fully quantum-mechanical studies....

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

Science.gov (United States)

Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581

Non--Local Approach to the Analysis of the Stress Distribution in Granular Systems.

Science.gov (United States)

Scott, J. E.; Kenkre, V. M.; Hurd, A. J.

1998-03-01

A continuum mechanical theory of the stress distribution in granular materials is presented, where the transformation of the vertical spatial coordinate into a formal time variable converts the study of the static stress distribution into a generally non--Markoffian, i.e., memory-possessing (non-local) propagation analysis. Previous treatments (J. -P). Bouchaud, M. E. Cates, and P. Claudin, J. Phys. I France 5, 639 (1995). (C. -h). Liu, S. R. Nagel, D. A. Schecter, S. N. Coppersmith, S. Majumdar, O. Narayan, and T. A. Witten, Science 269, 513 (1995). are shown to be particular cases of our theory corresponding to, respectively, wave-like and dif fusive limits of the general evolution. Calculations are presented for the example of ceramic or metal powder compaction in dies, with emphasis on the understanding of previously unexplained features as seen in experimental data found in the literature o ver the past 50 years. Specific proposals for new experimental investigations are presented.

Conformal symmetry and nonlinear extensions of nonlocal gravity

CERN Document Server

Cusin, Giulia; Maggiore, Michele; Mancarella, Michele

2016-01-01

We study two nonlinear extensions of the nonlocal $R\\,\\Box^{-2}R$ gravity theory. We extend this theory in two different ways suggested by conformal symmetry, either replacing $\\Box^{-2}$ with $(-\\Box + R/6)^{-2}$, which is the operator that enters the action for a conformally-coupled scalar field, or replacing $\\Box^{-2}$ 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 $w_{\\rm DE}\\simeq -1.01$, which very closely mimics $\\Lambda$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 primordia...

Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics

Science.gov (United States)

Nourhani, Amir; Crespi, Vincent H.; Lammert, Paul E.

2015-06-01

We present a self-consistent nonlocal feedback theory for the phoretic propulsion mechanisms of electrocatalytic micromotors or nanomotors. These swimmers, such as bimetallic platinum and gold rods catalyzing decomposition of hydrogen peroxide in aqueous solution, have received considerable theoretical attention. In contrast, the heterogeneous electrochemical processes with nonlocal feedback that are the actual "engines" of such motors are relatively neglected. We present a flexible approach to these processes using bias potential as a control parameter field and a locally-open-circuit reference state, carried through in detail for a spherical motor. While the phenomenological flavor makes meaningful contact with experiment easier, required inputs can also conceivably come from, e.g., Frumkin-Butler-Volmer kinetics. Previously obtained results are recovered in the weak-heterogeneity limit and improved small-basis approximations tailored to structural heterogeneity are presented. Under the assumption of weak inhomogeneity, a scaling form is deduced for motor speed as a function of fuel concentration and swimmer size. We argue that this form should be robust and demonstrate a good fit to experimental data.

On the continuum limit of a Z4 lattice gauge theory

International Nuclear Information System (INIS)

Pena, A.; Socolovsky, M.

1983-01-01

The continuum limit of a Z 4 gauge plus matter lattice theory is identified with massless scalar and vector fields with quartic self-interactions phi 4 and (AμAμ) 2 , respectively. The analysis is based on the mean field approximation after gauge fixing. (orig.)

Nonlocal Boltzmann theory of plasma channels

International Nuclear Information System (INIS)

Yu, S.S.; Melendez, R.E.

1983-01-01

The mathematical framework for the LLNL code NUTS is developed. This code is designed to study the evolution of an electron-beam-generated plasma channel at all pressures. The Boltzmann treatment of the secondary electrons presented include all inertial, nonlocal, electric and magnetic effects, as well as effects of atomic collisions. Field equations are advanced simultaneously and self-consistently with the evolving plasma currents

Nonlocality and short-range wetting phenomena.

Science.gov (United States)

Parry, A O; Romero-Enrique, J M; Lazarides, A

2004-08-20

We propose a nonlocal interfacial model for 3D short-range wetting at planar and nonplanar walls. The model is characterized by a binding-potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tubelike fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong nonperturbative influence of nonlocality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.

Nonlocality and Short-Range Wetting Phenomena

Science.gov (United States)

Parry, A. O.; Romero-Enrique, J. M.; Lazarides, A.

2004-08-01

We propose a nonlocal interfacial model for 3D short-range wetting at planar and nonplanar walls. The model is characterized by a binding-potential functional depending only on the bulk Ornstein-Zernike correlation function, which arises from different classes of tubelike fluctuations that connect the interface and the substrate. The theory provides a physical explanation for the origin of the effective position-dependent stiffness and binding potential in approximate local theories and also obeys the necessary classical wedge covariance relationship between wetting and wedge filling. Renormalization group and computer simulation studies reveal the strong nonperturbative influence of nonlocality at critical wetting, throwing light on long-standing theoretical problems regarding the order of the phase transition.

Sensitivity filtering from a continuum mechanics perspective

DEFF Research Database (Denmark)

Sigmund, Ole; Maute, Kurt

2012-01-01

In topology optimization filtering is a popular approach for preventing numerical instabilities. This short note shows that the well-known sensitivity filtering technique, that prevents checkerboards and ensures mesh-independent designs in density-based topology optimization, is equivalent to min...... to minimizing compliance for nonlocal elasticity problems known from continuum mechanics. Hence, the note resolves the long-standing quest for finding an explanation and physical motivation for the sensitivity filter....

Surface effects on static bending of nanowires based on non-local elasticity theory

Directory of Open Access Journals (Sweden)

Quan Wu

2015-10-01

Full Text Available The surface elasticity and non-local elasticity effects on the elastic behavior of statically bent nanowires are investigated in the present investigation. Explicit solutions are presented to evaluate the surface stress and non-local elasticity effects with various boundary conditions. Compared with the classical Euler beam, a nanowire with surface stress and/or non-local elasticity can be either stiffer or less stiff, depending on the boundary conditions. The concept of surface non-local elasticity was proposed and its physical interpretation discussed to explain the combined effect of surface elasticity and non-local elasticity. The effect of the nanowire size on its elastic bending behavior was investigated. The results obtained herein are helpful to characterize mechanical properties of nanowires and aid nanowire-based devices design.

Entanglement and nonlocality in multi-particle systems

Science.gov (United States)

Reid, Margaret D.; He, Qiong-Yi; Drummond, Peter D.

2012-02-01

Entanglement, the Einstein-Podolsky-Rosen (EPR) paradox and Bell's failure of local-hiddenvariable (LHV) theories are three historically famous forms of "quantum nonlocality". We give experimental criteria for these three forms of nonlocality in multi-particle systems, with the aim of better understanding the transition from microscopic to macroscopic nonlocality. We examine the nonlocality of N separated spin J systems. First, we obtain multipartite Bell inequalities that address the correlation between spin values measured at each site, and then we review spin squeezing inequalities that address the degree of reduction in the variance of collective spins. The latter have been particularly useful as a tool for investigating entanglement in Bose-Einstein condensates (BEC). We present solutions for two topical quantum states: multi-qubit Greenberger-Horne-Zeilinger (GHZ) states, and the ground state of a two-well BEC.

The small length scale effect for a non-local cantilever beam: a paradox solved.

Science.gov (United States)

Challamel, N; Wang, C M

2008-08-27

Non-local continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with microstructures or nanostructures. This paper presents some simplified non-local elastic beam models, for the bending analyses of small scale rods. Integral-type or gradient non-local models abandon the classical assumption of locality, and admit that stress depends not only on the strain value at that point but also on the strain values of all points on the body. There is a paradox still unresolved at this stage: some bending solutions of integral-based non-local elastic beams have been found to be identical to the classical (local) solution, i.e. the small scale effect is not present at all. One example is the Euler-Bernoulli cantilever nanobeam model with a point load which has application in microelectromechanical systems and nanoelectromechanical systems as an actuator. In this paper, it will be shown that this paradox may be overcome with a gradient elastic model as well as an integral non-local elastic model that is based on combining the local and the non-local curvatures in the constitutive elastic relation. The latter model comprises the classical gradient model and Eringen's integral model, and its application produces small length scale terms in the non-local elastic cantilever beam solution.

Nonlocal quasinormal modes for arbitrarily shaped three-dimensional plasmonic resonators

DEFF Research Database (Denmark)

Kamandar Dezfouli, Mohsen; Tserkezis, Christos; Mortensen, N. Asger

2017-01-01

Nonlocal effects have been shown to be responsible for a variety of non-trivial optical effects in small-size plasmonic nanoparticles, beyond classical electrodynamics. However, it is not clear whether optical mode descriptions can be applied to such extreme confinement regimes. Here, we present...... quasinormal modes, even at the single mode level. We exemplify the use of this theory by calculating the Purcell factors of single quantum emitters, the electron energy-loss spectroscopy spatial maps, as well as the Mollow triplet spectra of field-driven quantum dots with and without nonlocal effects...... for different size nanoresonators. Our nonlocal quasinormal mode theory offers a reliable and efficient technique to study both classical and quantum optical problems in nanoplasmonics....

Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators.

Science.gov (United States)

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.

The charge-asymmetric nonlocally determined local-electric (CANDLE) solvation model

Energy Technology Data Exchange (ETDEWEB)

Sundararaman, Ravishankar; Goddard, William A. [Joint Center for Artificial Photosynthesis, Pasadena, California 91125 (United States)

2015-02-14

Many important applications of electronic structure methods involve molecules or solid surfaces in a solvent medium. Since explicit treatment of the solvent in such methods is usually not practical, calculations often employ continuum solvation models to approximate the effect of the solvent. Previous solvation models either involve a parametrization based on atomic radii, which limits the class of applicable solutes, or based on solute electron density, which is more general but less accurate, especially for charged systems. We develop an accurate and general solvation model that includes a cavity that is a nonlocal functional of both solute electron density and potential, local dielectric response on this nonlocally determined cavity, and nonlocal approximations to the cavity-formation and dispersion energies. The dependence of the cavity on the solute potential enables an explicit treatment of the solvent charge asymmetry. With four parameters per solvent, this “CANDLE” model simultaneously reproduces solvation energies of large datasets of neutral molecules, cations, and anions with a mean absolute error of 1.8 kcal/mol in water and 3.0 kcal/mol in acetonitrile.

Analytic perturbation theory for screened Coulomb potential: full continuum wave function

International Nuclear Information System (INIS)

Bechler, A.; Ennan, Mc J.; Pratt, R.H.

1979-01-01

An analytic perturbation theory developed previously is used to find a continuum screened-Coulomb wave function characterized by definite asymptotic momentum. This wave function satisfies an inhomogeneous partial differential equation which is solved in parabolic coordinates; the solution depends on both parabolic variables. We calculate partial wave projections of this solution and show that we can choose to add a solution of the homogeneous equation such that the partial wave projections become equal to the normalized continuum radial function found previously. However, finding the unique solution with given asymptotic linear momentum will require either using boundary conditions to determine the unique needed solution of the homogeneous equation or equivalently specifying the screened-Coulomb phase-shifts. (author)

Bosonization, dual transformation and non-local hidden symmetry in two dimensions

International Nuclear Information System (INIS)

Hata, Hiroyuki

1985-01-01

The non-local hidden symmetry is investigated in the bosonized non-abelian Thirring model and the dual representation of the chiral model. In these representations the first non-local symmetry is spontaneously broken in naive pertubation theory. (orig.)

Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory

KAUST Repository

Ball, John M.

2010-07-20

We define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially homogeneous and inhomogeneous systems. In the mean-field approach the main macroscopic variable, the Q-tensor order parameter, is defined in terms of the second moment of a probability distribution function. This definition imposes certain constraints on the eigenvalues of the Q-tensor order parameter, which may be interpreted as physical constraints. We define a thermotropic bulk potential which blows up whenever the eigenvalues of the Q-tensor order parameter approach physically unrealistic values. As a consequence, the minimizers of this continuum energy functional have physically realistic order parameters in all temperature regimes. We study the asymptotics of this bulk potential and show that this model also predicts a first-order nematic-isotropic phase transition, whilst respecting the physical constraints. In contrast, in the Landau-de Gennes framework the Q-tensor order parameter is often defined independently of the probability distribution function, and the theory makes physically unrealistic predictions about the equilibrium order parameters in the low-temperature regime. Copyright © Taylor & Francis Group, LLC.

Deriving appropriate boundary conditions, and accelerating position-jump simulations, of diffusion using non-local jumping

International Nuclear Information System (INIS)

Taylor, P R; Baker, R E; Yates, C A

2015-01-01

In this paper we explore lattice-based position-jump models of diffusion, and the implications of introducing non-local jumping; particles can jump to a range of nearby boxes rather than only to their nearest neighbours. We begin by deriving conditions for equivalence with traditional local jumping models in the continuum limit. We then generalize a previously postulated implementation of the Robin boundary condition for a non-local process of arbitrary maximum jump length, and present a novel implementation of flux boundary conditions, again generalized for a non-local process of arbitrary maximum jump length. In both these cases we validate our results using stochastic simulation. We then proceed to consider two variations on the basic diffusion model: a hybrid local/non-local scheme suitable for models involving sharp concentration gradients, and the implementation of biased jumping. In all cases we show that non-local jumping can deliver substantial time savings for stochastic simulations. (paper)

Quantum nonlocality does not exist.

Science.gov (United States)

Tipler, Frank J

2014-08-05

Quantum nonlocality is shown to be an artifact of the Copenhagen interpretation, in which each observed quantity has exactly one value at any instant. In reality, all physical systems obey quantum mechanics, which obeys no such rule. Locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the many-worlds interpretation (MWI). Using the MWI, I show that the quantum side of Bell's inequality, generally believed nonlocal, is really due to a series of three measurements (not two as in the standard, oversimplified analysis), all three of which have only local effects. Thus, experiments confirming "nonlocality" are actually confirming the MWI. The mistaken interpretation of nonlocality experiments depends crucially on a question-begging version of the Born interpretation, which makes sense only in "collapse" versions of quantum theory, about the meaning of the modulus of the wave function, so I use the interpretation based on the MWI, namely that the wave function is a world density amplitude, not a probability amplitude. This view allows the Born interpretation to be derived directly from the Schrödinger equation, by applying the Schrödinger equation to both the observed and the observer.

The General Theory of Homogenization A Personalized Introduction

CERN Document Server

Tartar, Luc

2010-01-01

Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of Francois Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science,

Quantum Nonlocality and Beyond: Limits from Nonlocal Computation

Science.gov (United States)

Linden, Noah; Popescu, Sandu; Short, Anthony J.; Winter, Andreas

2007-11-01

We address the problem of “nonlocal computation,” in which separated parties must compute a function without any individual learning anything about the inputs. Surprisingly, entanglement provides no benefit over local classical strategies for such tasks, yet stronger nonlocal correlations allow perfect success. This provides intriguing insights into the limits of quantum information processing, the nature of quantum nonlocality, and the differences between quantum and stronger-than-quantum nonlocal correlations.

Experimental studies of the large Debye length probe theory in a continuum plasma

International Nuclear Information System (INIS)

Kamitsuma, M.; Chen, S.

1977-01-01

The Laplace limit probe theory for continuum plasmas, i.e., probe theory under the condition r/sub p//lambda/sub D/→0, where r/sub p/ is probe radius and lambda/sub D/ is Debye length, has been experimentally studied. The results show that the application limit of this theory is r/sub p//lambda/sub D/=0.44 for a spherical probe and r/sub p//lambda/sub D/=0.23 for a cylindrical probe

Target continuum distorted-wave theory for collisions of fast protons with atomic hydrogen

International Nuclear Information System (INIS)

Crothers, D.S.F.; Dunseath, K.M.

1990-01-01

By considering the target continuum distorted-wave (TCDW) theory as the high-energy limit of the half-way house variational continuum distorted-wave theory, it is shown not only that there is no intermediate elastic divergence but also that the second-order amplitude based on a purely elastic intermediate state is of order υ -6 and is thus negligible. The residual inelastic TCDW theory is developed to second-order at high velocities. It is used to describe charge exchange during collisions of fast protons with atomic hydrogen. Using an on-shell peaking approximation and considering 1s-1s capture it is shown that the residual purely second-order transition amplitude comprises two terms, one real term of order υ -6 and one purely imaginary term of order υ -7 ln υ. At 5 MeV laboratory energy, it is shown that these are negligible. It is also shown that the υ -5 first-order term gives a differential cross section in very good agreement with an experiment at all angles including forward, interference minimum, Thomas maximum and large angles, particularly having folded our theory over experimental resolution. (author)

A Non-local Model for Transient Moisture Flow in Unsaturated Soils Based on the Peridynamic Theory

Science.gov (United States)

Jabakhanji, R.; Mohtar, R. H.

2012-12-01

A non-local, gradient free, formulation of the porous media flow problem in unsaturated soils was derived. It parallels the peridynamic theory, a non-local reformulation of solid mechanics presented by Silling. In the proposed model, the evolution of the state of a material point is driven by pairwise interactions with other points across finite distances. Flow and changes in moisture are the result of these interactions. Instead of featuring local gradients, the proposed model expresses the flow as a functional integral of the hydraulic potential field. The absence of spatial gradients, undefined at or on discontinuities, makes the model a good candidate for flow simulations in fractured soils. It also lends itself to coupling with peridynamic mechanical models for simulating crack formation triggered by shrinkage and swelling, and assessing their potential impact on a wide range of processes, such as infiltration, contaminant transport, slope stability and integrity of clay barriers. A description of the concept and an outline of the derivation and numerical implementation are presented. Simulation results of infiltration and drainage for 1D, single and two-layers soil columns, for three different soil types are also presented. The same simulations are repeated using HYDRUS-1D, a computer model using the classic local flow equation. We show that the proposed non-local formulation successfully reproduces the results from HYDRUS-1D. S.A. Silling, "Reformulation of Elasticity Theory for Discontinuities and Long-range Forces," Journal of the Mechanics and Physics of Solids 48, no. 1 (January 2000): 175-209. J. Simunek, M. Sejna, and M.T. Van Genuchten, "The HYDRUS-1D Software Package for Simulating the One-dimensional Movement of Water, Heat, and Multiple Solutes in Variably-saturated Media," University of California, Riverside, Research Reports 240 (2005).

On the origin of nonlocal damping in plasmonic monomers and dimers

Science.gov (United States)

Tserkezis, Christos; Yan, Wei; Hsieh, Wenting; Sun, Greg; Khurgin, Jacob B.; Wubs, Martijn; Mortensen, N. Asger

2017-09-01

The origin and importance of nonlocal damping is discussed through simulations with the generalized nonlocal optical response (GNOR) theory, in conjunction with time-dependent density functional theory (TDDFT) calculations and equivalent circuit modeling, for some of the most typical plasmonic architectures: metal-dielectric interfaces, metal-dielectric-metal gaps, spherical nanoparticles and nanoparticle dimers. It is shown that diffusive damping, as introduced by the convective-diffusive GNOR theory, describes well the enhanced losses and plasmon broadening predicted by ab initio calculations in few-nm particles or few-to-sub-nm gaps. Through the evaluation of a local effective dielectric function, it is shown that absorptive losses appear dominantly close to the metal surface, in agreement with TDDFT and the mechanism of Landau damping due to generation of electron-hole pairs near the interface. Diffusive nonlocal theories provide therefore an efficient means to tackle plasmon damping when electron tunneling can be safely disregarded, without the need to resort to more accurate, but time-consuming fully quantum-mechanical studies.

Nanoplasmonics: Exploring nonlocal and quantum effects

DEFF Research Database (Denmark)

Mortensen, N. Asger

2016-01-01

Plasmonics is commonly understood within classical electrodynamics with local-response constitutive relations. However, possibilities for nonlocal dynamics and quantum effects emerge with strong spatial confinement in plasmonic nanostructures. This talks reviews recent theory and experiments...

Nonlocal interactions and Bell's inequality

International Nuclear Information System (INIS)

Garuccio, A.; Selleri, F.

1976-01-01

It is shown that natural extensions of the local hidden variable theories to include nonlocal effects still lead to a full validity of Bell's inequality. It is conjectured that the essential point expressed by this inequality is not locality, but the wave-particle dualism

Quantum cybernetics: a new perspective for Nelson's stochastic theory, nonlocality, and the Klein-Gordon equation

Science.gov (United States)

Grössing, Gerhard

2002-04-01

The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a “particle”, which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or “cybernetic”, relationships between “particles” and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.

Accuracy of local exchange in the calculation of continuum wavefunctions

International Nuclear Information System (INIS)

Biava, D A; Bartschat, K; Saha, H P; Madison, D H

2002-01-01

It is well known that electron exchange can play an important role in electron-impact elastic, inelastic and ionization scattering from atoms and molecules. The proper theoretical treatment of exchange yields an inhomogeneous differential equation with a non-local exchange operator. To simplify the calculation, a local approximation is often made for this non-local operator. In this paper, we examine the accuracy of this approximation for the calculation of elastic scattering continuum waves in the presence of an argon ion with a single vacancy in the p-shell. It is found that one can reliably use the local exchange approximation for ionization leading to s-state vacancies but not p-state vacancies

Breathing multichimera states in nonlocally coupled phase oscillators

Science.gov (United States)

Suda, Yusuke; Okuda, Koji

2018-04-01

Chimera states for the one-dimensional array of nonlocally coupled phase oscillators in the continuum limit are assumed to be stationary states in most studies, but a few studies report the existence of breathing chimera states. We focus on multichimera states with two coherent and incoherent regions and numerically demonstrate that breathing multichimera states, whose global order parameter oscillates temporally, can appear. Moreover, we show that the system exhibits a Hopf bifurcation from a stationary multichimera to a breathing one by the linear stability analysis for the stationary multichimera.

A Monte Carlo procedure for Hamiltonians with small nonlocal correction terms

International Nuclear Information System (INIS)

Mack, G.; Pinn, K.

1986-03-01

We consider lattice field theories whose Hamiltonians contain small nonlocal correction terms. We propose to do simulations for an auxiliarly polymer system with field dependent activities. If a nonlocal correction term to the Hamiltonian is small, it need to be evaluated only rarely. (orig.)

Robustness of the far-field response of nonlocal plasmonic ensembles

DEFF Research Database (Denmark)

Tserkezis, Christos; Maack, Johan Rosenkrantz; Liu, Zhaowei

2016-01-01

Contrary to classical predictions, the optical response of few-nm plasmonic particles depends on particle size due to effects such as nonlocality and electron spill-out. Ensembles of such nanoparticles are therefore expected to exhibit a nonclassical inhomogeneous spectral broadening due to size...... distribution. For a normal distribution of free-electron nanoparticles, and within the simple nonlocal hydrodynamic Drude model, both the nonlocal blueshift and the plasmon linewidth are shown to be considerably affected by ensemble averaging. Size-variance effects tend however to conceal nonlocality...... to a lesser extent when the homogeneous size-dependent broadening of individual nanoparticles is taken into account, either through a local size-dependent damping model or through the Generalized Nonlocal Optical Response theory. The role of ensemble averaging is further explored in realistic distributions...

Unexpected strong attraction in the presence of continuum bound state

International Nuclear Information System (INIS)

Delfino, A.; Frederico, T.

1992-06-01

The result of few-particle ground-state calculation employing a two-particle non-local potential supporting a continuum bound state in addition to a negative-energy bound state has occasionally revealed unexpected large attraction in producing a very strongly bound ground state. In the presence of the continuum bound state the difference of phase shift between zero and infinite energies has an extra jump of φ as in the presence of an additional bound state. The wave function of the continuum bound state is identical with that of a strongly bound negative-energy state, which leads us to postulate a pseudo bound state in the two-particle system in order to explain the unexpected attraction. The role of the Pauli forbidden states is expected to be similar to these pseudo states. (author)

Nonlocality and entanglement in qubit systems

Energy Technology Data Exchange (ETDEWEB)

Batle, J [Departament de Fisica, Universitat de les Illes Balears, 07122 Palma de Mallorca (Spain); Casas, M, E-mail: vdfsjbv4@uib.es [Departament de Fisica and IFISC-CSIC, Universitat de les Illes Balears, 07122 Palma de Mallorca (Spain)

2011-11-04

Nonlocality and quantum entanglement constitute two special aspects of the quantum correlations existing in quantum systems, which are of paramount importance in quantum-information theory. Traditionally, they have been regarded as identical (equivalent, in fact, for pure two qubit states, that is, Gisin's Theorem), yet they constitute different resources. Describing nonlocality by means of the violation of several Bell inequalities, we obtain by direct optimization those states of two qubits that maximally violate a Bell inequality, in terms of their degree of mixture as measured by either their participation ratio R = 1/Tr({rho}{sup 2}) or their maximum eigenvalue {lambda}{sub max}. This optimum value is obtained as well, which coincides with previous results. Comparison with entanglement is performed too. An example of an application is given in the XY model. In this novel approximation, we also concentrate on the nonlocality for linear combinations of pure states of two qubits, providing a closed form for their maximal nonlocality measure. The case of Bell diagonal mixed states of two qubits is also extensively studied. Special attention concerning the connection between nonlocality and entanglement for mixed states of two qubits is paid to the so-called maximally entangled mixed states. Additional aspects for the case of two qubits are also described in detail. Since we deal with qubit systems, we will perform an analogous study for three qubits, employing similar tools. Relation between distillability and nonlocality is explored quantitatively for the whole space of states of three qubits. We finally extend our analysis to four-qubit systems, where nonlocality for generalized Greenberger-Horne-Zeilinger states of arbitrary number of parties is computed. (paper)

Limits on nonlocal correlations from the structure of the local state space

International Nuclear Information System (INIS)

Janotta, Peter; Gogolin, Christian; Barrett, Jonathan; Brunner, Nicolas

2011-01-01

The outcomes of measurements on entangled quantum systems can be nonlocally correlated. However, while it is easy to write down toy theories allowing arbitrary nonlocal correlations, those allowed in quantum mechanics are limited. Quantum correlations cannot, for example, violate a principle known as macroscopic locality, which implies that they cannot violate Tsirelson's bound. This paper shows that there is a connection between the strength of nonlocal correlations in a physical theory and the structure of the state spaces of individual systems. This is illustrated by a family of models in which local state spaces are regular polygons, where a natural analogue of a maximally entangled state of two systems exists. We characterize the nonlocal correlations obtainable from such states. The family allows us to study the transition between classical, quantum and super-quantum correlations by varying only the local state space. We show that the strength of nonlocal correlations - in particular whether the maximally entangled state violates Tsirelson's bound or not-depends crucially on a simple geometric property of the local state space, known as strong self-duality. This result is seen to be a special case of a general theorem, which states that a broad class of entangled states in probabilistic theories-including, by extension, all bipartite classical and quantum states-cannot violate macroscopic locality. Finally, our results show that models exist that are locally almost indistinguishable from quantum mechanics, but can nevertheless generate maximally nonlocal correlations.

Molecular-state close-coupling theory including continuum states. I. Derivation of close-coupled equations

International Nuclear Information System (INIS)

Thorson, W.R.; Bandarage, G.

1988-01-01

We formulate a close-coupling theory of slow ion-atom collisions based on molecular (adiabatic) electronic states, and including the electronic continuum. The continuum is represented by packet states spanning it locally and constructed explicitly from exact continuum states. Particular attention is given to two fundamental questions: (1) Unbound electrons can escape from the local region spanned by the packet states. We derive close-coupled integral equations correctly including the escape effects; the ''propagator'' generated by these integral equations does not conserve probability within the close-coupled basis. Previous molecular-state formulations including the continuum give no account of escape effects. (2) Nonadiabatic couplings of adiabatic continuum states with the same energy are singular, reflecting the fact that an adiabatic description of continuum behavior is not valid outside a local region. We treat these singularities explicitly and show that an accurate representation of nonadiabatic couplings within the local region spanned by a set of packet states is well behaved. Hence an adiabatic basis-set description can be used to describe close coupling to the continuum in a local ''interaction region,'' provided the effects of escape are included. In principle, the formulation developed here can be extended to a large class of model problems involving many-electron systems and including models for Penning ionization and collisional detachment processes

An analytical method for free vibration analysis of Timoshenko beam theory applied to cracked nanobeams using a nonlocal elasticity model

International Nuclear Information System (INIS)

Torabi, K.; Nafar Dastgerdi, J.

2012-01-01

This paper is concerned with the free transverse vibration of cracked nanobeams modeled after Eringen's nonlocal elasticity theory and Timoshenko beam theory. The cracked beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in rotational displacement due to bending which is proportional to bending moment transmitted by the cracked section. The governing equations of cracked nanobeams with two symmetric and asymmetric boundary conditions are derived; then these equations are solved analytically based on concerning basic standard trigonometric and hyperbolic functions. Besides, the frequency parameters and the vibration modes of cracked nanobeams for variant crack positions, crack ratio, and small scale effect parameters are calculated. The vibration solutions obtained provide a better representation of the vibration behavior of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. - Highlights: ► The free vibration analysis of cracked nanobeams is investigated. ► This study is based on the theory of nonlocal elasticity and Timoshenko beam theory. ► The small scale effect parameter greatly affects the value of natural frequencies. ► Crack reduces the natural frequencies, causes a discontinuity in the cracked section.

An analytical method for free vibration analysis of Timoshenko beam theory applied to cracked nanobeams using a nonlocal elasticity model

Energy Technology Data Exchange (ETDEWEB)

Torabi, K., E-mail: kvntrb@KashanU.ac.ir; Nafar Dastgerdi, J., E-mail: J.nafardastgerdi@me.iut.ac.ir

2012-08-31

This paper is concerned with the free transverse vibration of cracked nanobeams modeled after Eringen's nonlocal elasticity theory and Timoshenko beam theory. The cracked beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in rotational displacement due to bending which is proportional to bending moment transmitted by the cracked section. The governing equations of cracked nanobeams with two symmetric and asymmetric boundary conditions are derived; then these equations are solved analytically based on concerning basic standard trigonometric and hyperbolic functions. Besides, the frequency parameters and the vibration modes of cracked nanobeams for variant crack positions, crack ratio, and small scale effect parameters are calculated. The vibration solutions obtained provide a better representation of the vibration behavior of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant. - Highlights: Black-Right-Pointing-Pointer The free vibration analysis of cracked nanobeams is investigated. Black-Right-Pointing-Pointer This study is based on the theory of nonlocal elasticity and Timoshenko beam theory. Black-Right-Pointing-Pointer The small scale effect parameter greatly affects the value of natural frequencies. Black-Right-Pointing-Pointer Crack reduces the natural frequencies, causes a discontinuity in the cracked section.

Two- and three-dimensional nonlocal density functional theory for inhomogeneous fluids. 1. Algorithms and parallelization

International Nuclear Information System (INIS)

Frink, L.J.D.; Salinger, A.G.

2000-01-01

Fluids adsorbed near surfaces, near macromolecules, and in porous materials are inhomogeneous, exhibiting spatially varying density distributions. This inhomogeneity in the fluid plays an important role in controlling a wide variety of complex physical phenomena including wetting, self-assembly, corrosion, and molecular recognition. One of the key methods for studying the properties of inhomogeneous fluids in simple geometries has been density functional theory (DFT). However, there has been a conspicuous lack of calculations in complex two- and three-dimensional geometries. The computational difficulty arises from the need to perform nested integrals that are due to nonlocal terms in the free energy functional. These integral equations are expensive both in evaluation time and in memory requirements; however, the expense can be mitigated by intelligent algorithms and the use of parallel computers. This paper details the efforts to develop efficient numerical algorithms so that nonlocal DFT calculations in complex geometries that require two or three dimensions can be performed. The success of this implementation will enable the study of solvation effects at heterogeneous surfaces, in zeolites, in solvated (bio)polymers, and in colloidal suspensions

Ab initio translationally invariant nonlocal one-body densities from no-core shell-model theory

Science.gov (United States)

Burrows, M.; Elster, Ch.; Popa, G.; Launey, K. D.; Nogga, A.; Maris, P.

2018-02-01

Background: It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from ab initio no-core shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. Purpose: Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wave functions up to now has only been developed for local densities. Results: A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of 4He, 6Li, 12C, and 16O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space. Conclusions: We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and cannot be described with simple functional forms.

Hyperbolic metamaterials: Nonlocal response regularizes broadband supersingularity

DEFF Research Database (Denmark)

Yan, Wei; Wubs, Martijn; Mortensen, N. Asger

2012-01-01

We study metamaterials known as hyperbolic media that in the usual local-response approximation exhibit hyperbolic dispersion and an associated broadband singularity in the density of states. Instead, from the more microscopic hydrodynamic Drude theory we derive qualitatively different optical...... properties of these metamaterials, due to the free-electron nonlocal optical response of their metal constituents. We demonstrate that nonlocal response gives rise to a large-wavevector cutoff in the dispersion that is inversely proportional to the Fermi velocity of the electron gas, but also for small...

Constitutive relationships and models in continuum theories of multiphase flows

International Nuclear Information System (INIS)

Decker, R.

1989-09-01

In April, 1989, a workshop on constitutive relationships and models in continuum theories of multiphase flows was held at NASA's Marshall Space Flight Center. Topics of constitutive relationships for the partial or per phase stresses, including the concept of solid phase pressure are discussed. Models used for the exchange of mass, momentum, and energy between the phases in a multiphase flow are also discussed. The program, abstracts, and texts of the presentations from the workshop are included

Non-locality of non-Abelian anyons

International Nuclear Information System (INIS)

Brennen, G K; Iblisdir, S; Pachos, J K; Slingerland, J K

2009-01-01

Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.

Non-locality of non-Abelian anyons

Science.gov (United States)

Brennen, G. K.; Iblisdir, S.; Pachos, J. K.; Slingerland, J. K.

2009-10-01

Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history. The information encoded in anyons is inherently non-local even in the single subsystem level making the treatment of anyons non-conventional. We describe a protocol to reveal the non-locality of anyons in terms of correlations in the outcomes of measurements in two separated regions. This gives a clear operational measure of non-locality for anyonic states and it opens up the possibility to test Bell inequalities in quantum Hall liquids or spin lattices.

Nonlinear static analysis of single layer annular/circular graphene sheets embedded in Winkler–Pasternak elastic matrix based on non-local theory of Eringen

Directory of Open Access Journals (Sweden)

Shahriar Dastjerdi

2016-06-01

Full Text Available Nonlinear bending analysis of orthotropic annular/circular graphene sheets has been studied based on the non-local elasticity theory. The first order shear deformation theory (FSDT is applied in combination with the nonlinear Von-Karman strain field. The obtained differential equations are solved by using two methods, first the differential quadrature method (DQM and a new semi-analytical polynomial method (SAPM which is innovated by the authors. Applying the DQM or SAPM, the differential equations are transformed to nonlinear algebraic equations system. Then the Newton–Raphson iterative scheme is used. First, the obtained results from DQM and SAPM are compared and it is concluded that although the SAPM’s formulation is considerably simpler than DQM, however, the SAPM’s results are so close to DQM. The results are validated with available papers. Finally, the effects of small scale parameter on the results, the comparison between local and non-local theories, and linear to nonlinear analyses are investigated.

Conceptual Nonlocality

Directory of Open Access Journals (Sweden)

David A. Grandy

2007-08-01

Full Text Available Nonlocality is a puzzling issue in modern physics. I propose that, aside from the experimental determination of nonlocality, the concept of atomistic lightmdash;discrete, self-bounded photonsmdash;breaks down toward something like nonlocality when subjected to philosophical scrutiny. Louis de Broglie made a similar argument regarding the material atom: the concept of the classical atom, when interrogated, collapses upon itself to offer a glimpse of wave-particle duality. Light atoms or photons, I argue, similarly collapse toward the contradictory possibility of nonlocality.

The statistical strength of nonlocality proofs

NARCIS (Netherlands)

Dam, van W.; Gill, R.D.; Grünwald, P.D.

2005-01-01

There exist numerous proofs of Bell's theorem, stating that quantum mechanics is incompatible with local realistic theories of nature. Here the strength of such nonlocality proofs is defined in terms of the amount of evidence against local realism provided by the corresponding experiments.

The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow

Energy Technology Data Exchange (ETDEWEB)

Mohammadimehr, M., E-mail: mmohammadimehr@kashanu.ac.ir [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of); Mohammadi-Dehabadi, A.A. [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of); Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran (Iran, Islamic Republic of); Maraghi, Z. Khoddami [Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, P.O. Box: 87317-53153, Kashan (Iran, Islamic Republic of)

2017-04-01

In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.

The effect of non-local higher order stress to predict the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow

International Nuclear Information System (INIS)

Mohammadimehr, M.; Mohammadi-Dehabadi, A.A.; Maraghi, Z. Khoddami

2017-01-01

In this research, the effect of non-local higher order stress on the nonlinear vibration behavior of carbon nanotube conveying viscous nanoflow resting on elastic foundation is investigated. Physical intuition reveals that increasing nanoscale stress leads to decrease the stiffness of nanostructure which firstly established by Eringen's non-local elasticity theory (previous nonlocal method) while many of papers have concluded otherwise at microscale based on modified couple stress, modified strain gradient theories and surface stress effect. The non-local higher order stress model (new nonlocal method) is used in this article that has been studied by few researchers in other fields and the results from the present study show that the trend of the new nonlocal method and size dependent effect including modified couple stress theory is the same. In this regard, the nonlinear motion equations are derived using a variational principal approach considering essential higher-order non-local terms. The surrounded elastic medium is modeled by Pasternak foundation to increase the stability of system where the fluid flow may cause system instability. Effects of various parameters such as non-local parameter, elastic foundation coefficient, and fluid flow velocity on the stability and dimensionless natural frequency of nanotube are investigated. The results of this research show that the small scale parameter based on higher order stress help to increase the natural frequency which has been approved by other small scale theories such as strain gradient theory, modified couple stress theory and experiments, and vice versa for previous nonlocal method. This study may be useful to measure accurately the vibration characteristics of nanotubes conveying viscous nanoflow and to design nanofluidic devices for detecting blood Glucose.

Torsion of cracked nanorods using a nonlocal elasticity model

International Nuclear Information System (INIS)

Loya, J A; Aranda-Ruiz, J; Fernández-Sáez, J

2014-01-01

This paper presents a nonlocal cracked-rod model from which we have analysed the torsional vibrations of a carbon nanotube with a circumferential crack. Several types of boundary conditions, including the consideration of a buckyball at the end of the nanotube, have been studied. The nonlocal Eringen elasticity theory is used to formulate the problem. The cracked rod is modelled by dividing the cracked element into two segments connected by a torsional linear spring whose stiffness is related to the crack severity. The effect of the nonlocal small-scale parameter, crack severity, cracked section position, different boundary conditions and attached mass are examined in this work. (paper)

Two-dimensional linear elasticity theory of magneto-electro-elastic plates considering surface and nonlocal effects for nanoscale device applications

Science.gov (United States)

Wang, Wenjun; Li, Peng; Jin, Feng

2016-09-01

A novel two-dimensional linear elastic theory of magneto-electro-elastic (MEE) plates, considering both surface and nonlocal effects, is established for the first time based on Hamilton’s principle and the Lee plate theory. The equations derived are more general, suitable for static and dynamic analyses, and can also be reduced to the piezoelectric, piezomagnetic, and elastic cases. As a specific application example, the influences of the surface and nonlocal effects, poling directions, piezoelectric phase materials, volume fraction, damping, and applied magnetic field (i.e., constant applied magnetic field and time-harmonic applied magnetic field) on the magnetoelectric (ME) coupling effects are first investigated based on the established two-dimensional plate theory. The results show that the ME coupling coefficient has an obvious size-dependent characteristic owing to the surface effects, and the surface effects increase the ME coupling effects significantly when the plate thickness decreases to its critical thickness. Below this critical thickness, the size-dependent effect is obvious and must be considered. In addition, the output power density of a magnetic energy nanoharvester is also evaluated using the two-dimensional plate theory obtained, with the results showing that a relatively larger output power density can be achieved at the nanoscale. This study provides a mathematical tool which can be used to analyze the mechanical properties of nanostructures theoretically and numerically, as well as evaluating the size effect qualitatively and quantitatively.

Morphing Continuum Theory: A First Order Approximation to the Balance Laws

Science.gov (United States)

Wonnell, Louis; Cheikh, Mohamad Ibrahim; Chen, James

2017-11-01

Morphing Continuum Theory is constructed under the framework of Rational Continuum Mechanics (RCM) for fluid flows with inner structure. This multiscale theory has been successfully emplyed to model turbulent flows. The framework of RCM ensures the mathematical rigor of MCT, but contains new material constants related to the inner structure. The physical meanings of these material constants have yet to be determined. Here, a linear deviation from the zeroth-order Boltzmann-Curtiss distribution function is derived. When applied to the Boltzmann-Curtiss equation, a first-order approximation of the MCT governing equations is obtained. The integral equations are then related to the appropriate material constants found in the heat flux, Cauchy stress, and moment stress terms in the governing equations. These new material properties associated with the inner structure of the fluid are compared with the corresponding integrals, and a clearer physical interpretation of these coefficients emerges. The physical meanings of these material properties is determined by analyzing previous results obtained from numerical simulations of MCT for compressible and incompressible flows. The implications for the physics underlying the MCT governing equations will also be discussed. This material is based upon work supported by the Air Force Office of Scientific Research under Award Number FA9550-17-1-0154.

Loop quantization as a continuum limit

International Nuclear Information System (INIS)

Manrique, Elisa; Oeckl, Robert; Weber, Axel; Zapata, Jose A

2006-01-01

We present an implementation of Wilson's renormalization group and a continuum limit tailored for loop quantization. The dynamics of loop-quantized theories is constructed as a continuum limit of the dynamics of effective theories. After presenting the general formalism we show as a first explicit example the 2D Ising field theory, an interacting relativistic quantum field theory with local degrees of freedom quantized by loop quantization techniques

A Systems-Theoretical Generalization of Non-Local Correlations

Science.gov (United States)

von Stillfried, Nikolaus

Non-local correlations between quantum events are not due to a causal interaction in the sense of one being the cause for the other. In principle, the correlated events can thus occur simultaneously. Generalized Quantum Theory (GQT) formalizes the idea that non-local phenomena are not exclusive to quantum mechanics, e.g. due to some specific properties of (sub)atomic particles, but that they instead arise as a consequence of the way such particles are arranged into systems. Non-local phenomena should hence occur in any system which fulfils the necessary systems-theoretical parameters. The two most important parameters with respect to non-local correlations seem to be a conserved global property of the system as a whole and sufficient degrees of freedom of the corresponding property of its subsystems. Both factors place severe limitations on experimental observability of the phenomena, especially in terms of replicability. It has been suggested that reported phenomena of a so-called synchronistic, parapsychological or paranormal kind could be understood as instances of systems-inherent non-local correlations. From a systems-theoretical perspective, their phenomenology (including the favorable conditions for their occurrence and their lack of replicability) displays substantial similarities to non-local correlations in quantum systems and matches well with systems-theoretical parameters, thus providing circumstantial evidence for this hypothesis.

Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams

Science.gov (United States)

Ebrahimi, Farzad; Reza Barati, Mohammad

2016-09-01

In this work, a size-dependent curved beam model is developed to take into account the effects of nonlocal stresses on the buckling behavior of curved magneto-electro-elastic FG nanobeams for the first time. The governing differential equations are derived based on the principle of virtual work and Euler-Bernoulli beam theory. The power-law function is employed to describe the spatially graded magneto-electro-elastic properties. By extending the radius of the curved nanobeam to infinity, the results of straight nonlocal FG beams can be rendered. The effects of magnetic potential, electric voltage, opening angle, nonlocal parameter, power-law index and slenderness ratio on buckling loads of curved MEE-FG nanobeams are studied.

Nonlocality, Entanglement Witnesses and Supra-correlations

Science.gov (United States)

2012-04-01

quantum non-locality, non-signaling theories, Popescu-Rohrlich boxes, EPR 1. INTRODUCTION Physics imposes limits on the correlations that can be...References [1] J.S. Bell, “On the Einstein Podolsky Rosen paradox ,” Physics 1, 195 (1964). [2] B. Tsirelson, “Quantum Generalizations of Bell’s

A generalized nonlocal vector calculus

Science.gov (United States)

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.

Continuum orbital approximations in weak-coupling theories for inelastic electron scattering

International Nuclear Information System (INIS)

Peek, J.M.; Mann, J.B.

1977-01-01

Two approximations, motivated by heavy-particle scattering theory, are tested for weak-coupling electron-atom (ion) inelastic scattering theory. They consist of replacing the one-electron scattering orbitals by their Langer uniform approximations and the use of an average trajectory approximation which entirely avoids the necessity for generating continuum orbitals. Numerical tests for a dipole-allowed and a dipole-forbidden event, based on Coulomb-Born theory with exchange neglected, reveal the error trends. It is concluded that the uniform approximation gives a satisfactory prediction for traditional weak-coupling theories while the average approximation should be limited to collision energies exceeding at least twice the threshold energy. The accuracy for both approximations is higher for positive ions than for neutral targets. Partial-wave collision-strength data indicate that greater care should be exercised in using these approximations to predict quantities differential in the scattering angle. An application to the 2s 2 S-2p 2 P transition in Ne VIII is presented

Pion form factor in QCD sum rules, local duality approach, and O(A2) fractional analytic perturbation theory

International Nuclear Information System (INIS)

Bakulev, Alexander P.

2010-01-01

Using the results on the electromagnetic pion Form Factor (FF) obtained in the O(α s ) QCD sum rules with non-local condensates [A.P. Bakulev, A.V. Pimikov, and N.G. Stefanis, Phys. Rev. D79 (2009) 093010] we determine the effective continuum threshold for the local duality approach. Then we apply it to construct the O(α s 2 ) estimation of the pion FF in the framework of the fractional analytic perturbation theory.

A continuum theory of edge dislocations

Science.gov (United States)

Berdichevsky, V. L.

2017-09-01

Continuum theory of dislocation aims to describe the behavior of large ensembles of dislocations. This task is far from completion, and, most likely, does not have a "universal solution", which is applicable to any dislocation ensemble. In this regards it is important to have guiding lines set by benchmark cases, where the transition from a discrete set of dislocations to a continuum description is made rigorously. Two such cases have been considered recently: equilibrium of dislocation walls and screw dislocations in beams. In this paper one more case is studied, equilibrium of a large set of 2D edge dislocations placed randomly in a 2D bounded region. The major characteristic of interest is energy of dislocation ensemble, because it determines the structure of continuum equations. The homogenized energy functional is obtained for the periodic dislocation ensembles with a random contents of the periodic cell. Parameters of the periodic structure can change slowly on distances of order of the size of periodic cells. The energy functional is obtained by the variational-asymptotic method. Equilibrium positions are local minima of energy. It is confirmed the earlier assertion that energy density of the system is the sum of elastic energy of averaged elastic strains and microstructure energy, which is elastic energy of the neutralized dislocation system, i.e. the dislocation system placed in a constant dislocation density field making the averaged dislocation density zero. The computation of energy is reduced to solution of a variational cell problem. This problem is solved analytically. The solution is used to investigate stability of simple dislocation arrays, i.e. arrays with one dislocation in the periodic cell. The relations obtained yield two outcomes: First, there is a state parameter of the system, dislocation polarization; averaged stresses affect only dislocation polarization and cannot change other characteristics of the system. Second, the structure of

Einstein locality, EPR locality, and the significance for science of the nonlocal character of quantum theory

International Nuclear Information System (INIS)

Stapp, H.P.

1985-10-01

The immense difference between Einstein locality and EPR locality is discussed. The latter provides a basis for establishing the nonlocal character of quantum theory, whereas the former does not. A model representing Heisenberg's idea of physical reality is introduced. It is nondeterministic and holistic: the objects, measuring devices, and their environment are treated as an inseparable entity, with, however, macroscopically localizable attributes. The EPR principle that no disturbance can propagate faster than light is imposed without assuming any structure incompatible with orthodox quantum thinking. This locality requirement renders the model incompatible with rudimentary predictions of quantum theory. A more general proof not depending on any model is also given. A recent argument that purports to show that quantum theory is compatible with EPR locality is examined. It illustrates the importance of the crucial one-world assumption. The significance for science of the failure of EPR locality is discussed

Subquantum nonlocal correlations induced by the background random field

Energy Technology Data Exchange (ETDEWEB)

Khrennikov, Andrei, E-mail: Andrei.Khrennikov@lnu.s [International Center for Mathematical Modelling in Physics and Cognitive Sciences, Linnaeus University, Vaexjoe (Sweden); Institute of Information Security, Russian State University for Humanities, Moscow (Russian Federation)

2011-10-15

We developed a purely field model of microphenomena-prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction-the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology-for Gaussian random fields with covariance operators corresponding to factorizable quantum states).

Subquantum nonlocal correlations induced by the background random field

International Nuclear Information System (INIS)

Khrennikov, Andrei

2011-01-01

We developed a purely field model of microphenomena-prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of quantum mechanics (QM) including correlations for entangled systems, but also gives a possibility to go beyond QM, i.e. to make predictions of phenomena that could be observed at the subquantum level. In this paper, we discuss one such prediction-the existence of nonlocal correlations between prequantum random fields corresponding to all quantum systems. (And by PCSFT, quantum systems are represented by classical Gaussian random fields and quantum observables by quadratic forms of these fields.) The source of these correlations is the common background field. Thus all prequantum random fields are 'entangled', but in the sense of classical signal theory. On the one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random background. On the other hand, it demonstrates total generality of such correlations. They exist even for distinguishable quantum systems in factorizable states (by PCSFT terminology-for Gaussian random fields with covariance operators corresponding to factorizable quantum states).

Extrapolation of lattice gauge theories to the continuum limit

International Nuclear Information System (INIS)

Duncan, A.; Vaidya, H.

1978-01-01

The problem of extrapolating lattice gauge theories from the strong-coupling phase to the continuum critical point is studied for the Abelian (U(1)) and non-Abelian (SU(2)) theories in three (space--time) dimensions. A method is described for obtaining the asymptotic behavior, for large β, of such thermodynamic quantities and correlation functions as the free energy and Wilson loop function. Certain general analyticity and positivity properties (in the complex β-plane) are shown to lead, after appropriate analytic remappings, to a Stieltjes property of these functions. Rigorous theorems then guarantee uniform and monotone convergence of the Pade approximants, with exact pointwise upper and lower bounds. The first three Pade's are computed for both the free energy and the Wilson function. For the free energy, satisfactory agreement is with the asymptotic behavior computed by an explicit lattice calculation. The strong-coupling series for the Wilson function is found to be considerably more unstable in the lower order terms - correspondingly, convergence of the Pade's is found to be slower than in the free-energy case. It is suggested that higher-order calculations may allow a reasonably accurate determination of the string constant for the SU(2) theory. 14 references

Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axial load

International Nuclear Information System (INIS)

Li, C; Yu, J L; Lim, C W

2011-01-01

This paper investigates the natural frequency, steady-state resonance and stability for the transverse vibrations of a nanobeam subjected to a variable initial axial force, including axial tension and axial compression, based on nonlocal elasticity theory. It is reported that the nonlocal nanoscale has significant effects on vibration behavior, which results in a new effective nonlocal bending moment different to but dependent on the corresponding nonlocal bending moment. The effects of nonlocal nanoscale and the variation of initial axial force on the natural frequency as well as the instability regions are analyzed by the perturbation method. It concludes that both the nonlocal nanoscale and the initial tension, including static and dynamic tensions, cause an increase in natural frequency, while an initial compression causes the natural frequency to decrease. Instability regions are also greatly influenced by the nonlocal nanoscale and initial tension and they become smaller with stronger nonlocal effects or larger initial tension

Nonlocal teleparallel cosmology.

Science.gov (United States)

Bahamonde, Sebastian; Capozziello, Salvatore; Faizal, Mir; Nunes, Rafael C

2017-01-01

Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + [Formula: see text] observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction.

Nonlocal teleparallel cosmology

Energy Technology Data Exchange (ETDEWEB)

Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Capozziello, Salvatore [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); Gran Sasso Science Institute, L' Aquila (Italy); Compl. Univ. di Monte S. Angelo, Naples (Italy); INFN, Napoli (Italy); Faizal, Mir [University of British Columbia - Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Lethbridge, AB (Canada); Nunes, Rafael C. [Universidade Federal de Juiz de Fora, Departamento de Fisica, Juiz de Fora, MG (Brazil)

2017-09-15

Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + H{sub 0} observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction. (orig.)

Hyperbolic conservation laws in continuum physics

CERN Document Server

Dafermos, Constantine M

2016-01-01

This is a masterly exposition and an encyclopedic presentation of the theory of hyperbolic conservation laws. It illustrates the essential role of continuum thermodynamics in providing motivation and direction for the development of the mathematical theory while also serving as the principal source of applications. The reader is expected to have a certain mathematical sophistication and to be familiar with (at least) the rudiments of analysis and the qualitative theory of partial differential equations, whereas prior exposure to continuum physics is not required. The target group of readers would consist of (a) experts in the mathematical theory of hyperbolic systems of conservation laws who wish to learn about the connection with classical physics; (b) specialists in continuum mechanics who may need analytical tools; (c) experts in numerical analysis who wish to learn the underlying mathematical theory; and (d) analysts and graduate students who seek introduction to the theory of hyperbolic systems of conser...

The sheaf-theoretic structure of non-locality and contextuality

International Nuclear Information System (INIS)

Abramsky, Samson; Brandenburger, Adam

2011-01-01

We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, in a setting that generalizes the familiar probability tables used in non-locality theory to arbitrary measurement covers; this includes Kochen-Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. We distinguish a proper hierarchy of strengths of no-go theorems, and show that three leading examples—due to Bell, Hardy and Greenberger, Horne and Zeilinger, respectively—occupy successively higher levels of this hierarchy. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling; this is based on a result showing that the linear subspaces generated by the non-contextual and no-signalling models, over an arbitrary measurement cover, coincide. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. A general setting is developed for the Kochen-Specker-type results, as generic, model-independent proofs of maximal contextuality, and a new combinatorial condition is given, which generalizes the ‘parity proofs’ commonly found in the literature. We also show how our abstract setting can be represented in quantum mechanics. This leads to a strengthening of the usual no-signalling theorem, which shows that quantum mechanics obeys no-signalling for arbitrary families of commuting observables, not just those represented on different factors of a tensor product. (paper)

A nonlocal strain gradient model for dynamic deformation of orthotropic viscoelastic graphene sheets under time harmonic thermal load

Science.gov (United States)

Radwan, Ahmed F.; Sobhy, Mohammed

2018-06-01

This work presents a nonlocal strain gradient theory for the dynamic deformation response of a single-layered graphene sheet (SLGS) on a viscoelastic foundation and subjected to a time harmonic thermal load for various boundary conditions. Material of graphene sheets is presumed to be orthotropic and viscoelastic. The viscoelastic foundation is modeled as Kelvin-Voigt's pattern. Based on the two-unknown plate theory, the motion equations are obtained from the dynamic version of the virtual work principle. The nonlocal strain gradient theory is established from Eringen nonlocal and strain gradient theories, therefore, it contains two material scale parameters, which are nonlocal parameter and gradient coefficient. These scale parameters have two different effects on the graphene sheets. The obtained deflection is compared with that predicted in the literature. Additional numerical examples are introduced to illustrate the influences of the two length scale coefficients and other parameters on the dynamic deformation of the viscoelastic graphene sheets.

Non-local quantal Noether identities and their applications

International Nuclear Information System (INIS)

Li Ziping

2002-01-01

Based on the phase-space generating functional for a system with a singular high-order Lagrangian, the quantal canonical Noether identities under the local and non-local transformation in phase space for such system have been derived. For a gauge-invariant system with a higher-order Lagrangian, the quantal Noether identities under the local and non-local transformation in configuration space have also been derived. it has been pointed out that in certain cases the quantal Noether identities may be converted to the conservation laws at the quantum level. This algorithm to derive the quantal conservation laws is significantly different from the first quantal Noether theorem. The applications to the non-Abelian CS theories with higher-order derivatives are given. The conserved quantities at the quantum level for some local and non-local transformation are found respectively

Nonlocal transport in hot plasma. Part I

International Nuclear Information System (INIS)

Brantov, A. V.; Bychenkov, V. Yu.

2013-01-01

The problem of describing charged particle transport in hot plasma under the conditions in which the ratio of the electron mean free path to the gradient length is not too small is one of the key problems of plasma physics. However, up to now, there was a deficit of the systematic interpretation of the current state of this problem, which, in most studies, is formulated as the problem of nonlocal transport. In this review, we fill this gap by presenting a self-consistent linear theory of nonlocal transport for small plasma perturbations and an arbitrary collisionality from the classical highly collisional hydrodynamic regime to the collisionless regime. We describe a number of nonlinear transport models and demonstrate the application of the nonclassical transport theory to the solution of some problems of plasma physics, first of all for plasmas produced by nanosecond laser pulses with intensities of 10 13 –10 16 W/cm 2

Lattice gravity near the continuum limit

International Nuclear Information System (INIS)

Feinberg, G.; Friedberg, R.; Lee, T.D.; Ren, H.C.

1984-01-01

We prove that the lattice gravity always approaches the usual continuum limit when the link length l -> 0, provided that certain general boundary conditions are satisfied. This result holds for any lattice, regular or irregular. Furthermore, for a given lattice, the deviation from its continuum limit can be expressed as a power series in l 2 . General formulas for such a perturbative calculation are given, together with a number of illustrative examples, including the graviton propagator. The lattice gravity satisfies all the invariance properties of Einstein's theory of general relativity. In addition, it is symmetric under a new class of transformations that are absent in the usual continuum theory. The possibility that the lattice theory (with a nonzero l) may be more fundamental is discussed. (orig.)

On the application of the partition of unity method for nonlocal response of low-dimensional structures

Science.gov (United States)

Natarajan, Sundararajan

2014-12-01

The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen's nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

Nonlocality versus complementarity: a conservative approach to the information problem

International Nuclear Information System (INIS)

Giddings, Steven B

2011-01-01

A proposal for resolution of the information paradox is that 'nice slice' states, which have been viewed as providing a sharp argument for information loss, do not in fact do so as they do not give a fully accurate description of the quantum state of a black hole. This however leaves an information problem, which is to provide a consistent description of how information escapes when a black hole evaporates. While a rather extreme form of nonlocality has been advocated in the form of complementarity, this paper argues that is not necessary, and more modest nonlocality could solve the information problem. One possible distinguishing characteristic of scenarios is the information retention time. The question of whether such nonlocality implies acausality, and particularly inconsistency, is briefly addressed. The need for such nonlocality, and its apparent tension with our empirical observations of local quantum field theory, may be a critical missing piece in understanding the principles of quantum gravity.

Quantifying multipartite nonlocality via the size of the resource

Science.gov (United States)

Curchod, Florian John; Gisin, Nicolas; Liang, Yeong-Cherng

2015-01-01

The generation of (Bell-)nonlocal correlations, i.e., correlations leading to the violation of a Bell-like inequality, requires the usage of a nonlocal resource, such as an entangled state. When given a correlation (a collection of conditional probability distributions) from an experiment or from a theory, it is desirable to determine the extent to which the participating parties would need to collaborate nonlocally for its (re)production. Here, we propose to achieve this via the minimal group size (MGS) of the resource, i.e., the smallest number of parties that need to share a given type of nonlocal resource for the above-mentioned purpose. In addition, we provide a general recipe—based on the lifting of Bell-like inequalities—to construct MGS witnesses for nonsignaling resources starting from any given ones. En route to illustrating the applicability of this recipe, we also show that when restricted to the space of full-correlation functions, nonsignaling resources are as powerful as unconstrained signaling resources. Explicit examples of correlations where their MGS can be determined using this recipe and other numerical techniques are provided.

Chimera and modulated drift states in a ring of nonlocally coupled oscillators with heterogeneous phase lags

Science.gov (United States)

Choe, Chol-Ung; Kim, Ryong-Son; Ri, Ji-Song

2017-09-01

We consider a ring of phase oscillators with nonlocal coupling strength and heterogeneous phase lags. We analyze the effects of heterogeneity in the phase lags on the existence and stability of a variety of steady states. A nonlocal coupling with heterogeneous phase lags that allows the system to be solved analytically is suggested and the stability of solutions along the Ott-Antonsen invariant manifold is explored. We present a complete bifurcation diagram for stationary patterns including the uniform drift and modulated drift states as well as chimera state, which reveals that the stable modulated drift state and a continuum of metastable drift states could occur due to the heterogeneity of the phase lags. We verify our theoretical results using the direct numerical simulations of the model system.

Quasiclassical R-matrix theory of inelastic processes in collisions of electrons with HCl molecules

International Nuclear Information System (INIS)

Fabrikant, I.I.

1991-01-01

The R-matrix theory for the vibrational excitation and dissociative attachment in e-HCl collisions is developed. Only one pole in the R-matrix expansion is included. This allows for making a connection between the R-matrix and the nonlocal-complex-potential theories, and for obtaining the expression for the dissociative-attachment cross section without using the R-matrix radius in the internuclear coordinate. All matrix elements in the equation for the vibrational-excitation and dissociative-attachment amplitudes are calculated using the quasiclassical approach. We study how the results depend on the number of vibrational levels of the neutral molecule included in the theory and show how to exclude the vibrational continuum by a modification of the nonlocal-complex potential. The results for the vibrational-excitation cross sections are extremely sensitive to the behavior of the R-matrix potential curve near the point of crossing this curve with the potential curve of the neutral molecule. Particularly in some cases the cross section at the threshold peak exhibits the boomerang oscillations earlier found for HCl by Domcke [in Aspects of Electron-Molecule Scattering and Photoionization, edited by A. Herzenberg (AIP, New Haven, 1989), p. 169]. The dissociative-attachment cross sections are in reasonable agreement with experiment and with other theories

The morphing method as a flexible tool for adaptive local/non-local simulation of static fracture

KAUST Repository

Azdoud, Yan

2014-04-19

We introduce a framework that adapts local and non-local continuum models to simulate static fracture problems. Non-local models based on the peridynamic theory are promising for the simulation of fracture, as they allow discontinuities in the displacement field. However, they remain computationally expensive. As an alternative, we develop an adaptive coupling technique based on the morphing method to restrict the non-local model adaptively during the evolution of the fracture. The rest of the structure is described by local continuum mechanics. We conduct all simulations in three dimensions, using the relevant discretization scheme in each domain, i.e., the discontinuous Galerkin finite element method in the peridynamic domain and the continuous finite element method in the local continuum mechanics domain. © 2014 Springer-Verlag Berlin Heidelberg.

Extreme exotic calcium lambda hypernuclei in the relativistic continuum Hartree-Bogoliubov theory

International Nuclear Information System (INIS)

Lv Hongfeng

2008-01-01

Exotic calcium lambda hypernuclei properties with the neutron number of 20-400 by a step of 20 are discussed by employing the relativistic continuum Hartree-Bogoliubov theory with a zero range pairing interaction. The Bethe-Weizsaecker mass formula of a multi-strange system and the Woods-Saxon-type potential of lambda need to be modified for exotic calcium hypernuclei with unusual number of neutrons and lambdas. The possible neutron and lambda limits of exotic Ca lambda hypernuclei are also investigated. (authors)

A non-local hidden-variable model that violates Leggett-type inequalities

Energy Technology Data Exchange (ETDEWEB)

Zela, F de [Departamento de Ciencias, Seccion Fisica, Pontificia Universidad Catolica del Peru, Apartado 1761, Lima (Peru)

2008-12-19

Recent experiments of Groeblacher et al proved the violation of a Leggett-type inequality that was claimed to be valid for a broad class of non-local hidden-variable theories. The impossibility of constructing a non-local and realistic theory, unless it entails highly counterintuitive features, seems thus to have been experimentally proved. This would bring us close to a definite refutation of realism. Indeed, realism was proved to be also incompatible with locality, according to a series of experiments testing Bell inequalities. The present paper addresses the said experiments of Groeblacher et al and presents an explicit, contextual and realistic, model that reproduces the predictions of quantum mechanics. It thus violates the Leggett-type inequality that was established with the aim of ruling out a supposedly broad class of non-local models. We can thus conclude that plausible contextual, realistic, models are still tenable. This restates the possibility of a future completion of quantum mechanics by a realistic and contextual theory which is not in a class containing only highly counterintuitive models. The class that was ruled out by the experiments of Groeblacher et al is thus proved to be a limited one, arbitrarily separating models that physically belong in the same class.

A non-local hidden-variable model that violates Leggett-type inequalities

International Nuclear Information System (INIS)

Zela, F de

2008-01-01

Recent experiments of Groeblacher et al proved the violation of a Leggett-type inequality that was claimed to be valid for a broad class of non-local hidden-variable theories. The impossibility of constructing a non-local and realistic theory, unless it entails highly counterintuitive features, seems thus to have been experimentally proved. This would bring us close to a definite refutation of realism. Indeed, realism was proved to be also incompatible with locality, according to a series of experiments testing Bell inequalities. The present paper addresses the said experiments of Groeblacher et al and presents an explicit, contextual and realistic, model that reproduces the predictions of quantum mechanics. It thus violates the Leggett-type inequality that was established with the aim of ruling out a supposedly broad class of non-local models. We can thus conclude that plausible contextual, realistic, models are still tenable. This restates the possibility of a future completion of quantum mechanics by a realistic and contextual theory which is not in a class containing only highly counterintuitive models. The class that was ruled out by the experiments of Groeblacher et al is thus proved to be a limited one, arbitrarily separating models that physically belong in the same class

Pre-buckling responses of Timoshenko nanobeams based on the integral and differential models of nonlocal elasticity: an isogeometric approach

Science.gov (United States)

Norouzzadeh, A.; Ansari, R.; Rouhi, H.

2017-05-01

Differential form of Eringen's nonlocal elasticity theory is widely employed to capture the small-scale effects on the behavior of nanostructures. However, paradoxical results are obtained via the differential nonlocal constitutive relations in some cases such as in the vibration and bending analysis of cantilevers, and recourse must be made to the integral (original) form of Eringen's theory. Motivated by this consideration, a novel nonlocal formulation is developed herein based on the original formulation of Eringen's theory to study the buckling behavior of nanobeams. The governing equations are derived according to the Timoshenko beam theory, and are represented in a suitable vector-matrix form which is applicable to the finite-element analysis. In addition, an isogeometric analysis (IGA) is conducted for the solution of buckling problem. Construction of exact geometry using non-uniform rational B-splines and easy implementation of geometry refinement tools are the main advantages of IGA. A comparison study is performed between the predictions of integral and differential nonlocal models for nanobeams under different kinds of end conditions.

Computational Continuum Mechanics

CERN Document Server

Shabana, Ahmed A

2011-01-01

This text presents the theory of continuum mechanics using computational methods. Ideal for students and researchers, the second edition features a new chapter on computational geometry and finite element analysis.

Shape Changing Nonlocal Molecular Deformations in a Nematic Liquid Crystal

International Nuclear Information System (INIS)

Kavitha, L.; Venkatesh, M.; Gopi, D.

2010-07-01

The nature of nonlinear molecular deformations in a homeotropically aligned nematic liquid crystal (NLC) is presented. We start from the basic dynamical equation for the director axis of a NLC with elastic deformation mapped onto an integro-differential perturbed Nonlinear Schroedinger equation which includes the nonlocal term. By invoking the modified extended tangent hyperbolic function method aided with symbolic computation, we obtain a series of solitary wave solutions. Under the influence of the nonlocality induced by the reorientation nonlinearity due to fluctuations in the molecular orientation, the solitary wave exhibits shape changing property for different choices of parameters. This intriguing property, as a result of the relation between the coherence of the solitary deformation and the nonlocality, reveals a strong need for deeper understanding in the theory of self-localization in NLC systems. (author)

Generalized ward identities for non-local transformation

International Nuclear Information System (INIS)

Li Ziping; Li Ruijie

2002-01-01

Based on the phase-space generating functional of Green function for a system with a singular higher-order Lagrangian, the generalized canonical Ward identities under the local and non-local transformation in phase space for such a system have been derived. Starting from the configuration-space generating functional for a gauge-invariant system, the generalized Ward identities were deduced under the local, non-local and global transformation, respectively. The applications to the non-Abelian Chern-Simons theories with higher derivatives were given. Some relationships among the proper vertices have been deduced, in which one does not need to carry out the integration over canonical momenta in phase-space generating functional. The Ward-Takahashi identities for BRS transformation are also obtained

Soliton-induced nonlocal resonances observed through high-intensity tunable spectrally compressed second-harmonic peaks

DEFF Research Database (Denmark)

Zhou, Binbin; Guo, Hairun; Bache, Morten

2014-01-01

Experimental data of femtosecond thick-crystal second-harmonic generation show that when tuning away from phase matching, a dominating narrow spectral peak appears in the second harmonic that can be tuned over hundreds of nanometers by changing the phase-mismatch parameter. Traditional theory...... and the nonlocal theory indirectly proves that we have observed a soliton-induced nonlocal resonance. The soliton exists in the self-defocusing regime of the cascaded nonlinear interaction and in the normal dispersion regime of the crystal, and needs high input intensities to become excited....

Giant resonances in the deformed continuum

International Nuclear Information System (INIS)

Nakatsukasa, T.; Yabana, K.

2004-01-01

Giant resonances in the continuum for deformed nuclei are studied with the time-dependent Hartree-Fock (TDHF) theory in real time and real space. The continuum effect is effectively taken into account by introducing a complex Absorbing Boundary Condition (ABC). (orig.)

Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

Energy Technology Data Exchange (ETDEWEB)

Green, Jeremy; Jansen, Karl; Steffens, Fernanda [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC

2017-07-15

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Nonperturbative renormalization of nonlocal quark bilinears for quasi-PDFs on the lattice using an auxiliary field

International Nuclear Information System (INIS)

Green, Jeremy; Jansen, Karl; Steffens, Fernanda

2017-07-01

Quasi-PDFs provide a path toward an ab initio calculation of parton distribution functions (PDFs) using lattice QCD. One of the problems faced in calculations of quasi-PDFs is the renormalization of a nonlocal operator. By introducing an auxiliary field, we can replace the nonlocal operator with a pair of local operators in an extended theory. On the lattice, this is closely related to the static quark theory. In this approach, we show how to understand the pattern of mixing that is allowed by chiral symmetry breaking, and obtain a master formula for renormalizing the nonlocal operator that depends on three parameters. We present an approach for nonperturbatively determining these parameters and use perturbation theory to convert to the MS scheme. Renormalization parameters are obtained for two lattice spacings using Wilson twisted mass fermions and for different discretizations of the Wilson line in the nonlocal operator. Using these parameters we show the effect of renormalization on nucleon matrix elements with pion mass approximately 370 MeV, and compare renormalized results for the two lattice spacings. The renormalized matrix elements are consistent among the different Wilson line discretizations and lattice spacings.

Magnetic field and contact resistance dependence of non-local charge imbalance

International Nuclear Information System (INIS)

Kleine, A; Baumgartner, A; Trbovic, J; Schoenenberger, C; Golubev, D S; Zaikin, A D

2010-01-01

Crossed Andreev reflection (CAR) in metallic nanostructures, a possible basis for solid-state electron entangler devices, is usually investigated by detecting non-local voltages in multi-terminal superconductor/normal metal devices. This task is difficult because other subgap processes may mask the effects of CAR. One of these processes is the generation of charge imbalance (CI) and the diffusion of non-equilibrium quasi-particles in the superconductor. Here we demonstrate a characteristic dependence of non-local CI on a magnetic field applied parallel to the superconducting wire, which can be understood by a generalization of the standard description of CI to non-local experiments. These results can be used to distinguish CAR and CI and to extract CI relaxation times in superconducting nanostructures. In addition, we investigate the dependence of non-local CI on the resistance of the injector and detector contacts and demonstrate a quantitative agreement with a recent theory using only material and junction characteristics extracted from separate direct measurements.

Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory

International Nuclear Information System (INIS)

Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.

1996-01-01

We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a open-quote no goclose quotes for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a open-quotes continuum limitclose quotes in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined

Second Order Impulsive Retarded Differential Inclusions with Nonlocal Conditions

Directory of Open Access Journals (Sweden)

Hernán R. Henríquez

2014-01-01

Full Text Available In this work we establish some existence results for abstract second order Cauchy problems modeled by a retarded differential inclusion involving nonlocal and impulsive conditions. Our results are obtained by using fixed point theory for the measure of noncompactness.

Clear evidence of a continuum theory of 4D Euclidean simplicial quantum gravity

International Nuclear Information System (INIS)

Egawa, H.S.; Horata, S.; Yukawa, T.

2002-01-01

Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (N X ) and gauge fields (N A ) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent γ (4) is estimated. Furthermore, we compare our numerical results with Background-Metric-Independent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity

Numerically robust and efficient nonlocal electron transport in 2D DRACO simulations

Science.gov (United States)

Cao, Duc; Chenhall, Jeff; Moses, Greg; Delettrez, Jacques; Collins, Tim

2013-10-01

An improved implicit algorithm based on Schurtz, Nicolai and Busquet (SNB) algorithm for nonlocal electron transport is presented. Validation with direct drive shock timing experiments and verification with the Goncharov nonlocal model in 1D LILAC simulations demonstrate the viability of this efficient algorithm for producing 2D lagrangian radiation hydrodynamics direct drive simulations. Additionally, simulations provide strong incentive to further modify key parameters within the SNB theory, namely the ``mean free path.'' An example 2D polar drive simulation to study 2D effects of the nonlocal flux as well as mean free path modifications will also be presented. This research was supported by the University of Rochester Laboratory for Laser Energetics.

Nonlocal superconducting correlations in graphene in the quantum Hall regime

Science.gov (United States)

Beconcini, Michael; Polini, Marco; Taddei, Fabio

2018-05-01

We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nat. Phys. 13, 693 (2017), 10.1038/nphys4084]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-Büttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair edge and with a wide superconducting region (as compared to the superconducting coherence length), CAR exhibits large oscillations as a function of the magnetic field due to interference effects. This results in sign changes of the nonlocal resistance.

Continuum gauge fields from lattice gauge fields

International Nuclear Information System (INIS)

Goeckeler, M.; Kronfeld, A.S.; Schierholz, G.; Wiese, U.J.

1993-01-01

On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant and complies with geometrical constructions of the topological charge on the lattice, is given in this paper. The procedure is explicitly carried out in the U(1) theory in two dimensions, where it leads to simple results. (orig.)

Post-Newtonian parameter γ in generalized non-local gravity

Science.gov (United States)

Zhang, Xue; Wu, YaBo; Yang, WeiQiang; Zhang, ChengYuan; Chen, BoHai; Zhang, Nan

2017-10-01

We investigate the post-Newtonian parameter γ and derive its formalism in generalized non-local (GNL) gravity, which is the modified theory of general relativity (GR) obtained by adding a term m 2 n-2 R☐-n R to the Einstein-Hilbert action. Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields ϕ i in addition to the metric tensor g μν, the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters γ, we can compare our expressions and results with those in Hohmann and Järv et al. (2016), as well as current observational constraints on the values of γ in Will (2006). Hence, we draw restrictions on the nonminimal coupling terms F̅ around their background values.

Nonlocal, yet translation invariant, constraints for rotationally invariant slave bosons

Science.gov (United States)

Ayral, Thomas; Kotliar, Gabriel

The rotationally-invariant slave boson (RISB) method is a lightweight framework allowing to study the low-energy properties of complex multiorbital problems currently out of the reach of more comprehensive, yet more computationally demanding methods such as dynamical mean field theory. In the original formulation of this formalism, the slave-boson constraints can be made nonlocal by enlarging the unit cell and viewing the quantum states enclosed in this new unit cell as molecular levels. In this work, we extend RISB to constraints which are nonlocal while preserving translation invariance. We apply this extension to the Hubbard model.

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

Science.gov (United States)

Zhen, Ya-Xin

2017-02-01

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.

Weakly nonlocal symplectic structures, Whitham method and weakly nonlocal symplectic structures of hydrodynamic type

International Nuclear Information System (INIS)

Maltsev, A Ya

2005-01-01

We consider the special type of field-theoretical symplectic structures called weakly nonlocal. The structures of this type are, in particular, very common for integrable systems such as KdV or NLS. We introduce here the special class of weakly nonlocal symplectic structures which we call weakly nonlocal symplectic structures of hydrodynamic type. We investigate then the connection of such structures with the Whitham averaging method and propose the procedure of 'averaging' the weakly nonlocal symplectic structures. The averaging procedure gives the weakly nonlocal symplectic structure of hydrodynamic type for the corresponding Whitham system. The procedure also gives 'action variables' corresponding to the wave numbers of m-phase solutions of the initial system which give the additional conservation laws for the Whitham system

Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity

International Nuclear Information System (INIS)

Biswas, Tirthabir; Koivisto, Tomi; Mazumdar, Anupam

2010-01-01

One of the greatest problems of standard cosmology is the Big Bang singularity. Previously it has been shown that non-local ghostfree higher-derivative modifications of Einstein gravity in the ultra-violet regime can admit non-singular bouncing solutions. In this paper we study in more details the dynamical properties of the equations of motion for these theories of gravity in presence of positive and negative cosmological constants and radiation. We find stable inflationary attractor solutions in the presence of a positive cosmological constant which renders inflation geodesically complete, while in the presence of a negative cosmological constant a cyclic universe emerges. We also provide an algorithm for tracking the super-Hubble perturbations during the bounce and show that the bouncing solutions are free from any perturbative instability

Experimental test of Bell's inequality with a proton pair and quantum nonlocality

International Nuclear Information System (INIS)

Sakai, Hideyuki; Saito, Takaaki

2009-01-01

One of the most profound feature of quantum mechanics is the non-locality of entangled system. Einstein-Podolsky-Rosen (EPR) criticized this non-locality from the classical view point, realistic local theory. This criticism is known as the EPR paradox which has been thought as a philosophical argument between Copenhagen interpretation and EPR rather than the experimental issue. About 30 years later, John Bell found the inequality which is amenable to experiments. We succeeded to measure the spin correlation of an entangled proton pair in high accuracy which disagrees with Bell's inequality and confirmed the nonlocality of quantum mechanics in the massive Fermion pair. This short article introduces our experiment. The difference between present experiment and photon experiments is briefly mentioned. (author)

Notes on nonlocal projective measurements in relativistic systems

International Nuclear Information System (INIS)

Lin, Shih-Yuin

2014-01-01

In quantum mechanical bipartite systems, naive extensions of von Neumann’s projective measurement to nonlocal variables can produce superluminal signals and thus violate causality. We analyze the projective quantum nondemolition state-verification in a two-spin system and see how the projection introduces nonlocality without entanglement. For the ideal measurements of “R-nonlocal” variables, we argue that causality violation can be resolved by introducing further restrictions on the post-measurement states, which makes the measurement “Q-nonlocal”. After we generalize these ideas to quantum mechanical harmonic oscillators, we look into the projective measurements of the particle number of a single mode or a wave-packet of a relativistic quantum field in Minkowski space. It turns out that the causality-violating terms in the expectation values of the local operators, generated either by the ideal measurement of the “R-nonlocal” variable or the quantum nondemolition verification of a Fock state, are all suppressed by the IR and UV cutoffs of the theory. Thus relativistic quantum field theories with such projective measurements are effectively causal

Non-local Effects of Conformal Anomaly

Science.gov (United States)

Meissner, Krzysztof A.; Nicolai, Hermann

2018-03-01

It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein's equations. The fact that Einstein's general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein's theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in D=4 for both the C^2 invariant and the Euler (Gauss-Bonnet) invariant can only be achieved for N-extended supergravity multiplets with N ≥ 5.

Comment on ''Canonical formalism for Lagrangians with nonlocality of finite extent''

International Nuclear Information System (INIS)

Llosa, Josep

2003-01-01

The paper by Woodward [Phys. Rev. A 62, 052105 (2000)] claimed to have proved that Lagrangian theories with a nonlocality of finite extent are necessarily unstable. In this Comment we propose that this conclusion is false

Vibration analysis of rotating nanobeam systems using Eringen's two-phase local/nonlocal model

Science.gov (United States)

Khaniki, Hossein Bakhshi

2018-05-01

Due to the inability of differential form of nonlocal elastic theory in modelling cantilever beams and inaccurate results for some type of boundaries, in this study, a reliable investigation on transverse vibrational behavior of rotating cantilever size-dependent beams is presented. Governing higher order equations are written in the framework of Eringen's two-phase local/nonlocal model and solved using a modified generalized differential quadrature method. In order to indicate the influence of different material and scale parameters, a comprehensive parametric study is presented. It is shown that increasing the nonlocality term leads to lower natural frequency terms for cantilever nanobeams especially for the fundamental frequency parameter which differential nonlocal model is unable to track appropriately. Moreover, it is shown that rotating speed and hub radius have a remarkable effect in varying the mechanical behavior of rotating cantilever nanobeams. This study is a step forward in analyzing nanorotors, nanoturbines, nanoblades, etc.

On the Activation of Quantum Nonlocality

Directory of Open Access Journals (Sweden)

Andrés Felipe Ducuara

2016-05-01

Full Text Available We report on some quantum properties of physical systems, namely, entanglement, nonlocality, k-copy nonlocality (superactivation of nonlocality, hidden nonlocality (activation of nonlocality through local filtering and the activation of nonlocality through tensoring and local filtering. The aim of this work is two-fold. First, we provide a review of the numerical procedures that must be followed in order to calculate the aforementioned properties, in particular, for any two-qubit system, and reproduce the bounds for two-qudit Werner states. Second, we use such numerical tools to calculate new bounds of these properties for two-qudit Isotropic states and two-qubit Hirsch states.

Nonlocal Sediment Transport on Steep Lateral Moraines, Eastern Sierra Nevada, California, USA

Science.gov (United States)

Doane, Tyler H.; Furbish, David Jon; Roering, Joshua J.; Schumer, Rina; Morgan, Daniel J.

2018-01-01

Recent work has highlighted the significance of long-distance particle motions in hillslope sediment transport. Such motions imply that the flux at a given hillslope position is appropriately described as a weighted function of surrounding conditions that influence motions reaching the given position. Although the idea of nonlocal sediment transport is well grounded in theory, limited field evidence has been provided. We test local and nonlocal formulations of the flux and compare their ability to reproduce land surface profiles of steep moraines in California. We show that nonlocal and nonlinear models better reproduce evolved land surface profiles, notably the amount of lowering and concavity near the moraine crest and the lengthening and straightening of the depositional apron. The analysis provides the first estimates of key parameters that set sediment entrainment rates and travel distances in nonlocal formulations and highlights the importance of correctly specifying the entrainment rate when modeling land surface evolution. Moraine evolution associated with nonlocal and nonlinear transport formulations, when described in terms of the evolution of the Fourier transform of the moraine surface, displays a distinct behavior involving growth of certain wave numbers, in contrast to the decay of all wave numbers associated with linear transport. Nonlinear and nonlocal formulations share key mathematical elements yielding a nonlinear relation between the flux and the land surface slope.

Full-potential multiple scattering theory with space-filling cells for bound and continuum states.

Science.gov (United States)

Hatada, Keisuke; Hayakawa, Kuniko; Benfatto, Maurizio; Natoli, Calogero R

2010-05-12

We present a rigorous derivation of a real-space full-potential multiple scattering theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the electron wavevector (either in the excited or ground state of the system under consideration) and R(b) is the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l(max) --> ∞ limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.

On the continuum theory of the two-fluid solar wind for small mass ratio

International Nuclear Information System (INIS)

Johnson, R.S.

1976-01-01

The continuum theory for the two-fluid solar wind is considered. The fluid is assumed to be a fully ionized neutral plasma of electrons and protons which is compressible, viscous and heat conducting with a constant Prandtl number and a viscosity proportional to (temperature) sup(ω), ω > 1. The gas is under the influence of a gravitational field centred on the Sun. It is assumed that the bulk velocity (at any point) is the same for both electrons and protons, but that an energy transfer can occur between the two species due to binary (Coulomb) collisions. The equations are non-dimensionalized and it is shown that the natural parameter to use in the construction of an asymptotic solution is the mass ratio. The limit mass ratio → zero corresponds to the small Prandtl number limit for the one-fluid theory developed by Johnson (Proc. R. Soc. (Lond) A; 347:537 (1976)). By using the method of matched asymptotic expansions, a solution is constructed that starts from the base of the corona and extends out to a diffuse shock layer. The results obtained exactly parallel the one-fluid theory and many details are identified and absorbed into this analysis. It is shown how the temperatures in the corona eventually become the well-known behaviours: rsup(-2/7) (electrons), rsup(-6/7) (protons) when ω = 5/2 and r is the radial coordinate. However, the continuum theory will probably have failed in the shock layer region - the more so since this occurs at about 100 light years distance - and further mathematical details are omitted. The numerical estimates given here compare tolerably well with the observed data and very favourably with other work on the same equations. (author)

Continuum capture in the three-body problem

International Nuclear Information System (INIS)

Sellin, I.A.

1980-01-01

The three-body problem, especially the problem of electron capture to the continuum in heavy particle collisions is reviewed. Major topics covered include: second born-induced asymmetry in electron capture to the continuum; historical context, links to other tests of atomic scattering theory; experiments characterizing the velocity distribution of ECC electrons; other atomic physics tests of high velocity Born expansions; atom capture; capture by positrons; and pion capture to the continuum

Pion polarizability in nonlocal quark model

International Nuclear Information System (INIS)

Efimov, G.V.; Okhlopkova, V.A.

1978-01-01

The γγ→ππ amplitude was calculated in nonlocal quark model in the fourth order on the perturbation theory. The coefficients of electric[a) and magnetic polarizability (β) determined are equal in magnitude and opposite in sign αsub(π+-)=βsub(π+-)=+0.014α/msub(π)sup(3), αsub(πsup(0))=-βsub(πsup(0))=-0.07α/msub(π)sup(3). The results have been compared with calculations in other models

Investigation of Perceptual-Motor Behavior Across the Expert Athlete to Disabled Patient Skill Continuum can Advance Theory and Practical Application.

Science.gov (United States)

Müller, Sean; Vallence, Ann-Maree; Winstein, Carolee

2017-12-14

A framework is presented of how theoretical predictions can be tested across the expert athlete to disabled patient skill continuum. Common-coding theory is used as the exemplar to discuss sensory and motor system contributions to perceptual-motor behavior. Behavioral and neural studies investigating expert athletes and patients recovering from cerebral stroke are reviewed. They provide evidence of bi-directional contributions of visual and motor systems to perceptual-motor behavior. Majority of this research is focused on perceptual-motor performance or learning, with less on transfer. The field is ripe for research designed to test theoretical predictions across the expert athlete to disabled patient skill continuum. Our view has implications for theory and practice in sports science, physical education, and rehabilitation.

Multipartite fully nonlocal quantum states

International Nuclear Information System (INIS)

Almeida, Mafalda L.; Cavalcanti, Daniel; Scarani, Valerio; Acin, Antonio

2010-01-01

We present a general method for characterizing the quantum correlations obtained after local measurements on multipartite systems. Sufficient conditions for a quantum system to be fully nonlocal according to a given partition, as well as being (genuinely) multipartite fully nonlocal, are derived. These conditions allow us to identify all completely connected graph states as multipartite fully nonlocal quantum states. Moreover, we show that this feature can also be observed in mixed states: the tensor product of five copies of the Smolin state, a biseparable and bound entangled state, is multipartite fully nonlocal.

Extent of multiparticle quantum nonlocality

International Nuclear Information System (INIS)

Jones, Nick S.; Linden, Noah; Massar, Serge

2005-01-01

It is well known that entangled quantum states are nonlocal: the corrrelations between local measurements carried out on these states cannot be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are more nonlocal than bipartite ones in the sense that even some nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely, we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalizes work of Svetlichny and others in which it was showed that a particular class of classical nonlocal models, the 'separable' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition

Continuum mechanics of single-substance bodies

CERN Document Server

Eringen, A Cemal

1975-01-01

Continuum Physics, Volume II: Continuum Mechanics of Single-Substance Bodies discusses the continuum mechanics of bodies constituted by a single substance, providing a thorough and precise presentation of exact theories that have evolved during the past years. This book consists of three parts-basic principles, constitutive equations for simple materials, and methods of solution. Part I of this publication is devoted to a discussion of basic principles irrespective of material geometry and constitution that are valid for all kinds of substances, including composites. The geometrical notions, k

Non-local modeling of materials

DEFF Research Database (Denmark)

Niordson, Christian Frithiof

2002-01-01

Numerical studies of non-local plasticity effects on different materials and problems are carried out. Two different theories are used. One is of lower order in that it retains the structure of a conventional plasticity boundary value problem, while the other is of higher order and employs higher...... order stresses as work conjugates to higher order strains and uses higher order boundary conditions. The influence of internal material length parameters is studied, and the effects of higher order boundary conditions are analyzed. The focus of the thesis is on metal-matrix composites, and non...

Physics of the continuum of borromean nuclei

Energy Technology Data Exchange (ETDEWEB)

Vaagen, J S; Rogde, T [Dept. of Physics, Univ. of Bergen (Norway); Danilin, B V [RRC The Kurchatov Inst., Kurchatov, Moscow (Russian Federation); Ershov, S N [JINR, Dubna, Moscow (Russian Federation); Thompson, I J [Dept. of Physics, Univ. of Surrey, Guildford (United Kingdom); Zhukov, M V [Chalmers Univ. of Technology and Goeteborg Univ., Goeteborg (Sweden); RNBT Collaboration

1998-06-01

The continuum states of two-neutron halo nuclei are calculated in the method of hyperspherical harmonics. Using DWIA theory appropriate for dilute halo matter we have probed the structure of the low-lying {sup 6}He continuum via calculations of charge-exchange and inelastic scattering. (orig.)

Robustness of the Rabi Splitting under Nonlocal Corrections in Plexcitonics

DEFF Research Database (Denmark)

Tserkezis, Christos; Wubs, Martijn; Mortensen, N. Asger

2018-01-01

separations, either coated with or encapsulating an excitonic layer. Through detailed simulations based on the generalized nonlocal optical response theory, which simultaneously accounts both for modal shifts due to screening and for surface-enhanced Landau damping, we show that, contrary to expectations...... architectures with ultrafine geometrical details....

Continuum mechanics for engineers

CERN Document Server

Mase, G Thomas; Mase, George E

2009-01-01

Continuum TheoryContinuum MechanicsStarting OverNotationEssential MathematicsScalars, Vectors and Cartesian TensorsTensor Algebra in Symbolic Notation - Summation ConventionIndicial NotationMatrices and DeterminantsTransformations of Cartesian TensorsPrincipal Values and Principal DirectionsTensor Fields, Tensor CalculusIntegral Theorems of Gauss and StokesStress PrinciplesBody and Surface Forces, Mass DensityCauchy Stress PrincipleThe Stress TensorForce and Moment Equilibrium; Stress Tensor SymmetryStress Transformation LawsPrincipal Stresses; Principal Stress DirectionsMaximum and Minimum Stress ValuesMohr's Circles For Stress Plane StressDeviator and Spherical Stress StatesOctahedral Shear StressKinematics of Deformation and MotionParticles, Configurations, Deformations and MotionMaterial and Spatial CoordinatesLangrangian and Eulerian DescriptionsThe Displacement FieldThe Material DerivativeDeformation Gradients, Finite Strain TensorsInfinitesimal Deformation TheoryCompatibility EquationsStretch RatiosRot...

The nonlocal electron kinetics for a low-pressure glow discharge dusty plasma

Science.gov (United States)

Liang, Yonggan; Wang, Ying; Li, Hui; Tian, Ruihuan; Yuan, Chengxun; Kudryavtsev, A. A.; Rabadanov, K. M.; Wu, Jian; Zhou, Zhongxiang; Tian, Hao

2018-05-01

The nonlocal electron kinetic model based on the Boltzmann equation is developed in low-pressure argon glow discharge dusty plasmas. The additional electron-dust elastic and inelastic collision processes are considered when solving the kinetic equation numerically. The orbital motion limited theory and collision enhanced collection approximation are employed to calculate the dust surface potential. The electron energy distribution function (EEDF), effective electron temperature Teff, and dust surface potential are investigated under different plasma and dust conditions by solving the Boltzmann and the dust charging current balance equations self-consistently. A comparison of the calculation results obtained from nonlocal and local kinetic models is made. It is shown that the appearance of dust particles leads to a deviation of the EEDF from its original profile for both nonlocal and local kinetic models. With the increase in dust density and size, the effective electron temperature and dust surface potential decrease due to the high-energy electron loss on the dust surface. Meanwhile, the nonlocal and local results differ much from each other under the same calculation condition. It is concluded that, for low-pressure (PR ≤ 1 cm*Torr) glow discharge dusty plasmas, the existence of dust particles will amplify the difference of local and nonlocal EEDFs, which makes the local kinetic model more improper to determine the main parameters of the positive column. The nonlocal kinetic model should be used for the calculation of the EEDFs and dusty plasma parameters.

The periodic sℓ(2|1) alternating spin chain and its continuum limit as a bulk logarithmic conformal field theory at c=0

International Nuclear Information System (INIS)

Gainutdinov, A.M.; Read, N.; Saleur, H.; Vasseur, R.

2015-01-01

The periodic sℓ(2|1) alternating spin chain encodes (some of) the properties of hulls of percolation clusters, and is described in the continuum limit by a logarithmic conformal field theory (LCFT) at central charge c=0. This theory corresponds to the strong coupling regime of a sigma model on the complex projective superspace CP 1|1 =U(2|1)/(U(1)×U(1|1)), and the spectrum of critical exponents can be obtained exactly. In this paper we push the analysis further, and determine the main representation theoretic (logarithmic) features of this continuum limit by extending to the periodic case the approach of http://dx.doi.org/10.1016/j.nuclphysb.2007.03.033 [N. Read and H. Saleur, Nucl. Phys. B 777 (2007) 316]. We first focus on determining the representation theory of the finite size spin chain with respect to the algebra of local energy densities provided by a representation of the affine Temperley-Lieb algebra at fugacity one. We then analyze how these algebraic properties carry over to the continuum limit to deduce the structure of the space of states as a representation over the product of left and right Virasoro algebras. Our main result is the full structure of the vacuum module of the theory, which exhibits Jordan cells of arbitrary rank for the Hamiltonian.

Quadratic solitons for negative effective second-harmonic diffraction as nonlocal solitons with periodic nonlocal response function

DEFF Research Database (Denmark)

Esbensen, B.K.; Bache, Morten; Krolikowski, W.

2012-01-01

We employ the formal analogy between quadratic and nonlocal solitons to investigate analytically the properties of solitons and soliton bound states in second-harmonic generation in the regime of negative diffraction or dispersion of the second harmonic. We show that in the nonlocal description...... this regime corresponds to a periodic nonlocal response function. We then use the strongly nonlocal approximation to find analytical solutions of the families of single bright solitons and their bound states in terms of Mathieu functions....

On the non-local obstruction to interacting higher spins in flat space

Energy Technology Data Exchange (ETDEWEB)

Taronna, Massimo [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium)

2017-05-04

Owing to a renewed interest in flat space higher spin gauge theories, in this note we provide further details and clarifications on the results presented in arXiv:1107.5843 and arXiv: 1209.5755, which investigated their locality properties. Focusing, for simplicity, on quartic couplings with one of the external legs having non-zero integer spin (which can be considered as a prototype for Weinberg-type arguments), we review the appearance of 1/◻ non-localities. In particular, we emphasise that it appears to be not possible to eliminate all of the aforementioned non-localities in the general quartic Noether procedure solution with a judicious choice of coupling constants and spectrum. We also discuss the light-cone gauge fixing in d=4, and argue that the non-local obstruction discussed in the covariant language cannot be avoided using light-cone gauge formalism.

Certifying the absence of quantum nonlocality

OpenAIRE

Miller, Carl A.; Shi, Yaoyun

2016-01-01

Quantum nonlocality is an inherently non-classical feature of quantum mechanics and manifests itself through violation of Bell inequalities for nonlocal games. We show that in a fairly general setting, a simple extension of a nonlocal game can certify instead the absence of quantum nonlocality. Through contraposition, our result implies that a super-classical performance for such a game ensures that a player's output is unpredictable to the other player. Previously such output unpredictabilit...

Bell's theorem, accountability and nonlocality

International Nuclear Information System (INIS)

Vona, Nicola; Liang, Yeong-Cherng

2014-01-01

Bell's theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner (2011 Nature Commun. 2 411), we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’. (paper)

Optical Beams in Nonlocal Nonlinear Media

DEFF Research Database (Denmark)

Królikowski, W.; Bang, Ole; Wyller, J.

2003-01-01

We discuss propagation of optical beams in nonlocal Kerr-like media with the nonlocality of general form. We study the effect of nonlocality on modulational instability of the plane wave fronts, collapse of finite beams and formation of spatial solitons....

Nonlocal optical effects on the Goos–Hänchen shifts at multilayered hyperbolic metamaterials

International Nuclear Information System (INIS)

Chen, Chih-Wei; Bian, Tingting; Chiang, Hai-Pang; Leung, P T

2016-01-01

The lateral beam shift of light incident on a multilayered hyperbolic metamaterial (HMM) is investigated using a theoretical model which emphasizes the nonlocal optical response of the indefinite material. By applying an effective local response theory formulated recently in the literature, it is found that nonlocal effects only affect p polarized light in this Goos–Hänchen (GH) shift of the incident beam; leading to a blue-shifted peak for positive shifts at high frequencies and red-shifted dip for negative shifts at low frequencies in the GH shift spectrum. An account for the observed phenomenon is given by referring to the ‘Brewster condition’ for the reflected wave from the HMM. This observation thus provides a relatively direct probe for the nonlocal response of the HMM. (paper)

Quantum objects. Non-local correlation, causality and objective indefiniteness in the quantum world

International Nuclear Information System (INIS)

Jaeger, Gregg

2014-01-01

Presents interpretation of quantum mechanics, advances in quantum foundations and philosophy of quantum mechanics. Explains non-locality and its relationship to causality and probability in quantum theory. Displays foundational characteristics of quantum physic to understand conceptual origins of the unusual nature of quantum phenomena. Describes relationship of subsystems and space-time. Gives a careful review of existing views. Confronts the old approaches with recent results and approaches from quantum information theory. Delivers a clear and thorough analysis of the quantum events in the context of relativistic space-time, which impacts the problem of creating a theory of quantum gravity. Supplies a detailed discussion of non-local correlation within and beyond the bounds set by standard quantum mechanics, which impacts the foundations of information theory. Gives a detailed discussion of probabilistic causation (central to contemporary accounts of causation) in quantum mechanics and relativity. Leads a thorough discussion of the nature of ''quantum potentiality,'' the novel form of existence arising for the first time in quantum mechanics. This monograph identifies the essential characteristics of the objects described by current quantum theory and considers their relationship to space-time. In the process, it explicates the senses in which quantum objects may be consistently considered to have parts of which they may be composed or into which they may be decomposed. The book also demonstrates the degree to which reduction is possible in quantum mechanics, showing it to be related to the objective indefiniteness of quantum properties and the strong non-local correlations that can occur between the physical quantities of quantum subsystems. Careful attention is paid to the relationships among such property correlations, physical causation, probability, and symmetry in quantum theory. In this way, the text identifies and clarifies the conceptual grounds

Quantum objects. Non-local correlation, causality and objective indefiniteness in the quantum world

Energy Technology Data Exchange (ETDEWEB)

Jaeger, Gregg [Boston Univ., MA (United States). Natural Sciences and Mathematics

2014-07-01

Presents interpretation of quantum mechanics, advances in quantum foundations and philosophy of quantum mechanics. Explains non-locality and its relationship to causality and probability in quantum theory. Displays foundational characteristics of quantum physic to understand conceptual origins of the unusual nature of quantum phenomena. Describes relationship of subsystems and space-time. Gives a careful review of existing views. Confronts the old approaches with recent results and approaches from quantum information theory. Delivers a clear and thorough analysis of the quantum events in the context of relativistic space-time, which impacts the problem of creating a theory of quantum gravity. Supplies a detailed discussion of non-local correlation within and beyond the bounds set by standard quantum mechanics, which impacts the foundations of information theory. Gives a detailed discussion of probabilistic causation (central to contemporary accounts of causation) in quantum mechanics and relativity. Leads a thorough discussion of the nature of ''quantum potentiality,'' the novel form of existence arising for the first time in quantum mechanics. This monograph identifies the essential characteristics of the objects described by current quantum theory and considers their relationship to space-time. In the process, it explicates the senses in which quantum objects may be consistently considered to have parts of which they may be composed or into which they may be decomposed. The book also demonstrates the degree to which reduction is possible in quantum mechanics, showing it to be related to the objective indefiniteness of quantum properties and the strong non-local correlations that can occur between the physical quantities of quantum subsystems. Careful attention is paid to the relationships among such property correlations, physical causation, probability, and symmetry in quantum theory. In this way, the text identifies and clarifies the

Nonlocal response in thin-film waveguides: Loss versus nonlocality and breaking of complementarity

DEFF Research Database (Denmark)

Raza, Søren; Christensen, Thomas; Wubs, Martijn

2013-01-01

the Thomas-Fermi internal kinetic energy of the free electrons in the metal. We derive the nonlocal dispersion relations of the three waveguide structures taking into account also retardation and interband effects, and examine the delicate interplay between nonlocal response and absorption losses...

Nonlocal symmetries and nonlocal conservation laws of Maxwell's equations

International Nuclear Information System (INIS)

Anco, S.C.; Bluman, G.

1997-01-01

Nonlocal symmetries are obtained for Maxwell's equations in three space-time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the constants of motion arising from local conservation laws for space-time symmetries. These nine constants of motion represent additional conserved quantities for the electromagnetic field in three space endash time dimensions. copyright 1997 American Institute of Physics

Robust non-local median filter

Science.gov (United States)

Matsuoka, Jyohei; Koga, Takanori; Suetake, Noriaki; Uchino, Eiji

2017-04-01

This paper describes a novel image filter with superior performance on detail-preserving removal of random-valued impulse noise superimposed on natural gray-scale images. The non-local means filter is in the limelight as a way of Gaussian noise removal with superior performance on detail preservation. By referring the fundamental concept of the non-local means, we had proposed a non-local median filter as a specialized way for random-valued impulse noise removal so far. In the non-local processing, the output of a filter is calculated from pixels in blocks which are similar to the block centered at a pixel of interest. As a result, aggressive noise removal is conducted without destroying the detailed structures in an original image. However, the performance of non-local processing decreases enormously in the case of high noise occurrence probability. A cause of this problem is that the superimposed noise disturbs accurate calculation of the similarity between the blocks. To cope with this problem, we propose an improved non-local median filter which is robust to the high level of corruption by introducing a new similarity measure considering possibility of being the original signal. The effectiveness and validity of the proposed method are verified in a series of experiments using natural gray-scale images.

Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

Directory of Open Access Journals (Sweden)

Diem Dang Huan

2015-12-01

Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

A morphing approach to couple state-based peridynamics with classical continuum mechanics

KAUST Repository

Han, Fei

2016-01-04

A local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

A morphing approach to couple state-based peridynamics with classical continuum mechanics

KAUST Repository

Han, Fei; Lubineau, Gilles; Azdoud, Yan; Askari, Abe

2016-01-01

A local/nonlocal coupling technique called the morphing method is developed to couple classical continuum mechanics with state-based peridynamics. State-based peridynamics, which enables the description of cracks that appear and propagate spontaneously, is applied to the key domain of a structure, where damage and fracture are considered to have non-negligible effects. In the rest of the structure, classical continuum mechanics is used to reduce computational costs and to simultaneously satisfy solution accuracy and boundary conditions. Both models are glued by the proposed morphing method in the transition region. The morphing method creates a balance between the stiffness tensors of classical continuum mechanics and the weighted coefficients of state-based peridynamics through the equivalent energy density of both models. Linearization of state-based peridynamics is derived by Taylor approximations based on vector operations. The discrete formulation of coupled models is also described. Two-dimensional numerical examples illustrate the validity and accuracy of the proposed technique. It is shown that the morphing method, originally developed for bond-based peridynamics, can be successfully extended to state-based peridynamics through the original developments presented here.

Improved non-local electron thermal transport model for two-dimensional radiation hydrodynamics simulations

Science.gov (United States)

Cao, Duc; Moses, Gregory; Delettrez, Jacques

2015-08-01

An implicit, non-local thermal conduction algorithm based on the algorithm developed by Schurtz, Nicolai, and Busquet (SNB) [Schurtz et al., Phys. Plasmas 7, 4238 (2000)] for non-local electron transport is presented and has been implemented in the radiation-hydrodynamics code DRACO. To study the model's effect on DRACO's predictive capability, simulations of shot 60 303 from OMEGA are completed using the iSNB model, and the computed shock speed vs. time is compared to experiment. Temperature outputs from the iSNB model are compared with the non-local transport model of Goncharov et al. [Phys. Plasmas 13, 012702 (2006)]. Effects on adiabat are also examined in a polar drive surrogate simulation. Results show that the iSNB model is not only capable of flux-limitation but also preheat prediction while remaining numerically robust and sacrificing little computational speed. Additionally, the results provide strong incentive to further modify key parameters within the SNB theory, namely, the newly introduced non-local mean free path. This research was supported by the Laboratory for Laser Energetics of the University of Rochester.

EPR paradox, quantum nonlocality and physical reality

International Nuclear Information System (INIS)

Kupczynski, M

2016-01-01

Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are

EPR paradox, quantum nonlocality and physical reality

Science.gov (United States)

Kupczynski, M.

2016-03-01

Eighty years ago Einstein, Podolsky and Rosen demonstrated that instantaneous reduction of wave function, believed to describe completely a pair of entangled physical systems, led to EPR paradox. The paradox disappears in statistical interpretation of quantum mechanics (QM) according to which a wave function describes only an ensemble of identically prepared physical systems. QM predicts strong correlations between outcomes of measurements performed on different members of EPR pairs in far-away locations. Searching for an intuitive explanation of these correlations John Bell analysed so called local realistic hidden variable models and proved that correlations consistent with these models satisfy Bell inequalities which are violated by some predictions of QM and by experimental data. Several different local models were constructed and inequalities proven. Some eminent physicists concluded that Nature is definitely nonlocal and that it is acting according to a law of nonlocal randomness. According to these law perfectly random, but strongly correlated events, can be produced at the same time in far away locations and a local and causal explanation of their occurrence cannot be given. We strongly disagree with this conclusion and we prove the contrary by analysing in detail some influential finite sample proofs of Bell and CHSH inequalities and so called Quantum Randi Challenges. We also show how one can win so called Bell's game without violating locality of Nature. Nonlocal randomness is inconsistent with local quantum field theory, with standard model in elementary particle physics and with causal laws and adaptive dynamics prevailing in the surrounding us world. The experimental violation of Bell-type inequalities does not prove the nonlocality of Nature but it only confirms a contextual character of quantum observables and gives a strong argument against counterfactual definiteness and against a point of view according to which experimental outcomes are produced

An anthology of non-local QFT and QFT on non-commutative spacetime

Science.gov (United States)

Schroer, Bert

2005-09-01

Ever since the appearance of renormalization theory, there have been several differently motivated attempts at non-localized (in the sense of not generated by pointlike fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review in the light of previous results on this subject.

An anthology of non-local QFT and QFT on non-commutative spacetime

International Nuclear Information System (INIS)

Schroer, Bert

2005-01-01

Ever since the appearance of renormalization theory, there have been several differently motivated attempts at non-localized (in the sense of not generated by pointlike fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review in the light of previous results on this subject

Some loopholes to save quantum nonlocality

Science.gov (United States)

Accardi, Luigi

2005-02-01

The EPR-chameleon experiment has closed a long standing debate between the supporters of quantum nonlocality and the thesis of quantum probability according to which the essence of the quantum pecularity is non Kolmogorovianity rather than non locality. The theory of adaptive systems (symbolized by the chameleon effect) provides a natural intuition for the emergence of non-Kolmogorovian statistics from classical deterministic dynamical systems. These developments are quickly reviewed and in conclusion some comments are introduced on recent attempts to "reconstruct history" on the lines described by Orwell in "1984".

An anthology of non-local QFT and QFT on noncommutative spacetime

International Nuclear Information System (INIS)

Schroer, Bert; E-mail schroer@cbpf.br

2004-05-01

Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review of contemporary ideas in the light of previous results on this subject. (author)

Nonlocality and localizability in quantum mechanics

International Nuclear Information System (INIS)

Matsuno, K.

1989-01-01

Nonlocality of simultaneous spatial correlation of a quantum phenomenon as demonstrated in various versions of Einstein-Podolsky-Rosen type experiment reduces to nonlocality of the measurement apparatus in the sense that the eigen-wavefunctions for the apparatus are completely specified in a manner of being independent of whatever object it may measure. Nonlocality of the measurement apparatus however serves as no more than a good approximation to reality at best. The theoretical imposition of nonlocality of the measurement apparatus as an approximation is compatible with the actual locality of quantum mechanics that dispenses with an agent claiming globally simultaneous specifiability of boundary conditions, though the genuine locality of quantum mechanics has to be examined without employing the nonlocality of the measurement apparatus. The actual locality of quantum mechanics is intrinsically irreversible in its development

The effect of nonlocal dielectric response on the surface-enhanced Raman and fluorescence spectra of molecular systems

Science.gov (United States)

Wei, Yong; Pei, Huan; Li, Li; Zhu, Yanying

2018-06-01

We present a theoretical study on the influence of the nonlocal dielectric response on surface-enhanced resonant Raman scattering (SERRS) and fluorescence (SEF) spectra of a model molecule confined in the center of a Ag nanoparticle (NP) dimer. In the simulations, the nonlocal dielectric response caused by the electron–hole pair generation in Ag NPs was computed with the d-parameter theory, and the scattering spectra of a model molecule representing the commonly used fluorescent dye rhodamine 6G (R6G) were obtained by density-matrix calculations. The influence of the separation between Ag NP dimers on the damping rate and scattering spectra with and without the nonlocal response were systematically analyzed. The results show that the nonlocal dielectric response is very sensitive to the gap distance of the NP dimers, and it undergoes much faster decay with the increase of the separation than the radiative and energy transfer rates. The Raman and fluorescence peaks as simulated with the nonlocal dielectric response are relative weaker than that without the nonlocal effect for smaller NP separations because the extra decay rates of the nonlocal effect could reduce both the population of the excited state and the interband coherence between the ground and excited states. Our result also indicates that the nonlocal effect is more prominent on the SEF process than the SERRS process.

Discretization independence implies non-locality in 4D discrete quantum gravity

Science.gov (United States)

Dittrich, Bianca; Kamiński, Wojciech; Steinhaus, Sebastian

2014-12-01

The 4D Regge action is invariant under 5-1 and 4-2 Pachner moves, which define a subset of (local) changes of the triangulation. Given this fact, one might hope to find a local path integral measure that makes the quantum theory invariant under these moves and hence makes the theory partially triangulation invariant. We show that such a local invariant path integral measure does not exist for the 4D linearized Regge theory. To this end we uncover an interesting geometric interpretation for the Hessian of the 4D Regge action. This geometric interpretation will allow us to prove that the determinant of the Hessian of the 4D Regge action does not factorize over four-simplices or subsimplices. It furthermore allows us to determine configurations where this Hessian vanishes, which only appears to be the case in degenerate backgrounds or if one allows for different orientations of the simplices. We suggest a non-local measure factor that absorbs the non-local part of the determinant of the Hessian under 5-1 moves as well as a local measure factor that is preserved for very special configurations.

Discretization independence implies non-locality in 4D discrete quantum gravity

International Nuclear Information System (INIS)

Dittrich, Bianca; Kamiński, Wojciech; Steinhaus, Sebastian

2014-01-01

The 4D Regge action is invariant under 5–1 and 4–2 Pachner moves, which define a subset of (local) changes of the triangulation. Given this fact, one might hope to find a local path integral measure that makes the quantum theory invariant under these moves and hence makes the theory partially triangulation invariant. We show that such a local invariant path integral measure does not exist for the 4D linearized Regge theory. To this end we uncover an interesting geometric interpretation for the Hessian of the 4D Regge action. This geometric interpretation will allow us to prove that the determinant of the Hessian of the 4D Regge action does not factorize over four-simplices or subsimplices. It furthermore allows us to determine configurations where this Hessian vanishes, which only appears to be the case in degenerate backgrounds or if one allows for different orientations of the simplices. We suggest a non-local measure factor that absorbs the non-local part of the determinant of the Hessian under 5–1 moves as well as a local measure factor that is preserved for very special configurations. (paper)

Non-classical solutions of a continuum model for rock descriptions

Directory of Open Access Journals (Sweden)

Mikhail A. Guzev

2014-06-01

Full Text Available The strain-gradient and non-Euclidean continuum theories are employed for construction of non-classical solutions of continuum models. The linear approximation of both models' results in identical structures in terms of their kinematic and stress characteristics. The solutions obtained in this study exhibit a critical behaviour with respect to the external loading parameter. The conclusions are obtained based on an investigation of the solution for the scalar curvature in the non-Euclidean continuum theory. The proposed analysis enables us to use different theoretical approaches for description of rock critical behaviour under different loading conditions.

Nonlocal quantum effective actions in Weyl-Flat spacetimes

Science.gov (United States)

Bautista, Teresa; Benevides, André; Dabholkar, Atish

2018-06-01

Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite N corrections in holography. We describe how the quantum effective actions summarizing these effects can be computed efficiently for Weyl-flat metrics by integrating the Weyl anomaly or, equivalently, the local renormalization group equation. This method relies only on the local Schwinger-DeWitt expansion of the heat kernel and allows for a re-summation of the anomalous leading large logarithms of the scale factor, log a( x), in situations where the Weyl factor changes by several e-foldings. As an illustration, we obtain the quantum effective action for the Yang-Mills field coupled to massless matter, and the self-interacting massless scalar field. Our action reduces to the nonlocal action obtained using the Barvinsky-Vilkovisky covariant perturbation theory in the regime R 2 ≪ ∇2 R for a typical curvature scale R, but has a greater range of validity effectively re-summing the covariant perturbation theory to all orders in curvatures. In particular, it is applicable also in the opposite regime R 2 ≫ ∇2 R, which is often of interest in cosmology.

Non-Local Effects in Kaonic Atoms

International Nuclear Information System (INIS)

Lutz, M.; Florkowski, W.

2000-01-01

Optical potentials with non-local (gradient) terms are used to describe the spectra of kaonic atoms. The strength of the non-local terms is determined from a many-body calculation of the kaon self energy in nuclear matter. We find that the non-local terms are quantitatively important and the results depend strongly on the way the gradient terms are arranged. Phenomenologically successful description is obtained for p-wave like optical potentials. It is suggested that the microscopic form of the non-local interaction terms is obtained systematically by means of a semi-classical expansion of the nucleus structure. (author)

Non-local effects in kaonic atoms

International Nuclear Information System (INIS)

Lutz, M.; Florkowski, W.

2000-04-01

Optical potentials with non-local (gradient) terms are used to describe the spectra of kaonic atoms. The strength of the non-local terms is determined from a many-body calculation of the kaon self-energy in nuclear matter. The optical potentials show strong non-linearities in the nucleon density and sizeable non-local terms. We find that the non-local terms are quantitatively important and the results depend strongly on the way the gradient terms are arranged. Phenomenologically successful fits are obtained for p-wave like optical potentials. It is suggested that the microscopic form of the non-local interaction terms is obtained systematically by means of a semi-classical expansion of the nucleus structure. We conclude that a microscopic description of kaonic atom data requires further detailed studies of the microscopic K - nuclear dynamics. (orig.)

Chimera Type Behavior in Nonlocal Coupling System with Two Different Inherent Frequencies

Science.gov (United States)

Lin, Larry; Li, Ping-Cheng; Tseng, Hseng-Che

2014-03-01

From the research of Kuramoto and Strogatz, arrays of identical oscillators can display a remarkable pattern, named chimera state, in which phase-locked oscillators coexist with drifting ones in nonlocal coupling oscillator system. We consider further in this study, two groups of oscillators with different inherent frequencies and arrange them in a ring. When the difference of the inherent frequencies is within some specific parameter range, oscillators of nonlocal coupling system show two distinct chimera states. When the parameter value exceeds some threshold value, two chimera states disappear. They show different features. The statistical dynamic behavior of the system can be described by Kuramoto theory.

Nonlocal microstructure-dependent dynamic stability of refined porous FG nanoplates in hygro-thermal environments

Science.gov (United States)

Reza Barati, Mohammad

2017-10-01

Based on the generalized nonlocal strain gradient theory (NSGT), dynamic modeling and analysis of nanoporous inhomogeneous nanoplates is presented. Therefore, it is possible to capture both stiffness-softening and stiffness-hardening effects for a more accurate dynamic analysis of nanoplates. The nanoplate is in hygro-thermal environments and is subjected to an in-plane harmonic load. Porosities are incorporated to the model based on a modified rule of mixture. Modeling of the porous nanoplate is conducted according to a refined four-variable plate theory with fewer field variables than in the first-order plate theory. The governing equations and related classical and nonclassical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. It is shown that porosities, moisture rise, temperature rise, nonlocal parameter, strain gradient parameter, material gradation, elastic foundation and uniform dynamic load have a remarkable influence on the dynamic behavior of nanoscale plates.

Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

Directory of Open Access Journals (Sweden)

Dhakne Machindra B.

2017-04-01

Full Text Available In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

Stable rotating dipole solitons in nonlocal media

DEFF Research Database (Denmark)

Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.

2006-01-01

We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons.......We present the first example of stable rotating two-soliton bound states in nonlinear optical media with nonlocal response. We show that, in contrast to media with local response, nonlocality opens possibilities to generate stable azimuthons....

Continuum modeling of twinning, amorphization, and fracture: theory and numerical simulations

Science.gov (United States)

Clayton, J. D.; Knap, J.

2018-03-01

A continuum mechanical theory is used to model physical mechanisms of twinning, solid-solid phase transformations, and failure by cavitation and shear fracture. Such a sequence of mechanisms has been observed in atomic simulations and/or experiments on the ceramic boron carbide. In the present modeling approach, geometric quantities such as the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors. After development of the general nonlinear theory, a first problem class considers simple shear deformation of a single crystal of this material. For homogeneous fields or stress-free states, algebraic systems or ordinary differential equations are obtained that can be solved by numerical iteration. Results are in general agreement with atomic simulation, without introduction of fitted parameters. The second class of problems addresses the more complex mechanics of heterogeneous deformation and stress states involved in deformation and failure of polycrystals. Finite element calculations, in which individual grains in a three-dimensional polycrystal are fully resolved, invoke a partially linearized version of the theory. Results provide new insight into effects of crystal morphology, activity or inactivity of different inelasticity mechanisms, and imposed deformation histories on strength and failure of the aggregate under compression and shear. The importance of incorporation of inelastic shear deformation in realistic models of amorphization of boron carbide is noted, as is a greater reduction in overall strength of polycrystals containing one or a few dominant flaws rather than many diffusely distributed microcracks.

Unified criteria for multipartite quantum nonlocality

Energy Technology Data Exchange (ETDEWEB)

Cavalcanti, E. G. [Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111 (Australia); He, Q. Y.; Reid, M. D. [Centre for Atom Optics and Ultrafast Spectroscopy and Centre for Quantum-Atom Optics (Australian Research Council), Swinburne University of Technology, Melbourne (Australia); Wiseman, H. M. [Centre for Quantum Dynamics, Griffith University, Brisbane, Queensland 4111 (Australia); Centre for Quantum Computation and Communication Technology (Australian Research Council), Griffith University, Brisbane, Queensland 4111 (Australia)

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.

Unified criteria for multipartite quantum nonlocality

International Nuclear Information System (INIS)

Cavalcanti, E. G.; He, Q. Y.; Reid, M. D.; Wiseman, H. M.

2011-01-01

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.

Improved non-local electron thermal transport model for two-dimensional radiation hydrodynamics simulations

International Nuclear Information System (INIS)

Cao, Duc; Moses, Gregory; Delettrez, Jacques

2015-01-01

An implicit, non-local thermal conduction algorithm based on the algorithm developed by Schurtz, Nicolai, and Busquet (SNB) [Schurtz et al., Phys. Plasmas 7, 4238 (2000)] for non-local electron transport is presented and has been implemented in the radiation-hydrodynamics code DRACO. To study the model's effect on DRACO's predictive capability, simulations of shot 60 303 from OMEGA are completed using the iSNB model, and the computed shock speed vs. time is compared to experiment. Temperature outputs from the iSNB model are compared with the non-local transport model of Goncharov et al. [Phys. Plasmas 13, 012702 (2006)]. Effects on adiabat are also examined in a polar drive surrogate simulation. Results show that the iSNB model is not only capable of flux-limitation but also preheat prediction while remaining numerically robust and sacrificing little computational speed. Additionally, the results provide strong incentive to further modify key parameters within the SNB theory, namely, the newly introduced non-local mean free path. This research was supported by the Laboratory for Laser Energetics of the University of Rochester

Improved non-local electron thermal transport model for two-dimensional radiation hydrodynamics simulations

Energy Technology Data Exchange (ETDEWEB)

Cao, Duc; Moses, Gregory [University of Wisconsin—Madison, 1500 Engineering Drive, Madison, Wisconsin 53706 (United States); Delettrez, Jacques [Laboratory for Laser Energetics of the University of Rochester, 250 East River Road, Rochester, New York 14623 (United States)

2015-08-15

An implicit, non-local thermal conduction algorithm based on the algorithm developed by Schurtz, Nicolai, and Busquet (SNB) [Schurtz et al., Phys. Plasmas 7, 4238 (2000)] for non-local electron transport is presented and has been implemented in the radiation-hydrodynamics code DRACO. To study the model's effect on DRACO's predictive capability, simulations of shot 60 303 from OMEGA are completed using the iSNB model, and the computed shock speed vs. time is compared to experiment. Temperature outputs from the iSNB model are compared with the non-local transport model of Goncharov et al. [Phys. Plasmas 13, 012702 (2006)]. Effects on adiabat are also examined in a polar drive surrogate simulation. Results show that the iSNB model is not only capable of flux-limitation but also preheat prediction while remaining numerically robust and sacrificing little computational speed. Additionally, the results provide strong incentive to further modify key parameters within the SNB theory, namely, the newly introduced non-local mean free path. This research was supported by the Laboratory for Laser Energetics of the University of Rochester.

Nonlocal neoclassical transport in tokamak and spherical torus experiments

International Nuclear Information System (INIS)

Wang, W. X.; Rewoldt, G.; Tang, W. M.; Hinton, F. L.; Manickam, J.; Zakharov, L. E.; White, R. B.; Kaye, S.

2006-01-01

Large ion orbits can produce nonlocal neoclassical effects on ion heat transport, the ambipolar radial electric field, and the bootstrap current in realistic toroidal plasmas. Using a global δf particle simulation, it is found that the conventional local, linear gradient-flux relation is broken for the ion thermal transport near the magnetic axis. With regard to the transport level, it is found that details of the ion temperature profile determine whether the transport is higher or lower when compared with the predictions of standard neoclassical theory. Particularly, this nonlocal feature is suggested to exist in the National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)], being consistent with NSTX experimental evidence. It is also shown that a large ion temperature gradient can increase the bootstrap current. When the plasma rotation is taken into account, the toroidal rotation gradient can drive an additional parallel flow for the ions and then additional bootstrap current, either positive or negative, depending on the gradient direction. Compared with the carbon radial force balance estimate for the neoclassical poloidal flow, our nonlocal simulation predicts a significantly deeper radial electric field well at the location of an internal transport barrier of an NSTX discharge

Plasmon-enhanced fluorescence near nonlocal metallic nanospheres

DEFF Research Database (Denmark)

Tserkezis, Christos; Stefanou, N.; Wubs, Martijn

Spontaneous emission and fluorescence of organic molecules are known to strongly depend on the local electromagnetic environment. Plasmonic nanoparticles are widely explored as templates for controlling light-matter interactions, and can be tailored to optimize the fluorescence rate (Ȗem......) and the generalized nonlocal optical response (GNOR) theory [2] shows that a significant decrease in fluorescence enhancement is obtained for emitters close to small metallic nanospheres or thin metallic nanoshells, while the optimum emitter position is also affected. In this respect, our recent work introduces...

Nonlocal diffusion and applications

CERN Document Server

Bucur, Claudia

2016-01-01

Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.

Towards a test of non-locality without 'supplementary assumptions'

International Nuclear Information System (INIS)

Barbieri, M.; De Martini, F.; Di Nepi, G.; Mataloni, P.

2005-01-01

We have experimentally tested the non-local properties of the two-photon states generated by a high brilliance source of entanglement which virtually allows the direct measurement of the full set of photon pairs created by the basic QED process implied by the parametric quantum scattering. Standard Bell measurements and Bell's inequality violation test have been realized over the entire cone of emission of the degenerate pairs. By the same source we have verified Hardy's ladder theory up to the 20th step and the contradiction between the standard quantum theory and the local realism has been tested for 41% of entangled pairs

Modulational instability in nonlocal nonlinear Kerr media

DEFF Research Database (Denmark)

Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens

2001-01-01

We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function. For a defoc...

Continuum mechanical and computational aspects of material behavior

Energy Technology Data Exchange (ETDEWEB)

Fried, Eliot; Gurtin, Morton E.

2000-02-10

The focus of the work is the application of continuum mechanics to materials science, specifically to the macroscopic characterization of material behavior at small length scales. The long-term goals are a continuum-mechanical framework for the study of materials that provides a basis for general theories and leads to boundary-value problems of physical relevance, and computational methods appropriate to these problems supplemented by physically meaningful regularizations to aid in their solution. Specific studies include the following: the development of a theory of polycrystalline plasticity that incorporates free energy associated with lattice mismatch between grains; the development of a theory of geometrically necessary dislocations within the context of finite-strain plasticity; the development of a gradient theory for single-crystal plasticity with geometrically necessary dislocations; simulations of dynamical fracture using a theory that allows for the kinking and branching of cracks; computation of segregation and compaction in flowing granular materials.

Unified criteria for multipartite quantum nonlocality

Science.gov (United States)

Cavalcanti, E. G.; He, Q. Y.; Reid, M. D.; Wiseman, H. M.

2011-09-01

Wiseman and co-workers [H. M. Wiseman, S. J. Jones, and A. C. Doherty, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.98.140402 98, 140402, (2007)] proposed a distinction among the nonlocality classes of Bell's nonlocality, Einstein-Podolsky-Rosen (EPR) paradox or steering, and entanglement based on whether or not an overseer trusts each party in a bipartite scenario where they are asked to demonstrate entanglement. Here we extend that concept to the multipartite case and derive inequalities that progressively test for those classes of nonlocality, with different thresholds for each level. This framework includes the three classes of nonlocality above in special cases and introduces a family of others.

Nonlocality of classical electrodynamics of point particles, and violation of Bell's inequalities

International Nuclear Information System (INIS)

Carati, A.; Galagni, L.

1999-01-01

This study shows that Bell's inequalities are violated in a model of two charged particles interacting with two potential barriers, which mimic the measuring instruments; the motion in the nonrelativistic version, and the role of the hidden variables is played by the initial accelerations. The essential nonlocality property of the system is induced by the celebrated Dirac's non-runway condition, which makes the measuring instruments have a certain influence on the observed system, by determining the domain of definition of the hidden variable (the Bopp-Haag phenomenon). So this model strongly supports E. Nelson's suggestion, namely that nonlocality properties suited to violate Bell's inequalities appear in classical field theories when regularizing cutoff are removed

Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models

Science.gov (United States)

Ma, Li-Hong; Ke, Liao-Liang; Wang, Yi-Ze; Wang, Yue-Sheng

2017-02-01

This paper makes the first attempt to investigate the dispersion behavior of waves in magneto-electro-elastic (MEE) nanobeams. The Euler nanobeam model and Timoshenko nanobeam model are developed in the formulation based on the nonlocal theory. By using the Hamilton's principle, we derive the governing equations which are then solved analytically to obtain the dispersion relations of MEE nanobeams. Results are presented to highlight the influences of the thermo-electro-magnetic loadings and nonlocal parameter on the wave propagation characteristics of MEE nanobeams. It is found that the thermo-electro-magnetic loadings can lead to the occurrence of the cut-off wave number below which the wave can't propagate in MEE nanobeams.

Abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm

Directory of Open Access Journals (Sweden)

Wang Rong-Nian

2011-01-01

Full Text Available Abstract In the present paper, we deal with the Cauchy problems of abstract fractional integro-differential equations involving nonlocal initial conditions in α-norm, where the operator A in the linear part is the generator of a compact analytic semigroup. New criterions, ensuring the existence of mild solutions, are established. The results are obtained by using the theory of operator families associated with the function of Wright type and the semigroup generated by A, Krasnoselkii's fixed point theorem and Schauder's fixed point theorem. An application to a fractional partial integro-differential equation with nonlocal initial condition is also considered. Mathematics subject classification (2000 26A33, 34G10, 34G20

Locality or non-locality in quantum mechanics: hidden variables without ''spooky action-at-a-distance''

International Nuclear Information System (INIS)

Aharonov, Y.; Scully, M.

2001-01-01

The folklore notion of the ''Non-Locality of Quantum Mechanics'' is examined from the point of view of hidden-variables theories according to Belinfante's classification in his Survey of Hidden Variables Theories. It is here shown that in the case of EPR, there exist hidden variables theories that successfully reproduce quantum-mechanical predictions, but which are explicitly local. Since such theories do not fall into Belinfante's classification, we propose an expanded classification which includes similar theories, which we term as theories of the ''third'' kind. Causal implications of such theories are explored. (orig.)

Robustness of multiparty nonlocality to local decoherence

International Nuclear Information System (INIS)

Jang, Sung Soon; Cheong, Yong Wook; Kim, Jaewan; Lee, Hai-Woong

2006-01-01

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

Nonlocal strain gradient based wave dispersion behavior of smart rotating magneto-electro-elastic nanoplates

Science.gov (United States)

Ebrahimi, Farzad; Dabbagh, Ali

2017-02-01

Main object of the present research is an exact investigation of wave propagation responses of smart rotating magneto-electro-elastic (MEE) graded nanoscale plates. In addition, effective material properties of functionally graded (FG) nanoplate are presumed to be calculated using the power-law formulations. Also, it has been tried to cover both softening and stiffness-hardening behaviors of nanostructures by the means of employing nonlocal strain gradient theory (NSGT). Due to increasing the accuracy of the presented model in predicting shear deformation effects, a refined higher-order plate theory is introduced. In order to cover the most enormous circumstances, maximum amount of load generated by plate’s rotation is considered. Furthermore, utilizing a developed form of Hamilton’s principle, containing magneto-electric effects, the nonlocal governing equations of MEE-FG rotating nanoplates are derived. An analytical solution is obtained to solve the governing equations and validity of the solution method is proven by comparing results from present method with those of former attempts. At last, outcomes are plotted in the framework of some figures to show the influences of various parameters such as wave number, nonlocality, length scale parameter, magnetic potential, electric voltage, gradient index and angular velocity on wave frequency, phase velocity and escape frequency of the examined nanoplate.

Continuum solutions of the Klein-Gordon equation

International Nuclear Information System (INIS)

Jansen, G.; Pusch, M.; Soff, G.

1987-10-01

We construct explicit solutions of the Klein-Gordon equation for continuum states. The role of the energy in the single-particle Klein-Gordon theory is elucidated. Special emphasis is laid on the determination of resonance states in the continuum for overcritical potentials. As examples for long-range interaction we depict solutions for the Coulomb potential of a point-like nucleus as an extended nucleus. The square-well potential and the exponential potential are treated to exemplify pecularities of short-range interactions. We also derive continuum solutions for a scalar interaction of square-well type. Finally we discuss the behaviour of a spin-0 particle in an external homogeneous magnetic field. (orig.)

Investigating dynamic characteristics of porous double-layered FG nanoplates in elastic medium via generalized nonlocal strain gradient elasticity

Science.gov (United States)

Reza Barati, Mohammad

2017-09-01

For the first time, a vibrating porous double-nanoplate system under in-plane periodic loads is modeled via the generalized nonlocal strain gradient theory (NSGT). Based on the proposed theory, one can examine both stiffness-softening and stiffness-hardening effects for a more accurate analysis of nanoplates. Nanopores or nanovoids are incorporated to the model based on a modified rule of mixture. Modeling of porous double-layered nanoplate is conducted according to a refined four-variable plate theory with fewer field variables than first-order plate theory. The governing equations and related classical and nonclassical boundary conditions are derived based on Hamilton's principle. These equations are solved for hinged nanoplates via Galerkin's method. It is shown that porosities, nonlocal parameter, strain gradient parameter, material gradation, interlayer stiffness, elastic foundation, side-to-thickness and aspect ratios have a notable impact on the vibration behavior of nanoporous materials.

Theory of a spheroidal probe in low-density continuum plasmas

International Nuclear Information System (INIS)

Kamitsuma, M.; Teii, S.

1982-01-01

A spheroidal probe theory for a low-density continuum plasma, i.e., one where the electron density is N/sub e/ 8 cm -3 and the gas pressure is P> or approx. =1 Torr has been developed using a spheroidal coordinate system in order to properly take into account the effect of the finite length of the probe. The numerical results of both the electron- and the ion-current characteristics are obtained for various values of R/sub p//lambda/sub D/ ranging from 0 to 1, epsilon = T/sub i//T/sub e/ from 0.1 to 1, and C/sub p/ = L/sub p//2R/sub p/ from 1 to 100, where lambda/sub D/ is the Debye length, R/sub p/ and L/sub p/ are the probe radius and the probe length, T/sub i/ and T/sub e/ are the ion and the electron temperature, respectively. Using these results, new methods to determine the electron temperature and the plasma space potential (consequently, the electron density) by practical measurements are also proposed and discussed

Set theory and the continuum hypothesis

CERN Document Server

Cohen, Paul J

2008-01-01

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The independence of the continuum hypothesis is the focus of this study by Paul J. Cohen. It presents not only an accessible technical explanation of the author's landmark proof but also a fine introduction to mathematical logic. An emeritus professor of mathematics at Stanford University, Dr. Cohen won two of the most prestigious awards in mathematics: in 1964, he was awarded the American Mathematical Society's Bôcher Prize for analysis; and in 1966, he received the Fields Medal for Logic.

Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.

Science.gov (United States)

Jin, Leisheng; Li, Lijie

2017-12-01

In this work, nonlinear dynamics of silicon nanowire resonator considering nonlocal effect has been investigated. For the first time, dynamical parameters (e.g., resonant frequency, Duffing coefficient, and the damping ratio) that directly influence the nonlinear dynamics of the nanostructure have been derived. Subsequently, by calculating their response with the varied nonlocal coefficient, it is unveiled that the nonlocal effect makes more obvious impacts at the starting range (from zero to a small value), while the impact of nonlocal effect becomes weaker when the nonlocal term reaches to a certain threshold value. Furthermore, to characterize the role played by nonlocal effect in exerting influence on nonlinear behaviors such as bifurcation and chaos (typical phenomena in nonlinear dynamics of nanoscale devices), we have calculated the Lyapunov exponents and bifurcation diagram with and without nonlocal effect, and results shows the nonlocal effect causes the most significant effect as the device is at resonance. This work advances the development of nanowire resonators that are working beyond linear regime.

Geophysical Field Theory

International Nuclear Information System (INIS)

Eloranta, E.

2003-11-01

The geophysical field theory includes the basic principles of electromagnetism, continuum mechanics, and potential theory upon which the computational modelling of geophysical phenomena is based on. Vector analysis is the main mathematical tool in the field analyses. Electrostatics, stationary electric current, magnetostatics, and electrodynamics form a central part of electromagnetism in geophysical field theory. Potential theory concerns especially gravity, but also electrostatics and magnetostatics. Solid state mechanics and fluid mechanics are central parts in continuum mechanics. Also the theories of elastic waves and rock mechanics belong to geophysical solid state mechanics. The theories of geohydrology and mass transport form one central field theory in geophysical fluid mechanics. Also heat transfer is included in continuum mechanics. (orig.)

Plasmonic nanostructures: local versus nonlocal response

DEFF Research Database (Denmark)

Toscano, Giuseppe; Wubs, Martijn; Xiao, Sanshui

2010-01-01

, and hence it is sensitive to possible narrow resonances that may arise due to strong electronic quantum confinement in the metal. This feature allows us to accurately determine which geometries are strongly affected by nonlocal response, for example regarding applications based on electric field enhancement......We study the importance of taking the nonlocal optical response of metals into account for accurate determination of optical properties of nanoplasmonic structures. Here we focus on the computational physics aspects of this problem, and in particular we report on the nonlocal-response package...... that we wrote for state-of the art numerical software, enabling us to take into account the nonlocal material response of metals for any arbitrarily shaped nanoplasmonic structures, without much numerical overhead as compared to the standard local response. Our method is a frequency-domain method...

On deformation of complex continuum immersed in a plane space

Science.gov (United States)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-05-01

The present paper is devoted to mathematical modelling of complex continua deformations considered as immersed in an external plane space. The complex continuum is defined as a differential manifold supplied with metrics induced by the external space. A systematic derivation of strain tensors by notion of isometric immersion of the complex continuum into a plane space of a higher dimension is proposed. Problem of establishing complete systems of irreducible objective strain and extrastrain tensors for complex continuum immersed in an external plane space is resolved. The solution to the problem is obtained by methods of the field theory and the theory of rational algebraic invariants. Strain tensors of the complex continuum are derived as irreducible algebraic invariants of contravariant vectors of the external space emerging as functional arguments in the complex continuum action density. Present analysis is restricted to rational algebraic invariants. Completeness of the considered systems of rational algebraic invariants is established for micropolar elastic continua. Rational syzygies for non-quadratic invariants are discussed. Objective strain tensors (indifferent to frame rotations in the external plane space) for micropolar continuum are alternatively obtained by properly combining multipliers of polar decompositions of deformation and extra-deformation gradients. The latter is realized only for continua immersed in a plane space of the equal mathematical dimension.

Nonlocal higher order evolution equations

KAUST Repository

Rossi, Julio D.; Schö nlieb, Carola-Bibiane

2010-01-01

In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove

A behavioral continuum synthesizing Neutralization Theory, situational ethics and juvenile delinquency.

Science.gov (United States)

Norris, T D; Dodder, R A

1979-01-01

This paper develops some ideas in Matza's Neutralization theory into a continuum containing four categories ranging from extreme goodness to rebellion. We labeled these categories as Moral Absolute, Situational Ethic, Neutralization, and Rebellious Absolute. We discuss the percentages expected in each category and hypothesize that involvement in delinquency will increase progressively across these four categories. The rationale behind this hypothesis is that youth in the United States are viewed as being socialized to accept absolute norms but also to allow exceptions to these norms for particular situations, and that delinquent youth extend these exceptions to zones wider than are tolerated by law officers and wider than are generally accepted. A modified version of the Nye-Short self-reported delinquency scale and measures of normative oreintation which we constructed were used in a mail-out questionnaire to public school students (N = 351). We view our findings as being basically consistent with these expectations.

Experimental Greenberger-Horne-Zeilinger-Type Six-Photon Quantum Nonlocality.

Science.gov (United States)

Zhang, Chao; Huang, Yun-Feng; Wang, Zhao; Liu, Bi-Heng; Li, Chuan-Feng; Guo, Guang-Can

2015-12-31

Quantum nonlocality gives us deeper insight into quantum physics. In addition, quantum nonlocality has been further recognized as an essential resource for device-independent quantum information processing in recent years. Most experiments of nonlocality are performed using a photonic system. However, until now, photonic experiments of nonlocality have involved at most four photons. Here, for the first time, we experimentally demonstrate the six-photon quantum nonlocality in an all-versus-nothing manner based on a high-fidelity (88.4%) six-photon Greenberger-Horne-Zeilinger state. Our experiment pushes multiphoton nonlocality studies forward to the six-photon region and might provide a larger photonic system for device-independent quantum information protocols.

A hybrid local/non-local framework for the simulation of damage and fracture

KAUST Repository

Azdoud, Yan

2014-01-01

Recent advances in non-local continuum models, notably peridynamics, have spurred a paradigm shift in solid mechanics simulation by allowing accurate mathematical representation of singularities and discontinuities. This doctoral work attempts to extend the use of this theory to a community more familiar with local continuum models. In this communication, a coupling strategy - the morphing method -, which bridges local and non-local models, is presented. This thesis employs the morphing method to ease use of the non-local model to represent problems with failure-induced discontinuities. First, we give a quick review of strategies for the simulation of discrete degradation, and suggest a hybrid local/non-local alternative. Second, we present the technical concepts involved in the morphing method and evaluate the quality of the coupling. Third, we develop a numerical tool for the simulation of the hybrid model for fracture and damage and demonstrate its capabilities on numerical model examples

Performance-based shape optimization of continuum structures

International Nuclear Information System (INIS)

Liang Qingquan

2010-01-01

This paper presents a performance-based optimization (PBO) method for optimal shape design of continuum structures with stiffness constraints. Performance-based design concepts are incorporated in the shape optimization theory to achieve optimal designs. In the PBO method, the traditional shape optimization problem of minimizing the weight of a continuum structure with displacement or mean compliance constraints is transformed to the problem of maximizing the performance of the structure. The optimal shape of a continuum structure is obtained by gradually eliminating inefficient finite elements from the structure until its performance is maximized. Performance indices are employed to monitor the performance of optimized shapes in an optimization process. Performance-based optimality criteria are incorporated in the PBO method to identify the optimum from the optimization process. The PBO method is used to produce optimal shapes of plane stress continuum structures and plates in bending. Benchmark numerical results are provided to demonstrate the effectiveness of the PBO method for generating the maximum stiffness shape design of continuum structures. It is shown that the PBO method developed overcomes the limitations of traditional shape optimization methods in optimal design of continuum structures. Performance-based optimality criteria presented can be incorporated in any shape and topology optimization methods to obtain optimal designs of continuum structures.

On a class of nonlocal wave equations from applications

Science.gov (United States)

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.

Hyperspherical effective interaction for nonlocal potentials

International Nuclear Information System (INIS)

Barnea, N.; Leidemann, W.; Orlandini, G.

2010-01-01

The effective interaction hyperspherical-harmonics method, formulated for local forces, is generalized to accommodate nonlocal interactions. As for local potentials this formulation retains the separation of the hyper-radial part leading solely to a hyperspherical effective interaction. By applying the method to study ground-state properties of 4 He with a modern effective-field-theory nucleon-nucleon potential model (Idaho-N3LO), one finds a substantial acceleration in the convergence rate of the hyperspherical-harmonics series. Also studied are the binding energies of the six-body nuclei 6 He and 6 Li with the JISP16 nuclear force. Again an excellent convergence is observed.

Gap solitons under competing local and nonlocal nonlinearities

International Nuclear Information System (INIS)

Kuo, Kuan-Hsien; Lin Yuanyao; Lee, Ray-Kuang; Malomed, Boris A.

2011-01-01

We analyze the existence, bifurcations, and shape transformations of one-dimensional gap solitons (GSs) in the first finite band gap induced by a periodic potential built into materials with local self-focusing and nonlocal self-defocusing nonlinearities. Originally stable on-site GS modes become unstable near the upper edge of the band gap with the introduction of the nonlocal self-defocusing nonlinearity with a small nonlocality radius. Unstable off-site GSs bifurcate into a new branch featuring single-humped, double-humped, and flat-top modes due to the competition between local and nonlocal nonlinearities. The mechanism underlying the complex bifurcation pattern and cutoff effects (termination of some bifurcation branches) is illustrated in terms of the shape transformation under the action of the varying degree of the nonlocality. The results of this work suggest a possibility of optical-signal processing by means of the competing nonlocal and local nonlinearities.

Bistable traveling waves for a competitive-cooperative system with nonlocal delays

Science.gov (United States)

Tian, Yanling; Zhao, Xiao-Qiang

2018-04-01

This paper is devoted to the study of bistable traveling waves for a competitive-cooperative reaction and diffusion system with nonlocal time delays. The existence of bistable waves is established by appealing to the theory of monotone semiflows and the finite-delay approximations. Then the global stability of such traveling waves is obtained via a squeezing technique and a dynamical systems approach.

Nonlocal higher order evolution equations

KAUST Repository

Rossi, Julio D.

2010-06-01

In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.

Simulated small-angle scattering patterns for a plastically deformed model composite material

NARCIS (Netherlands)

Shenoy, V.B.; Cleveringa, H.H.M.; Phillips, R.; Giessen, E. van der; Needleman, A.

2000-01-01

The small-angle scattering patterns predicted by discrete dislocation plasticity versus local and non-local continuum plasticity theory are compared in a model problem. The problem considered is a two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to

Quantum Monte Carlo calculations with chiral effective field theory interactions

Energy Technology Data Exchange (ETDEWEB)

Tews, Ingo

2015-10-12

The neutron-matter equation of state connects several physical systems over a wide density range, from cold atomic gases in the unitary limit at low densities, to neutron-rich nuclei at intermediate densities, up to neutron stars which reach supranuclear densities in their core. An accurate description of the neutron-matter equation of state is therefore crucial to describe these systems. To calculate the neutron-matter equation of state reliably, precise many-body methods in combination with a systematic theory for nuclear forces are needed. Chiral effective field theory (EFT) is such a theory. It provides a systematic framework for the description of low-energy hadronic interactions and enables calculations with controlled theoretical uncertainties. Chiral EFT makes use of a momentum-space expansion of nuclear forces based on the symmetries of Quantum Chromodynamics, which is the fundamental theory of strong interactions. In chiral EFT, the description of nuclear forces can be systematically improved by going to higher orders in the chiral expansion. On the other hand, continuum Quantum Monte Carlo (QMC) methods are among the most precise many-body methods available to study strongly interacting systems at finite densities. They treat the Schroedinger equation as a diffusion equation in imaginary time and project out the ground-state wave function of the system starting from a trial wave function by propagating the system in imaginary time. To perform this propagation, continuum QMC methods require as input local interactions. However, chiral EFT, which is naturally formulated in momentum space, contains several sources of nonlocality. In this Thesis, we show how to construct local chiral two-nucleon (NN) and three-nucleon (3N) interactions and discuss results of first QMC calculations for pure neutron systems. We have performed systematic auxiliary-field diffusion Monte Carlo (AFDMC) calculations for neutron matter using local chiral NN interactions. By

Revealing Hidden Einstein-Podolsky-Rosen Nonlocality

Science.gov (United States)

Walborn, S. P.; Salles, A.; Gomes, R. M.; Toscano, F.; Souto Ribeiro, P. H.

2011-04-01

Steering is a form of quantum nonlocality that is intimately related to the famous Einstein-Podolsky-Rosen (EPR) paradox that ignited the ongoing discussion of quantum correlations. Within the hierarchy of nonlocal correlations appearing in nature, EPR steering occupies an intermediate position between Bell nonlocality and entanglement. In continuous variable systems, EPR steering correlations have been observed by violation of Reid’s EPR inequality, which is based on inferred variances of complementary observables. Here we propose and experimentally test a new criterion based on entropy functions, and show that it is more powerful than the variance inequality for identifying EPR steering. Using the entropic criterion our experimental results show EPR steering, while the variance criterion does not. Our results open up the possibility of observing this type of nonlocality in a wider variety of quantum states.

Relativistic Inverse Scattering Problem for a Superposition of a Nonlocal Separable and a Local Quasipotential

International Nuclear Information System (INIS)

Chernichenko, Yu.D.

2005-01-01

Within the relativistic quasipotential approach to quantum field theory, the relativistic inverse scattering problem is solved for the case where the total quasipotential describing the interaction of two relativistic spinless particles having different masses is a superposition of a nonlocal separable and a local quasipotential. It is assumed that the local component of the total quasipotential is known and that there exist bound states in this local component. It is shown that the nonlocal separable component of the total interaction can be reconstructed provided that the local component, an increment of the phase shift, and the energies of bound states are known

Quasi-Continuum Reduction of Field Theories: A Route to Seamlessly Bridge Quantum and Atomistic Length-Scales with Continuum

Science.gov (United States)

2016-04-01

May - Nov 1998; Nov 1998. 4. TITLE. Enter title and subtitle with volume number and part number, if applicable . On classified documents, enter the...The non-local (extended) electrostatic interactions involve the kernel 1/|r−r′|, which is the Green’s function of the Laplace operator. These...trivial transformation of the generalized eigenvalue problem (3) to a standard eigenvalue problem as HΨ̃ i = h i MΨ̃ i ⇒ HΨ̃ i = hi M1/2M1/2Ψ̃ i

Hyperbolic metamaterial lens with hydrodynamic nonlocal response

OpenAIRE

Yan, Wei; Mortensen, N. Asger; Wubs, Martijn

2013-01-01

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 cu...

Frustrated Brownian Motion of Nonlocal Solitary Waves

International Nuclear Information System (INIS)

Folli, V.; Conti, C.

2010-01-01

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.

Nonlocality, Correlations, and Magnetotransport in a Spatially Modulated Two-Dimensional Electron Gas

Science.gov (United States)

Raichev, O. E.

2018-04-01

It is shown that the classical commensurability phenomena in weakly modulated two-dimensional electron systems is a manifestation of the intrinsic properties of the correlation functions describing a homogeneous electron gas in a magnetic field. The theory demonstrates the importance for consideration of nonlocal response and removes the gap between classical and quantum approaches to magnetotransport in such systems.

Scattering theory for lattice phi4sub(D+1) theory

International Nuclear Information System (INIS)

Garczynski, W.

1983-01-01

Feynman rules are derived for a lattice version of the phi 4 sub(D+1) theory. The lattice values are transcribed, via a quasicontinual representation, into a continuous, non-local in spatial variables field theory, which is then quantized by the path integral method. (orig.)

Some generalizations of the nonlocal transformations approach

Directory of Open Access Journals (Sweden)

V. A. Tychynin

2015-02-01

Full Text Available Some generalizations of a method of nonlocal transformations are proposed: a con­nection of given equations via prolonged nonlocal transformations and finding of an adjoint solution to the solutions of initial equation are considered. A concept of nonlocal transformation with additional variables is introduced, developed and used for searching symmetries of differential equations. A problem of inversion of the nonlocal transforma­tion with additional variables is investigated and in some cases solved. Several examples are presented. Derived technique is applied for construction of the algorithms and for­mulae of generation of solutions. The formulae derived are used for construction of exact solutions of some nonlinear equations.

Phase structure of 3D Z(N) lattice gauge theories at finite temperature: Large-N and continuum limits

International Nuclear Information System (INIS)

Borisenko, O.; Chelnokov, V.; Gravina, M.; Papa, A.

2014-01-01

We study numerically three-dimensional Z(N) lattice gauge theories at finite temperature, for N=5,6,8,12,13 and 20 on lattices with temporal extension N t =2,4,8. For each model, we locate phase transition points and determine critical indices. We propose also the scaling of critical points with N. The data obtained enable us to verify the scaling near the continuum limit for the Z(N) models at finite temperatures

Magnetic-field-induced nonlocal effects on the vortex interactions in twin-free YBa₂Cu₃O₇

DEFF Research Database (Denmark)

White, J. S.; Heslop, R. W.; Holmes, A. T.

2011-01-01

measurements demonstrate how the influence of anisotropy on the VL, which in theory can be parameterized as nonlocal corrections, becomes progressively important with increasing magnetic field, and suppressed by increasing the temperature toward Tc. The data indicate that nonlocality due to different...... anisotropies plays an important role in determining the VL properties....

Nonlocal effective actions in semiclassical gravity: Thermal effects in stationary geometries

Science.gov (United States)

Elías, M.; Mazzitelli, F. D.; Trombetta, L. G.

2017-11-01

We compute the gravitational effective action by integrating out quantum matter fields in a weak gravitational field, using the Schwinger-Keldysh (in-in) formalism. We pay particular attention to the role of the initial quantum state in the structure of the nonlocal terms in the effective action, with an eye to nonlinear completions of the theory that may be relevant in astrophysics and cosmology. In this first paper we consider a quantum scalar field in thermal equilibrium, in a stationary gravitational field. We obtain a covariant expression for the nonlocal effective action, which can be expressed in terms of the curvature tensor, the four-velocity of the thermal bath, and the local Tolman temperature. We discuss the connection between the results for ultrastatic and static metrics through conformal transformations, and the main features of the thermal corrections to the semiclassical Einstein equations.

Attraction of nonlocal dark optical solitons

DEFF Research Database (Denmark)

Nikolov, Nikola Ivanov; Neshev, Dragomir; Krolikowski, Wieslaw

2004-01-01

We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states...

Optimizing plasmon-enhanced fluorescence with nonlocal metallic nanospheres

DEFF Research Database (Denmark)

Tserkezis, Christos; Stefanou, Nikolaos; Wubs, Martijn

, through the recent Generalized Nonlocal Optical Response (GNOR) theory, the concurrent contribution of modal shifts and nonradiative losses, together with a reduced emitter excitation rate due to the decreased field intensity, lead always to a strong reduction of fluorescence (see Fig. 1). Finally, we...... identify situations where the common, intuitive recipe of tuning the NP modes to match λem can in fact lead to strong fluorescence quenching, instead of the anticipated enhancement. Our results highlight the necessity for careful modeling and design of plasmon-field-enhancement based applications....

Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling

KAUST Repository

Hackett-Jones, Emily J.; Landman, Kerry A.; Fellner, Klemens

2012-01-01

both attractive and repulsive singularities. Currently, no existence theory for such potentials is available. We develop and compare two complementary solution methods, a continuous pseudoinverse method and a discrete stochastic lattice approach

One-loop effective action for non-local modified Gauss-Bonnet gravity in de Sitter space

Energy Technology Data Exchange (ETDEWEB)

Cognola, Guido; Zerbini, Sergio [Universita di Trento (Italy); Istituto Nazionale di Fisica Nucleare Gruppo Collegato di Trento, Dipartimento di Fisica, Trento (Italy); Elizalde, Emilio [Consejo Superior de Investigaciones Cientificas (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Facultat Ciencies, Bellaterra (Barcelona) (Spain); Nojiri, Shin' ichi [Nagoya University, Department of Physics, Nagoya (Japan); Odintsov, Sergei D. [Consejo Superior de Investigaciones Cientificas (ICE/CSIC) and Institut d' Estudis Espacials de Catalunya (IEEC), Facultat Ciencies, Bellaterra (Barcelona) (Spain); ICREA, Barcelona (Spain); TSPU, Center of Theor. Phys., Tomsk (Russian Federation)

2009-12-15

We discuss the classical and quantum properties of non-local modified Gauss-Bonnet gravity in de Sitter space, using its equivalent representation via string-inspired local scalar-Gauss-Bonnet gravity with a scalar potential. A classical, multiple de Sitter universe solution is found where one of the de Sitter phases corresponds to the primordial inflationary epoch, while the other de Sitter space solution - the one with the smallest Hubble rate - describes the late-time acceleration of our universe. A Chameleon scenario for the theory under investigation is developed, and it is successfully used to show that the theory complies with gravitational tests. An explicit expression for the one-loop effective action for this non-local modified Gauss-Bonnet gravity in the de Sitter space is obtained. It is argued that this effective action might be an important step towards the solution of the cosmological constant problem. (orig.)

Solving Two -Dimensional Diffusion Equations with Nonlocal Boundary Conditions by a Special Class of Padé Approximants

Directory of Open Access Journals (Sweden)

Mohammad Siddique

2010-08-01

Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.

Higgs mechanism in light-front quantized field theory

Energy Technology Data Exchange (ETDEWEB)

Srivastava, P P

1993-12-31

The spontaneous symmetry breaking of continuous symmetry in light-front quantized scalar field theory is studied following the standard Dirac procedure for constrained dynamical systems. A non-local constraint is found to follow. The values of the constant backgrounds fields (zero modes) at the tree level, as a consequence, are shown to given by minimizing the light-front energy. The zero modes are shown to commute with the non-zero ones and the isovector built from them is seen to characterize a (non-perturbative) vacuum state and the corresponding physical sector. The infinite degeneracy of the vacuum is described by the continuum of the allowed orientations of this background isovector in the isospin space. The symmetry generators in the quantized field theory annihilate the vacuum is contrast to the case of equal-time quantization. Not all of them are conserved and the conserved ones determine the surviving symmetry of the quantum theory Lagrangian. The criteria for determining the background isovector and the counting of the number of Goldstone bosons goes as in the equal-time case. A demonstration in favour of the absence of Goldstone bosons in two dimensions is also found. Finally, is extended to an understanding of the Higgs mechanism in light-front frame. (author). 13 refs.

Higgs mechanism in light-front quantized field theory

International Nuclear Information System (INIS)

Srivastava, P.P.

1992-01-01

The spontaneous symmetry breaking of continuous symmetry in light-front quantized scalar field theory is studied following the standard Dirac procedure for constrained dynamical systems. A non-local constraint is found to follow. The values of the constant backgrounds fields (zero modes) at the tree level, as a consequence, are shown to given by minimizing the light-front energy. The zero modes are shown to commute with the non-zero ones and the isovector built from them is seen to characterize a (non-perturbative) vacuum state and the corresponding physical sector. The infinite degeneracy of the vacuum is described by the continuum of the allowed orientations of this background isovector in the isospin space. The symmetry generators in the quantized field theory annihilate the vacuum is contrast to the case of equal-time quantization. Not all of them are conserved and the conserved ones determine the surviving symmetry of the quantum theory Lagrangian. The criteria for determining the background isovector and the counting of the number of Goldstone bosons goes as in the equal-time case. A demonstration in favour of the absence of Goldstone bosons in two dimensions is also found. Finally, is extended to an understanding of the Higgs mechanism in light-front frame. (author). 13 refs

Defining and testing a granular continuum element

Energy Technology Data Exchange (ETDEWEB)

Rycroft, Chris H.; Kamrin, Ken; Bazant, Martin Z.

2007-12-03

Continuum mechanics relies on the fundamental notion of amesoscopic volume "element" in which properties averaged over discreteparticles obey deterministic relationships. Recent work on granularmaterials suggests a continuum law may be inapplicable, revealinginhomogeneities at the particle level, such as force chains and slow cagebreaking. Here, we analyze large-scale Discrete-Element Method (DEM)simulations of different granular flows and show that a "granularelement" can indeed be defined at the scale of dynamical correlations,roughly three to five particle diameters. Its rheology is rather subtle,combining liquid-like dependence on deformation rate and solid-likedependence on strain. Our results confirm some aspects of classicalplasticity theory (e.g., coaxiality of stress and deformation rate),while contradicting others (i.e., incipient yield), and can guide thedevelopment of more realistic continuum models.

The right inferior frontal gyrus processes nested non-local dependencies in music.

Science.gov (United States)

Cheung, Vincent K M; Meyer, Lars; Friederici, Angela D; Koelsch, Stefan

2018-02-28

Complex auditory sequences known as music have often been described as hierarchically structured. This permits the existence of non-local dependencies, which relate elements of a sequence beyond their temporal sequential order. Previous studies in music have reported differential activity in the inferior frontal gyrus (IFG) when comparing regular and irregular chord-transitions based on theories in Western tonal harmony. However, it is unclear if the observed activity reflects the interpretation of hierarchical structure as the effects are confounded by local irregularity. Using functional magnetic resonance imaging (fMRI), we found that violations to non-local dependencies in nested sequences of three-tone musical motifs in musicians elicited increased activity in the right IFG. This is in contrast to similar studies in language which typically report the left IFG in processing grammatical syntax. Effects of increasing auditory working demands are moreover reflected by distributed activity in frontal and parietal regions. Our study therefore demonstrates the role of the right IFG in processing non-local dependencies in music, and suggests that hierarchical processing in different cognitive domains relies on similar mechanisms that are subserved by domain-selective neuronal subpopulations.

Nonlocal transformation optics.

Science.gov (United States)

Castaldi, Giuseppe; Galdi, Vincenzo; Alù, Andrea; Engheta, Nader

2012-02-10

We show that the powerful framework of transformation optics may be exploited for engineering the nonlocal response of artificial electromagnetic materials. Relying on the form-invariant properties of coordinate-transformed Maxwell's equations in the spectral domain, we derive the general constitutive "blueprints" of transformation media yielding prescribed nonlocal field-manipulation effects and provide a physically incisive and powerful geometrical interpretation in terms of deformation of the equifrequency contours. In order to illustrate the potentials of our approach, we present an example of application to a wave-splitting refraction scenario, which may be implemented via a simple class of artificial materials. Our results provide a systematic and versatile framework which may open intriguing venues in dispersion engineering of artificial materials.

Occurrence of exact R{sup 2} inflation in non-local UV-complete gravity

Energy Technology Data Exchange (ETDEWEB)

Koshelev, Alexey S. [Departamento de Física and Centro de Matemática e Aplicações (CMA-UBI),Universidade da Beira Interior, 6200 Covilhã (Portugal); Theoretische Natuurkunde, Vrije Universiteit Brussel, and The International Solvay Institutes,Pleinlaan 2, B-1050 Brussels (Belgium); Modesto, Leonardo [Department of Physics, Southern University of Science and Technology, Shenzhen 518055 (China); Department of Physics & Center for Field Theory and Particle Physics, Fudan University,200433 Shanghai (China); Rachwał, Lesław [Department of Physics & Center for Field Theory and Particle Physics, Fudan University,200433 Shanghai (China); Starobinsky, Alexei A. [L.D. Landau Institute for Theoretical Physics RAS, Moscow 119334 (Russian Federation); Kazan Federal University, Kazan 420008, Republic of Tatarstan (Russian Federation)

2016-11-10

The R+R{sup 2}, shortly named “R{sup 2}” (“Starobinsky”) inflationary model, represents a fully consistent example of a one-parameter inflationary scenario. This model has a “graceful exit” from inflation and provides a mechanism for subsequent creation and final thermalization of the standard matter. Moreover, it produces a very good fit of the observed spectrum of primordial perturbations. In the present paper we show explicitly that the R{sup 2} inflationary spacetime is an exact solution of a range of weakly non-local (quasi-polynomial) gravitational theories, which provide an ultraviolet completion of the R{sup 2} theory. These theories are ghost-free, super-renormalizable or finite at quantum level, and perturbatively unitary. Their spectrum consists of the graviton and the scalaron that is responsible for driving the inflation. Notably, any further extension of the spectrum leads to propagating ghost degrees of freedom. We are aimed at presenting a detailed construction of such theories in the so called Weyl basis. Further, we give a special account to the cosmological implications of this theory by considering perturbations during inflation. The highlight of the non-local model is the prediction of a modified, in comparison to a local R{sup 2} model, value for the ratio of tensor and scalar power spectra r, depending on the parameters of the theory. The relevant parameters are under control to be successfully confronted with existing observational data. Furthermore, the modified r can surely meet future observational constraints.

Gradient effects in a new class of electro-elastic bodies

Science.gov (United States)

Arvanitakis, Antonios

2018-06-01

Continuum theories for electro-elastic solids suggest the development of electric field or polarization-based models. Advanced versions of these models are the so-called gradient models, i.e., polarization gradient and electric field gradient models, which prove to be more than capable of explaining the behavior of a continuum in a wider range of length scales. In this work, implicit constitutive relations for electro-elastic bodies are considered with the introduction of polarization and electric field gradient effects. In this sense, the new class of electro-elastic bodies extends even further to account for nonlocality in constitutive equations, besides strain-limiting behavior and polarization saturation for large values of stresses and electric field, respectively. Nonlocality in constitutive equations is essential in modeling various phenomena.

Phase structure of 3D Z(N) lattice gauge theories at finite temperature: Large-N and continuum limits

Energy Technology Data Exchange (ETDEWEB)

Borisenko, O., E-mail: oleg@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine); Chelnokov, V., E-mail: chelnokov@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 03680 Kiev (Ukraine); Gravina, M., E-mail: gravina@fis.unical.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy); Papa, A., E-mail: papa@fis.unical.it [Dipartimento di Fisica, Università della Calabria, and Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Cosenza, I-87036 Arcavacata di Rende, Cosenza (Italy)

2014-11-15

We study numerically three-dimensional Z(N) lattice gauge theories at finite temperature, for N=5,6,8,12,13 and 20 on lattices with temporal extension N{sub t}=2,4,8. For each model, we locate phase transition points and determine critical indices. We propose also the scaling of critical points with N. The data obtained enable us to verify the scaling near the continuum limit for the Z(N) models at finite temperatures.

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

Science.gov (United States)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

Nonlocal exchange and kinetic-energy density functionals for electronic systems

International Nuclear Information System (INIS)

Glossman, M.D.; Rubio, A.; Balbas, L.C.; Alonso, J.A.

1992-01-01

The nonlocal weighted density approximation (WDA) to the exchange and kinetic-energy functionals of many electron systems proposed several years ago by Alonso and Girifalco is used to compute, within the framework of density functional theory, the ground-state electronic density and total energy of noble gas atoms and of neutral jellium-like sodium clusters containing up to 500 atoms. These results are compared with analogous calculations using the well known Thomas-Fermi-Weizsacker-Dirac (TFWD) approximations for the kinetic (TFW) and exchange (D) energy density functionals. An outstanding improvement of the total and exchange energies, of the density at the nucleus and of the expectation values is obtained for atoms within the WDA scheme. For sodium clusters the authors notice a sizeable contribution of the nonlocal effects to the total energy and to the density profiles. In the limit of very large clusters these effects should affect the surface energy of the bulk metal

Continuum and crystal strain gradient plasticity with energetic and dissipative length scales

Science.gov (United States)

Faghihi, Danial

This work, standing as an attempt to understand and mathematically model the small scale materials thermal and mechanical responses by the aid of Materials Science fundamentals, Continuum Solid Mechanics, Misro-scale experimental observations, and Numerical methods. Since conventional continuum plasticity and heat transfer theories, based on the local thermodynamic equilibrium, do not account for the microstructural characteristics of materials, they cannot be used to adequately address the observed mechanical and thermal response of the micro-scale metallic structures. Some of these cases, which are considered in this dissertation, include the dependency of thin films strength on the width of the sample and diffusive-ballistic response of temperature in the course of heat transfer. A thermodynamic-based higher order gradient framework is developed in order to characterize the mechanical and thermal behavior of metals in small volume and on the fast transient time. The concept of the thermal activation energy, the dislocations interaction mechanisms, nonlocal energy exchange between energy carriers and phonon-electrons interactions are taken into consideration in proposing the thermodynamic potentials such as Helmholtz free energy and rate of dissipation. The same approach is also adopted to incorporate the effect of the material microstructural interface between two materials (e.g. grain boundary in crystals) into the formulation. The developed grain boundary flow rule accounts for the energy storage at the grain boundary due to the dislocation pile up as well as energy dissipation caused by the dislocation transfer through the grain boundary. Some of the abovementioned responses of small scale metallic compounds are addressed by means of the numerical implementation of the developed framework within the finite element context. In this regard, both displacement and plastic strain fields are independently discretized and the numerical implementation is performed in

Nonlocal electron kinetics and spectral line emission in the positive column of an argon glow discharge

International Nuclear Information System (INIS)

Golubovskii, Yu; Kalanov, D; Gorchakov, S; Uhrlandt, D

2015-01-01

Modern non-local electron kinetics theory predicts several interesting effects connected with spectral line emission from the positive column in the range of low and medium pressures and currents. Some theoretical works describe non-monotonic behavior of the radial profiles of line emission at intermediate pressures and currents between the validity ranges of the non-local and local approximation of the electron kinetics. Despite a great number of publications, there have been no systematic measurements attempting to confirm these theoretical predictions through experiments. In this work the radial profiles of the line emission from the positive column of an argon glow discharge have been measured with high spatial resolution and new effects caused by the narrowing and broadening of the spatial emission profiles with dependence on discharge conditions have been discovered. The effect of intensity maximum shift predicted by theory using a self-consistent model was not found in the experiment. The properties of the spectral line radiation are influenced by the peculiarities of the formation of the high-energy tail of the electron energy distribution function. An interpretation of the observed effects based on the non-local character of the electron kinetics in radially inhomogeneous fields is given. The obtained experimental data are compared with the results of calculations. (paper)

Effects of two-temperature parameter and thermal nonlocal parameter on transient responses of a half-space subjected to ramp-type heating

Science.gov (United States)

Xue, Zhang-Na; Yu, Ya-Jun; Tian, Xiao-Geng

2017-07-01

Based upon the coupled thermoelasticity and Green and Lindsay theory, the new governing equations of two-temperature thermoelastic theory with thermal nonlocal parameter is formulated. To more realistically model thermal loading of a half-space surface, a linear temperature ramping function is adopted. Laplace transform techniques are used to get the general analytical solutions in Laplace domain, and the inverse Laplace transforms based on Fourier expansion techniques are numerically implemented to obtain the numerical solutions in time domain. Specific attention is paid to study the effect of thermal nonlocal parameter, ramping time, and two-temperature parameter on the distributions of temperature, displacement and stress distribution.

Tests of non-local interferences in kaon physics at asymmetric φ-factories

International Nuclear Information System (INIS)

Eberhard, P.H.

1993-01-01

Tests of non-local interference effects in the two-kaon system are proposed. The first kind of tests consists of measuring the amount of destructive interference between K S → K L regeneration processes of two distant kaons. The second kind deals with constructive interference. These tests could be performed at an asymmetric φ-factory. Estimates are given of the number of events predicted by orthodox quantum mechanics and kaon regeneration theory in various suitable experimental conditions. The impact on local theories if the predictions of quantum mechanics hold is discussed

Spatial buckling analysis of current-carrying nanowires in the presence of a longitudinal magnetic field accounting for both surface and nonlocal effects

Science.gov (United States)

Foroutan, Shahin; Haghshenas, Amin; Hashemian, Mohammad; Eftekhari, S. Ali; Toghraie, Davood

2018-03-01

In this paper, three-dimensional buckling behavior of nanowires was investigated based on Eringen's Nonlocal Elasticity Theory. The electric current-carrying nanowires were affected by a longitudinal magnetic field based upon the Lorentz force. The nanowires (NWs) were modeled based on Timoshenko beam theory and the Gurtin-Murdoch's surface elasticity theory. Generalized Differential Quadrature (GDQ) method was used to solve the governing equations of the NWs. Two sets of boundary conditions namely simple-simple and clamped-clamped were applied and the obtained results were discussed. Results demonstrated the effect of electric current, magnetic field, small-scale parameter, slenderness ratio, and nanowires diameter on the critical compressive buckling load of nanowires. As a key result, increasing the small-scale parameter decreased the critical load. By the same token, increasing the electric current, magnetic field, and slenderness ratio resulted in a decrease in the critical load. As the slenderness ratio increased, the effect of nonlocal theory decreased. In contrast, by expanding the NWs diameter, the nonlocal effect increased. Moreover, in the present article, the critical values of the magnetic field of strength and slenderness ratio were revealed, and the roles of the magnetic field, slenderness ratio, and NWs diameter on higher buckling loads were discussed.

Reassessment of the nonlocality of correlation boxes

Energy Technology Data Exchange (ETDEWEB)

Costa, A.P.; Parisio, Fernando, E-mail: parisio@df.ufpe.br

2017-01-15

Correlation boxes are hypothetical systems usually designed to produce the maximal algebraic violation of a Bell inequality, beyond the quantum bound and without superluminal signalling. The fact that these systems show stronger correlations than those presented by maximally entangled quantum states, as the spin singlet, has been regarded as a demonstration that the former are more nonlocal than the latter. By applying an alternative, consistent measure of nonlocality to a family of correlation boxes, we show that this conclusion is not necessarily true. Complementarily, we define a class of systems displaying subquantum correlations which, nevertheless, are more nonlocal than the singlet state, showing that the extent of the numeric violation of an inequality may have little to do with the degree of nonlocality, especially in the case of correlation boxes.

Gradient models in molecular biophysics: progress, challenges, opportunities

Science.gov (United States)

Bardhan, Jaydeep P.

2013-12-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g., molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding nonlocal dielectric response. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain, and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost 40 years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The review concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics.

Gauge unification, non-local breaking, open strings

International Nuclear Information System (INIS)

Trapletti, M.

2005-01-01

The issue of non-local GUT symmetry breaking is addressed in the context of open string model building. We study Z N xZ M ' orbifolds with all the GUT-breaking orbifold elements acting freely, as rotations accompanied by translations in the internal space. We consider open strings quantized on these backgrounds, distinguishing whether the translational action is parallel or perpendicular to the D-branes. GUT breaking is impossible in the purely perpendicular case, non-local GUT breaking is instead allowed in the purely parallel case. In the latter, the scale of breaking is set by the compactification moduli, and there are no fixed points with reduced gauge symmetry, where dangerous explicit GUT-breaking terms could be located. We investigate the mixed parallel+perpendicular case in a Z 2 xZ 2 ' example, having also a simplified field theory realization. It is a new S 1 /Z 2 xZ 2 ' orbifold-GUT model, with bulk gauge symmetry SU(5)xSU(5) broken locally to the Standard Model gauge group. In spite of the locality of the GUT symmetry breaking, there is no localized contribution to the running of the coupling constants, and the unification scale is completely set by the length of S 1

Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory

Directory of Open Access Journals (Sweden)

A. Farajpour

Full Text Available Carbon nanotubes are a new class of microtubule-stabilizing agents since they interact with protein microtubules in living cells, interfering with cell division and inducing apoptosis. In the present work, a modified beam model is developed to investigate the effect of carbon nanotubes on the buckling of microtubule bundles in living cell. A realistic interaction model is employed using recent experimental data on the carbon nanotube-stabilized microtubules. Small scale and surface effects are taken into account applying the nonlocal strain gradient theory and surface elasticity theory. Pasternak model is used to describe the normal and shearing effects of enclosing filament matrix on the buckling behavior of the system. An exact solution is obtained for the buckling growth rates of the mixed bundle in viscoelastic surrounding cytoplasm. The present results are compared with those reported in the open literature for single microtubules and an excellent agreement is found. Finally, the effects of different parameters such as the size, chirality, position and surface energy of carbon nanotubes on the buckling growth rates of microtubule bundles are studied. It is found that the buckling growth rate may increase or decrease by adding carbon nanotubes, depending on the diameter and chirality of carbon nanotubes. Keywords: Microtubules, Carbon nanotubes, Buckling, Size effects

Classification of scalar and dyadic nonlocal optical response models

DEFF Research Database (Denmark)

Wubs, Martijn

2015-01-01

Nonlocal optical response is one of the emerging effects on the nanoscale for particles made of metals or doped semiconductors. Here we classify and compare both scalar and tensorial nonlocal response models. In the latter case the nonlocality can stem from either the longitudinal response...

A new treatment of nonlocality in scattering process

Science.gov (United States)

Upadhyay, N. J.; Bhagwat, A.; Jain, B. K.

2018-01-01

Nonlocality in the scattering potential leads to an integro-differential equation. In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schrödinger equation is usually handled by approximating r,{r}{\\prime }-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method is accurate and valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off 12C, 56Fe and 100Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in reasonable accord with the experiments.

Ring vortex solitons in nonlocal nonlinear media

DEFF Research Database (Denmark)

Briedis, D.; Petersen, D.E.; Edmundson, D.

2005-01-01

We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single...... or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....

Inverse dualization and non-local dualities between Einstein gravity and supergravities

International Nuclear Information System (INIS)

Chen Chiangmei; Gal'tsov, Dmitri V; Sharakin, Sergei A

2002-01-01

We investigate non-local dualities between suitably compactified higher dimensional Einstein gravity and supergravities which can be revealed if one reinterprets the dualized Kaluza-Klein 2-forms in D>4 as antisymmetric forms belonging to supergravities. We find several examples of such a correspondence including one between the six-dimensional Einstein gravity and the four-dimensional Einstein-Maxwell-dilaton-axion theory (truncated N=4 supergravity), and others between the compactified eleven- and ten-dimensional supergravities and the eight- or ten-dimensional pure gravity. The Killing spinor equation of the D=11 supergravity is shown to be equivalent to the geometric Killing spinor equation in the dual gravity. We give several examples of using new dualities for solution generation and demonstrate how p-branes can be interpreted as non-local duals of pure gravity solutions. New supersymmetric solutions are presented including M2 subset of 5-brane with two rotation parameters

Microscopic tunneling theory of long Josephson junctions

DEFF Research Database (Denmark)

Grønbech-Jensen, N.; Hattel, Søren A.; Samuelsen, Mogens Rugholm

1992-01-01

We present a numerical scheme for solving a nonlinear partial integro-differential equation with nonlocal time dependence. The equation describes the dynamics in a long Josephson junction modeled by use of the microscopic theory for tunneling between superconductors. We demonstrate that the detai......We present a numerical scheme for solving a nonlinear partial integro-differential equation with nonlocal time dependence. The equation describes the dynamics in a long Josephson junction modeled by use of the microscopic theory for tunneling between superconductors. We demonstrate...

Static third-harmonic lines in widely variable fiber continuum generation

Science.gov (United States)

Tu, Haohua; Zhao, Youbo; Liu, Yuan; Boppart, Stephen A.

2014-01-01

An intriguing phenomenon of third-harmonic generation under fiber continuum generation is the emission of an anharmonic signal. One popular interpretation of this effect has developed into a general theory of fiber third-harmonic generation. Here we produce "static" third-harmonic lines dictated fully by fiber properties independent of pump parameters, in contrast to the signals of all known phase-matched nonlinear optical processes that vary dynamically with these parameters. We argue that the anharmonic signal is an illusion of the continuum generation, that it is in fact harmonic, and that this theory should be reevaluated.

A Generalized Nonlocal Calculus with Application to the Peridynamics Model for Solid Mechanics

OpenAIRE

Alali, Bacim; Liu, Kuo; Gunzburger, Max

2014-01-01

A nonlocal vector calculus was introduced in [2] that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion models. A generalization 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...

Collapse arrest and soliton stabilization in nonlocal nonlinear media

DEFF Research Database (Denmark)

Bang, Ole; Krolikowski, Wieslaw; Wyller, John

2002-01-01

that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric and have a positive definite Fourier spectrum, but can otherwise be of completely arbitrary shape and degree of nonlocality...

Quantum scattering theory on the momentum lattice

International Nuclear Information System (INIS)

Rubtsova, O. A.; Pomerantsev, V. N.; Kukulin, V. I.

2009-01-01

A new approach based on the wave-packet continuum discretization method recently developed by the present authors for solving quantum-mechanical scattering problems for atomic and nuclear scattering processes and few-body physics is described. The formalism uses the complete continuum discretization scheme in terms of the momentum stationary wave-packet basis, which leads to formulation of the scattering problem on a lattice in the momentum space. The solution of the few-body scattering problem can be found in the approach from linear matrix equations with nonsingular matrix elements, averaged on energy over lattice cells. The developed approach is illustrated by the solution of numerous two- and three-body scattering problems with local and nonlocal potentials below and well above the three-body breakup threshold.

Nonlinear continuum mechanics and large inelastic deformations

CERN Document Server

Dimitrienko, Yuriy I

2010-01-01

This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...

Non-local magnetoresistance in YIG/Pt nanostructures

Energy Technology Data Exchange (ETDEWEB)

Goennenwein, Sebastian T. B., E-mail: goennenwein@wmi.badw.de; Pernpeintner, Matthias; Gross, Rudolf; Huebl, Hans [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Walther-Meißner-Str. 8, 85748 Garching (Germany); Nanosystems Initiative Munich (NIM), Schellingstraße 4, 80799 München (Germany); Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching (Germany); Schlitz, Richard; Ganzhorn, Kathrin [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Walther-Meißner-Str. 8, 85748 Garching (Germany); Physik-Department, Technische Universität München, James-Franck-Str. 1, 85748 Garching (Germany); Althammer, Matthias [Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, Walther-Meißner-Str. 8, 85748 Garching (Germany)

2015-10-26

We study the local and non-local magnetoresistance of thin Pt strips deposited onto yttrium iron garnet. The local magnetoresistive response, inferred from the voltage drop measured along one given Pt strip upon current-biasing it, shows the characteristic magnetization orientation dependence of the spin Hall magnetoresistance. We simultaneously also record the non-local voltage appearing along a second, electrically isolated, Pt strip, separated from the current carrying one by a gap of a few 100 nm. The corresponding non-local magnetoresistance exhibits the symmetry expected for a magnon spin accumulation-driven process, confirming the results recently put forward by Cornelissen et al. [“Long-distance transport of magnon spin information in a magnetic insulator at room temperature,” Nat. Phys. (published online 14 September 2015)]. Our magnetotransport data, taken at a series of different temperatures as a function of magnetic field orientation, rotating the externally applied field in three mutually orthogonal planes, show that the mechanisms behind the spin Hall and the non-local magnetoresistance are qualitatively different. In particular, the non-local magnetoresistance vanishes at liquid Helium temperatures, while the spin Hall magnetoresistance prevails.

Continuum (scaling) limits of lattice field theories (triviality of lambda/phi/4 in D greater than or equal to dimensions)

International Nuclear Information System (INIS)

Frohlich, J.

1983-01-01

The author describes some recent techniques for constructing the continuum (= scaling) limit of lattice field theories, including the one- and two- component lambda/less than or equal to→/phi// 4 theories and the Ising and rotator models in a space (- imaginary time) of dimension d >greater than or equal to 4. These techniques should have applications to other related models, like the selfavoiding random walk in five or more dimensions and bond percolation in seven or more dimensions. Some plausible conjectures concerning the Gaussian nature of the scaling limit of the d greater than or equal to 2 dimensional rotator model and the d greater than or equal to 4 dimensional U(1) lattice gauge theory in the low temperature (weak coupling) phase are described

Non-local ground-state functional for quantum spin chains with translational broken symmetry

Energy Technology Data Exchange (ETDEWEB)

Libero, Valter L.; Penteado, Poliana H.; Veiga, Rodrigo S. [Universidade de Sao Paulo (IFSC/USP), Sao Carlos, SP (Brazil). Inst. de Fisica

2011-07-01

Full text. Thanks to the development and use of new materials with special doping, it becomes relevant the study of Heisenberg spin-chains with broken translational symmetry, induced for instance by finite-size effects, bond defects or by impurity spin in the chain. The exact numerical results demands huge computational efforts, due to the size of the Hilbert space involved and the lack of symmetry to exploit. Density Functional Theory (DFT) has been considered a simple alternative to obtain ground-state properties for such systems. Usually, DFT starts with a uniform system to build the correlation energy and after implement a local approximation to construct local functionals. Based on our prove of the Hohenberg-Kohn theorem for Heisenberg models, and in order to describe more realistic models, we have recently developed a non-local exchange functional for the ground-state energy of quantum-spin chains. A alternating-bond chain is used to obtain the correlation energy and a local unit-cell approximation - LUCA, is defined in the context of DFT. The alternating chain is a good starting point to construct functionals since it is intrinsically non-homogeneous, therefore instead of the usual local approximation (like LDA for electronic systems) we need to introduce an approximation based upon a unit cell concept, that renders a non-local functional in the bond exchange interaction. The agreement with exact numerical data (obtained only for small chains, although the functional can be applied for chains with arbitrary size) is significantly better than in our previous local formulation, even for chains with several ferromagnetic or antiferromagnetic bond defects. These results encourage us to extend the concept of LUCA for chains with alternating-spin magnitudes. We also have constructed a non-local functional based on an alternating-spin chain, instead of a local alternating-bond, using spin-wave-theory. Because of its non-local nature, this functional is expected to

Non-local ground-state functional for quantum spin chains with translational broken symmetry

International Nuclear Information System (INIS)

Libero, Valter L.; Penteado, Poliana H.; Veiga, Rodrigo S.

2011-01-01

Full text. Thanks to the development and use of new materials with special doping, it becomes relevant the study of Heisenberg spin-chains with broken translational symmetry, induced for instance by finite-size effects, bond defects or by impurity spin in the chain. The exact numerical results demands huge computational efforts, due to the size of the Hilbert space involved and the lack of symmetry to exploit. Density Functional Theory (DFT) has been considered a simple alternative to obtain ground-state properties for such systems. Usually, DFT starts with a uniform system to build the correlation energy and after implement a local approximation to construct local functionals. Based on our prove of the Hohenberg-Kohn theorem for Heisenberg models, and in order to describe more realistic models, we have recently developed a non-local exchange functional for the ground-state energy of quantum-spin chains. A alternating-bond chain is used to obtain the correlation energy and a local unit-cell approximation - LUCA, is defined in the context of DFT. The alternating chain is a good starting point to construct functionals since it is intrinsically non-homogeneous, therefore instead of the usual local approximation (like LDA for electronic systems) we need to introduce an approximation based upon a unit cell concept, that renders a non-local functional in the bond exchange interaction. The agreement with exact numerical data (obtained only for small chains, although the functional can be applied for chains with arbitrary size) is significantly better than in our previous local formulation, even for chains with several ferromagnetic or antiferromagnetic bond defects. These results encourage us to extend the concept of LUCA for chains with alternating-spin magnitudes. We also have constructed a non-local functional based on an alternating-spin chain, instead of a local alternating-bond, using spin-wave-theory. Because of its non-local nature, this functional is expected to

Efficient linear criterion for witnessing Einstein-Podolsky-Rosen nonlocality under many-setting local measurements

Science.gov (United States)

Zheng, Yu-Lin; Zhen, Yi-Zheng; Chen, Zeng-Bing; Liu, Nai-Le; Chen, Kai; Pan, Jian-Wei

2017-01-01

The striking and distinctive nonlocal features of quantum mechanics were discovered by Einstein, Podolsky, and Rosen (EPR) beyond classical physics. At the core of the EPR argument, it was "steering" that Schrödinger proposed in 1935. Besides its fundamental significance, quantum steering opens up a novel application for quantum communication. Recent work has precisely characterized its properties; however, witnessing the EPR nonlocality remains a big challenge under arbitrary local measurements. Here we present an alternative linear criterion and complement existing results to efficiently testify steering for high-dimensional system in practice. By developing a novel and analytical method to tackle the maximization problem in deriving the bound of a steering criterion, we show how observed correlations can reveal powerfully the EPR nonlocality in an easily accessed manner. Although the criteria is not necessary and sufficient, it can recover some of the known results under a few settings of local measurements and is applicable even if the size of the system or the number of measurement settings are high. Remarkably, a deep connection is explicitly established between the steering and amount of entanglement. The results promise viable paths for secure communication with an untrusted source, providing optional loophole-free tests of the EPR nonlocality for high-dimensional states, as well as motivating solutions for other related problems in quantum information theory.

Nonlocal superelastic model of size-dependent hardening and dissipation in single crystal Cu-Al-Ni shape memory alloys.

Science.gov (United States)

Qiao, Lei; Rimoli, Julian J; Chen, Ying; Schuh, Christopher A; Radovitzky, Raul

2011-02-25

We propose a nonlocal continuum model to describe the size-dependent superelastic effect observed in recent experiments of single crystal Cu-Al-Ni shape memory alloys. The model introduces two length scales, one in the free energy and one in the dissipation, which account for the size-dependent hardening and dissipation in the loading and unloading response of micro- and nanopillars subject to compression tests. The information provided by the model suggests that the size dependence observed in the dissipation is likely to be associated with a nonuniform evolution of the distribution of the austenitic and martensitic phases during the loading cycle. © 2011 American Physical Society

Controllable nonlocal behaviour by cascaded second-harmonic generation of fs pulses

DEFF Research Database (Denmark)

Bache, Morten; Bang, Ole; Krolikowski, Wieslaw

2008-01-01

Second-harmonic generation (SHG) of ultra-short pulses can act as a prototypical nonlocal nonlinear model, since the strength and nature of the temporal nonlocality can be controlled through the phase-mismatch parameter. The presence of a group-velocity mismatch namely implies that when the phase...... mismatch is small the nonlocal response function becomes oscillatory, while for large phase mismatch it becomes localized. In the transition between the two regimes the strength of the nonlocality diverges, and the system goes from a weakly nonlocal to a strongly nonlocal state. When simulating soliton...... compression to few-cycle pulses in the cascaded quadratic soliton compressor, the spectral content of the full coupled SHG model is predicted by the nonlocal model even when few-cycle pulses are interacting....

Tight Bell Inequalities and Nonlocality in Weak Measurement

Science.gov (United States)

Waegell, Mordecai

A general class of Bell inequalities is derived based on strict adherence to probabilistic entanglement correlations observed in nature. This derivation gives significantly tighter bounds on local hidden variable theories for the well-known Clauser-Horne-Shimony-Holt (CHSH) inequality, and also leads to new proofs of the Greenberger-Horne-Zeilinger (GHZ) theorem. This method is applied to weak measurements and reveals nonlocal correlations between the weak value and the post-selection, which rules out various classical models of weak measurement. Implications of these results are discussed. Fetzer-Franklin Fund of the John E. Fetzer Memorial Trust.

Analysis of nonlocal phonon thermal conductivity simulations showing the ballistic to diffusive crossover

Science.gov (United States)

Allen, Philip B.

2018-04-01

Simulations [e.g., X. W. Zhou et al., Phys. Rev. B 79, 115201 (2009), 10.1103/PhysRevB.79.115201] show nonlocal effects of the ballistic/diffusive crossover. The local temperature has nonlinear spatial variation not contained in the local Fourier law j ⃗(r ⃗) =-κ ∇ ⃗T (r ⃗) . The heat current j ⃗(r ⃗) depends not just on the local temperature gradient ∇ ⃗T (r ⃗) but also on temperatures at points r⃗' within phonon mean free paths, which can be micrometers long. This paper uses the Peierls-Boltzmann transport theory in nonlocal form to analyze the spatial variation Δ T (r ⃗) . The relaxation-time approximation (RTA) is used because the full solution is very challenging. Improved methods of extrapolation to obtain the bulk thermal conductivity κ are proposed. Callaway invented an approximate method of correcting RTA for the q ⃗ (phonon wave vector or crystal momentum) conservation of N (Normal as opposed to Umklapp) anharmonic collisions. This method is generalized to the nonlocal case where κ (k ⃗) depends on the wave vector of the current j ⃗(k ⃗) and temperature gradient i k ⃗Δ T (k ⃗) .

Classical and non-classical effective medium theories: New perspectives

International Nuclear Information System (INIS)

Tsukerman, Igor

2017-01-01

Highlights: • Advanced non-asymptotic and nonlocal homogenization theories of metamaterials, valid in electrostatics and electrodynamics. • Classical theories (Clausius–Mossotti, Lorenz–Lorentz, Maxwell Garnett) fit well into the proposed framework. • Nonlocal effects can be included in the model, making order-of-magnitude accuracy improvements possible. • A challenging problem for future research is to determine what effective tensors are attainable for given constituents of a metamaterial. - Abstract: Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius–Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.

Classical and non-classical effective medium theories: New perspectives

Energy Technology Data Exchange (ETDEWEB)

Tsukerman, Igor, E-mail: igor@uakron.edu

2017-05-18

Highlights: • Advanced non-asymptotic and nonlocal homogenization theories of metamaterials, valid in electrostatics and electrodynamics. • Classical theories (Clausius–Mossotti, Lorenz–Lorentz, Maxwell Garnett) fit well into the proposed framework. • Nonlocal effects can be included in the model, making order-of-magnitude accuracy improvements possible. • A challenging problem for future research is to determine what effective tensors are attainable for given constituents of a metamaterial. - Abstract: Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius–Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.

Existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay

Directory of Open Access Journals (Sweden)

V. Vijayakumar

2014-09-01

Full Text Available In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory.

Microscopic theory of light exotic nuclei. Shell Models Embedded in the Continuum

International Nuclear Information System (INIS)

Bennaceur, K.

1999-01-01

The recent advances in experimental nuclear physics make it possible to study nuclear systems far from the beta stability line. The discovery of new phenomena, like halos or neutron skins, requires the development of new theoretical models which enable to study these systems. The first part of this work is devoted to the development and the applications of the Shell Model Embedded in the Continuum (SMEC). This new formalism allows to take into account the correlations between the bound and scattering states of loosely bound nuclei. SMEC is applied here to the study of the spectroscopy of the Mirror nuclei 8 B- 8 Li and 17 F- 17 O. It can also be used to calculate the cross sections of the elastic scattering, the Coulomb breakup processes and the radiative n,p capture processes. The results concerning the reactions of astrophysical interest: 18 O(p, γ) 17 F and 7 Be(p, γ) 8 B, are discussed in details. This last reaction is very important because the disintegration of 8 B is the main source of High energy neutrinos in the sun. The second part of this work is related to the analysis of pairing interaction for weakly bound nuclei. We have developed a new approach, based on the Hartree-Fock-Bogolyubov (HFB) theory, that allows to study the pairing correlations between bound and scattering states, both resonant and not resonant ones. The 'particle-hole' potential is replaced by a model potential for which the solutions are analytically known. This method allows to analyse the effect of pairing on bound and resonant states, independently of their energy position. We have clearly demonstrated that the non-resonant continuum plays a crucial role in the loosely bound nuclei and that solving the HFB equations in the coordinate space is the only method that permits to treat this problem correctly. (author)

Theoretical atomic-force-microscopy study of a stepped surface: Nonlocal effects in the probe

International Nuclear Information System (INIS)

Girard, C.

1991-01-01

The interaction force between a metallic tip and a nonplanar dielectric surface is derived from a nonlocal formalism. A general formulation is given for the case of a spherical tip of nanometer size and for surfaces of arbitrary shapes (stepped surfaces and single crystals adsorbed on a planar surface). The dispersion part of the attractive force is obtained from a nonlocal theory expressed in terms of generalized electric susceptibilities of the two constituents. Implications for atomic force microscopy in attractive modes are discussed. In this context, the present model indicates two different forms of corrugation: those due to the protuberance present on the tip leading to atomic corrugations; nanometer-sized corrugations detected in the attractive region by the spherical part of the tip

Nonlocal plasticity effects on interaction of different size voids

DEFF Research Database (Denmark)

Tvergaard, Viggo; Niordson, Christian Frithiof

2004-01-01

A nonlocal elastic-plastic material model is used to show that the rate of void growth is significantly reduced when the voids are small enough to be comparable with a characteristic material length. For a very small void in the material between much larger voids the competition between...... dimensional array of spherical voids. It is shown that the high growth rate of very small voids predicted by conventional plasticity theory is not realistic when the effect of a characteristic length, dependent on the dislocation structure, is accounted for. (C) 2003 Elsevier Ltd. All rights reserved....

Non-locality versus entanglement in the neutral kaon system

International Nuclear Information System (INIS)

Ableitinger, A.; Bertlmann, R.A.; Durstberger, K.; Hiesmayr, B.C.; Krammer, P.

2006-01-01

Full text: Particle physics has become an interesting testing ground for fundamental questions of quantum mechanics (QM). The entangled massive meson-antimeson systems are specially suitable as they offer a unique laboratory to test various aspects of particle physics (CP violation, CPT violation, . . . ) as well to test foundations of QM (local realistic theories versus QM, Bell inequalities, decoherence effects, quantum marking and erasure concepts, . . . ). For the neutral kaon system we show that nonlocality detected by the violation of a Bell inequality and entanglement are indeed different concepts. (author)

Peridynamics as a rigorous coarse-graining of atomistics for multiscale materials design

International Nuclear Information System (INIS)

Lehoucq, Richard B.; Aidun, John Bahram; Silling, Stewart Andrew; Sears, Mark P.; Kamm, James R.; Parks, Michael L.

2010-01-01

This report summarizes activities undertaken during FY08-FY10 for the LDRD Peridynamics as a Rigorous Coarse-Graining of Atomistics for Multiscale Materials Design. The goal of our project was to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. The goal of our project is to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. Our coarse-graining overcomes the intrinsic limitation of coupling atomistics with classical continuum mechanics via the FEM (finite element method), SPH (smoothed particle hydrodynamics), or MPM (material point method); namely, that classical continuum mechanics assumes a local force interaction that is incompatible with the nonlocal force model of atomistic methods. Therefore FEM, SPH, and MPM inherit this limitation. This seemingly innocuous dichotomy has far reaching consequences; for example, classical continuum mechanics cannot resolve the short wavelength behavior associated with atomistics. Other consequences include spurious forces, invalid phonon dispersion relationships, and irreconcilable descriptions/treatments of temperature. We propose a statistically based coarse-graining of atomistics via peridynamics and so develop a first of a kind mesoscopic capability to enable consistent, thermodynamically sound, atomistic-to-continuum (AtC) multiscale material simulation. Peridynamics (PD) is a microcontinuum theory that assumes nonlocal forces for describing long-range material interaction. The force interactions occurring at finite distances are naturally accounted for in PD. Moreover, PDs nonlocal force model is entirely consistent with those used by atomistics methods, in stark contrast to classical continuum mechanics. Hence, PD can be employed for mesoscopic phenomena that are beyond the realms of classical continuum mechanics and

Microscopic optical potentials derived from ab initio translationally invariant nonlocal one-body densities

Science.gov (United States)

Gennari, Michael; Vorabbi, Matteo; Calci, Angelo; Navrátil, Petr

2018-03-01

Background: The nuclear optical potential is a successful tool for the study of nucleon-nucleus elastic scattering and its use has been further extended to inelastic scattering and other nuclear reactions. The nuclear density of the target nucleus is a fundamental ingredient in the construction of the optical potential and thus plays an important role in the description of the scattering process. Purpose: In this paper we derive a microscopic optical potential for intermediate energies using ab initio translationally invariant nonlocal one-body nuclear densities computed within the no-core shell model (NCSM) approach utilizing two- and three-nucleon chiral interactions as the only input. Methods: The optical potential is derived at first order within the spectator expansion of the nonrelativistic multiple scattering theory by adopting the impulse approximation. Nonlocal nuclear densities are derived from the NCSM one-body densities calculated in the second quantization. The translational invariance is generated by exactly removing the spurious center-of-mass (COM) component from the NCSM eigenstates. Results: The ground-state local and nonlocal densities of He 4 ,6 ,8 , 12C, and 16O are calculated and applied to optical potential construction. The differential cross sections and the analyzing powers for the elastic proton scattering off these nuclei are then calculated for different values of the incident proton energy. The impact of nonlocality and the COM removal is discussed. Conclusions: The use of nonlocal densities has a substantial impact on the differential cross sections and improves agreement with experiment in comparison to results generated with the local densities especially for light nuclei. For the halo nuclei 6He and 8He, the results for the differential cross section are in a reasonable agreement with the data although a more sophisticated model for the optical potential is required to properly describe the analyzing powers.

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

OpenAIRE

Nigg, Simon E.; Tiwari, Rakesh P.; Walter, Stefan; Schmidt, Thomas L.

2014-01-01

Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the produced photon pairs can be used to violate a Bell inequality, unambiguo...

Spiraling solitons and multipole localized modes in nonlocal nonlinear media

International Nuclear Information System (INIS)

Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.; Bang, Ole; Krolikowski, Wieslaw; Kivshar, Yuri S.

2007-01-01

We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form

Spiralling solitons and multipole localized modes in nonlocal nonlinear media

DEFF Research Database (Denmark)

Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan

2007-01-01

We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form....

Prediction of Reduction Potentials of Copper Proteins with Continuum Electrostatics and Density Functional Theory.

Science.gov (United States)

Fowler, Nicholas J; Blanford, Christopher F; Warwicker, Jim; de Visser, Sam P

2017-11-02

Blue copper proteins, such as azurin, show dramatic changes in Cu 2+ /Cu + reduction potential upon mutation over the full physiological range. Hence, they have important functions in electron transfer and oxidation chemistry and have applications in industrial biotechnology. The details of what determines these reduction potential changes upon mutation are still unclear. Moreover, it has been difficult to model and predict the reduction potential of azurin mutants and currently no unique procedure or workflow pattern exists. Furthermore, high-level computational methods can be accurate but are too time consuming for practical use. In this work, a novel approach for calculating reduction potentials of azurin mutants is shown, based on a combination of continuum electrostatics, density functional theory and empirical hydrophobicity factors. Our method accurately reproduces experimental reduction potential changes of 30 mutants with respect to wildtype within experimental error and highlights the factors contributing to the reduction potential change. Finally, reduction potentials are predicted for a series of 124 new mutants that have not yet been investigated experimentally. Several mutants are identified that are located well over 10 Å from the copper center that change the reduction potential by more than 85 mV. The work shows that secondary coordination sphere mutations mostly lead to long-range electrostatic changes and hence can be modeled accurately with continuum electrostatics. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Nonlocal non-Markovian effects in dephasing environments

International Nuclear Information System (INIS)

Xie Dong; Wang An-Min

2014-01-01

We study the nonlocal non-Markovian effects through local interactions between two subsystems and the corresponding two environments. It has been found that the initial correlations between two environments can turn a Markovian to a non-Markovian regime with extra control on the local interaction time. We further research the nonlocal non-Markovian effects from two situations: without extra control, the nonlocal non-Markovian effects only appear under the condition that two local dynamics are non-Markovian–non-Markovian (both of the two local dynamics are non-Markovian) or Markovian–non-Markovian, but not under the condition of Markovian–Markovian; with extra control, the nonlocal non-Markovian effects can occur under the condition of Markovian–Markovian. It shows that the function of correlations between two environments has an upper bound, which makes a flow of information from the environment back to the global system beginning finitely earlier than that back to one of the two local systems, not infinitely. Then, we proposed two special ways to distribute classical correlations between two environments without initial correlations. Finally, from numerical solutions in the spin star configuration, we found that the self-correlation (internal correlation) of each environment promotes the nonlocal non-Markovian effects. (general)

Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model

Energy Technology Data Exchange (ETDEWEB)

Ghorbanpour Arani, A., E-mail: aghorban@kashanu.ac.ir [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of); Institute of Nanoscience and Nanotechnology, University of Kashan, Kashan (Iran, Islamic Republic of); Zarei, M.Sh.; Amir, S.; Khoddami Maraghi, Z. [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of)

2013-02-01

In this work nonlinear vibration of double-walled carbon nanotube (DWCNT) embedded in an elastic medium and subjected to an axial fluid flow (incompressible and non-viscose) is investigated. The elastic medium is simulated using Pasternak foundation in which adjacent layer interactions are assumed to have been coupled by van der Waals (VdW) force. The higher-order equation of motion is derived using Hamilton's principle and nonlocal-nonlinear shell theory. Galerkin and averaging methods are adopted to solve the higher-order governing equations. Elastic medium, small scale parameter, velocity and fluid density are taken into account to calculate the effects of axial and circumferential wave numbers in this study. Results reveal that increasing circumferential wave number, leads to enhanced nonlinearity. Critical flow velocities of DWCNT are inversely related to the non-local parameter (e{sub 0}a), so that increase in the later lead to reduced critical flow velocities.

Revival of the Deser-Woodard nonlocal gravity model: Comparison of the original nonlocal form and a localized formulation

Science.gov (United States)

Park, Sohyun

2018-02-01

We examine the origin of two opposite results for the growth of perturbations in the Deser-Woodard (DW) nonlocal gravity model. One group previously analyzed the model in its original nonlocal form and showed that the growth of structure in the DW model is enhanced compared to general relativity (GR) and thus concluded that the model was ruled out. Recently, however, another group has reanalyzed it by localizing the model and found that the growth in their localized version is suppressed even compared to the one in GR. The question was whether the discrepancy originates from an intrinsic difference between the nonlocal and localized formulations or is due to their different implementations of the subhorizon limit. We show that the nonlocal and local formulations give the same solutions for the linear perturbations as long as the initial conditions are set the same. The different implementations of the subhorizon limit lead to different transient behaviors of some perturbation variables; however, they do not affect the growth of matter perturbations at the sub-horizon scale much. In the meantime, we also report an error in the numerical calculation code of the former group and verify that after fixing the error the nonlocal version also gives the suppressed growth. Finally, we discuss two alternative definitions of the effective gravitational constant taken by the two groups and some open problems.

Size-dependent nonlocal effects in plasmonic semiconductor particles

DEFF Research Database (Denmark)

Maack, Johan Rosenkrantz; Mortensen, N. Asger; Wubs, Martijn

2017-01-01

Localized surface plasmons (LSP) in semiconductor particles are expected to exhibit spatial nonlocal response effects as the geometry enters the nanometer scale. To investigate these nonlocal effects, we apply the hydrodynamic model to nanospheres of two different semiconductor materials: intrinsic...... InSb and n-doped GaAs. Our results show that the semiconductors indeed display nonlocal effects, and that these effects are even more pronounced than in metals. In a 150 nm InSb particle at 300 K, the LSP frequency is blueshifted 35%, which is orders of magnitude larger than the blueshift in a metal...... particle of the same size. This property, together with their tunability, makes semiconductors a promising platform for experiments in nonlocal effects. Copyright (C)EPLA, 2017...

Is Quantum Gravity a Super-Quantum Theory?

OpenAIRE

Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; Takeuchi, Tatsu

2013-01-01

We argue that quantum gravity should be a super-quantum theory, that is, a theory whose non-local correlations are stronger than those of canonical quantum theory. As a super-quantum theory, quantum gravity should display distinct experimentally observable super-correlations of entangled stringy states.

The quantum and the continuum : Einstein's dichotomous legacies

International Nuclear Information System (INIS)

Majumdar, Parthasarathi

2015-01-01

This talk begins with a summary of some of Einstein's seminal contributions in the quantum domain, like Brownian motion and the Light Quantum Hypothesis, as well as on the spacetime continuum enshrined in the theories of special and general relativity. Following up on Einstein's rationale for postulating the Light Quantum Hypothesis, we attempt to point to a possible dichotomy in his thinking about these two legacies of his, which may have been noticed by him, but was not much discussed by him in the public domain. One may speculate that this may have had something to do with his well-known distaste for the probability interpretation of quantum mechanics as a fundamental interpretation. We argue that Einstein's general relativity theory itself contains the seeds of a dramatic modification of our ideas of the Einsteinian spacetime continuum, thus underlining the dichotomy even more strongly. We then survey one modern attempt to resolve the dichotomy, at least partly, by bringing into the spacetime continuum, aspects of quantum mechanics with its underlying statistical interpretation, an approach which Einstein may not have whole-heartedly endorsed, but which seems to work so far, with good prospects for the future. (author)

YM2: Continuum expectations, lattice convergence, and lassos

International Nuclear Information System (INIS)

Driver, B.K.

1989-01-01

The two dimensional Yang-Mills theory (YM 2 ) is analyzed in both the continuum and the lattice. In the complete axial gauge the continuum theory may be defined in terms of a Lie algebra valued white noise, and parallel translation may be defined by stochastic differential equations. This machinery is used to compute the expectations of gauge invariant functions of the parallel translation operators along a collection of curves C. The expectation values are expressed as finite dimensional integrals with densities that are products of the heat kernel on the structure group. The time parameters of the heat kernels are determined by the areas enclosed by the collection C, and the arguments are determined by the crossing topologies of the curves in C. The expectations for the Wilson lattice models have a similar structure, and from this it follows that in the limit of small lattice spacing the lattice expectations converge to the continuum expectations. It is also shown that the lasso variables advocated by L. Gross exist and are sufficient to generate all the measurable functions on the YM 2 -measure space. (orig.)

Localized solutions for a nonlocal discrete NLS equation

International Nuclear Information System (INIS)

Ben, Roberto I.; Cisneros Ake, Luís; Minzoni, A.A.; Panayotaros, Panayotis

2015-01-01

We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces

Localized solutions for a nonlocal discrete NLS equation

Energy Technology Data Exchange (ETDEWEB)

Ben, Roberto I. [Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, 1613 Los Polvorines (Argentina); Cisneros Ake, Luís [Department of Mathematics, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 México D.F. (Mexico); Minzoni, A.A. [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico); Panayotaros, Panayotis, E-mail: panos@mym.iimas.unam.mx [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico)

2015-09-04

We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces.

A far wing line shape theory and its application to the foreign-broadened water continuum absorption. III

Science.gov (United States)

Ma, Q.; Tipping, R. H.

1992-01-01

The far wing line shape theory developed previously and applied to the calculation of the continuum absorption of pure water vapor is extended to foreign-broadened continua. Explicit results are presented for H2O-N2 and H2O-CO2 in the frequency range from 0 to 10,000/cm. For H2O-N2 the positive and negative resonant frequency average line shape functions and absorption coefficients are computed for a number of temperatures between 296 and 430 K for comparison with available laboratory data. In general the agreement is very good.

Experimental nonlocal steering of Bohmian trajectories.

Science.gov (United States)

Xiao, Ya; Kedem, Yaron; Xu, Jin-Shi; Li, Chuan-Feng; Guo, Guang-Can

2017-06-26

Interpretations of quantum mechanics (QM), or proposals for underlying theories, that attempt to present a definite realist picture, such as Bohmian mechanics, require strong non-local effects. Naively, these effects would violate causality and contradict special relativity. However if the theory agrees with QM the violation cannot be observed directly. Here, we demonstrate experimentally such an effect: we steer the velocity and trajectory of a Bohmian particle using a remote measurement. We use a pair of photons and entangle the spatial transverse position of one with the polarization of the other. The first photon is sent to a double-slit-like apparatus, where its trajectory is measured using the technique of Weak Measurements. The other photon is projected to a linear polarization state. The choice of polarization state, and the result, steer the first photon in the most intuitive sense of the word. The effect is indeed shown to be dramatic, while being easy to visualize. We discuss its strength and what are the conditions for it to occur.

Asymmetric continuum extreme processes in solids and fluids

CERN Document Server

Teisseyre, Roman

2014-01-01

This book deals with a class of basic deformations in asymmetric continuum theory. It describes molecular deformations and transport velocities in fluids, strain deformations in solids as well as the molecular transport, important in fracture processes.

The quantum handshake entanglement, nonlocality and transactions

CERN Document Server

Cramer, John G

2016-01-01

This book shines bright light into the dim recesses of quantum theory, where the mysteries of entanglement, nonlocality, and wave collapse have motivated some to conjure up multiple universes, and others to adopt a "shut up and calculate" mentality. After an extensive and accessible introduction to quantum mechanics and its history, the author turns attention to his transactional model. Using a quantum handshake between normal and time-reversed waves, this model provides a clear visual picture explaining the baffling experimental results that flow daily from the quantum physics laboratories of the world. To demonstrate its powerful simplicity, the transactional model is applied to a collection of counter-intuitive experiments and conceptual problems.

Relativistic continuum random phase approximation in spherical nuclei

International Nuclear Information System (INIS)

Daoutidis, Ioannis

2009-01-01

Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)

Relativistic continuum random phase approximation in spherical nuclei

Energy Technology Data Exchange (ETDEWEB)

Daoutidis, Ioannis

2009-10-01

Covariant density functional theory is used to analyze the nuclear response in the external multipole fields. The investigations are based on modern functionals with zero range and density dependent coupling constants. After a self-consistent solution of the Relativistic Mean Field (RMF) equations for the nuclear ground states multipole giant resonances are studied within the Relativistic Random Phase Approximation (RRPA), the small amplitude limit of the time-dependent RMF. The coupling to the continuum is treated precisely by calculating the single particle Greens-function of the corresponding Dirac equation. In conventional methods based on a discretization of the continuum this was not possible. The residual interaction is derived from the same RMF Lagrangian. This guarantees current conservation and a precise decoupling of the Goldstone modes. For nuclei with open shells pairing correlations are taken into account in the framework of BCS theory and relativistic quasiparticle RPA. Continuum RPA (CRPA) presents a robust method connected with an astonishing reduction of the numerical effort as compared to conventional methods. Modes of various multipolarities and isospin are investigated, in particular also the newly discovered Pygmy modes in the vicinity of the neutron evaporation threshold. The results are compared with conventional discrete RPA calculations as well as with experimental data. We find that the full treatment of the continuum is essential for light nuclei and the study of resonances in the neighborhood of the threshold. (orig.)

Numerical fluid solutions for nonlocal electron transport in hot plasmas: Equivalent diffusion versus nonlocal source

International Nuclear Information System (INIS)

Colombant, Denis; Manheimer, Wallace

2010-01-01

Flux limitation and preheat are important processes in electron transport occurring in laser produced plasmas. The proper calculation of both of these has been a subject receiving much attention over the entire lifetime of the laser fusion project. Where nonlocal transport (instead of simple single flux limit) has been modeled, it has always been with what we denote the equivalent diffusion solution, namely treating the transport as only a diffusion process. We introduce here a new approach called the nonlocal source solution and show it is numerically viable for laser produced plasmas. It turns out that the equivalent diffusion solution generally underestimates preheat. Furthermore, the advance of the temperature front, and especially the preheat, can be held up by artificial 'thermal barriers'. The nonlocal source method of solution, on the other hand more accurately describes preheat and can stably calculate the solution for the temperature even if the heat flux is up the gradient.

A non-local shell model of hydrodynamic and magnetohydrodynamic turbulence

Energy Technology Data Exchange (ETDEWEB)

Plunian, F [Laboratoire de Geophysique Interne et Tectonophysique, CNRS, Universite Joseph Fourier, Maison des Geosciences, BP 53, 38041 Grenoble Cedex 9 (France); Stepanov, R [Institute of Continuous Media Mechanics, Korolyov 1, 614013 Perm (Russian Federation)

2007-08-15

We derive a new shell model of magnetohydrodynamic (MHD) turbulence in which the energy transfers are not necessarily local. Like the original MHD equations, the model conserves the total energy, magnetic helicity, cross-helicity and volume in phase space (Liouville's theorem) apart from the effects of external forcing, viscous dissipation and magnetic diffusion. The model of hydrodynamic (HD) turbulence is derived from the MHD model setting the magnetic field to zero. In that case the conserved quantities are the kinetic energy and the kinetic helicity. In addition to a statistically stationary state with a Kolmogorov spectrum, the HD model exhibits multiscaling. The anomalous scaling exponents are found to depend on a free parameter {alpha} that measures the non-locality degree of the model. In freely decaying turbulence, the infra-red spectrum also depends on {alpha}. Comparison with theory suggests using {alpha} = -5/2. In MHD turbulence, we investigate the fully developed turbulent dynamo for a wide range of magnetic Prandtl numbers in both kinematic and dynamic cases. Both local and non-local energy transfers are clearly identified.

The Asymptotic Expansion of Lattice Loop Integrals Around the Continuum Limit

International Nuclear Information System (INIS)

Becher, Thomas G

2002-01-01

We present a method of computing any one-loop integral in lattice perturbation theory by systematically expanding around its continuum limit. At any order in the expansion in the lattice spacing, the result can be written as a sum of continuum loop integrals in analytic regularization and a few genuine lattice integrals (''master integrals''). These lattice master integrals are independent of external momenta and masses and can be computed numerically. At the one-loop level, there are four master integrals in a theory with only bosonic fields, seven in HQET and sixteen in QED or QCD with Wilson fermions

Nonlocality, no-signalling, and Bellʼs theorem investigated by Weyl conformal differential geometry

Science.gov (United States)

De Martini, Francesco; Santamato, Enrico

2014-12-01

The principles and methods of conformal quantum geometrodynamics based on Weyl differential geometry are presented. The theory applied to the case of the relativistic single quantum spin-\\frac{1}{2} leads to a novel and unconventional derivation of the Dirac equation. The further extension of the theory to the case of two-spins-\\frac{1}{2} in the EPR entangled state and to the related violation of Bell inequalities leads, by an exact non-relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality.

Nonlocality, no-signalling, and Bell's theorem investigated by Weyl conformal differential geometry

International Nuclear Information System (INIS)

Martini, Francesco De; Santamato, Enrico

2014-01-01

The principles and methods of conformal quantum geometrodynamics based on Weyl differential geometry are presented. The theory applied to the case of the relativistic single quantum spin-(1/2) leads to a novel and unconventional derivation of the Dirac equation. The further extension of the theory to the case of two-spins-(1/2) in the EPR entangled state and to the related violation of Bell inequalities leads, by an exact non-relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality. (paper)

Medical education and cognitive continuum theory: an alternative perspective on medical problem solving and clinical reasoning.

Science.gov (United States)

Custers, Eugène J F M

2013-08-01

Recently, human reasoning, problem solving, and decision making have been viewed as products of two separate systems: "System 1," the unconscious, intuitive, or nonanalytic system, and "System 2," the conscious, analytic, or reflective system. This view has penetrated the medical education literature, yet the idea of two independent dichotomous cognitive systems is not entirely without problems.This article outlines the difficulties of this "two-system view" and presents an alternative, developed by K.R. Hammond and colleagues, called cognitive continuum theory (CCT). CCT is featured by three key assumptions. First, human reasoning, problem solving, and decision making can be arranged on a cognitive continuum, with pure intuition at one end, pure analysis at the other, and a large middle ground called "quasirationality." Second, the nature and requirements of the cognitive task, as perceived by the person performing the task, determine to a large extent whether a task will be approached more intuitively or more analytically. Third, for optimal task performance, this approach needs to match the cognitive properties and requirements of the task. Finally, the author makes a case that CCT is better able than a two-system view to describe medical problem solving and clinical reasoning and that it provides clear clues for how to organize training in clinical reasoning.

Causality and local determinism versus quantum nonlocality

International Nuclear Information System (INIS)

Kupczynski, M

2014-01-01

The entanglement and the violation of Bell and CHSH inequalities in spin polarization correlation experiments (SPCE) is considered to be one of the biggest mysteries of Nature and is called quantum nonlocality. In this paper we show once again that this conclusion is based on imprecise terminology and on the lack of understanding of probabilistic models used in various proofs of Bell and CHSH theorems. These models are inconsistent with experimental protocols used in SPCE. This is the only reason why Bell and CHSH inequalities are violated. A probabilistic non-signalling description of SPCE, consistent with quantum predictions, is possible and it depends explicitly on the context of each experiment. It is also deterministic in the sense that the outcome is determined by supplementary local parameters describing both physical signals and measuring instruments. The existence of such description gives additional arguments that quantum theory is emergent from some more detailed theory respecting causality and local determinism. If quantum theory is emergent then there exist perhaps some fine structures in time-series of experimental data which were not predicted by quantum theory. In this paper we explain how a systematic search for such fine structures can be done. If such reproducible fine structures were found it would show that quantum theory is not predictably complete, which would be a major discovery.

Gradient Models in Molecular Biophysics: Progress, Challenges, Opportunities.

Science.gov (United States)

Bardhan, Jaydeep P

2013-12-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g. molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding features such as nonlocal dielectric response, and nonlinearities resulting from dielectric saturation. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost forty years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The paper concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics.

Gradient Models in Molecular Biophysics: Progress, Challenges, Opportunities

Science.gov (United States)

Bardhan, Jaydeep P.

2014-01-01

In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g. molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding features such as nonlocal dielectric response, and nonlinearities resulting from dielectric saturation. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost forty years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The paper concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics. PMID:25505358

Construction of local and non-local conservation laws for non-linear field equations

International Nuclear Information System (INIS)

Vladimirov, V.S.; Volovich, I.V.

1984-08-01

A method of constructing conserved currents for non-linear field equations is presented. More explicitly for non-linear equations, which can be derived from compatibility conditions of some linear system with a parameter, a procedure of obtaining explicit expressions for local and non-local currents is developed. Some examples such as the classical Heisenberg spin chain and supersymmetric Yang-Mills theory are considered. (author)

Investigation on plasmonic responses in multilayered nanospheres including asymmetry and spatial nonlocal effects

Science.gov (United States)

Dong, Tianyu; Shi, Yi; Liu, Hui; Chen, Feng; Ma, Xikui; Mittra, Raj

2017-12-01

In this work, we present a rigorous approach for analyzing the optical response of multilayered spherical nano-particles comprised of either plasmonic metal or dielectric, when there is no longer radial symmetry and when nonlocality is included. The Lorenz-Mie theory is applied, and a linearized hydrodynamic Drude model as well as the general nonlocal optical response model for the metals are employed. Additional boundary conditions, viz., the continuity of normal components of polarization current density and the continuity of first-order pressure of free electron density, respectively, are incorporated when handling interfaces involving metals. The application of spherical addition theorems, enables us to express a spherical harmonic about one origin to spherical harmonics about a different origin, and leads to a linear system of equations for the inward- and outward-field modal coefficients for all the layers in the nanoparticle. Scattering matrices at interfaces are obtained and cascaded to obtain the expansion coefficients, to yield the final solution. Through extensive modelling of stratified concentric and eccentric metal-involved spherical nanoshells illuminating by a plane wave, we show that, within a nonlocal description, significant modifications of plasmonic response appear, e.g. a blue-shift in the extinction / scattering spectrum and a broadening spectrum of the resonance. In addition, it has been demonstrated that core-shell nanostructures provide an option for tunable Fano-resonance generators. The proposed method shows its capability and flexibility to analyze the nonlocal response of eccentric hybrid metal-dielectric multilayer structures as well as adjoined metal-involved nanoparticles, even when the number of layers is large.

Wave propagation in fluid-conveying viscoelastic carbon nanotubes under longitudinal magnetic field with thermal and surface effect via nonlocal strain gradient theory

Science.gov (United States)

Zhen, Yaxin; Zhou, Lin

2017-03-01

Based on nonlocal strain gradient theory, wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes (SWCNTs) is studied in this paper. With consideration of thermal effect and surface effect, wave equation is derived for fluid-conveying viscoelastic SWCNTs under longitudinal magnetic field utilizing Euler-Bernoulli beam theory. The closed-form expressions are derived for the frequency and phase velocity of the wave motion. The influences of fluid flow velocity, structural damping coefficient, temperature change, magnetic flux and surface effect are discussed in detail. SWCNTs’ viscoelasticity reduces the wave frequency of the system and the influence gets remarkable with the increase of wave number. The fluid in SWCNTs decreases the frequency of wave propagation to a certain extent. The frequency (phase velocity) gets larger due to the existence of surface effect, especially when the diameters of SWCNTs and the wave number decrease. The wave frequency increases with the increase of the longitudinal magnetic field, while decreases with the increase of the temperature change. The results may be helpful for better understanding the potential applications of SWCNTs in nanotechnology.

Sign-changing solutions for non-local elliptic equations

Directory of Open Access Journals (Sweden)

Huxiao Luo

2017-07-01

Full Text Available This article concerns the existence of sign-changing solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet boundary conditions, $$\\displaylines{ -\\mathcal{L}_Ku=f(x,u,\\quad x\\in \\Omega, \\cr u=0,\\quad x\\in \\mathbb{R}^n\\setminus\\Omega, }$$ where $\\Omega\\subset\\mathbb{R}^n\\; (n\\geq2$ is a bounded, smooth domain and the nonlinear term f satisfies suitable growth assumptions. By using Brouwer's degree theory and Deformation Lemma and arguing as in [2], we prove that there exists a least energy sign-changing solution. Our results generalize and improve some results obtained in [27

Specker's parable of the overprotective seer: A road to contextuality, nonlocality and complementarity

International Nuclear Information System (INIS)

Liang, Yeong-Cherng; Spekkens, Robert W.; Wiseman, Howard M.

2011-01-01

In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations, the counter-intuitive features of which he dramatized using a parable about a seer, who sets an impossible prediction task to his daughter's suitors. We revisit this example here, using it as an entree to three central concepts in quantum foundations: contextuality, Bell-nonlocality, and complementarity. Specifically, we show that Specker's parable offers a narrative thread that weaves together a large number of results, including the following: the impossibility of measurement-noncontextual and outcome-deterministic ontological models of quantum theory (the 1967 Kochen-Specker theorem), in particular, the recent state-specific pentagram proof of Klyachko; the impossibility of Bell-local models of quantum theory (Bell's theorem), especially the proofs by Mermin and Hardy and extensions thereof; the impossibility of a preparation-noncontextual ontological model of quantum theory; the existence of triples of positive operator valued measures (POVMs) that can be measured jointly pairwise but not triplewise. Along the way, several novel results are presented: a generalization of a theorem by Fine connecting the existence of a joint distribution over outcomes of counterfactual measurements to the existence of a measurement-noncontextual and outcome-deterministic ontological model; a generalization of Klyachko's proof of the Kochen-Specker theorem from pentagrams to a family of star polygons; a proof of the Kochen-Specker theorem in the style of Hardy's proof of Bell's theorem (i.e., one that makes use of the failure of the transitivity of implication for counterfactual statements); a categorization of contextual and Bell-nonlocal correlations in terms of frustrated networks; a derivation of a new inequality testing preparation noncontextuality; some novel results on the joint measurability of POVMs and the question of whether these can be modeled noncontextually. Finally

Derivation of Electromagnetism from the Elastodynamics of the Spacetime Continuum

Directory of Open Access Journals (Sweden)

Millette P. A.

2013-04-01

Full Text Available We derive Electromagnetism from the Elastodynamics of the Spacetime Continuum based on the identification of the theory’s antisymmetric rotation tensor with the elec- tromagnetic field-strength tensor. The theory provides a physical explanation of the electromagnetic potential, which arises from transverse ( shearing displacements of the spacetime continuum, in contrast to mass which arises from longitudinal (dilatational displacements. In addition, the theory provides a physical explanation of the current density four-vector, as the 4-gradient of the volume dilatation of the spacetime con- tinuum. The Lorentz condition is obtained directly from the theory. In addition, we obtain a generalization of Electromagnetism for the situation where a volume force is present, in the general non-macroscopic case. Maxwell’s equations are found to remain unchanged, but the current density has an additional term proportional to the volume force.

Frequency chirpings in Alfven continuum

Science.gov (United States)

Wang, Ge; Berk, Herb; Breizman, Boris; Zheng, Linjin

2017-10-01

We have used a self-consistent mapping technique to describe both the nonlinear wave-energetic particle resonant interaction and its spatial mode structure that depends upon the resonant energetic particle pressure. At the threshold for the onset of the energetic particle mode (EPM), strong chirping emerges in the lower continuum close to the TAE gap and then, driven by strong continuum damping, chirps rapidly to lower frequencies in the Alfven continuum. An adiabatic theory was developed that accurately replicated the results from the simulation where the nonlinearity was only due to the EPM resonant particles. The results show that the EPM-trapped particles have their action conserved during the time of rapid chirping. This adiabaticity enabled wave trapped particles to be confined within their separatrix, and produce even larger resonant structures, that can produce a large amplitude mode far from linearly predicted frequencies. In the present work we describe the effect of additional MHD nonlinearity to this calculation. We studied how the zonal flow component and its nonlinear feedback to the fundamental frequency and found that the MHD nonlinearity doesn't significantly alter the frequency chirping response that is predicted by the calculation that neglects the MHD nonlinearity.

Energy dependence of nonlocal optical potentials

Science.gov (United States)

Lovell, A. E.; Bacq, P.-L.; Capel, P.; Nunes, F. M.; Titus, L. J.

2017-11-01

Recently, a variety of studies have shown the importance of including nonlocality in the description of reactions. The goal of this work is to revisit the phenomenological approach to determining nonlocal optical potentials from elastic scattering. We perform a χ2 analysis of neutron elastic scattering data off 40Ca, 90Zr, and 208Pb at energies E ≈5 -40 MeV, assuming a Perey and Buck [Nucl. Phys. 32, 353 (1962), 10.1016/0029-5582(62)90345-0] or Tian et al. [Int. J. Mod. Phys. E 24, 1550006 (2015), 10.1142/S0218301315500068] nonlocal form for the optical potential. We introduce energy and asymmetry dependencies in the imaginary part of the potential and refit the data to obtain a global parametrization. Independently of the starting point in the minimization procedure, an energy dependence in the imaginary depth is required for a good description of the data across the included energy range. We present two parametrizations, both of which represent an improvement over the original potentials for the fitted nuclei as well as for other nuclei not included in our fit. Our results show that, even when including the standard Gaussian nonlocality in optical potentials, a significant energy dependence is required to describe elastic-scattering data.

On a non-local gas dynamics like integrable hierarchy

International Nuclear Information System (INIS)

Brunelli, Jose Carlos; Das, Ashok

2004-01-01

We study a new hierarchy of equations derived from the system of isentropic gas dynamics equations where the pressure is a non-local function of the density. We show that the hierarchy of equations is integrable. We construct the two compatible Hamiltonian structures and show that the first structure has three distinct Casimirs while the second has one. The existence of Casimirs allows us to extend the flows to local ones. We construct an infinite series of commuting local Hamiltonians as well as three infinite series (related to the three Casimirs) of non-local charges. We discuss the zero curvature formulation of the system where we obtain a simple expression for the non-local conserved charges, which also clarifies the existence of the three series from a Lie algebraic point of view. We point out that the non-local hierarchy of Hunter-Zheng equations can be obtained from our non-local flows when the dynamical variables are properly constrained. (author)

Protecting nonlocality of multipartite states by feed-forward control

Science.gov (United States)

Li, Xiao-Gang; Zou, Jian; Shao, Bin

2018-06-01

Nonlocality is a useful resource in quantum communication and quantum information processing. In practical quantum communication, multipartite entangled states must be distributed between different users in different places through a channel. However, the channel is usually inevitably disturbed by the environment in quantum state distribution processing and then the nonlocality of states will be weakened and even lost. In this paper, we use a feed-forward control scheme to protect the nonlocality of the Bell and GHZ states against dissipation. We find that this protection scheme is very effective, specifically, for the Bell state, we can increase the noise threshold from 0.5 to 0.98, and for GHZ state from 0.29 to 0.96. And we also find that entanglement is relatively easier to be protected than nonlocality. For our scheme, protecting entanglement is equivalent to protecting the state in the case of Bell state, while protecting nonlocality is not.

Time-nonlocal kinetic equations, jerk and hyperjerk in plasmas and solar physics

Science.gov (United States)

El-Nabulsi, Rami Ahmad

2018-06-01

The simulation and analysis of nonlocal effects in fluids and plasmas is an inherently complicated problem due to the massive breadth of physics required to describe the nonlocal dynamics. This is a multi-physics problem that draws upon various miscellaneous fields, such as electromagnetism and statistical mechanics. In this paper we strive to focus on one narrow but motivating mathematical way: the derivation of nonlocal plasma-fluid equations from a generalized nonlocal Liouville derivative operator motivated from Suykens's nonlocal arguments. The paper aims to provide a guideline toward modeling nonlocal effects occurring in plasma-fluid systems by means of a generalized nonlocal Boltzmann equation. The generalized nonlocal equations of fluid dynamics are derived and their implications in plasma-fluid systems are addressed, discussed and analyzed. Three main topics were discussed: Landau damping in plasma electrodynamics, ideal MHD and solar wind. A number of features were revealed, analyzed and confronted with recent research results and observations.

Skin cancer interventions across the cancer control continuum: Review of technology, environment, and theory.

Science.gov (United States)

Taber, Jennifer M; Dickerman, Barbra A; Okhovat, Jean-Phillip; Geller, Alan C; Dwyer, Laura A; Hartman, Anne M; Perna, Frank M

2018-06-01

The National Cancer Institute's Skin Cancer Intervention across the Cancer Control Continuum model was developed to summarize research and identify gaps concerning skin cancer interventions. We conducted a mapping review to characterize whether behavioral interventions addressing skin cancer prevention and control from 2000 to 2015 included (1) technology, (2) environmental manipulations (policy and/or built environment), and (3) a theoretical basis. We included 86 studies with a randomized controlled or quasi-experimental design that targeted behavioral intervention in skin cancer for children and/or adults; seven of these were dissemination or implementation studies. Of the interventions described in the remaining 79 articles, 57 promoted only prevention behaviors (e.g., ultraviolet radiation protection), five promoted only detection (e.g., skin examinations), 10 promoted both prevention and detection, and seven focused on survivorship. Of the 79 non-dissemination studies, two-thirds used some type of technology (n=52; 65.8%). Technology specific to skin cancer was infrequently used: UVR photography was used in 15.2% of studies (n=12), reflectance spectroscopy was used in 12.7% (n=10), and dermatoscopes (n=1) and dosimeters (n=2) were each used in less than 3%. Ten studies (12.7%) targeted the built environment. Fifty-two (65.8%) of the studies included theory-based interventions. The most common theories were Social Cognitive Theory (n=20; 25.3%), Health Belief Model (n=17; 21.5%), and the Theory of Planned Behavior/Reasoned Action (n=12; 15.2%). Results suggest that skin cancer specific technology and environmental manipulations are underutilized in skin cancer behavioral interventions. We discuss implications of these results for researchers developing skin cancer behavioral interventions. Copyright © 2017. Published by Elsevier Inc.

NLOM - a program for nonlocal optical model calculations

International Nuclear Information System (INIS)

Kim, B.T.; Kyum, M.C.; Hong, S.W.; Park, M.H.; Udagawa, T.

1992-01-01

A FORTRAN program NLOM for nonlocal optical model calculations is described. It is based on a method recently developed by Kim and Udagawa, which utilizes the Lanczos technique for solving integral equations derived from the nonlocal Schroedinger equation. (orig.)

Continuum-level modelling of cellular adhesion and matrix production in aggregates.

Science.gov (United States)

Geris, Liesbet; Ashbourn, Joanna M A; Clarke, Tim

2011-05-01

Key regulators in tissue-engineering processes such as cell culture and cellular organisation are the cell-cell and cell-matrix interactions. As mathematical models are increasingly applied to investigate biological phenomena in the biomedical field, it is important, for some applications, that these models incorporate an adequate description of cell adhesion. This study describes the development of a continuum model that represents a cell-in-gel culture system used in bone-tissue engineering, namely that of a cell aggregate embedded in a hydrogel. Cell adhesion is modelled through the use of non-local (integral) terms in the partial differential equations. The simulation results demonstrate that the effects of cell-cell and cell-matrix adhesion are particularly important for the survival and growth of the cell population and the production of extracellular matrix by the cells, concurring with experimental observations in the literature.

Black hole information, unitarity, and nonlocality

OpenAIRE

Giddings, Steven B.

2006-01-01

The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. The leading contender is nonlocality. Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. Suggestions that such dynamics arises from ultra-planckian modes in Hawking's derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. However, no simul...

Non-classical continuum mechanics a dictionary

CERN Document Server

Maugin, Gérard A

2017-01-01

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, every entry is followed by a cross-reference to other related subject entries in the dictionary.

Quantum non-locality and relativity metaphysical intimations of modern physics

CERN Document Server

Maudlin, Tim

2011-01-01

The third edition of Quantum Non-Locality and Relativity has been carefully updated to reflect significant developments, including a new chapter covering important recent work in the foundations of physics. A new edition of the premier philosophical study of Bell's Theorem and its implication for the relativistic account of space and timeDiscusses Roderich Tumiulka's explicit, relativistic theory that can reproduce the quantum mechanical violation of Bell's inequality. Discusses the "Free Will Theorem" of John Conway and Simon KochenIntroduces philosophers to the relevant physics and demonstra

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Energy Technology Data Exchange (ETDEWEB)

Nigg, Simon E.; Tiwari, Rakesh P.; Walter, Stefan; Schmidt, Thomas L. [Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel (Switzerland)

2015-07-01

Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the produced photon pairs can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Science.gov (United States)

Nigg, Simon E.; Tiwari, Rakesh P.; Walter, Stefan; Schmidt, Thomas L.

2015-03-01

Based on the Bardeen-Cooper-Schrieffer theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the photon pairs produced can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.

Nonlocal gravity. Conceptual aspects and cosmological predictions

Science.gov (United States)

Belgacem, Enis; Dirian, Yves; Foffa, Stefano; Maggiore, Michele

2018-03-01

Even if the fundamental action of gravity is local, the corresponding quantum effective action, that includes the effect of quantum fluctuations, is a nonlocal object. These nonlocalities are well understood in the ultraviolet regime but much less in the infrared, where they could in principle give rise to important cosmological effects. Here we systematize and extend previous work of our group, in which it is assumed that a mass scale Λ is dynamically generated in the infrared, giving rise to nonlocal terms in the quantum effective action of gravity. We give a detailed discussion of conceptual aspects related to nonlocal gravity (including causality, degrees of freedom, ambiguities related to the boundary conditions of the nonlocal operator, scenarios for the emergence of a dynamical scale in the infrared) and of the cosmological consequences of these models. The requirement of providing a viable cosmological evolution severely restricts the form of the nonlocal terms, and selects a model (the so-called RR model) that corresponds to a dynamical mass generation for the conformal mode. For such a model: (1) there is a FRW background evolution, where the nonlocal term acts as an effective dark energy with a phantom equation of state, providing accelerated expansion without a cosmological constant. (2) Cosmological perturbations are well behaved. (3) Implementing the model in a Boltzmann code and comparing with observations we find that the RR model fits the CMB, BAO, SNe, structure formation data and local H0 measurements at a level statistically equivalent to ΛCDM. (4) Bayesian parameter estimation shows that the value of H0 obtained in the RR model is higher than in ΛCDM, reducing to 2.0σ the tension with the value from local measurements. (5) The RR model provides a prediction for the sum of neutrino masses that falls within the limits set by oscillation and terrestrial experiments (in contrast to ΛCDM, where letting the sum of neutrino masses vary as a free

Assessing continuum postulates in simulations of granular flow

Energy Technology Data Exchange (ETDEWEB)

Rycroft, Chris; Kamrin, Ken; Bazant, Martin

2008-08-26

Continuum mechanics relies on the fundamental notion of a mesoscopic volume"element" in which properties averaged over discrete particles obey deterministic relationships. Recent work on granular materials suggests a continuum law may be inapplicable, revealing inhomogeneities at the particle level, such as force chains and slow cage breaking. Here, we analyze large-scale three-dimensional Discrete-Element Method (DEM) simulations of different granular flows and show that an approximate"granular element" defined at the scale of observed dynamical correlations (roughly three to five particle diameters) has a reasonable continuum interpretation. By viewing all the simulations as an ensemble of granular elements which deform and move with the flow, we can track material evolution at a local level. Our results confirm some of the hypotheses of classical plasticity theory while contradicting others and suggest a subtle physical picture of granular failure, combining liquid-like dependence on deformation rate and solid-like dependence on strain. Our computational methods and results can be used to guide the development of more realistic continuum models, based on observed local relationships betweenaverage variables.

Global stability and pattern formation in a nonlocal diffusive Lotka-Volterra competition model

Science.gov (United States)

Ni, Wenjie; Shi, Junping; Wang, Mingxin

2018-06-01

A diffusive Lotka-Volterra competition model with nonlocal intraspecific and interspecific competition between species is formulated and analyzed. The nonlocal competition strength is assumed to be determined by a diffusion kernel function to model the movement pattern of the biological species. It is shown that when there is no nonlocal intraspecific competition, the dynamics properties of nonlocal diffusive competition problem are similar to those of classical diffusive Lotka-Volterra competition model regardless of the strength of nonlocal interspecific competition. Global stability of nonnegative constant equilibria are proved using Lyapunov or upper-lower solution methods. On the other hand, strong nonlocal intraspecific competition increases the system spatiotemporal dynamic complexity. For the weak competition case, the nonlocal diffusive competition model may possess nonconstant positive equilibria for some suitably large nonlocal intraspecific competition coefficients.

Dynamic response of multiple nanobeam system under a moving nanoparticle

Directory of Open Access Journals (Sweden)

Shahrokh Hosseini Hashemi

2018-03-01

Full Text Available In this article, nonlocal continuum based model of multiple nanobeam system (MNBS under a moving nanoparticle is investigated using Eringen’s nonlocal theory. Beam layers are assumed to be coupled by winkler elastic medium and the nonlocal Euler-Bernoulli beam theory is used to model each layer of beam. The Hamilton’s principle, Eigen function technique and the Laplace transform method are employed to solve the governing equations. Analytical solutions of the transverse displacements for MNBs with simply supported boundary condition are presented for double layered and three layered MNBSs. For higher number of layers, the governing set of equations is solved numerically and the results are presented. This study shows that small-scale parameter has a significant effect on dynamic response of MNBS under a moving nanoparticle. Sensitivity of dynamical deflection to variation of nonlocal parameter, stiffness of Winkler elastic medium and number of nanobeams are presented in nondimensional form for each layer. Keywords: Dynamic response, Analytical solution, Moving particle, Nanobeam, Multi-layered nanobeam

Atom-to-continuum methods for gaining a fundamental understanding of fracture.

Energy Technology Data Exchange (ETDEWEB)

McDowell, David Lynn (Georgia Institute of Technology, Atlanta, GA); Reedy, Earl David, Jr.; Templeton, Jeremy Alan; Jones, Reese E.; Moody, Neville Reid; Zimmerman, Jonathan A.; Belytschko, Ted. (Northwestern University, Evanston, IL); Zhou, Xiao Wang; Lloyd, Jeffrey T. (Georgia Institute of Technology, Atlanta, GA); Oswald, Jay (Northwestern University, Evanston, IL); Delph, Terry J. (Lehigh University, Bethlehem, PA); Kimmer, Christopher J. (Indiana University Southeast, New Albany, IN)

2011-08-01

This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. Under this aegis we developed new theory and a number of novel techniques to describe the fracture process at the atomic scale. These developments ranged from a material-frame connection between molecular dynamics and continuum mechanics to an atomic level J integral. Each of the developments build upon each other and culminated in a cohesive zone model derived from atomic information and verified at the continuum scale. This report describes an Engineering Sciences Research Foundation (ESRF) project to characterize and understand fracture processes via molecular dynamics modeling and atom-to-continuum methods. The effort is predicated on the idea that processes and information at the atomic level are missing in engineering scale simulations of fracture, and, moreover, are necessary for these simulations to be predictive. In this project we developed considerable new theory and a number of novel techniques in order to describe the fracture process at the atomic scale. Chapter 2 gives a detailed account of the material-frame connection between molecular dynamics and continuum mechanics we constructed in order to best use atomic information from solid systems. With this framework, in Chapter 3, we were able to make a direct and elegant extension of the classical J down to simulations on the scale of nanometers with a discrete atomic lattice. The technique was applied to cracks and dislocations with equal success and displayed high fidelity with expectations from continuum theory. Then, as a prelude to extension of the atomic J to finite temperatures, we explored the quasi-harmonic models as efficient and accurate surrogates of atomic lattices undergoing thermo-elastic processes (Chapter 4). With this in hand, in Chapter 5 we provide evidence that, by using the appropriate

A Nonlocal Peridynamic Plasticity Model for the Dynamic Flow and Fracture of Concrete.

Energy Technology Data Exchange (ETDEWEB)

Vogler, Tracy; Lammi, Christopher James

2014-10-01

A nonlocal, ordinary peridynamic constitutive model is formulated to numerically simulate the pressure-dependent flow and fracture of heterogeneous, quasi-brittle ma- terials, such as concrete. Classical mechanics and traditional computational modeling methods do not accurately model the distributed fracture observed within this family of materials. The peridynamic horizon, or range of influence, provides a characteristic length to the continuum and limits localization of fracture. Scaling laws are derived to relate the parameters of peridynamic constitutive model to the parameters of the classical Drucker-Prager plasticity model. Thermodynamic analysis of associated and non-associated plastic flow is performed. An implicit integration algorithm is formu- lated to calculate the accumulated plastic bond extension and force state. The gov- erning equations are linearized and the simulation of the quasi-static compression of a cylinder is compared to the classical theory. A dissipation-based peridynamic bond failure criteria is implemented to model fracture and the splitting of a concrete cylinder is numerically simulated. Finally, calculation of the impact and spallation of a con- crete structure is performed to assess the suitability of the material and failure models for simulating concrete during dynamic loadings. The peridynamic model is found to accurately simulate the inelastic deformation and fracture behavior of concrete during compression, splitting, and dynamically induced spall. The work expands the types of materials that can be modeled using peridynamics. A multi-scale methodology for simulating concrete to be used in conjunction with the plasticity model is presented. The work was funded by LDRD 158806.

Black hole information, unitarity, and nonlocality

International Nuclear Information System (INIS)

Giddings, Steven B.

2006-01-01

The black hole information paradox apparently indicates the need for a fundamentally new ingredient in physics. The leading contender is nonlocality. Possible mechanisms for the nonlocality needed to restore unitarity to black hole evolution are investigated. Suggestions that such dynamics arise from ultra-Planckian modes in Hawking's derivation are investigated and found not to be relevant, in a picture using smooth slices spanning the exterior and interior of the horizon. However, no simultaneous description of modes that have fallen into the black hole and outgoing Hawking modes can be given without appearance of a large kinematic invariant, or other dependence on ultra-Planckian physics. This indicates that a reliable argument for information loss has not been constructed, and that strong gravitational dynamics is important. Such dynamics has been argued to be fundamentally nonlocal in extreme situations, such as those required to investigate the fate of information

On nonlocal symmetries of some shallow water equations

Energy Technology Data Exchange (ETDEWEB)

Reyes, Enrique G [Departamento de Matematicas y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2 Santiago (Chile)

2007-04-27

A recent construction of nonlocal symmetries for the Korteweg-de Vries, Camassa-Holm and Hunter-Saxton equations is reviewed, and it is pointed out that-in the Camassa-Holm and Hunter-Saxton case-these symmetries can be considered as (nonlocal) symmetries of integro-differential equations.

Continuum Mechanics

CERN Document Server

Romano, Antonio

2010-01-01

This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors' previous book, Continuum Mechanics using Mathematica(R), this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.Specific topics, which have been chosen to show the power of continuum mechanics to characterize the experimental behavior of real phenomena, include: * various aspects of nonlin

Modulational instability and nonlocality management in coupled NLS systems

International Nuclear Information System (INIS)

Doktorov, Evgeny V; Molchan, Maxim A

2007-01-01

The modulational instability of two interacting waves in a nonlocal Kerr-type medium is considered analytically and numerically. For a generic choice of wave amplitudes, we give a complete description of stable/unstable regimes for zero group-velocity mismatch. It is shown that nonlocality suppresses considerably the growth rate and bandwidth of instability. For nonzero group-velocity mismatch we perform a geometrical analysis of a nonlocality management which can provide stability of waves otherwise unstable in a local medium

Inconsistency of Minkowski higher-derivative theories

Energy Technology Data Exchange (ETDEWEB)

Aglietti, Ugo G. [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)

2017-02-15

We show that Minkowski higher-derivative quantum field theories are generically inconsistent, because they generate nonlocal, non-hermitian ultraviolet divergences, which cannot be removed by means of standard renormalization procedures. By ''Minkowski theories'' we mean theories that are defined directly in Minkowski spacetime. The problems occur when the propagators have complex poles, so that the correlation functions cannot be obtained as the analytic continuations of their Euclidean versions. The usual power counting rules fail and are replaced by much weaker ones. Self-energies generate complex divergences proportional to inverse powers of D'Alembertians. Three-point functions give more involved nonlocal divergences, which couple to infrared effects. We illustrate the violations of the locality and hermiticity of counterterms in scalar models and higher-derivative gravity. (orig.)

A non-local variable for general relativity