Nonlocal continuum field theories
2002-01-01
Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unif...
Nonlocal Theories in Continuum Mechanics
Directory of Open Access Journals (Sweden)
M. Jirásek
2004-01-01
Full Text Available The purpose of this paper is to explain why the standard continuum theory fails to properly describe certain mechanical phenomena and how the description can be improved by enrichments that incorporate the influence of gradients or weighted spatial averages of strain or of an internal variable. Three typical mechanical problems that require such enrichments are presented: (i dispersion of short elastic waves in heterogeneous or discrete media, (ii size effects in microscale elastoplasticity, in particular with the size dependence of the apparent hardening modulus, and (iii localization of strain and damage in quasibrittle structures and with the resulting transitional size effect. Problems covered in the examples encompass static and dynamic phenomena, linear and nonlinear behavior, and three constitutive frameworks, namely elasticity, plasticity and continuum damage mechanics. This shows that enrichments of the standard continuum theory can be useful in a wide range of mechanical problems.
Bardhan, Jaydeep P
2011-09-14
We study the energetics of burying charges, ion pairs, and ionizable groups in a simple protein model using nonlocal continuum electrostatics. Our primary finding is that the nonlocal response leads to markedly reduced solvent screening, comparable to the use of application-specific protein dielectric constants. Employing the same parameters as used in other nonlocal studies, we find that for a sphere of radius 13.4 Å containing a single +1e charge, the nonlocal solvation free energy varies less than 18 kcal/mol as the charge moves from the surface to the center, whereas the difference in the local Poisson model is ∼35 kcal/mol. Because an ion pair (salt bridge) generates a comparatively more rapidly varying Coulomb potential, energetics for salt bridges are even more significantly reduced in the nonlocal model. By varying the central parameter in nonlocal theory, which is an effective length scale associated with correlations between solvent molecules, nonlocal-model energetics can be varied from the standard local results to essentially zero; however, the existence of the reduction in charge-burial penalties is quite robust to variations in the protein dielectric constant and the correlation length. Finally, as a simple exploratory test of the implications of nonlocal response, we calculate glutamate pK(a) shifts and find that using standard protein parameters (ε(protein) = 2-4), nonlocal results match local-model predictions with much higher dielectric constants. Nonlocality may, therefore, be one factor in resolving discrepancies between measured protein dielectric constants and the model parameters often used to match titration experiments. Nonlocal models may hold significant promise to deepen our understanding of macromolecular electrostatics without substantially increasing computational complexity.
Nonlocal continuum theories of beams for the analysis of carbon nanotubes
Reddy, J. N.; Pang, S. D.
2008-01-01
The equations of motion of the Euler-Bernoulli and Timoshenko beam theories are reformulated using the nonlocal differential constitutive relations of Eringen [International Journal of Engineering Science 10, 1-16 (1972)]. The equations of motion are then used to evaluate the static bending, vibration, and buckling responses of beams with various boundary conditions. Numerical results are presented using the nonlocal theories to bring out the effect of the nonlocal behavior on deflections, buckling loads, and natural frequencies of carbon nanotubes.
Wang, Yi-Ze; Li, Feng-Ming
2016-08-01
Structures under parametric load can be induced to the parametric instability in which the excitation frequency is located the instability region. In the present work, the parametric instability of double-walled carbon nanotubes is studied. The axial harmonic excitation is considered and the nonlocal continuum theory is applied. The critical equation is derived as the Mathieu form by the Galerkin's theory and the instability condition is presented with the Bolotin's method. Numerical calculations are performed and it can be seen that the van der Waals interaction can enhance the stability of double-walled nanotubes under the parametric excitation. The parametric instability becomes more obvious with the matrix stiffness decreasing and small scale coefficient increasing. The parametric instability is going to be more significant for higher mode numbers. For the nanosystem with the soft matrix and higher mode number, the small scale coefficient and the ratio of the length to the diameter have obvious influences on the starting point of the instability region.
Wang, Yi-Ze; Wang, Yue-Sheng; Ke, Liao-Liang
2016-09-01
In the present work, the nonlinear vibration of a carbon nanotube which is subjected to the external parametric excitation is studied. By the nonlocal continuum theory and nonlinear von Kármán beam theory, the governing equation of the carbon nanotube is derived with the consideration of the large deformation. The principle parametric resonance of the nanotube is discussed and the approximation explicit solution is presented by the multiple scale method. Numerical calculations are performed. It can be observed that when the mode number is 1, the stable region can be significantly changed by the parametric excitation, length-to-diameter ratio and matrix stiffness. This phenomenon becomes different to appear if the mode number increases. Moreover, the small scale effects have great influences on the positive bifurcation point for the short carbon nanotube, and the nonlocal continuum theory can present the proper model.
Axial buckling scrutiny of doubly orthogonal slender nanotubes via nonlocal continuum theory
Energy Technology Data Exchange (ETDEWEB)
Kiani, Keivan [K.N. Toosi University of Technolog, Tehran (Iran, Islamic Republic of)
2015-10-15
Using nonlocal Euler-Bernoulli beam theory, buckling behavior of elastically embedded Doubly orthogonal single-walled carbon nanotubes (DOSWCNTs) is studied. The nonlocal governing equations are obtained. In fact, these are coupled fourth-order integroordinary differential equations which are very difficult to be solved explicitly. As an alternative solution, Galerkin approach in conjunction with assumed mode method is employed, and the axial compressive buckling load of the nanosystem is evaluated. For DOSWCNTs with simply supported tubes, the influences of the slenderness ratio, aspect ratio, intertube free space, small-scale parameter, and properties of the surrounding elastic matrix on the axial buckling load of the nanosystem are addressed. The proposed model could be considered as a pivotal step towards better understanding the buckling behavior of more complex nanosystems such as doubly orthogonal membranes or even jungles of carbon nanotubes.
Wave propagation in nanostructures nonlocal continuum mechanics formulations
Gopalakrishnan, Srinivasan
2013-01-01
Wave Propagation in Nanostructures describes the fundamental and advanced concepts of waves propagating in structures that have dimensions of the order of nanometers. The book is fundamentally based on non-local elasticity theory, which includes scale effects in the continuum model. The book predominantly addresses wave behavior in carbon nanotubes and graphene structures, although the methods of analysis provided in this text are equally applicable to other nanostructures. The book takes the reader from the fundamentals of wave propagation in nanotubes to more advanced topics such as rotating nanotubes, coupled nanotubes, and nanotubes with magnetic field and surface effects. The first few chapters cover the basics of wave propagation, different modeling schemes for nanostructures and introduce non-local elasticity theories, which form the building blocks for understanding the material provided in later chapters. A number of interesting examples are provided to illustrate the important features of wave behav...
Nonlocal and quasilocal field theories
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
Acausality in Nonlocal Gravity Theory
Zhang, Ying-li; Sasaki, Misao; Zhao, Gong-Bo
2016-01-01
We investigate the nonlocal gravity theory by deriving nonlocal equations of motion using the traditional variation principle in a homogeneous background. We focus on a class of models with a linear nonlocal modification term in the action. It is found that the resulting equations of motion contain the advanced Green's function, implying that there is an acausality problem. As a consequence, a divergence arises in the solutions due to contributions from the future infinity unless the Universe will go back to the radiation dominated era or become the Minkowski spacetime in the future. We also discuss the relation between the original nonlocal equations and its biscalar-tensor representation and identify the auxiliary fields with the corresponding original nonlocal terms. Finally, we show that the acusality problem cannot be avoided by any function of nonlocal terms in the action.
Aggregation patterns from nonlocal interactions: Discrete stochastic and continuum modeling
Hackett-Jones, Emily J.
2012-04-17
Conservation equations governed by a nonlocal interaction potential generate aggregates from an initial uniform distribution of particles. We address the evolution and formation of these aggregating steady states when the interaction potential has 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, and formally show a connection between the two. Interesting aggregation patterns involving multiple peaks for a simple doubly singular attractive-repulsive potential are determined. For a swarming Morse potential, characteristic slow-fast dynamics in the scaled inverse energy is observed in the evolution to steady state in both the continuous and discrete approaches. The discrete approach is found to be remarkably robust to modifications in movement rules, related to the potential function. The comparable evolution dynamics and steady states of the discrete model with the continuum model suggest that the discrete stochastic approach is a promising way of probing aggregation patterns arising from two- and three-dimensional nonlocal interaction conservation equations. © 2012 American Physical Society.
Bassani, J.L.; Needleman, A.; Giessen, E. van der
2001-01-01
A two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to macroscopic shear is considered using both discrete dislocation plasticity and a nonlocal continuum crystal plasticity theory. Only single slip is permitted in the matrix material. The discrete dislocati
Coupling of nonlocal and local continuum models by the Arlequinapproach
Han, Fei
2011-08-09
The objective of this work is to develop and apply the Arlequin framework to couple nonlocal and local continuum mechanical models. A mechanically-based model of nonlocal elasticity, which involves both contact and long-range forces, is used for the \\'fine scale\\' description in which nonlocal interactions are considered to have non-negligible effects. Classical continuum mechanics only involving local contact forces is introduced for the rest of the structure where these nonlocal effects can be neglected. Both models overlap in a coupling subdomain called the \\'gluing area\\' in which the total energy is separated into nonlocal and local contributions by complementary weight functions. A weak compatibility is ensured between kinematics of both models using Lagrange multipliers over the gluing area. The discrete formulation of this specific Arlequin coupling framework is derived and fully described. The validity and limits of the technique are demonstrated through two-dimensional numerical applications and results are compared against those of the fully nonlocal elasticity method. © 2011 John Wiley & Sons, Ltd.
Nonlocal scalar quantum field theory from causal sets
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano
2015-03-01
We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.
Nonlocal Scalar Quantum Field Theory from Causal Sets
Belenchia, Alessio; Liberati, Stefano
2014-01-01
We study a non-local scalar quantum field theory in flat spacetime derived from the dynamics of a scalar field on a causal set. We show that this non-local QFT contains a continuum of massive modes in any dimension. In 2 dimensions the Hamiltonian is positive definite and therefore the quantum theory is well-defined. In 4-dimensions, we show that the unstable modes of the non-local d'Alembertian are propagated via the so called Wheeler propagator and hence do not appear in the asymptotic states. In the free case studied here the continuum of massive mode are shown to not propagate in the asymptotic states. However the Hamiltonian is not positive definite, therefore potential issues with the quantum theory remain. Finally, we conclude with hints toward what kind of phenomenology one might expect from such non-local QFTs.
Institute of Scientific and Technical Information of China (English)
戴天民
2003-01-01
The purpose is to reestablish the balance laws of momentum, angular momentumand energy and to derive the corresponding local and nonlocal balance equations formicromorphic continuum mechanics and couple stress theory. The desired results formicromorphic continuum mechanics and couple stress theory are naturally obtained via directtransitions and reductions from the coupled conservation law of energy for micropolarcontinuum theory, respectively. The basic balance laws and equation s for micromorphiccontinuum mechanics and couple stress theory are constituted by combining these resultsderived here and the traditional conservation laws and equations of mass and microinertiaand the entropy inequality. The incomplete degrees of the former related continuum theoriesare clarified. Finally, some special cases are conveniently derived.
Institute of Scientific and Technical Information of China (English)
Sarp Adali
2012-01-01
Equations governing the vibrations and buckling of multilayered orthotropic graphene sheets can be expressed as a system of n partial differential equations where n refers to the number of sheets.This description is based on the continuum model of the graphene sheets which can also take the small scale effects into account by employing a nonlocal theory.In the present article a variational principle is derived for the nonlocal elastic theory of rectangular graphene sheets embedded in an elastic medium and undergoing transverse vibrations.Moreover the graphene sheets are subject to biaxial compression.Rayleigh quotients are obtained for the frequencies of freely vibrating graphene sheets and for the buckling load. The influence of small scale effects on the frequencies and the buckling load can be observed qualiatively from the expressions of the Rayleigh quotients.Elastic medium is modeled as a combination of Winkler and Pasternak foundations acting on the top and bottom layers of the mutilayered nano-structure.Natural boundary conditions of the problem are derived using the variational principle formulated in the study.It is observed that free boundaries lead to coupled boundary conditions due to nonlocal theory used in the continuum formulation while the local (classical) elasticity theory leads to uncoupled boundary conditions.The mathematical methods used in the study involve calculus of variations and the semi-inverse method for deriving the variational integrals.
Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures
Energy Technology Data Exchange (ETDEWEB)
Rafii-Tabar, Hashem, E-mail: rafii-tabar@nano.ipm.ac.ir [Department of Medical Physics and Biomedical Engineering, Faculty of Medicine, Shahid Beheshti University of Medical Sciences, Tehran (Iran, Islamic Republic of); 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)
2016-06-06
Insight into the mechanical characteristics of nanoscopic structures is of fundamental interest and indeed poses a great challenge to the research communities around the world. These structures are ultra fine in size and consequently performing standard experiments to measure their various properties is an extremely difficult and expensive endeavor. Hence, to predict the mechanical characteristics of the nanoscopic structures, different theoretical models, numerical modeling techniques, and computer-based simulation methods have been developed. Among several proposed approaches, the nonlocal continuum-based modeling is of particular significance because the results obtained from this modeling for different nanoscopic structures are in very good agreement with the data obtained from both experimental and atomistic-based studies. A review of the essentials of this model together with its applications is presented here. Our paper is a self contained presentation of the nonlocal elasticity theory and contains the analysis of the recent works employing this model within the field of nanoscopic structures. In this review, the concepts from both the classical (local) and the nonlocal elasticity theories are presented and their applications to static and dynamic behavior of nanoscopic structures with various morphologies are discussed. We first introduce the various nanoscopic structures, both carbon-based and non carbon-based types, and then after a brief review of the definitions and concepts from classical elasticity theory, and the basic assumptions underlying size-dependent continuum theories, the mathematical details of the nonlocal elasticity theory are presented. A comprehensive discussion on the nonlocal version of the beam, the plate and the shell theories that are employed in modeling of the mechanical properties and behavior of nanoscopic structures is then provided. Next, an overview of the current literature discussing the application of the nonlocal models
Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures
Rafii-Tabar, Hashem; Ghavanloo, Esmaeal; Fazelzadeh, S. Ahmad
2016-06-01
Insight into the mechanical characteristics of nanoscopic structures is of fundamental interest and indeed poses a great challenge to the research communities around the world. These structures are ultra fine in size and consequently performing standard experiments to measure their various properties is an extremely difficult and expensive endeavor. Hence, to predict the mechanical characteristics of the nanoscopic structures, different theoretical models, numerical modeling techniques, and computer-based simulation methods have been developed. Among several proposed approaches, the nonlocal continuum-based modeling is of particular significance because the results obtained from this modeling for different nanoscopic structures are in very good agreement with the data obtained from both experimental and atomistic-based studies. A review of the essentials of this model together with its applications is presented here. Our paper is a self contained presentation of the nonlocal elasticity theory and contains the analysis of the recent works employing this model within the field of nanoscopic structures. In this review, the concepts from both the classical (local) and the nonlocal elasticity theories are presented and their applications to static and dynamic behavior of nanoscopic structures with various morphologies are discussed. We first introduce the various nanoscopic structures, both carbon-based and non carbon-based types, and then after a brief review of the definitions and concepts from classical elasticity theory, and the basic assumptions underlying size-dependent continuum theories, the mathematical details of the nonlocal elasticity theory are presented. A comprehensive discussion on the nonlocal version of the beam, the plate and the shell theories that are employed in modeling of the mechanical properties and behavior of nanoscopic structures is then provided. Next, an overview of the current literature discussing the application of the nonlocal models
Nonlocal and quasi-local field theories
Tomboulis, E T
2015-01-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasi-local (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasi-local kernels all acausal effects are confined within the compact support regi...
Quantum theory of nonlocal nonlinear Schrodinger equation
Vyas, Vivek M
2015-01-01
Nonlocal nonlinear Schrodinger model is quantised and exactly solved using the canonical framework. It is found that the usual canonical quantisation of the model leads to a theory with pathological inner product. This problem is resolved by constructing another inner product over the vector space of the theory. The resultant theory is found to be identical to that of nonrelativistic bosons with delta function interaction potential, devoid of any nonlocality. The exact eigenstates are found using the Bethe ansatz technique.
A morphing strategy to couple non-local to local continuum mechanics
Lubineau, Gilles
2012-06-01
A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. © 2012 Elsevier Ltd.
Hu, Yan-Gao; Liew, K M; Wang, Q
2011-12-01
Free transverse, longitudinal and torsional vibrations of single-walled carbon nanotubes (SWCNTs) are investigated through nonlocal beam model, nonlocal rod model and verified by molecular dynamics (MD) simulations. The nonlocal Timoshenko beam model offers a better prediction of the fundamental frequencies of shorter SWCNTs, such as a (5, 5) SWCNT shorter than 3.5 nm, than local beam models. The nonlocal rod model is employed to study the longitudinal and torsional vibrations of SWCNT and found to enable a good prediction of the MD results for shorter SWCNTs. Nonlocal and local continuum models provide a good agreement with MD results for relatively longer SWCNTs, such as (5, 5) SWCNTs longer than 3.5 nm. The scale parameter in nonlocal beam and rod models is estimated by calibrations from MD results.
Quantum Theory of Continuum Optomechanics
Rakich, Peter
2016-01-01
We present the basic ingredients of continuum optomechanics, i.e. the suitable extension of cavity-optomechanical concepts to the interaction of photons and phonons in an extended waveguide. We introduce a real-space picture and argue which coupling terms may arise in leading order in the spatial derivatives. This picture allows us to discuss quantum noise, dissipation, and the correct boundary conditions at the waveguide entrance. The connections both to optomechanical arrays as well as to the theory of Brillouin scattering in waveguides are highlighted. We identify the 'strong coupling regime' of continuum optomechanics that may be accessible in future experiments.
An expedition to continuum theory
Müller, Wolfgang H
2014-01-01
This book introduces field theory as required in solid and fluid mechanics as well as in electromagnetism. It also presents the necessary mathematical framework, namely tensor algebra and tensor calculus, by using an inductive approach, which makes it particularly suitable for beginners. In general, the book can be used in undergraduate classes on continuum theory and, more specifically, in courses on continuum mechanics, for students of physics and engineering alike. The benefits for the readers consist of providing a sound basis of the subject as a whole and of training their ability for solving specific problems in a rational manner. For this purpose the general laws of nature in terms of the balances for mass, momentum, and energy are applied and combined with constitutive relations, which are material specific. Various examples and homework problems illustrate how to use the theory in daily practice. Numerous mini-biographies have been added to the mathematical text for diversion and amusement.
Kiani, Keivan
2011-10-01
The potential applications of nanoplates in energy storage, chemical and biological sensors, solar cells, field emission, and transporting of nanocars have been attracted the attentions of the nanotechnology community to them during recent years. Herein, the later application of nanoplates from nonlocal elastodynamic point of view is of interest. To this end, dynamic response of a nanoplate subjected to a moving nanoparticle is examined within the context of nonlocal continuum theory of Eringen. The fully simply supported nanoplate is modeled based on the nonlocal Kirchhoff, Mindlin, and higher-order plate theories. The non-dimensional equations of motion of the nonlocal plate models are established. The effects of moving nanoparticle's weight and existing friction between the surfaces of the moving nanoparticle and nanoplate on the in-plane and out-of-plane vibrations of the nanoplate are incorporated into the formulations of the proposed models. The eigen function expansion and the Laplace transform methods are employed for discretization of the governing equations in the spatial and the time domains, respectively. The analytical expressions of the dynamic deformation field associated with each nonlocal plate theory are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight path (an opened path) as well as an ellipse path (a closed path). The dynamic in-plane forces and moments of each nonlocal plate model are also derived. Furthermore, the critical velocity and the critical angular velocity of the moving nanoparticle for the proposed models are expressed analytically for the aforementioned paths. Part II of this work consists in a comprehensive parametric study where the effects of influential parameters on dynamic response of the proposed nonlocal plate models are scrutinized in some detail.
Analytical theory of dark nonlocal solitons
DEFF Research Database (Denmark)
Kong, Qian; Wang, Qi; Bang, Ole;
2010-01-01
We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality.......We investigate properties of dark solitons in nonlocal materials with an arbitrary degree of nonlocality. We employ the variational technique and describe dark solitons, for the first time to our knowledge, in the whole range of degree of nonlocality....
Dynamics in Nonlocal Cosmological Models Derived from String Field Theory
Joukovskaya, Liudmila
2007-01-01
A general class of nonlocal cosmological models is considered. A new method for solving nonlocal Friedmann equations is proposed, and solutions of the Friedmann equations with nonlocal operator are presented. The cosmological properties of these solutions are discussed. Especially indicated is $p$-adic cosmological model in which we have obtained nonsingular bouncing solution and string field theory tachyon model in which we have obtained full solution of nonlocal Friedmann equations with $w=...
Self-localized states for electron transfer in nonlocal continuum deformable media
Energy Technology Data Exchange (ETDEWEB)
Cisneros-Ake, Luis A., E-mail: cisneros@esfm.ipn.mx
2016-08-19
We consider the problem of electron transport in a deformable continuum medium subjected to an external harmonic substrate potential. We then consider the quasi-stationary state of the full problem to find a Gross–Pitaevskii type equation with a nonlocal external potential, which is solved by variational and numerical means (considered as the exact solution) to find the parameter conditions for the existence of self-localized solutions. The variational approach predicts a threshold on the on-site or nonlocality parameter where localized solutions cease to exist from the Non-Linear Schrödinger soliton limit. A numerical continuation of stationary state solutions in the corresponding discrete system is used to confirm the prediction of the turning value in the on-site term. We finally study the full stationary state and make use of an approximation, proposed by Briedis et al. [17], for the nonlocal term, corresponding to strong nonlocalities, to find analytic expressions for self-localized states in terms of the series solutions of a nonlinear modified Bessel equation. - Highlights: • Nonlocality overcomes nonlinearity at a threshold value to cease the existence of coherent solutions. • Variational and series expansion solutions predict the formation of coherent structures in nonlocal deformable media. • Full numerical solutions confirm the persistence of localized solutions.
Records Continuum: An Emerging Recordkeeping Theory
Directory of Open Access Journals (Sweden)
Chi-Shiou Lin
2007-12-01
Full Text Available This paper introduces Records Continuum, a recordkeeping theory emerging from the Australian archives and records management studies which gained international recognition in the 1990s. This paper first describes the background of the theory development. It goes on to explicate the theses of continuum theorists including the Records Continuum Diagram developed by Frank Upward. Finally, it offers some critiques on the theoretical propositions and discusses their implications on records and archival practices. [Article content in Chinese
Radial vibration of free anisotropic nanoparticles based on nonlocal continuum mechanics.
Ghavanloo, Esmaeal; Fazelzadeh, S Ahmad
2013-02-22
Radial vibration of spherical nanoparticles made of materials with anisotropic elasticity is theoretically investigated using nonlocal continuum mechanics. The anisotropic elastic model is reformulated using the nonlocal differential constitutive relations of Eringen. The nonlocal differential equation of radial motion is derived in terms of radial displacement. Cubic, hexagonal, trigonal and tetragonal symmetries of the elasticity are discussed. The suggested model is justified by a good agreement between the results given by the present model and available experimental data. Furthermore, the model is used to elucidate the effect of small scale on the vibration of several nanoparticles. Our results show that the small scale is essential for the radial vibration of the nanoparticles when the nanoparticle radius is smaller than 1.5 nm.
Internal noise-driven generalized Langevin equation from a nonlocal continuum model.
Sarkar, Saikat; Chowdhury, Shubhankar Roy; Roy, Debasish; Vasu, Ram Mohan
2015-08-01
Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree of freedom, is derived. The GLE features a memory-dependent multiplicative or internal noise, which appears upon recognizing that the microrotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the present GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum, a phenomenon that is ubiquitous across a broad class of response regimes in solids and fluids. This renders the proposed GLE a potentially useful model in such cases.
Twisted Backgrounds, PP-Waves and Nonlocal Field Theories
Alishahiha, M; Alishahiha, Mohsen; Ganor, Ori J.
2003-01-01
We study partially supersymmetric plane-wave like deformations of string theories and M-theory on brane backgrounds. These deformations are dual to nonlocal field theories. We calculate various expectation values of configurations of closed as well as open Wilson loops and Wilson surfaces in those theories. We also discuss the manifestation of the nonlocality structure in the supergravity backgrounds. A plane-wave like deformation of little string theory has also been studied.
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.
A continuum mechanical gradient theory with applications to fluid mechanics
Energy Technology Data Exchange (ETDEWEB)
Silber, G.; Alizadeh, M.; Benderoth, G. [Fachhochschule Frankfurt am Main (Germany). Lab. fuer Materialwissenschaften; Trostel, R
1998-11-01
A gradient theory of grade two based on an axiomatic conception of a nonlocal continuum theory for materials of grade n is presented. The total stress tensor of rank two in the equation of linear momentum contains two higher stress tensors of rank two and three. In the case of isotropic materials both the tensor of rank two and three are tensor-valued functions of the second order strain rate tensor and its first gradient so that the equation of motion is of order four. The necessary boundary conditions for real boundaries are generated by using so-called porosity tensors. This theory is applied to two experiments. To a velocity profile of a turbulent Couette flow of water and a Poiseuille flow of a blood like suspension. On the basis of these experimental data the material and porosity coefficients are identified by numerical algorithms like evolution strategies. (orig.) 23 refs.
Geometric continuum mechanics and induced beam theories
R Eugster, Simon
2015-01-01
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
Energy Technology Data Exchange (ETDEWEB)
Zenkour, A. M.; Alnefaie, K. A.; Abu-Hamdeh, N. H.; Aljinaid, A. A.; Aifanti, E. C. [King Abdulaziz University, Jeddah (Saudi Arabia); Abouelregal, A. E. [Mansoura University, Mansoura (Egypt)
2015-07-15
In this article, an Euler-Bernoulli beam model based upon nonlocal thermoelasticity theory without energy dissipation is used to study the vibration of a nanobeam subjected to ramp-type heating. Classical continuum theory is inherently size independent, while nonlocal elasticity exhibits size dependence. Among other things, this leads to a new expression for the effective nonlocal bending moment as contrasted to its classical counterpart. The thermal problem is addressed in the context of the Green-Naghdi (GN) theory of heat transport without energy dissipation. The governing partial differential equations are solved in the Laplace transform domain by the state space approach of modern control theory. Inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of nonlocality and ramping time parameters on the lateral vibration, temperature, displacement and bending moment are discussed.
Causal Set theory, non-locality and phenomenology
Belenchia, Alessio
2015-01-01
This proceeding is based on a talk prepared for the XIV Marcel Grossmann meeting. We review some results on causal set inspired non-local theories as well as work in progress concerning their phenomenology.
Noether's theorem in non-local field theories
Krivoruchenko, M I
2016-01-01
Explicit expressions are constructed for a locally conserved vector current associated with a continuous internal symmetry and for energy-momentum and angular-momentum density tensors associated with the Poincar\\'e group in field theories with higher-order derivatives and in non-local field theories. An example of non-local charged scalar field equations with broken C and CPT symmetries is considered. For this case, we find simple analytical expressions for the conserved currents.
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.
Slits, plates, and Poisson-Boltzmann theory in a local formulation of nonlocal electrostatics.
Paillusson, Fabien; Blossey, Ralf
2010-11-01
Polar liquids like water carry a characteristic nanometric length scale, the correlation length of orientation polarizations. Continuum theories that can capture this feature commonly run under the name of "nonlocal" electrostatics since their dielectric response is characterized by a scale-dependent dielectric function ε(q), where q is the wave vector; the Poisson(-Boltzmann) equation then turns into an integro-differential equation. Recently, "local" formulations have been put forward for these theories and applied to water, solvated ions, and proteins. We review the local formalism and show how it can be applied to a structured liquid in slit and plate geometries, and solve the Poisson-Boltzmann theory for a charged plate in a structured solvent with counterions. Our results establish a coherent picture of the local version of nonlocal electrostatics and show its ease of use when compared to the original formulation.
Incompressible turbulence as non-local field theory
Indian Academy of Sciences (India)
Mahendra K Verma
2005-03-01
It is well-known that incompressible turbulence is non-local in real space because sound speed is infinite in incompressible fluids. The equation in Fourier space indicates that it is non-local in Fourier space as well. However, the shell-to-shell energy transfer is local. Contrast this with Burgers equation which is local in real space. Note that the sound speed in Burgers equation is zero. In our presentation we will contrast these two equations using non-local field theory. Energy spectrum and renormalized parameters will be discussed.
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅰ)-MICROPOLAR CONTINUA
Institute of Scientific and Technical Information of China (English)
戴天民
2003-01-01
Based on the restudies of existing polar continuum theories rather completesystems of basic balance laws and equations for micropolar continuum theory are presented.In these new systems not only the additional angular momentum, surface moment and bodymoment produced by the linear momentum, surface force and body force, respectively, butalso the additional velocity produced by the angular velocity are considered. The newcoupled balance laws of linear momentum, angular momentum and energy arereestablished. From them the new coupled local and nonlocal balance equatiors arenaturally derived. Via contrast it can be clearly seen that the new results are believed to berather general and complete.
Saffari, Shahab; Hashemian, Mohammad; Toghraie, Davood
2017-09-01
Based on nonlocal Timoshenko beam theory, dynamic stability of functionally graded (FG) nanobeam under axial and thermal loading was investigated. Surface stress effects were implemented according to Gurtin-Murdoch continuum theory. Using power law distribution for FGM and von Karman geometric nonlinearity, governing equations were derived based on Hamilton's principle. The developed nonlocal models have the capability of interpreting small scale effects. Pasternak elastic medium was employed to represent the interaction of the FG nanobeam and the surrounding elastic medium. A parametric study was conducted to focus influences of the static load factor, temperature change, gradient index, nonlocal parameter, slenderness ratio, surface effect and springs constants of the elastic medium on the dynamic instability region (DIR) of the FG beam with simply-supported boundary conditions. It was found that differences between DIRs predicted by local and nonlocal beam theories are significant for beams with lower aspect ratio. Moreover, it was observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origin of the DIR to higher excitation frequency zone and leads to further stability. Considering surface stress effects shifts the DIR of FG beam to higher frequency zone, also increasing the gradient index enhances the frequency of DIR.
Low energy signatures of nonlocal field theories
Belenchia, Alessio; Benincasa, Dionigi M. T.; Martín-Martínez, Eduardo; Saravani, Mehdi
2016-09-01
The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by nonanalytic functions of the d'Alembertian operator □ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy nonlocality scales. This allows us to suggest a nuclear physics experiment (˜MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity.
Continuum mechanics concise theory and problems
Chadwick, P
1998-01-01
Written in response to the dearth of practical and meaningful textbooks in the field of fundamental continuum mechanics, this comprehensive treatment offers students and instructors an immensely useful tool. Its 115 solved problems and exercises not only provide essential practice but also systematically advance the understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations.Readers follow clear, formally precise steps through the central ideas of classical and modern continuum mechanics, expressed in a common, effici
DEFF Research Database (Denmark)
Hansen, Jesper S; Dyre, Jeppe C; Daivis, Peter
2015-01-01
This paper introduces the fundamental continuum theory governing momentum transport in isotropic nanofluidic systems. The theory is an extension of the classical Navier-Stokes equation, and includes coupling between translational and rotational degrees of freedom as well as nonlocal response...
DEFF Research Database (Denmark)
Hansen, Jesper S; Dyre, Jeppe C; Daivis, Peter;
2015-01-01
This paper introduces the fundamental continuum theory governing momentum transport in isotropic nanofluidic systems. The theory is an extension of the classical Navier-Stokes equation, and includes coupling between translational and rotational degrees of freedom as well as nonlocal response...
Generalized conservation laws in non-local field theories
Kegeles, Alexander; Oriti, Daniele
2016-04-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalized conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalization of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Generalised conservation laws in non-local field theories
Kegeles, Alexander
2015-01-01
We propose a geometrical treatment of symmetries in non-local field theories, where the non-locality is due to a lack of identification of field arguments in the action. We show that the existence of a symmetry of the action leads to a generalised conservation law, in which the usual conserved current acquires an additional non-local correction term, obtaining a generalisation of the standard Noether theorem. We illustrate the general formalism by discussing the specific physical example of complex scalar field theory of the type describing the hydrodynamic approximation of Bose-Einstein condensates. We expect our analysis and results to be of particular interest for the group field theory formulation of quantum gravity.
Nonlocal theory of longitudinal waves in thermoelastic bars
Directory of Open Access Journals (Sweden)
Esin Inan
1991-05-01
Full Text Available The longitudinal waves in thermoelastic bars are investigated in the context of nonlocal theory. Using integral forms of constitutive equations, balance of momenta and energy, field equations are obtained. Then the frequency equation is found in generalized form. To obtain tangible results, an approximate procedure is applied and numerical results are given for short waves.
Theory of nonlocal heat transport in fully ionized plasma
Energy Technology Data Exchange (ETDEWEB)
Maximov, A.V. (Tesla Labs., Inc., La Jolla, CA (United States)); Silin, V.P. (P.N. Lebedev Inst., Russian Academy of Sciences, Moscow (Russia))
1993-01-25
A new analytic solution of the electron kinetic equation describing the interacting of the electromagnetic heating field with plasma is obtained in the region of plasma parameters where the Spitzer-Harm classical theory is invalid. A novel expression for the nonlocal electron thermal conductivity is derived. (orig.).
To the non-local theory of cold nuclear fusion.
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.
Quantum theory is classical mechanics with non-local existence
Hegseth, John
2009-01-01
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized to allow many paths due to the non-local existence of particles in phase space. This principle allows a physical system to evolve non-locally in phase space while still allowing a representation that uses many classical paths. Whereas a point in phase space represents a classical system's state, I represent the state of a non-local system by a mixed trajectory. This formulation naturally leads to the transactional interpretation for resolving the paradoxes of the measurement problem. This principle also suggests a more flexible framework for formulating theories based on invariant actions and provides a single conceptual framework for discussing many areas of science.
Variational continuum multiphase poroelasticity theory and applications
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...
Unitarity and microscopic acausality in a nonlocal theory
Carone, Christopher D
2016-01-01
We consider unitarity and causality in a higher-derivative theory of infinite order, where propagators fall off more quickly in the ultraviolet due to the presence of a transcendental entire function of the momentum. Like Lee-Wick theories, these field theories might provide new avenues for addressing the hierarchy problem; unlike Lee-Wick theories, propagators do not have additional poles corresponding to unobserved particles with unusual properties. We consider microscopic acausality in these nonlocal theories. The acausal ordering of production and decay vertices for ordinary resonant particles may provide a phenomenologically distinct signature for these models.
Lim, C. W.; Zhang, G.; Reddy, J. N.
2015-05-01
In recent years there have been many papers that considered the effects of material length scales in the study of mechanics of solids at micro- and/or nano-scales. There are a number of approaches and, among them, one set of papers deals with Eringen's differential nonlocal model and another deals with the strain gradient theories. The modified couple stress theory, which also accounts for a material length scale, is a form of a strain gradient theory. The large body of literature that has come into existence in the last several years has created significant confusion among researchers about the length scales that these various theories contain. The present paper has the objective of establishing the fact that the length scales present in nonlocal elasticity and strain gradient theory describe two entirely different physical characteristics of materials and structures at nanoscale. By using two principle kernel functions, the paper further presents a theory with application examples which relates the classical nonlocal elasticity and strain gradient theory and it results in a higher-order nonlocal strain gradient theory. In this theory, a higher-order nonlocal strain gradient elasticity system which considers higher-order stress gradients and strain gradient nonlocality is proposed. It is based on the nonlocal effects of the strain field and first gradient strain field. This theory intends to generalize the classical nonlocal elasticity theory by introducing a higher-order strain tensor with nonlocality into the stored energy function. The theory is distinctive because the classical nonlocal stress theory does not include nonlocality of higher-order stresses while the common strain gradient theory only considers local higher-order strain gradients without nonlocal effects in a global sense. By establishing the constitutive relation within the thermodynamic framework, the governing equations of equilibrium and all boundary conditions are derived via the variational
Hidden Variable Theories and Quantum Nonlocality
Boozer, A. D.
2009-01-01
We clarify the meaning of Bell's theorem and its implications for the construction of hidden variable theories by considering an example system consisting of two entangled spin-1/2 particles. Using this example, we present a simplified version of Bell's theorem and describe several hidden variable theories that agree with the predictions of…
National Research Council Canada - National Science Library
Nami, Mohammad Rahim; Janghorban, Maziar
2013-01-01
.... In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates...
Institute of Scientific and Technical Information of China (English)
戴天民
2001-01-01
The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics. By combining new principles of virtual velocity and virtual angular velocity as well as of virtual stress and virtual couple stress with cross terms of incremental rate type a new principle of power and energy rate of incremental rate type with cross terms for micropolar continuum field theories is presented and from it all corresponding equations of motion and boundary conditions as well as power and energy rate equations of incremental rate type for micropolar and nonlocal micropolar continua with the help of generalized Piola's theorems in all and without any additional requirement are derived. Complete results for micromorphic continua could be similarly derived. The derived results in the present paper are believed to be new. They could be used to establish corresponding finite element methods of incremental rate type for generalized continuum mechanics.
Continuum regularization of quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Vibration analysis of defective graphene sheets using nonlocal elasticity theory
Namin, S. F. Asbaghian; Pilafkan, R.
2017-09-01
Many papers have studied the free vibration of graphene sheets. However, all this papers assumed their atomic structure free of any defects. Nonetheless, they actually contain some defects including single vacancy, double vacancy and Stone-Wales defects. This paper, therefore, investigates the free vibration of defective graphene sheets, rather than pristine graphene sheets, via nonlocal elasticity theory. Governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defective graphene sheets. Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different defect types are inspected for graphene sheets with clamped or simply-supported boundary conditions on all sides. It is shown that the natural frequencies of graphene sheets decrease by introducing defects to the atomic structure. Furthermore, it is found that the number of missing atoms, shapes and distributions of structural defects play a significant role in the vibrational behavior of graphene. The effect of vacancy defect reconstruction is also discussed in this paper.
Axial vibration analysis of nanocones based on nonlocal elasticity theory
Institute of Scientific and Technical Information of China (English)
Shu-Qi Guo; Shao-Pu Yang
2012-01-01
Carbon nanocones have quite fascinating electronic and structural properties,whose axial vibration is seldom investigated in previous studies.In this paper,based on a nonlocal elasticity theory,a nonuniform rod model is applied to investigate the small-scale effect and the nonuniform effect on axial vibration of nanocones.Using the modified Wentzel-Brillouin-Kramers (WBK) method,an asymptotic solution is obtained for the axial vibration of general nonuniform nanorods.Then,using similar procedure,the axial vibration of nanocones is analyzed for nonuniform parameters,mode number and nonlocal parameters.Explicit expressions are derived for mode frequencies of clamped-clamped and clamped-free boundary conditions.It is found that axial vibration frequencies are highly overestimated by the classical rod model because of ignorance of the effect of small length scale.
A continuum theory of edge dislocations
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
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.
On wave propagation characteristics in fluid saturated porous materials by a nonlocal Biot theory
Tong, Lihong; Yu, Yang; Hu, Wentao; Shi, Yufeng; Xu, Changjie
2016-09-01
A nonlocal Biot theory is developed by combing Biot theory and nonlocal elasticity theory for fluid saturated porous material. The nonlocal parameter is introduced as an independent variable for describing wave propagation characteristics in poroelastic material. A physical insight on nonlocal term demonstrates that the nonlocal term is a superposition of two effects, one is inertia force effect generated by fluctuation of porosity and the other is pore size effect inherited from nonlocal constitutive relation. Models for situations of excluding fluid nonlocal effect and including fluid nonlocal effect are proposed. Comparison with experiment confirms that model without fluid nonlocal effect is more reasonable for predicting wave characteristics in saturated porous materials. The negative dispersion is observed theoretically which agrees well with the published experimental data. Both wave velocities and quality factors as functions of frequency and nonlocal parameter are examined in practical cases. A few new physical phenomena such as backward propagation and disappearance of slow wave when exceeding critical frequency and disappearing shear wave in high frequency range, which were not predicted by Biot theory, are demonstrated.
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...
Spectral Dimension from Causal Set Nonlocal Dynamics
Belenchia, Alessio; Marciano, Antonino; Modesto, Leonardo
2015-01-01
We investigate the spectral dimension obtained from non-local continuum d'Alembertians derived from causal sets. We find a universal dimensional reduction to 2 dimensions, in all dimensions. We conclude by discussing the validity and relevance of our results within the broader context of quantum field theories based on these nonlocal dynamics.
Analysis of a micro piezoelectric vibration energy harvester by nonlocal elasticity theory
Directory of Open Access Journals (Sweden)
Hao Chen
2016-04-01
Full Text Available A theoretical model of a micro piezoelectric energy harvester is proposed based on the nonlocal elasticity theory, which is operated in the flexural mode for scavenging ambient vibration energy. A nonlocal scale is defined as the product of internal characteristic length and a constant related to the material. The dependences of performance of the harvester upon the nonlocal scale and the scale ratio of the nonlocal scale to the external characteristic parameter are investigated in detail. Numerical results show that output power of the harvester decreases, and resonance frequency reduces gradually at first then increases rapidly when nonlocal scale increases. The results of nonlocal elasticity theory are compared with that of classic beam theory. All the results are helpful for material and structure design of the micro piezoelectric energy harvester.
Energy Technology Data Exchange (ETDEWEB)
Anjomshoa, Amin; Tahani, Masoud [Ferdowsi University, Mashhad (Iran, Islamic Republic of)
2016-06-15
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.
An extended Coleman-Noll procedure for generalized continuum theories
Hütter, Geralf
2016-11-01
Within rational continuum mechanics, the Coleman-Noll procedure is established to derive requirements to constitutive equations. Aiming in particular at generalized continuum theories, the present contribution demonstrates how this procedure can be extended to yield additionally the underlying balance equations of stress-type quantities. This is demonstrated for micromorphic and strain gradient media as well as for the microforce theory. The relation between the extended Coleman-Noll procedure and the method of virtual powers is pointed out.
Directory of Open Access Journals (Sweden)
Houari M.S.A.
2014-04-01
Full Text Available In this work, the size-dependent buckling behavior of functionally graded (FG nanobeams is investigated on the basis of the nonlocal continuum model. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. In addition, Poisson’s ratio is assumed constant in the current model. The nanobeams is modelled according to the new first order shear beam theory with small deformation and the equilibrium equations are derived using the Hamilton’s principle. The Naviertype solution is developed for simply-supported boundary conditions, and exact formulas are proposed for the buckling load. The effects of nonlocal parameter, aspect ratio, various material compositions on the stability responses of the FG nanobeams are discussed.
DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory
National Research Council Canada - National Science Library
Setoodeh, AliReza; Derahaki, Morteza; Bavi, Navid
2015-01-01
Abstract To investigate the thermal buckling of curved carbon nanotubes (CCNTs) embedded in an elastic medium, nonlocal elasticity theory is employed in combination with the theory of thin curved beams...
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.
NEW PRINCIPLES OF WORK AND ENERGY AS WELL AS POWER AND ENERGY RATE FOR CONTINUUM FIELD THEORIES
Institute of Scientific and Technical Information of China (English)
戴天民
2001-01-01
New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola' s theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.
Nonlocal Elasticity Theory for Transient Analysis of Higher-Order Shear Deformable Nanoscale Plates
Directory of Open Access Journals (Sweden)
Woo-Young Jung
2014-01-01
Full Text Available The small scale effect on the transient analysis of nanoscale plates is studied. The elastic theory of the nano-scale plate is reformulated using Eringen’s nonlocal differential constitutive relations and higher-order shear deformation theory (HSDT. The equations of motion of the nonlocal theories are derived for the nano-scale plates. The Eringen’s nonlocal elasticity of Eringen has ability to capture the small scale effects and the higher-order shear deformation theory has ability to capture the quadratic variation of shear strain and consequently shear stress through the plate thickness. The solutions of transient dynamic analysis of nano-scale plate are presented using these theories to illustrate the effect of nonlocal theory on dynamic response of the nano-scale plates. On the basis of those numerical results, the relations between nonlocal and local theory are investigated and discussed, as are the nonlocal parameter, aspect ratio, side-to-thickness ratio, nano-scale plate size, and time step effects on the dynamic response. In order to validate the present solutions, the reference solutions are employed and examined. The results of nano-scale plates using the nonlocal theory can be used as a benchmark test for the transient analysis.
Michelitsch, Thomas; Riascos, Alejandro; Nowakowski, Andrzej F; Nicolleau, Franck C G A
2016-01-01
We introduce positive elastic potentials in the harmonic approximation leading by Hamilton's variational principle to fractional Laplacian matrices having the forms of power law matrix functions of the simple local Bornvon Karman Laplacian. The fractional Laplacian matrices are well defined on periodic and infinite lattices in $n=1,2,3,..$ dimensions. The present approach generalizes the central symmetric second differenceoperator (Born von Karman Laplacian) to its fractional central symmetric counterpart (Fractional Laplacian matrix).For non-integer powers of the Born von Karman Laplacian, the fractional Laplacian matrix is nondiagonal with nonzero matrix elements everywhere, corresponding to nonlocal behavior: For large lattices the matrix elements far from the diagonal expose power law asymptotics leading to continuum limit kernels of Riesz fractional derivative type. We present explicit results for the fractional Laplacian matrix in 1D for finite periodic and infinite linear chains and their Riesz fractio...
Equivalent bosonic theory for the massive Thirring model with non-local interaction
Li, Kang; Naon, Carlos
1997-01-01
We study, through path-integral methods, an extension of the massive Thirring model in which the interaction between currents is non-local. By examining the mass-expansion of the partition function we show that this non-local massive Thirring model is equivalent to a certain non-local extension of the sine-Gordon theory. Thus, we establish a non-local generalization of the famous Coleman's equivalence. We also discuss some possible applications of this result in the context of one-dimensional...
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.
Nami, Mohammad Rahim; Janghorban, Maziar
2013-12-30
In this article, a new higher order shear deformation theory based on trigonometric shear deformation theory is developed. In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates. In the present theory, the transverse shear stresses satisfy the traction free boundary conditions of the rectangular plates and these stresses can be calculated from the constitutive equations. The effects of different parameters such as nonlocal parameter and aspect ratio are investigated on both nondimensional deflections and deflection ratios. It may be important to mention that the present formulations are general and can be used for isotropic, orthotropic and anisotropic nanoplates.
Directory of Open Access Journals (Sweden)
Mohammad Rahim Nami
2013-12-01
Full Text Available In this article, a new higher order shear deformation theory based on trigonometric shear deformation theory is developed. In order to consider the size effects, the nonlocal elasticity theory is used. An analytical method is adopted to solve the governing equations for static analysis of simply supported nanoplates. In the present theory, the transverse shear stresses satisfy the traction free boundary conditions of the rectangular plates and these stresses can be calculated from the constitutive equations. The effects of different parameters such as nonlocal parameter and aspect ratio are investigated on both nondimensional deflections and deflection ratios. It may be important to mention that the present formulations are general and can be used for isotropic, orthotropic and anisotropic nanoplates.
Set theory and the continuum hypothesis
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.
Continuum theory of defects - Structural-analytical mechanics of materials
Likhachev, V. A.; Volkov, A. E.; Shudegov, V. E.
The fundamental concepts of the continuum theory of defects in crystals are examined including dislocations, disclinations, and planar defects. The principal plastic characteristics of materials are then calculated using these concepts. Elements of deformation theory for piecewise inhomogeneous bodies with a structural hierarchy and phase transformations are examined. The nature of the amorphous state is discussed.
Ebrahimi, Farzad; Reza Barati, Mohammad
2017-01-01
In this research, vibration characteristics of a flexoelectric nanobeam in contact with Winkler-Pasternak foundation is investigated based on the nonlocal elasticity theory considering surface effects. This nonclassical nanobeam model contains flexoelectric effect to capture coupling of strain gradients and electrical polarizations. Moreover, the nonlocal elasticity theory is employed to study the nonlocal and long-range interactions between the particles. The present model can degenerate into the classical model if the nonlocal parameter, flexoelectric and surface effects are omitted. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying a Galerkin-based solution. Natural frequencies are verified with those of previous papers on nanobeams. It is illustrated that flexoelectricity, nonlocality, surface stresses, elastic foundation and boundary conditions affects considerably the vibration frequencies of piezoelectric nanobeams.
On holographic entanglement entropy of non-local field theories
Pang, Da-Wei
2014-01-01
We study holographic entanglement entropy of non-local field theories both at extremality and finite temperature. The gravity duals, constructed in arXiv:1208.3469 [hep-th], are characterized by a parameter $w$. Both the zero temperature backgrounds and the finite temperature counterparts are exact solutions of Einstein-Maxwell-dilaton theory. For the extremal case we consider the examples with the entangling regions being a strip and a sphere. We find that the leading order behavior of the entanglement entropy always exhibits a volume law when the size of the entangling region is sufficiently small. We also clarify the condition under which the next-to-leading order result is universal. For the finite temperature case we obtain the analytic expressions both in the high temperature limit and in the low temperature limit. In the former case the leading order result approaches the thermal entropy, while the finite contribution to the entanglement entropy at extremality can be extracted by taking the zero temper...
Continuum Edge Gyrokinetic Theory and Simulations
Energy Technology Data Exchange (ETDEWEB)
Xu, X Q; Xiong, Z; Dorr, M R; Hittinger, J A; Bodi, K; Candy, J; Cohen, B I; Cohen, R H; Colella, P; Kerbel, G D; Krasheninnikov, S; Nevins, W M; Qin, H; Rognlien, T D; Snyder, P B; Umansky, M V
2007-01-09
The following results are presented from the development and application of TEMPEST, a fully nonlinear (full-f) five dimensional (3d2v) gyrokinetic continuum edge-plasma code. (1) As a test of the interaction of collisions and parallel streaming, TEMPEST is compared with published analytic and numerical results for endloss of particles confined by combined electrostatic and magnetic wells. Good agreement is found over a wide range of collisionality, confining potential, and mirror ratio; and the required velocity space resolution is modest. (2) In a large-aspect-ratio circular geometry, excellent agreement is found for a neoclassical equilibrium with parallel ion flow in the banana regime with zero temperature gradient and radial electric field. (3) The four-dimensional (2d2v) version of the code produces the first self-consistent simulation results of collisionless damping of geodesic acoustic modes and zonal flow (Rosenbluth-Hinton residual) with Boltzmann electrons using a full-f code. The electric field is also found to agree with the standard neoclassical expression for steep density and ion temperature gradients in the banana regime. In divertor geometry, it is found that the endloss of particles and energy induces parallel flow stronger than the core neoclassical predictions in the SOL. (5) Our 5D gyrokinetic formulation yields a set of nonlinear electrostatic gyrokinetic equations that are for both neoclassical and turbulence simulations.
Theory of nonlocal soliton interaction in nematic liquid crystals
DEFF Research Database (Denmark)
Rasmussen, Per Dalgaard; Bang, Ole; Krolikowski, Wieslaw
2005-01-01
We investigate interactions between spatial nonlocal bright solitons in nematic liquid crystals using an analytical “effective particle” approach as well as direct numerical simulations. The model predicts attraction of out-of-phase solitons and the existence of their stable bound state....... This nontrivial property is solely due to the nonlocal nature of the nonlinear response of the liquid crystals. We further predict and verify numerically the critical outwards angle and degree of nonlocality which determine the transition between attraction and repulsion of out-of-phase solitons....
Aspects of nonlocality in quantum field theory, quantum gravity and cosmology
Barvinsky, A. O.
2015-02-01
This paper contains a collection of essays on nonlocal phenomena in quantum field theory, gravity and cosmology. Mechanisms of nonlocal contributions to the quantum effective action are discussed within the covariant perturbation expansion in field strengths and spacetime curvatures. Euclidean version of the Schwinger-Keldysh technique for quantum expectation values is presented as a special rule of obtaining the nonlocal effective equations of motion for the mean quantum field from the Euclidean effective action. This rule is applied to a new model of ghost free nonlocal cosmology which can generate the de Sitter (dS) cosmological evolution at an arbitrary value of Λ — a model of dark energy with the dynamical scale selected by a kind of a scaling symmetry breaking mechanism. This model is shown to interpolate between the superhorizon phase of a scalar mediated gravity and the short distance general relativistic limit in a special metric frame related by a nonlocal conformal transformation to the original metric.
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.)
Directory of Open Access Journals (Sweden)
Woo-Young Jung
2013-01-01
Full Text Available Based on a nonlocal elasticity theory, a model for sigmoid functionally graded material (S-FGM nanoscale plate with first-order shear deformation is studied. The material properties of S-FGM nanoscale plate are assumed to vary according to sigmoid function (two power law distribution of the volume fraction of the constituents. Elastic theory of the sigmoid FGM (S-FGM nanoscale plate is reformulated using the nonlocal differential constitutive relations of Eringen and first-order shear deformation theory. The equations of motion of the nonlocal theories are derived using Hamilton’s principle. The nonlocal elasticity of Eringen has the ability to capture the small scale effect. The solutions of S-FGM nanoscale plate are presented to illustrate the effect of nonlocal theory on bending and vibration response of the S-FGM nanoscale plates. The effects of nonlocal parameters, power law index, aspect ratio, elastic modulus ratio, side-to-thickness ratio, and loading type on bending and vibration response are investigated. Results of the present theory show a good agreement with the reference solutions. These results can be used for evaluating the reliability of size-dependent S-FGM nanoscale plate models developed in the future.
Spectral dimension from nonlocal dynamics on causal sets
Belenchia, Alessio; Benincasa, Dionigi M. T.; Marcianò, Antonino; Modesto, Leonardo
2016-02-01
We investigate the spectral dimension obtained from nonlocal continuum d'Alembertians derived from causal sets. We find a universal dimensional reduction to two dimensions, in all dimensions. We conclude by discussing the validity and relevance of our results within the broader context of quantum field theories based on these nonlocal dynamics.
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.
Non-locality in quantum field theory due to general relativity
Energy Technology Data Exchange (ETDEWEB)
Calmet, Xavier; Croon, Djuna; Fritz, Christopher [University of Sussex, Physics and Astronomy, Brighton (United Kingdom)
2015-12-15
We show that general relativity coupled to a quantum field theory generically leads to non-local effects in the matter sector. These non-local effects can be described by non-local higher dimensional operators which remarkably have an approximate shift symmetry. When applied to inflationary models, our results imply that small non-Gaussianities are a generic feature of models based on general relativity coupled to matter fields. However, these effects are too small to be observable in the cosmic microwave background. (orig.)
Non-locality in quantum field theory due to general relativity
Energy Technology Data Exchange (ETDEWEB)
Calmet, Xavier, E-mail: x.calmet@sussex.ac.uk; Croon, Djuna, E-mail: d.croon@sussex.ac.uk; Fritz, Christopher, E-mail: c.fritz@sussex.ac.uk [Physics and Astronomy, University of Sussex, Falmer, BN1 9QH, Brighton (United Kingdom)
2015-12-19
We show that general relativity coupled to a quantum field theory generically leads to non-local effects in the matter sector. These non-local effects can be described by non-local higher dimensional operators which remarkably have an approximate shift symmetry. When applied to inflationary models, our results imply that small non-Gaussianities are a generic feature of models based on general relativity coupled to matter fields. However, these effects are too small to be observable in the cosmic microwave background.
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...
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.
Aspects of Nonlocality in Quantum Field Theory, Quantum Gravity and Cosmology
Barvinsky, A. O.
2014-01-01
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...
Theory of genuine tripartite nonlocality of Gaussian states.
Adesso, Gerardo; Piano, Samanta
2014-01-10
We investigate the genuine multipartite nonlocality of three-mode Gaussian states of continuous variable systems. For pure states, we present a simplified procedure to obtain the maximum violation of the Svetlichny inequality based on displaced parity measurements, and we analyze its interplay with genuine tripartite entanglement measured via Rényi-2 entropy. The maximum Svetlichny violation admits tight upper and lower bounds at fixed tripartite entanglement. For mixed states, no violation is possible when the purity falls below 0.86. We also explore a set of recently derived weaker inequalities for three-way nonlocality, finding violations for all tested pure states. Our results provide a strong signature for the nonclassical and nonlocal nature of Gaussian states despite their positive Wigner function, and lead to precise recipes for its experimental verification.
Low-Energy Signatures of Nonlocal Field Theories
Belenchia, Alessio; Martin-Martinez, Eduardo; Saravani, Mehdi
2016-01-01
The response of inertial particle detectors coupled to a scalar field satisfying nonlocal dynamics described by non-analytic functions of the d'Alembertian operator $\\Box$ is studied. We show that spontaneous emission processes of a low energy particle detector are very sensitive to high-energy non-locality scales. This allows us to suggest a nuclear physics experiment ($\\sim$ MeV energy scales) that outperforms the sensitivity of LHC experiments by many orders of magnitude. This may have implications for the falsifiability of theoretical proposals of quantum gravity.
Wang, Qi; E, Weinan; Liu, Chun; Zhang, Pingwen
2002-05-01
The Doi kinetic theory for flows of homogeneous, rodlike liquid crystalline polymers (LCPs) is extended to model flows of nonhomogeneous, rodlike LCPs through a nonlocal (long-range) intermolecular potential. The theory features (i) a nonlocal, anisotropic, effective intermolecular potential in an integral form that is consistent with the chemical potential, (ii) short-range elasticity as well as long-range isotropic and anisotropic elasticity, (iii) a closed-form stress expression accounting for the nonlocal molecular interaction, and (iv) an extra elastic body force exclusively associated with the integral form of the intermolecular potential. With the effective intermolecular potential, the theory is proven to be well posed in that it warrants a positive entropy production and thereby the second law of thermodynamics. Approximate theories are obtained by gradient expansions of the number density function in the free energy density.
Frequency Shift of Carbon-Nanotube-Based Mass Sensor Using Nonlocal Elasticity Theory
Directory of Open Access Journals (Sweden)
Lee Haw-Long
2010-01-01
Full Text Available Abstract The frequency equation of carbon-nanotube-based cantilever sensor with an attached mass is derived analytically using nonlocal elasticity theory. According to the equation, the relationship between the frequency shift of the sensor and the attached mass can be obtained. When the nonlocal effect is not taken into account, the variation of frequency shift with the attached mass on the sensor is compared with the previous study. According to this study, the result shows that the frequency shift of the sensor increases with increasing the attached mass. When the attached mass is small compared with that of the sensor, the nonlocal effect is obvious and increasing nonlocal parameter decreases the frequency shift of the sensor. In addition, when the location of the attached mass is closer to the free end, the frequency shift is more significant and that makes the sensor reveal more sensitive. When the attached mass is small, a high sensitivity is obtained.
Flaw-tolerance of nonlocal discrete systems and interpretation according to network theory
Directory of Open Access Journals (Sweden)
A. Infuso
2014-07-01
Full Text Available Discrete systems are modeled as a network of nodes (particles, molecules, or atoms linked by nonlinear springs to simulate the action of van der Waals forces. Such systems are nonlocal if links connecting non-adjacent nodes are introduced. For their topological characterization, a nonlocality index (NLI inspired by network theory is proposed. The mechanical response of 1D and 2D nonlocal discrete systems is predicted according to finite element (FE simulations based on a nonlinear spring element for large displacements implemented in the FE programme FEAP. Uniaxial force-displacement responses of intact and defective systems (with links or nodes removed are numerically simulated. Strain localization phenomena, size-scale effects and the ability to tolerate defects are investigated by varying the degree of nonlocality.
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...
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.
Vibration of nonuniform carbon nanotube with attached mass via nonlocal Timoshenko beam theory
Energy Technology Data Exchange (ETDEWEB)
Tang, Hai Li; Shen, Zhi Bin; Li, Dao Kui [National University of Defense Technology, Changsha (China)
2014-09-15
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.
Rashidian Vaziri, Mohammad Reza
2013-07-10
In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.
Cognitive continuum theory in interprofessional healthcare: A critical analysis.
Parker-Tomlin, Michelle; Boschen, Mark; Morrissey, Shirley; Glendon, Ian
2017-07-01
Effective clinical decision making is among the most important skills required by healthcare practitioners. Making sound decisions while working collaboratively in interprofessional healthcare teams is essential for modern healthcare planning, successful interventions, and patient care. The cognitive continuum theory (CCT) is a model of human judgement and decision making aimed at orienting decision-making processes. CCT has the potential to improve both individual health practitioner, and interprofessional team understanding about, and communication of, clinical decision-making processes. Examination of the current application of CCT indicates that this theory could strengthen interprofessional team clinical decision making (CDM). However, further research is needed before extending the use of this theoretical framework to a wider range of interprofessional healthcare team processes. Implications for research, education, practice, and policy are addressed.
Vibration analysis of single-walled carbon peapods based on nonlocal Timoshenko beam theory
Ghadiri, Majid; Hajbarati, Hamid; Safi, Mohsen
2017-04-01
In this article, vibration behavior of single-walled carbon nanotube encapsulating C60 molecules is studied using the Eringen's nonlocal elasticity theory within the frame work of Timoshenko beam theory. The governing equation and boundary conditions are derived using Hamilton's principle. It is considered that the nanopeapod is embedded in an elastic medium and the C60 molecules are modeled as lumped masses attached to the nanobeam. The Galerkin's method is applied to determine the natural frequency of the nanobeam with clamped-clamped boundary conditions. Effects of nonlocality, foundation stiffness, and ratio of the fullerenes' mass to the nanotube's mass on the natural frequencies are investigated. In addition, by vanishing effects of shear deformation and rotary inertia, the results based on Euler-Bernoulli beam theory are presented.
Continuum theory for cluster morphologies of soft colloids.
Kosmrlj, A; Pauschenwein, G J; Kahl, G; Ziherl, P
2011-06-01
We introduce a continuum description of the thermodynamics of colloids with a core-corona architecture. In the case of thick coronas, their overlap can be treated approximately by replacing the exact one-particle density distribution by a suitably shaped step profile, which provides a convenient way of modeling the spherical, columnar, lamellar, and inverted cluster morphologies predicted by numerical simulations and the more involved theories. We use the model to study monodisperse particles with the hard-core/square-shoulder pair interaction as the simplest representatives of the core-corona class. We derive approximate analytical expressions for the enthalpies of the cluster morphologies which offer a clear insight into the mechanisms at work, and we calculate the lattice spacing and the cluster size for all morphologies of the phase sequence as well as the phase-transition pressures. By comparing the results with the exact crystalline minimum-enthalpy configurations, we show that the accuracy of the theory increases with shoulder width. We discuss possible extensions of the theory that could account for the finite-temperature effects.
Understanding Construction Workers’ Risk Decisions Using Cognitive Continuum Theory
Directory of Open Access Journals (Sweden)
Cindy L. Menches
2016-09-01
Full Text Available During the course of performing daily tasks, construction workers encounter numerous hazards, such as ladders that are too short to reach the work area, energized electrical lines, or inadequate fall protection. When a hazard is encountered, the worker must make a rapid decision about how to respond and whether to take or avoid the risk. The goal of this research was to construct a theory about the influence of decision cues on intuitive and deliberative decision-making in high-hazard construction environments. Drawing from Cognitive Continuum Theory, the study specifies a framework for understanding why and how construction workers make decisions that lead to taking or avoiding physical risks when they encounter daily hazards. A secondary aim of the research was to construct a set of hypotheses about how specific decision cues influence whether a worker is more likely to engage their intuitive impulses or to use careful deliberation when responding to a hazard. These hypotheses are described and the efficacy of the hypotheses was evaluated using cross-tabulations and nonparametric measures of association. While most of the associations between decision cues and decision mode (i.e., intuition or deliberation identified in this data set were generally modest, none of the associations were statistically zero, thus indicating that further research is warranted based on theoretical grounds. A rigorous program of theory testing is the next logical step to the research.
A geometric theory of non-local two-qubit operations
Zhang, J; Whaley, K B; Sastry, S; Zhang, Jun; Vala, Jiri; Sastry, Shankar
2003-01-01
We study non-local two-qubit operations from a geometric perspective. By applying a Cartan decomposition to su(4), we find that the geometric structure of non-local gates is a 3-Torus. We derive the invariants for local transformations, and connect these local invariants to the coordinates of the 3-Torus. Since different points on the 3-Torus may correspond to the same local equivalence class, we use the Weyl group theory to reduce the symmetry. We show that the local equivalence classes of two-qubit gates are in one-to-one correspondence with the points in a tetrahedron except on the base. We then study the properties of perfect entanglers, that is, the two-qubit operations that can generate maximally entangled states from some initially separable states. We provide criteria to determine whether a given two-qubit gate is a perfect entangler and establish a geometric description of perfect entanglers by making use of the tetrahedral representation of non-local gates. We find that exactly half the non-local ga...
Barnaby, Neil
2008-01-01
We consider the possibility of realizing inflation in nonlocal field theories containing infinitely many derivatives. Such constructions arise naturally in string field theory and also in a number of toy models, such as the p-adic string. After reviewing the complications (ghosts and instabilities) that arise when working with high derivative theories we discuss the initial value problem and perturbative stability of theories with infinitely many derivatives. Next, we examine the inflationary dynamics and phenomenology of such theories. Nonlocal inflation can proceed even when the potential is naively too steep and generically predicts large nongaussianity in the Cosmic Microwave Background.
Tunneling of the 3rd Kind: A Test of the Effective Non-locality of Quantum Field Theory
Gardiner, S. A.; Gies, H.; Jaeckel, J.; Wallace, C. J.
2012-01-01
Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is non-local. In this Letter we argue that tunneling of the 3rd kind - where particles traverse a barrier by splitting into a pair of virtual particles which recombine only after a finite distance - provides a direct test of this non-locality. We sketch a quantum-optical setup to test this effect, and investigate observable effects in a simple toy model.
A continuum theory of surface piezoelectricity for nanodielectrics
Pan, XiaHui; Yu, ShouWen; Feng, XiQiao
2011-04-01
In this paper, a phenomenological continuum theory of surface piezoelectricity accounting for the linear superficial interplay between electricity and elasticity is formulated primarily for elastic dielectric materials. This theory is inspired by the physical idea that once completely relaxed, an insulating free dielectric surface will sustain a nontrivial spontaneous surface polarization in the normal direction together with a tangential self-equilibrated residual surface stress field. Under external loadings, the surface Helmholtz free energy density is identified as the characteristic function of such surfaces, with the in-plane strain tensor of surface and the surface free charge density as the independent state variables. New boundary conditions governing the surface piezoelectricity are derived through the variational method. The resulting concepts of charge-dependent surface stress and deformation-dependent surface electric field reflect the linear electromechanical coupling behavior of nanodielectric surfaces. As an illustrative example, an infinite radially polarizable piezoelectric nanotube with both inner and outer surfaces grounded is investigated. The novel phenomenon of possible surface-induced polarity inversion is predicted for thin enough nanotubes.
Burnett-Cattaneo continuum theory for shock waves.
Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon
2011-02-01
We model strong shock-wave propagation, both in the ideal gas and in the dense Lennard-Jones fluid, using a refinement of earlier work, which accounts for the cold compression in the early stages of the shock rise by a nonlinear, Burnett-like, strain-rate dependence of the thermal conductivity, and relaxation of kinetic-temperature components on the hot, compressed side of the shock front. The relaxation of the disequilibrium among the three components of the kinetic temperature, namely, the difference between the component in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, is accomplished at a much more quantitative level by a rigorous application of the Cattaneo-Maxwell relaxation equation to a reference solution, namely, the steady shock-wave solution of linear Navier-Stokes-Fourier theory, along with the nonlinear Burnett heat-flux term. Our new continuum theory is in nearly quantitative agreement with nonequilibrium molecular-dynamics simulations under strong shock-wave conditions, using relaxation parameters obtained from the reference solution.
Space-Time Quantization and Nonlocal Field Theory -Relativistic Second Quantization of Matrix Model
Tanaka, S
2000-01-01
We propose relativistic second quantization of matrix model of D particles in a general framework of nonlocal field theory based on Snyder-Yang's quantized space-time. Second-quantized nonlocal field is in general noncommutative with quantized space-time, but conjectured to become commutative with light cone time $X^+$. This conjecture enables us to find second-quantized Hamiltonian of D particle system and Heisenberg's equation of motion of second-quantized {\\bf D} field in close contact with Hamiltonian given in matrix model. We propose Hamilton's principle of Lorentz-invariant action of {\\bf D} field and investigate what conditions or approximations are needed to reproduce the above Heisenberg's equation given in light cone time. Both noncommutativities appearing in position coordinates of D particles in matrix model and in quantized space-time will be eventually unified through second quantization of matrix model.
Shock Waves Propagation in Scope of the Nonlocal Theory of Dynamical Plasticity
Khantuleva, Tatyana A.
2004-07-01
From the point of view of the modern statistical mechanics the problems on shock compression of solids require a reformulation in terms of highly nonequilibrium effects arising inside the wave front. The self-organization during the multiscale and multistage momentum and energy exchange are originated by the correlation function. The theory of dynamic plasticity has been developed by the author on the base of the self-consistent nonlocal hydrodynamic approach had been applied to the shock wave propagation in solids. Nonlocal balance equations describe both the reversible wave type transport at the initial stage and the diffusive (dissipative) one in the end. The involved inverse influence of the mesoeffects on the wave propagation makes the formulation of problems self-consistent and involves a concept of the cybernetic control close-loop.
Tang, Yugang; Liu, Ying; Zhao, Dong
2016-10-01
In this paper, the viscoelastic wave propagation in an embedded viscoelastic single-walled carbon nanotube (SWCNT) is studied based on the nonlocal strain gradient theory. The characteristic equation for the viscoelastic wave in SWCNTs is derived. The emphasis is placed on the influence of the tube diameter on the viscoelastic wave dispersion. A blocking diameter is observed, above which the wave could not propagate in SWCNTs. The results show that the blocking diameter is greatly dependent on the damping coefficient, the nonlocal and the strain gradient length scale parameters, as well as the Winkler modulus of the surrounding elastic medium. These findings may provide a prospective application of SWCNTs in nanodevices and nanocomposites.
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 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.
Serendipitous discoveries in nonlocal ghost-free gravity theory: dark energy and dark matter
Barvinsky, Andrei O
2011-01-01
We present a class of generally covariant nonlocal gravity models briefly reported in arXiv:1107.1463, which have a flat-space general relativistic (GR) limit and also possess a stable de Sitter (dS) or Anti-de Sitter (AdS) background with an arbitrary value of its cosmological constant. The nonlocal action of the theory is formulated in the Euclidean signature spacetime and is understood as an approximation to the quantum effective action (generating functional of one-particle irreducible diagrams) originating from fundamental quantum gravity theory. Using the known relation between the Schwinger-Keldysh technique for quantum expectation values and the Euclidean quantum field theory we derive from this action the {\\em causal} effective equations of motion for mean value of the metric field in the physical Lorentzian-signature spacetime. Thus we show that the (A)dS background of the theory carries as free propagating modes massless gravitons having two polarizations identical to those of the Einstein theory w...
Energy Technology Data Exchange (ETDEWEB)
Gao, Yuanwen, E-mail: ywgao@lzu.edu.cn [Key Laboratory of Mechanics on Western Disaster and Environment, Ministry of Education, Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000 (China); Lei, Fang-Ming [Key Laboratory of Mechanics on Western Disaster and Environment, Ministry of Education, Department of Mechanics and Engineering Science, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000 (China)
2009-09-25
Based on the nonlocal elastic theory, small scale effects are considered in the investigation of the mechanical properties of protein microtubules. A new prediction formula for the persistence lengths of microtubules with the consideration of the small scale effect is presented. Subsequently, the buckling of microtubules is studied based on a nonlocal elastic beam model. The predicted results of our model indicate that the length-dependence of persistence length is related not only to the shear terms, but also to the small scale effect. The Eular beam model, which is always considered unable to explain the length-dependence of microtubules, can capture the length-dependence of the persistence length of microtubules with the consideration of the small scale effect. The elastic buckling behaviors of microtubules in viscoelastic surrounding cytoplasm are also considered using the nonlocal Timoshenko beam model in this paper, and the results indicate that the small scale effect of microtubules also plays an important role in the buckling of microtubules.
Sedighi, H. M.; Yaghootian, A.
2016-01-01
This article presents a new asymptotic method to predict dynamic pull-in instability of nonlocal clamped-clamped carbon nanotubes (CNTs) near graphite sheets. Nonlinear governing equations of carbon nanotubes actuated by an electric field are derived. With due allowance for the van der Waals effects, the pull-in instability and the natural frequency-amplitude relationship are investigated by a powerful analytical method, namely, the parameter expansion method. It is demonstrated that retaining two terms in series expansions is sufficient to produce an acceptable solution. The obtained results from numerical methods verify the strength of the analytical procedure. The qualitative analysis of system dynamics shows that the equilibrium points of the autonomous system include center points and unstable saddle points. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.
Generating functional and large N limit of nonlocal 2D generalized Yang-Mills theories (nlgYM 2's)
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.
Theory of non-local point transformations - Part 2: General form and Gedanken experiment
Tessarotto, Massimo
2016-01-01
The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when expressed in arbitrary coordinate systems. It is shown that the solution permits to achieve an ideal (Gedanken) experiment realizing a suitable kind of phase-space transformation on point-particle classical dynamical systems. Applications of the theory are discussed both for diagonal and non-diagonal metric tensors.
Nonlocal quantum field theory without acausality and nonunitarity at quantum level: SUSY is the key
Addazi, Andrea
2015-01-01
The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality reappears at one loop. We suggest the the problem of acausality is, in a broad sense, similar to the one about anomalies in quantum field theory. By virtue of this analogy, we suggest that acausal diagrams resulting from the fermionic sector and the bosonic one might cancel each other, with a suitable content of fields and suitable symmetries. As a simple example, we show how supersymmetry can alleviate this problem in a simple and elegant way, i.e., by leading to exact cancellations of harmful diagrams, to all orders of perturbation theory, in the case of a nonlocal Wess-Zumino model. On the other hand, the same is true for a super Yang-Mills model, but in this case, other important acausal diagrams are also originating from supersymmetric D-terms. As a consequence, we conjecture ...
A generalized non-local optical response theory for plasmonic nanostructures.
Mortensen, N A; Raza, S; Wubs, M; Søndergaard, T; Bozhevolnyi, S I
2014-05-02
Metallic nanostructures exhibit a multitude of optical resonances associated with localized surface plasmon excitations. Recent observations of plasmonic phenomena at the sub-nanometre to atomic scale have stimulated the development of various sophisticated theoretical approaches 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 explains surprisingly well both the frequency shifts and size-dependent damping in individual metallic nanoparticles as well as the observed broadening of the crossover regime from bonding-dipole plasmons to charge-transfer plasmons in metal nanoparticle dimers, thus unravelling a classical broadening mechanism that even dominates the widely anticipated short circuiting by quantum tunnelling. We anticipate that our theory can be successfully applied in plasmonics to a wide class of conducting media, including doped semiconductors and low-dimensional materials such as graphene.
Translating caring theory across the continuum from inpatient to ambulatory care.
Tonges, Mary; McCann, Meghan; Strickler, Jeff
2014-06-01
While theory-based practice is a Magnet® characteristic, translating theories to practice remains challenging. As a result, theory-guided practice remains an ideal rather than a realized goal in many organizations. This article provides an overview of a research-derived caring theory, a translational model for theory-driven practice, implementation of a delivery model designed to translate theory across the acute and ambulatory care continuum, and resulting outcomes in oncology clinics and the emergency department.
Ebrahimi, Farzad; Barati, Mohammad Reza
2016-09-01
This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment. The theory contains two scale parameters corresponding to both nonlocal and strain gradient effects. A quasi-3D sinusoidal beam theory considering shear and normal deformations is employed to present the formulation. Mori-Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton's principle is employed to obtain the governing equations of nanobeam accounting for thickness stretching effect. These equations are solved analytically to find the wave frequencies and phase velocities of the FG nanobeam. It is indicated that wave dispersion behavior of FG nanobeams is significantly affected by temperature rise, nonlocality, length scale parameter and material composition.
Generalized continuum theories : Application to stress analysis in bone
Fatemi, J.; Keulen, F. van; Onck, P.R.
2002-01-01
Bone is a heterogeneous material with microstructural features. Continuum models of bone on the basis of classical elasticity ignore microstructure-related scale effects on the macroscopic mechanical properties. Consequently, these models do not provide a complete description of the mechanical
Equivalence between a bosonic theory and a massive non-local Thirring model at Finite Temperature
Manias, M V
1998-01-01
Using the path-integral bosonization procedure at Finite Temperature we study the equivalence between a massive Thirring model with non-local interaction between currents (NLMT) and a non-local extension of the sine-Gordon theory (NLSG). To this end we make a perturbative expansion in the mass parameter of the NLMT model and in the cosine term of the NLSG theory in order to obtain explicit expressions for the corresponding partition functions. We conclude that for certain relationship between NLMT and NLSG potentials both the fermionic and bosonic expansions are equal term by term. This result constitutes a generalization of Coleman's equivalence at T=0, when considering a Thirring model with bilocal potentials in the interaction term at Finite Temperature. The study of this model is relevant in connection with the physics of strongly correlated systems in one spatial dimension. Indeed, in the language of many-body non-relativistic systems, the relativistic mass term can be shown to represent the introduction...
Tunnelling of the 3rd kind: A test of the effective non-locality of quantum field theory
Gardiner, Simon A.; Gies, Holger; Jaeckel, Joerg; Wallace, Chris J.
2013-03-01
Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is non-local. In this letter we argue that tunnelling of the 3rd kind —where particles traverse a barrier by splitting into a pair of virtual particles which recombine only after a finite distance— provides a direct test of this non-locality. We sketch a quantum-optical setup to test this effect, and investigate observable effects in a simple toy model.
Lagrangian formulation of continuum with internal long-range interactions
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Based on a new definition of nonlocal variable,this paper establishes the Lagrangian formulation for continuum with internal long-range interactions.Distinguished from the existing theories,the nonlocal term in the Lagrangian formulation automatically satisfies the zero mean condition determined by the action and reaction law.By this formulation,elastic wave in a rod with the internal long-range interactions is investigated.The dispersion of the elastic wave is predicted.
Sound-speed inversion of the Sun using a nonlocal statistical convection theory
Zhang, Chunguang; Xiong, Darun; Christensen-Dalsgaard, Jørgen; 10.1088/2041-8205/759/1/L14
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 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.
Time-Dependent and/or Nonlocal Representations of Hilbert Spaces in Quantum Theory
Directory of Open Access Journals (Sweden)
M. Znojil
2010-01-01
Full Text Available A few recent innovations of the applicability of standard textbook Quantum Theory are reviewed. The three-Hilbert-space formulation of the theory (known from the interacting boson models in nuclear physics is discussed in its slightly broadened four-Hilbert-space update. Among applications involving several new scattering and bound-state problems the central role is played by models using apparently non-Hermitian (often called “crypto-Hermitian” Hamiltonians with real spectra. The formalism (originally inspired by the topical need for a mathematically consistent description of tobogganic quantum models is shown to admit even certain unusual nonlocal and/or “moving-frame” representations H(S of the standard physical Hilbert space of wave functions.
Filk, Thomas
2013-04-01
In this article I investigate several possibilities to define the concept of "temporal non-locality" within the standard framework of quantum theory. In particular, I analyze the notions of "temporally non-local states", "temporally non-local events" and "temporally non-local observables". The idea of temporally non-local events is already inherent in the standard formalism of quantum mechanics, and Basil Hiley recently defined an operator in order to measure the degree of such a temporal non-locality. The concept of temporally non-local states enters as soon as "clock-representing states" are introduced in the context of special and general relativity. It is discussed in which way temporally non-local measurements may find an interesting application for experiments which test temporal versions of Bell inequalities.
Surana, K. S.; Joy, A. D.; Reddy, J. N.
2017-03-01
This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory, we have (i) the usual displacements ( ±b \\varvec{u}) and (ii) three internal rotations ({}_i ±b \\varvec{Θ}) about the axes of a triad whose axes are parallel to the x-frame arising from the Jacobian of deformation (which are completely defined by the skew-symmetric part of the Jacobian of deformation), and (iii) three additional rotations ({}_e ±b \\varvec{Θ}) about the axes of the same triad located at each material point as additional three degrees of freedom referred to as Cosserat rotations. This gives rise to ±b \\varvec{u} and {}_e ±b \\varvec{{Θ} as six degrees of freedom at a material point. The internal rotations ({}_i ±b \\varvec{Θ}), often neglected in classical continuum mechanics, exist in all deforming solid continua as these are due to Jacobian of deformation. When the internal rotations {}_i ±b \\varvec{Θ} are resisted by the deforming matter, conjugate moment tensor arises that together with {}_i ±b \\varvec{Θ} may result in energy storage and/or dissipation, which must be accounted for in the conservation and the balance laws. The Cosserat rotations {}_e ±b \\varvec{Θ} also result in conjugate moment tensor which, together with {}_e ±b \\varvec{Θ}, may also result in energy storage and/or dissipation. The main focus of the paper is a consistent derivation of conservation and balance laws that incorporate aforementioned physics and associated constitutive theories for thermoelastic solids. The mathematical model derived here has closure, and the constitutive theories derived using two alternate approaches are in agreement with each other as well as with the condition resulting from the
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.
Free vibration of fractional viscoelastic Timoshenko nanobeams using the nonlocal elasticity theory
Ansari, R.; Faraji Oskouie, M.; Sadeghi, F.; Bazdid-Vahdati, M.
2015-11-01
In this article, the free vibration of a fractional viscoelastic Timoshenko nanobeam is studied through inserting fractional calculus as a viscoelastic material compatibility equations in nonlocal beam theory. The material properties of a single-walled carbon nanotube (SWCNT) are used and two solution procedures are proposed to solve the obtained equations in the time domain. The former is a semi-analytical approach in which the Galerkin scheme is employed to discretize the governing equations in the spatial domain and the obtained set of ordinary differential equations is solved using a direct numerical integration scheme. On the contrary, the latter is entirely numerical in which the governing equations of system on the spatial and time domains are first discretized using general differential quadrature (GDQ) technique and finite difference (FD) scheme, respectively and then the set of algebraic equations is solved to arrive at the time response of system under different boundary conditions. Considering the second solution procedure as the main approach, its validity and accuracy are verified by the semi-analytical approach which is more difficult to enter various boundary conditions. Numerical results are also presented to get an insight into the effects of fractional derivative order, nonlocal parameter, viscoelasticity coefficient and nanobeam length on the time response of fractional viscoelastic Timoshenko nanobeams under different boundary conditions.
The nonlocal theory solution of a Mode-I crack in functionally graded materials
Institute of Scientific and Technical Information of China (English)
LIANG Jun
2009-01-01
The behavior of a Mode-I finite crack in functionally graded materials is investigated using the non-local theory. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate vertical to the crack. The problem in this paper can be solved through the Fourier transform with the help of two pairs of dual integral equations, in which the unknown variables are jumps of displacements across crack surfaces. To solve dual integral equations, the jumps of displacements across crack surfaces are directly expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. Numerical examples are provided to show the effects of the crack length, the parameter describing the functionally graded materials, the lattice parameter of materials and the materials constants upon the stress fields near crack tips.
The nonlocal theory solution of a Mode-I crack in functionally graded materials
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The behavior of a Mode-I finite crack in functionally graded materials is investigated using the non-local theory. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate vertical to the crack. The problem in this paper can be solved through the Fourier transform with the help of two pairs of dual integral equations, in which the unknown variables are jumps of dis- placements across crack surfaces. To solve dual integral equations, the jumps of displacements across crack surfaces are directly expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solu- tions yield a finite stress at crack tips, thus allowing us to use the maximum stress as a fracture crite- rion. Numerical examples are provided to show the effects of the crack length, the parameter describ- ing the functionally graded materials, the lattice parameter of materials and the materials constants upon the stress fields near crack tips.
A Four-Dimensional Continuum Theory of Space-Time and the Classical Physical Fields
Directory of Open Access Journals (Sweden)
Suhendro I.
2007-10-01
Full Text Available In this work, we attempt to describe the classical physical fields of gravity, electromagnetism, and the so-called intrinsic spin (chirality in terms of a set of fully geometrized constitutive equations. In our formalism, we treat the four-dimensional space-time continuum as a deformable medium and the classical fields as intrinsic stress and spin fields generated by infinitesimal displacements and rotations in the space-time continuum itself. In itself, the unifying continuum approach employed herein may suggest a possible unified field theory of the known classical physical fields.
Dislocation patterning in a two-dimensional continuum theory of dislocations
Groma, István; Zaiser, Michael; Ispánovity, Péter Dusán
2016-06-01
Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but few of them (if any) are derived from microscopic considerations through systematic and controlled averaging procedures. In this paper we present a two-dimensional continuum theory that is obtained by systematic averaging of the equations of motion of discrete dislocations. It is shown that in the evolution equations of the dislocation densities diffusionlike terms neglected in earlier considerations play a crucial role in the length scale selection of the dislocation density fluctuations. It is also shown that the formulated continuum theory can be derived from an averaged energy functional using the framework of phase field theories. However, in order to account for the flow stress one has in that case to introduce a nontrivial dislocation mobility function, which proves to be crucial for the instability leading to patterning.
Institute of Scientific and Technical Information of China (English)
H.P. Zhu; Z.Y. Zhou; Q.F. Hou; A.B. YU
2011-01-01
Two approaches are widely used to describe particle systems:the continuum approach at macroscopic scale and the discrete approach at particle scale,Each has its own advantages and disadvantages in the modelling of particle systems.It is of paramount significance to develop a theory to overcome the disadvantages of the two approaches.Averaging method to link the discrete to continuum approach is a potential technique to develop such a theory.This paper introduces an averaging method,including the theory and its application to the particle flow in a hopper and the particle-fluid flow in an ironmaking blast furnace.
Universality and the approach to the continuum limit in lattice gauge theory
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.
Directory of Open Access Journals (Sweden)
H. Rouhi
2015-01-01
Full Text Available A nonlocal elastic shell model considering the small scale effects is developed to study the free vibrations of multiwalled carbon nanotubes subject to different types of boundary conditions. Based on the nonlocal elasticity and the Flügge shell theory, the governing equations are derived which include the interaction of van der Waals forces between adjacent and nonadjacent layers. To analytically solve the problem, the Rayleigh-Ritz method is employed. In the present analysis, different combinations of layerwise boundary conditions are taken into account. Some new intertube resonant frequencies and the associated noncoaxial vibrational modes are identified owing to incorporating circumferential modes into the shell model.
Theory connecting nonlocal sediment transport, earth surface roughness, and the Sadler effect
Schumer, Rina; Taloni, Alessandro; Furbish, David Jon
2017-03-01
Earth surface evolution, like many natural phenomena typified by fluctuations on a wide range of scales and deterministic smoothing, results in a statistically rough surface. We present theory demonstrating that scaling exponents of topographic and stratigraphic statistics arise from long-time averaging of noisy surface evolution rather than specific landscape evolution processes. This is demonstrated through use of "elastic" Langevin equations that generically describe disturbance from a flat earth surface using a noise term that is smoothed deterministically via sediment transport. When smoothing due to transport is a local process, the geologic record self organizes such that a specific Sadler effect and topographic power spectral density (PSD) emerge. Variations in PSD slope reflect the presence or absence and character of nonlocality of sediment transport. The range of observed stratigraphic Sadler slopes captures the same smoothing feature combined with the presence of long-range spatial correlation in topographic disturbance.
Energy Technology Data Exchange (ETDEWEB)
Biswas, Tirthabir [Department of Physics, St. Cloud State University, St. Cloud, MN 56301 U.S.A (United States); Koivisto, Tomi [Institute for Theoretical Physics and Spinoza Institute, Postbus 80.195, 3508 TD Utrecht (Netherlands); Mazumdar, Anupam, E-mail: tbiswas@loyno.edu, E-mail: T.S.Koivisto@uu.nl, E-mail: a.mazumdar@lancaster.ac.uk [Physics Department, Lancaster University, Lancaster, LA1 4YB (United Kingdom)
2010-11-01
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.
Mashhoon, B
2014-01-01
A brief account of the present status of the recent nonlocal generalization of Einstein's theory of gravitation is presented. The main physical assumptions that underlie this theory are described. We clarify the physical meaning and significance of Weitzenb\\"ock's torsion, and emphasize its intimate relationship with the gravitational field, characterized by the Riemannian curvature of spacetime. In this theory, nonlocality can simulate dark matter; in fact, in the Newtonian regime, we recover the phenomenological Tohline-Kuhn approach to modified gravity. To account for the observational data regarding dark matter, nonlocality is associated with a characteristic length scale of order 1 kpc. The confrontation of nonlocal gravity with observation is briefly discussed.
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.
NONLOCAL SYMMETRIES AND NONLOCAL RECURSION OPERATORS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
An expose about covering method on differential equations was given. The general formulae to determine nonlocal symmetries were derived which are analogous to the prolongation formulae of generalized symmetries. In addition, a new definition of nonlocal recursion operators was proposed, which gave a satisfactory explalnation in covering theory for the integro-differcntial recursion operators.
Non-locality in theories without the no-restriction hypothesis
Directory of Open Access Journals (Sweden)
Peter Janotta
2014-12-01
Full Text Available The framework of generalized probabilistic theories (GPT is a widely-used approach for studying the physical foundations of quantum theory. The standard GPT framework assumes the no-restriction hypothesis, in which the state space of a physical theory determines the set of measurements. However, this assumption is not physically motivated. In Janotta and Lal [Phys. Rev. A 87, 052131 (2013], it was shown how this assumption can be relaxed, and how such an approach can be used to describe new classes of probabilistic theories. This involves introducing a new, more general, definition of maximal joint state spaces, which we call the generalised maximal tensor product. Here we show that the generalised maximal tensor product recovers the standard maximal tensor product when at least one of the systems in a bipartite scenario obeys the no-restriction hypothesis. We also show that, under certain conditions, relaxing the no-restriction hypothesis for a given state space does not allow for stronger non-locality, although the generalized maximal tensor product may allow new joint states.
Nonlocal quantum field theory without acausality and nonunitarity at quantum level: Is SUSY the key?
Addazi, Andrea; Esposito, Giampiero
2015-05-01
The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality is expected to reappear at one loop. We suggest that the problem of acausality is, in a broad sense, similar to the one about anomalies in quantum field theory. By virtue of this analogy, we suggest that acausal diagrams resulting from the fermionic sector and the bosonic one might cancel each other, with a suitable content of fields and suitable symmetries. As a simple example, we show how supersymmetry can alleviate this problem in a simple and elegant way, i.e. by leading to exact cancellations of harmful diagrams, to all orders of perturbation theory. An infinite number of divergent diagrams cancel each other by virtue of the nonrenormalization theorem of supersymmetry. However, supersymmetry is not enough to protect a theory from all acausal divergences. For instance, acausal contributions to supersymmetric corrections to D-terms are not protected by supersymmetry. On the other hand, we show in detail how supersymmetry also helps in dealing with D-terms: divergences are not canceled but they become softer than in the nonsupersymmetric case. The supergraphs' formalism turns out to be a powerful tool to reduce the complexity of perturbative calculations.
A continuum theory for modeling the dynamics of crystalline materials.
Xiong, Liming; Chen, Youping; Lee, James D
2009-02-01
This paper introduces a multiscale field theory for modeling and simulation of the dynamics of crystalline materials. The atomistic formulation of a multiscale field theory is briefly introduced. Its applicability is discussed. A few application examples, including phonon dispersion relations of ferroelectric materials BiScO3 and MgO nano dot under compression are presented.
Size effects in single crystal thin films : nonlocal crystal plasticity simulations
Yefimov, S; van der Giessen, E
2005-01-01
Stress relaxation in single crystalline thin films on substrates subjected to thermal loading is studied using a recently proposed nonlocal continuum crystal plasticity theory. The theory is founded on a statistical-mechanics description of the collective behaviour of dislocations in multiple slip,
Adali, Sarp
2009-05-01
Variational principles are derived for multiwalled carbon nanotubes undergoing vibrations. Derivations are based on the continuum modeling with the Euler-Bernoulli beam representing the nanotubes and small scale effects taken into account via the nonlocal elastic theory. Hamilton's principle for multiwalled nanotubes is given and Rayleigh's quotient for the frequencies is derived for nanotubes undergoing free vibrations. Natural and geometric boundary conditions are derived which lead to a set of coupled boundary conditions due to nonlocal effects.
Ultra-nonlocality in density functional theory for photo-emission spectroscopy.
Uimonen, A-M; Stefanucci, G; van Leeuwen, R
2014-05-14
We derive an exact expression for the photocurrent of photo-emission spectroscopy using time-dependent current density functional theory (TDCDFT). This expression is given as an integral over the Kohn-Sham spectral function renormalized by effective potentials that depend on the exchange-correlation kernel of current density functional theory. We analyze in detail the physical content of this expression by making a connection between the density-functional expression and the diagrammatic expansion of the photocurrent within many-body perturbation theory. We further demonstrate that the density functional expression does not provide us with information on the kinetic energy distribution of the photo-electrons. Such information can, in principle, be obtained from TDCDFT by exactly modeling the experiment in which the photocurrent is split into energy contributions by means of an external electromagnetic field outside the sample, as is done in standard detectors. We find, however, that this procedure produces very nonlocal correlations between the exchange-correlation fields in the sample and the detector.
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.
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.
From the Kinetic Theory of Gases to Continuum Mechanics
Golse, François
2010-01-01
Recent results on the fluid dynamic limits of the Boltzmann equation based on the DiPerna-Lions theory of renormalized solutions are reviewed in this paper, with an emphasis on regimes where the velocity field behaves to leading order like that of an incompressible fluid with constant density.
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.
Low Energy Continuum and Lattice Effective Field Theories
Elhatisari, Serdar
In this thesis we investigate several constraints and their impacts on the short-range potentials in the low-energy limits of quantum mechanics.We also present lattice Monte Carlo calculations using the adiabatic projection method. In the first part we consider the constraints of causality and unitarity for the low-energy interactions of particles. We generalize Wigner's causality bound to the case of non-vanishing partial-wave mixing. Specifically we analyze the system of the low-energy interactions between protons and neutrons. We derive a general theorem that non-vanishing partial-wave mixing cannot be reproduced with zero-range interactions without violating causality or unitarity. We also analyze low-energy scattering for systems with arbitrary short-range interactions plus an attractive 1/ralpha tail for alpha ≥ 2. In particular, we focus on the case of alpha = 6 and we derive the constraints of causality and unitarity also for these systems and find that the van derWaals length scale dominates over parameters characterizing the short-distance physics of the interaction. This separation of scales suggests a separate universality class for physics characterizing interactions with an attractive 1{r6 tail. We argue that a similar universality class exists for any attractive potential 1/ralpha for alpha ≥ 2. In the second part of the thesis we present lattice Monte Carlo calculations of fermion-dimer scattering in the limit of zero-range interactions using the adiabatic projection method. The adiabatic projection method uses a set of initial cluster states and Euclidean time projection to give a systematically improvable description of the low-lying scattering cluster states in a finite volume. We use Luscher's finite-volume relations to determine the s-wave, p-wave, and d-wave phase shifts. For comparison, we also compute exact lattice results using Lanczos iteration and continuum results using the Skorniakov-Ter-Martirosian equation. For our Monte Carlo
Nonlocal String Theories on AdS{sub 3} x S{sup 3} and Stable Non-Supersymmetric Backgrounds
Energy Technology Data Exchange (ETDEWEB)
Silverstein, Eva M
2002-01-16
We exhibit a simple class of exactly marginal ''double-trace'' deformations of two dimensional CFTs which have AdS{sub 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{sub 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.
Ansari, R.; Faraji Oskouie, M.; Gholami, R.
2016-01-01
In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.
Multiphase Flow and Fluidization Continuum and Kinetic Theory Descriptions
Gidaspow, Dimitri
1994-01-01
Useful as a reference for engineers in industry and as an advanced level text for graduate engineering students, Multiphase Flow and Fluidization takes the reader beyond the theoretical to demonstrate how multiphase flow equations can be used to provide applied, practical, predictive solutions to industrial fluidization problems. Written to help advance progress in the emerging science of multiphase flow, this book begins with the development of the conservation laws and moves on through kinetic theory, clarifying many physical concepts (such as particulate viscosity and solids pressure) and i
Hidden-variable models for the spin singlet: I. Non-local theories reproducing quantum mechanics
Di Lorenzo, Antonio
2011-01-01
A non-local hidden variable model reproducing the quantum mechanical probabilities for a spin singlet is presented. The non-locality is concentrated in the distribution of the hidden variables. The model otherwise satisfies both the hypothesis of outcome independence, made in the derivation of Bell inequality, and of compliance with Malus's law, made in the derivation of Leggett inequality. It is shown through the prescription of a protocol that the non-locality can be exploited to send information instantaneously provided that the hidden variables can be measured, even though they cannot be controlled.
Non-local potentials with LS terms in algebraic scattering theory
Energy Technology Data Exchange (ETDEWEB)
Levay, Peter [Department of Theoretical Physics, Institute of Physics, Technical University of Budapest, Budapest (Hungary)
1997-10-21
The group theoretical analysis of Coulomb scattering based on the SO(3,1) group is revisited. Using matrix-valued differential operators, modifying the angular momentum and the Runge-Lenz vector used hitherto for the realization of the so(3,1) (Lorentz) algebra, we obtain a three-dimensional solvable two-channel scattering problem. The interaction term besides the Coulomb potential contains a non-local potential of LS-type. Using the momentum representation the S-matrix can be calculated analytically. By employing a canonical transformation, another solvable three-dimensional scattering problem is found, in agreement with the expectations of algebraic scattering theory. The potential in this case is of Poeschl-Teller type with an LS term. It is also pointed out that our matrix-valued realization of the so(3,1) algebra can be cast to an instructive form with the help of su(2) gauge fields. An interesting connection between gauge transformations and supersymmetry transformations of supersymmetric quantum mechanics is also observed. These results enable us to construct other solvable scattering problems by using su(2) gauge transformations. (author)
Directory of Open Access Journals (Sweden)
D. L. Hysell
Full Text Available Large-scale (l ~ 1 km waves in the daytime and night-time equatorial electrojet are studied using coherent scatter radar data from Jicamarca. Images of plasma irregularities within the main beam of the radar are formed using interferometry with multiple baselines. These images are analyzed according to nonlocal gradient drift instability theory and are also compared to nonlinear computer simulations carried out recently by Ronchi et al. (1991 and Hu and Bhattacharjee (1999. In the daytime, the large-scale waves assume a non-steady dynamical equilibrium state characterized by the straining and destruction of the waves by shear and diffusion followed by spontaneous regeneration as predicted by Ronchi et al. (1991. At night, when steep plasma density gradients emerge, slowly propagating large-scale vertically extended waves predominate. Eikonal analysis suggests that these waves are trapped (absolutely unstable or are nearly trapped (convectively unstable and are able to tunnel between altitude regions which are locally unstable. Intermediate-scale waves are mainly transient (convectively stable but can become absolutely unstable in narrow altitude bands determined by the background density profile. These characteristics are mainly consistent with the simulations presented by Hu and Bhattacharjee (1999. A new class of large-scale primary waves is found to occur along bands that sweep westward and downward from high altitudes through the E-region at twilight.
Key words. Ionosphere (equatorial ionosphere; ionospheric irregularities; plasma waves and instabilities
Time—dependent Theory of Raman Scattering with Pulses—Application to Continuum Raman Spectroscopy
Institute of Scientific and Technical Information of China (English)
Soo－Y.Lee
1995-01-01
A theory of real-time dependence of Raman scattering for a pulse-mode laser is developed within second-order perturbation theory and using the wavepacket terminology.We apply the theory to continuum Raman scattering for short and long pulses and varying pulse carrier frequency,For an initial ground virational state,it is shown that the rate of Raman emission as a funcition of time and pulse carrier frequency is structureless for all pulses,and for pulses that are longer than the dissociation time the rate also decays with the pulses.This is contrary to recently reported resonance fluorescence type structures at long times (M.Shapiro,J.Chem.Phys.99,2453(1993),We explain why such structures are unphysical for continuum Raman scattering.
Fully nonlocal quantum correlations
Aolita, Leandro; Acín, Antonio; Chiuri, Andrea; Vallone, Giuseppe; Mataloni, Paolo; Cabello, Adán
2011-01-01
Quantum mechanics is a nonlocal theory, but not as nonlocal as the no-signalling principle allows. However, there exist quantum correlations that exhibit maximal nonlocality: they are as nonlocal as any non-signalling correlations and thus have a local content, quantified by the fraction $p_L$ of events admitting a local description, equal to zero. Previous examples of maximal quantum nonlocality between two parties require an infinite number of measurements, and the corresponding Bell violation is not robust against noise. We show how every proof of the Kochen-Specker theorem gives rise to maximally nonlocal quantum correlations that involve a finite number of measurements and are robust against noise. We perform the experimental demonstration of a Bell test originating from the Peres-Mermin Kochen-Specker proof, providing an upper bound on the local content $p_L\\lesssim 0.22$.
Quantum Nonlocality and Reality
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
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jianming; Yang, Yang [Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming 650051, Yunnan (China)
2015-03-10
According to Hamilton’s principle, a new mathematical model and analytical solutions for nonlocal Timoshenko beam model (ANT) is established based on nonlocal elastic continuum theory when shear deformation and nonlocal effect are considered. The new ANT equilibrium equations and boundary conditions are derived for bending analysis of carbon nanotubes (CNTs) with simply supported, clamped and cantilever. The ANT deflection solutions demonstrate that the CNT stiffness is enhanced by the presence of nonlocal stress effects. Furthermore, the new ANT model concluded verifiable bending behaviors for a cantilever CNT with point load at the free end, which depends on the strength of nonlocal stress. Therefore, this new model will gives a better prediction for mechanical behaviors of nanostructures.
Norouzzadeh, A.; Ansari, R.
2017-04-01
Stress-strain relation in Eringen's nonlocal elasticity theory was originally formulated within the framework of an integral model. Due to difficulty of working with that integral model, the differential model of nonlocal constitutive equation is widely used for nanostructures. However, paradoxical results may be obtained by the differential model for some boundary and loading conditions. Presented in this article is a finite element analysis of Timoshenko nano-beams based on the integral model of nonlocal continuum theory without employing any simplification in the model. The entire procedure of deriving equations of motion is carried out in the matrix form of representation, and hence, they can be easily used in the finite element analysis. For comparison purpose, the differential counterparts of equations are also derived. To study the outcome of analysis based on the integral and differential models, some case studies are presented in which the influences of boundary conditions, nonlocal length scale parameter and loading factor are analyzed. It is concluded that, in contrast to the differential model, there is no paradox in the numerical results of developed integral model of nonlocal continuum theory for different situations of problem characteristics. So, resolving the mentioned paradoxes by means of a purely numerical approach based on the original integral form of nonlocal elasticity theory is the major contribution of present study.
Institute of Scientific and Technical Information of China (English)
周振功; 王彪
2001-01-01
The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a twodimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen' s for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non- local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.
Teng, Da; Cao, Qing; Wang, Kai
2017-05-01
We present an extension of the generalized nonlocal (GNL) optical response theory for the mode analysis of several plasmonic waveguides. We show that, compared with the local description, the imaginary part of the effective mode index is enlarged using the GNL response model. We ascribe this enlargement to the ‘effective’ surface modification and the induced charge diffusion. This result is quite different from that of the hydrodynamic model, where the imaginary part becomes smaller compared with that of the local model. Further, we investigate the influence of geometry parameters on propagation properties and find that the nonlocal effects are much more remarkable for smaller gap and sharper tip. Although the introduction of diffusion has a negative impact on the propagation length, it reveals the true physical insight and should be taken care when dealing with nanoplasmonic waveguide for photonic integration applications.
Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories
Gukov, Sergei
2013-01-01
We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases which are not distinguished by the Wilson-'t Hooft criterion. The long-distance behavior of loop and surface operators which are neither confined nor screened is controlled by a 4d TQFT. We construct these TQFTs for phases which are characterized by the presence of electrically and/or magnetically charged condensates. Interestingly, the TQFT describing a phase with a nonabelian monopole condensate is based on the theory of nonabelian gerbes. We also show that in phases with a dyonic condensate the low-energy theta-angle is quantized.
Large-N limit of the non-local 2D Yang-Mills and generalized Yang-Mills theories on a cylinder
Saaidi, K; Saaidi, Khaled; Khorrami, Mohammad
2002-01-01
The large-group behavior of the nonlocal YM$_2$'s and gYM$_2$'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 nonlocal YM$_2$'s on a cylinder with some special bounary conditions are also obtained.
On the one-loop effective potential in nonlocal supersymmetric theories
de Mello, E R Bezerra; Nascimento, J R; Petrov, A Yu
2016-01-01
Within the superfield approach, we consider the nonlocal generalization of the Wess-Zumino model and calculate the one-loop low-energy contributions to the effective action. Four different nonlocal models are considered, among which only the first model does not reduce to the standard Wess-Zumino model when we take the parameter of nonlocality of the model, $\\Lambda$, much greater than any energy scale; in addition, this model also depends on an extra parameter, $\\xi$. As to the other three models, the result looks like the renormalized effective potential for the usual Wess-Zumino model, where the normalization scale $\\mu$ is replaced by the $\\Lambda$. Moreover, the fourth model displays a divergence which can be eliminated through the appropriate wave function renormalization.
Mavrantzas, Vlasis G.; Beris, Antony N.; Leermakers, Frans; Fleer, Gerard J.
2005-11-01
Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n1,e and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction φ; both n1,e and φ enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z ⩽2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z =2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z ⩽2l, continuum for distances z >2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.
Renewal of basic laws and principles for polar continuum theories (Ⅺ)——consistency problems
Institute of Scientific and Technical Information of China (English)
DAI Tian-min
2007-01-01
Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅸ)-THERMOMECHANICS
Institute of Scientific and Technical Information of China (English)
DAI Tian-min
2005-01-01
The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified.
Biswas, T.; Koivisto, T.; Mazumdar, A.
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 d
Biswas, T.; Koivisto, T.; Mazumdar, A.
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
Energy Technology Data Exchange (ETDEWEB)
Sochichiu, Corneliu
2003-11-06
We discuss the continuum limits of Berenstein-Maldacena-Nastase matrix model. The special attention is paid to limits that give rise to Poisson bracket gauge field theories with gauge groups U(n) on the ordinary two sphere. The gauge group and the space depending on the degeneracy of the classical solution about which the model is considered. We compare these limits as well as different solutions in the framework of the same limit model. We show that these models fail to be equivalent in the continuum limit, i.e., the continuum limit does not commute with dualities of the matrix theory.
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.
Towards LHC physics with nonlocal Standard Model
Tirthabir Biswas; Nobuchika Okada
2015-01-01
We take a few steps towards constructing a string-inspired nonlocal extension of the Standard Model. We start by illustrating how quantum loop calculations can be performed in nonlocal scalar field theory. In particular, we show the potential to address the hierarchy problem in the nonlocal framework. Next, we construct a nonlocal abelian gauge model and derive modifications of the gauge interaction vertex and field propagators. We apply the modifications to a toy version of the nonlocal Stan...
Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory
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.
Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Nielsen, H.B. [Niels Bohr Inst., Kobenhavn (Denmark); Rugh, H.H. [Univ. of Warwick, Coventry (United Kingdom); Rugh, S.E. [Los Alamos National Lab., NM (United States)
1996-12-31
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 go{close_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 limit{close_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.
Extreme Exotic Calcium Lambda Hypernuclei in the Relativistic Continuum Hartree-Bogoliubov Theory
Institute of Scientific and Technical Information of China (English)
L(U) Hong-Feng
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-Weizs(a)cker mass formula of a multi-strange system and the Woods-Saxon-type potential of larnbda need to be modified for exotic calcium hypernuclei with unusual number of neutrons and lambdas. The possible neutron and lambda limits of exotic Ca larnbda hypernuclei are also investigated.
Ferrighi, Lara; Frediani, Luca; Ruud, Kenneth
2010-01-01
The theory and an implementation of the solvent contribution to the cubic response function for the polarizable continuum model for multiconfigurational self-consistent field wave functions is presented. The excited-state polarizability of benzene, para-nitroaniline, and nitrobenzene has been obtained from the double residue of the cubic response function calculated in the presence of an acetonitrile and dioxane solvent. The calculated excited-state polarizabilities are compared to results obtained from the linear response function of the explicitly optimized excited states.
Evolution of $N = 28$ shell closure in relativistic continuum Hartree-Bogoliubov theory
Xia, Xuewei
2015-01-01
The $N = 28$ shell gap in sulfur, argon, calcium and titanium isotopes is investigated in the framework of relativistic continuum Hartree-Bogoliubov (RCHB) theory. The evolutions of neutron shell gap, separation energy, single particle energy and pairing energy are analyzed, and it is found that $N = 28$ shell gap is quenched in sulfur isotopes but persists in argon, calcium and titanium isotopes. The evolution of $N = 28$ shell gap in $N = 28$ isotonic chain is discussed, and the erosion of $N = 28$ shell gap is understood with the evolution of potential with proton number.
Entanglement: A myth introducing non-locality in any quantum theory
Prikas, Athanasios
2007-01-01
The purposes of the present article are: a) To show that non-locality leads to the transfer of certain amounts of energy and angular momentum at very long distances, in an absolutely strange and unnatural manner, in any model reproducing the quantum mechanical results. b) To prove that non-locality is the result only of the zero spin state assumption for distant particles, which explains its presence in any quantum mechanical model. c) To reintroduce locality, simply by denying the existence of the zero spin state in nature (the so-called highly correlated, or EPR singlet state) for particles non-interacting with any known field. d) To propose a realizable experiment to clarify if two remote (and thus non-interacting with a known field) particles, supposed to be correlated as in Bell-type experiments, are actually in zero spin state.
Li, Xian-Fang; Tang, Guo-Jin; Shen, Zhi-Bin; Lee, Kang Yong
2015-01-01
Free vibration and mass detection of carbon nanotube-based sensors are studied in this paper. Since the mechanical properties of carbon nanotubes possess a size effect, the nonlocal beam model is used to characterize flexural vibration of nanosensors carrying a concentrated nanoparticle, where the size effect is reflected by a nonlocal parameter. For nanocantilever or bridged sensor, frequency equations are derived when a nanoparticle is carried at the free end or the middle, respectively. Exact resonance frequencies are numerically determined for clamped-free, simply-supported, and clamped-clamped resonators. Alternative approximations of fundamental frequency are given in closed form within the relative error less than 0.4%, 0.6%, and 1.4% for cantilever, simply-supported, and bridged sensors, respectively. Mass identification formulae are derived in terms of the frequency shift. Identified masses via the present approach coincide with those using the molecular mechanics approach and reach as low as 10(-24)kg. The obtained results indicate that the nonlocal effect decreases the resonance frequency except for the fundamental frequency of nanocantilever sensor. These results are helpful to the design of micro/nanomechanical zeptogram-scale biosensor.
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.
Observers in Spacetime and Nonlocality
Mashhoon, B
2012-01-01
Characteristics of observers in relativity theory are critically examined. For field measurements in Minkowski spacetime, the Bohr-Rosenfeld principle implies that the connection between actual (i.e., noninertial) and inertial observers must be nonlocal. Nonlocal electrodynamics of non-uniformly rotating observers is discussed and the consequences of this theory for the phenomenon of spin-rotation coupling are briefly explored.
Energy Technology Data Exchange (ETDEWEB)
Dastjerdi, Shahriar; Aliabadi, Sharifeh; Jabbarzadeh Mehrdad [Islamic Azad University, Tehran (Iran, Islamic Republic of)
2016-03-15
The constitutive equations of nano-plates embedded in elastic matrix are derived based on Eringen non-local elasticity theory. Considering the non-local differential constitutive relations of Eringen theory in Cartesian and cylindrical coordinates system based on the first and higher order shear deformation theories and using the Von Karman strain field, the equilibrium differential equations are derived in terms of generalized displacements and rotations. In addition, the obtained governing equations for single layer nano plates are developed for multi-layer nano-plates. Rectangular, annular/circular and sectorial nano-plates are considered. In the most of the investigations in non-local elasticity theory, the classical plate theory (CLPT) is used, however in this paper, the governing equations are derived based on both FSDT and HSDT theories because of obtaining more accurate results.
Causality, Nonlocality, and Negative Refraction.
Forcella, Davide; Prada, Claire; Carminati, Rémi
2017-03-31
The importance of spatial nonlocality in the description of negative refraction in electromagnetic materials has been put forward recently. We develop a theory of negative refraction in homogeneous and isotropic media, based on first principles, and that includes nonlocality in its full generality. The theory shows that both dissipation and spatial nonlocality are necessary conditions for the existence of negative refraction. It also provides a sufficient condition in materials with weak spatial nonlocality. These fundamental results should have broad implications in the theoretical and practical analyses of negative refraction of electromagnetic and other kinds of waves.
Clear Evidence of a Continuum Theory of 4D Euclidean Simplicial Quantum Gravity
Egawa, H 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 gamma^{(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.
Full-potential multiple scattering theory with space-filling cells for bound and continuum 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.
Directory of Open Access Journals (Sweden)
Maria Anna De Rosa
2014-01-01
Full Text Available The free vibration response of double-walled carbon nanotubes (DWCNTs is investigated. The DWCNTs are modelled as two beams, interacting between them through the van der Waals forces, and the nonlocal Euler-Bernoulli beam theory is used. The governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained employing two different approaches. In the first method, the two double-walled carbon nanotubes are discretized by means of the so-called “cell discretization method” (CDM in which each nanotube is reduced to a set of rigid bars linked together by elastic cells. The resulting discrete system takes into account nonlocal effects, constraint elasticities, and the van der Waals forces. The second proposed approach, belonging to the semianalytical methods, is an optimized version of the classical Rayleigh quotient, as proposed originally by Schmidt. The resulting conditions are solved numerically. Numerical examples end the paper, in which the two approaches give lower-upper bounds to the true values, and some comparisons with existing results are offered. Comparisons of the present numerical results with those from the open literature show an excellent agreement.
Waldecker, S. J.; Timofeyuk, N. K.
2016-09-01
The nonlocal dispersive optical model (NLDOM) nucleon potentials are used for the first time in the adiabatic analysis of a (d ,p ) reaction to generate distorted waves both in the entrance and exit channels. These potentials were designed and fitted by Mahzoon et al. [Phys. Rev. Lett. 112, 162503 (2014), 10.1103/PhysRevLett.112.162503] to constrain relevant single-particle physics in a consistent way by imposing the fundamental properties, such as nonlocality, energy-dependence and dispersive relations, that follow from the complex nature of nuclei. However, the NLDOM prediction for the 40Ca(d ,p )41Ca cross sections at low energy, typical for some modern radioactive beam ISOL (isotope separation online) facilities, is about 70% higher than the experimental data despite being reduced by the NLDOM spectroscopic factor of 0.73. This overestimation comes most likely either from insufficient absorption or due to constructive interference between ingoing and outgoing waves. This indicates strongly that additional physics arising from many-body effects is missing in the widely used current versions of (d ,p ) reaction theories.
De Rosa, Maria Anna; Lippiello, Maria
2014-01-01
The free vibration response of double-walled carbon nanotubes (DWCNTs) is investigated. The DWCNTs are modelled as two beams, interacting between them through the van der Waals forces, and the nonlocal Euler-Bernoulli beam theory is used. The governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained employing two different approaches. In the first method, the two double-walled carbon nanotubes are discretized by means of the so-called "cell discretization method" (CDM) in which each nanotube is reduced to a set of rigid bars linked together by elastic cells. The resulting discrete system takes into account nonlocal effects, constraint elasticities, and the van der Waals forces. The second proposed approach, belonging to the semianalytical methods, is an optimized version of the classical Rayleigh quotient, as proposed originally by Schmidt. The resulting conditions are solved numerically. Numerical examples end the paper, in which the two approaches give lower-upper bounds to the true values, and some comparisons with existing results are offered. Comparisons of the present numerical results with those from the open literature show an excellent agreement.
Disentangling Nonlocality and Teleportation
Hardy, L
1999-01-01
Quantum entanglement can be used to demonstrate nonlocality and to teleport a quantum state from one place to another. The fact that entanglement can be used to do both these things has led people to believe that teleportation is a nonlocal effect. In this paper it is shown that teleportation is conceptually independent of nonlocality. This is done by constructing a toy local theory in which cloning is not possible (without a no-cloning theory teleportation makes limited sense) but teleportation is. Teleportation in this local theory is achieved in an analogous way to the way it is done with quantum theory. This work provides some insight into what type of process teleportation is.
Quantum Noether identities for non-local transformations in higher-order derivatives theories
Li, Z P
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 sub e sub f sub f sup P in quantum canonical NIs instead of the classical I sup 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 Yan...
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.
Comparison of shock structure solutions using independent continuum and kinetic theory approaches
Fiscko, Kurt A.; Chapman, Dean R.
1988-01-01
A vehicle traversing the atmosphere will experience flight regimes at high altitudes in which the thickness of a hypersonic shock wave is not small compared to the shock standoff distance from the hard body. When this occurs, it is essential to compute accurate flow field solutions within the shock structure. In this paper, one-dimensional shock structure is investigated for various monatomic gases from Mach 1.4 to Mach 35. Kinetic theory solutions are computed using the Direct Simulation Monte Carlo method. Steady-state solutions of the Navier-Stokes equations and of a slightly truncated form of the Burnett equations are determined by relaxation to a steady state of the time-dependent continuum equations. Monte Carlo results are in excellent agreement with published experimental data and are used as bases of comparison for continuum solutions. For a Maxwellian gas, the truncated Burnett equations are shown to produce far more accurate solutions of shock structure than the Navier-Stokes equations.
Self-consistent elastic continuum theory of degenerate, equilibrium aperiodic solids.
Bevzenko, Dmytro; Lubchenko, Vassiliy
2014-11-07
We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state. The effective elastic constants are determined by the bare elastic constants of individual free energy minima of the liquid, the magnitude of built-in stress, and temperature, analogously to how the dielectric response of a polar liquid is determined by the dipole moment of the constituent molecules and temperature. In contrast with the dielectric constant--which is enhanced by adding polar molecules to the system--the elastic constants are down-renormalized by the relaxation of the built-in stress. The renormalization flow of the elastic constants has three fixed points, two of which are trivial and correspond to the uniform liquid state and an infinitely compressible solid, respectively. There is also a nontrivial fixed point at the Poisson ratio equal to 1/5, which corresponds to an isospin-like degeneracy between shear and uniform deformation. The present description predicts a discontinuous jump in the (finite frequency) shear modulus at the crossover from collisional to activated transport, consistent with the random first order transition theory.
Powell, Stephen; Chalker, J. T.
2008-10-01
We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.
A relativistic continuum Hartree-Bogoliubov theory description of N=3 isotones
Institute of Scientific and Technical Information of China (English)
HAN Rui; JI Juan-Xia; LI Jia-Xing
2011-01-01
The ground-state properties of N=3 isotones and mirror nuclei have been investigated in the Rrelativistic Continuum Hartree-Bogoliubov theory with the NLSH effective interaction.Pairing correlations are taken into account by a density-dependent δ-force.The calculations show that the proton density distributions of 8B and 9C have a long tail,the core has an increasing tendency of 9C and the paired off valence protons make the halo distribution shrink.The cross sections for the 8B(9C)+12C reaction which are consistent with the experimental data are calculated using the Glauber model.On the whole,we think that 8B is a one-proton halo nucleus and 9C is a two-proton halo nucleus.
Buyens, Boye; Montangero, Simone; Haegeman, Jutho; Verstraete, Frank; Van Acoleyen, Karel
2017-05-01
It has been established that matrix product states can be used to compute the ground state and single-particle excitations and their properties of lattice gauge theories at the continuum limit. However, by construction, in this formalism the Hilbert space of the gauge fields is truncated to a finite number of irreducible representations of the gauge group. We investigate quantitatively the influence of the truncation of the infinite number of representations in the Schwinger model, one-flavor QED2 , with a uniform electric background field. We compute the two-site reduced density matrix of the ground state and the weight of each of the representations. We find that this weight decays exponentially with the quadratic Casimir invariant of the representation which justifies the approach of truncating the Hilbert space of the gauge fields. Finally, we compute the single-particle spectrum of the model as a function of the electric background field.
Theory of non-local point transformations - Part 1: Representation of Teleparallel Gravity
Tessarotto, Massimo
2016-01-01
In this paper the extension of the functional setting customarily adopted in General Relativity (GR) is considered. For this purpose, an explicit solution of the so-called Einstein's\\ Teleparallel problem is sought. This is achieved by a suitable extension of the traditional concept of GR reference frame and is based on the notion of non-local point transformation (NLPT). In particular, it is shown that a solution to the said problem can be reached by introducing a suitable subset of transformations denoted here as \\textit{special} \\textit{NLPT}. These are found to realize a phase-space transformation connecting\\emph{\\}the flat Minkowski space-time with, in principle, an arbitrary curved space-time. The functional setting and basic properties of the new transformations are investigated.
Naka, S.; Toyoda, H.; Takanashi, T.; Umezawa, E.
2014-04-01
In kappa -Minkowski spacetime, the coordinates are Lie algebraic elements such that time and space coordinates do not commute, whereas space coordinates commute with each other. The noncommutativity is proportional to a Planck-length-scale constant kappa ^{-1}, which is a universal constant other than the velocity of light, under the kappa -Poincaré transformation. In this sense, the spacetime has a structure called "doubly special relativity." Such a noncommutative structure is known to be realized by SO(1,4) generators in 4-dimensional de Sitter space. In this paper, we try to construct a noncommutative spacetime having a commutative n-dimensional Minkowski spacetime based on AdS_{n+1} space with SO(2,n) symmetry. We also study an invariant wave equation corresponding to the first Casimir invariant of this symmetry as a nonlocal field equation expected to yield finite loop amplitudes.
Nonlocal gravity: Conformally flat spacetimes
Bini, Donato
2016-01-01
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity in two-dimensional spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein's field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of nonlocal gravity.
Exact Solutions in Nonlocal Linear Models
Vernov, S. Yu.
2008-01-01
A general class of cosmological models driven by a nonlocal scalar field inspired by the string field theory is studied. Using the fact that the considering linear nonlocal model is equivalent to an infinite number of local models we have found an exact special solution of the nonlocal Friedmann equations. This solution describes a monotonically increasing Universe with the phantom dark energy.
Kees, C. E.; Miller, C. T.; Dimakopoulos, A.; Farthing, M.
2016-12-01
The last decade has seen an expansion in the development and application of 3D free surface flow models in the context of environmental simulation. These models are based primarily on the combination of effective algorithms, namely level set and volume-of-fluid methods, with high-performance, parallel computing. These models are still computationally expensive and suitable primarily when high-fidelity modeling near structures is required. While most research on algorithms and implementations has been conducted in the context of finite volume methods, recent work has extended a class of level set schemes to finite element methods on unstructured methods. This work considers models of three-phase flow in domains containing air, water, and granular phases. These multi-phase continuum mechanical formulations show great promise for applications such as analysis of coastal and riverine structures. This work will consider formulations proposed in the literature over the last decade as well as new formulations derived using the thermodynamically constrained averaging theory, an approach to deriving and closing macroscale continuum models for multi-phase and multi-component processes. The target applications require the ability to simulate wave breaking and structure over-topping, particularly fully three-dimensional, non-hydrostatic flows that drive these phenomena. A conservative level set scheme suitable for higher-order finite element methods is used to describe the air/water phase interaction. The interaction of these air/water flows with granular materials, such as sand and rubble, must also be modeled. The range of granular media dynamics targeted including flow and wave transmision through the solid media as well as erosion and deposition of granular media and moving bed dynamics. For the granular phase we consider volume- and time-averaged continuum mechanical formulations that are discretized with the finite element method and coupled to the underlying air
A simple exposure-time theory for all time-nonlocal transport formulations and beyond.
Ginn, T. R.; Schreyer, L. G.
2016-12-01
Anomalous transport or better put, anomalous non-transport, of solutes or flowing water or suspended colloids or bacteria etc. has been the subject of intense analyses with multiple formulations appearing in scientific literature from hydrology to geomorphology to chemical engineering, to environmental microbiology to mathematical physics. Primary focus has recently been on time-nonlocal mass conservation formulations such as multirate mass transfer, fractional-time advection-dispersion, continuous-time random walks, and dual porosity modeling approaches, that employ a convolution with a memory function to reflect respective conceptual models of delays in transport. These approaches are effective or "proxy" ones that do not always distinguish transport from immobilzation delays, are generally without connection to measurable physicochemical properties, and involve variously fractional calculus, inverse Laplace or Fourier transformations, and/or complex stochastic notions including assumptions of stationarity or ergodicity at the observation scale. Here we show a much simpler approach to time-nonlocal (non-)transport that is free of all these things, and is based on expressing the memory function in terms of a rate of mobilization of immobilized mass that is a function of the continguous time immobilized. Our approach treats mass transfer completely independently from the transport process, and it allows specification of actual immobilization mechanisms or delays. To our surprize we found that for all practical purposes any memory function can be expressed this way, including all of those associated with the multi-rate mass transfer approaches, original powerlaw, different truncated powerlaws, fractional-derivative, etc. More intriguing is the fact that the exposure-time approach can be used to construct heretofore unseen memory functions, e.g., forms that generate oscillating tails of breakthrough curves such as may occur in sediment transport, forms for delay
Continuum theory of critical phenomena in polymer solutions: Formalism and mean field approximation
Goldstein, Raymond E.; Cherayil, Binny J.
1989-06-01
A theoretical description of the critical point of a polymer solution is formulated directly from the Edwards continuum model of polymers with two- and three-body excluded-volume interactions. A Hubbard-Stratonovich transformation analogous to that used in recent work on the liquid-vapor critical point of simple fluids is used to recast the grand partition function of the polymer solution as a functional integral over continuous fields. The resulting Landau-Ginzburg-Wilson (LGW) Hamiltonian is of the form of a generalized nonsymmetric n=1 component vector model, with operators directly related to certain connected correlation functions of a reference system. The latter is taken to be an ensemble of Gaussian chains with three-body excluded-volume repulsions, and the operators are computed in three dimensions by means of a perturbation theory that is rapidly convergent for long chains. A mean field theory of the functional integral yields a description of the critical point in which the power-law variations of the critical polymer volume fraction φc, critical temperature Tc, and critical amplitudes on polymerization index N are essentially identical to those found in the Flory-Huggins theory. In particular, we find φc ˜N-1/2, Tθ-Tc˜N-1/2 with (Tθ the theta temperature), and that the composition difference between coexisting phases varies with reduced temperature t as N-1/4t1/2. The mean field theory of the interfacial tension σ between coexisting phases near the critical point, developed by considering the LGW Hamiltonian for a weakly inhomogeneous solution, yields σ˜N-1/4t3/2, with the correlation length diverging as ξ˜N1/4t-1/2 within the same approximation, consistent with the mean field limit of de Gennes' scaling form. Generalizations to polydisperse systems are discussed.
Energy Technology Data Exchange (ETDEWEB)
Saaidi, K.; Sajadi, H.M. [Dept. of Physics, Univ. of Tehran (Iran)
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{sub 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({phi}) ={phi}{sup 2k} in nlgYM{sub 2} theories at the strong coupling phase (SCP) regime (A > A{sub c}) for large groups. In the specific {phi}{sup 4} model, we show that the theory has a third order phase transition. (orig.)
Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation
Directory of Open Access Journals (Sweden)
Arminjon Mayeul
2016-01-01
Full Text Available An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes’ thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton’s second law. This implies Einstein’s geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell’s equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a “free” photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.
Continuum dynamics and the electromagnetic field in the scalar ether theory of gravitation
Arminjon, Mayeul
2016-01-01
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time, but motion is governed by an extension of the relativistic form of Newton's second law. This implies Einstein's geodesic motion for free particles only in a constant gravitational field. In this work, equations governing the dynamics of a continuous medium subjected to gravitational and non-gravitational forces are derived. Then, the case where the non-gravitational force is the Lorentz force is investigated. The gravitational modification of Maxwell's equations is obtained under the requirement that a charged continuous medium, subjected to the Lorentz force, obeys the equation derived for continuum dynamics under external forces. These Maxwell equations are shown to be consistent with the dynamics of a "free" photon, and thus with the geometrical optics of this theory. However, these equations do not imply local charge conservation, except for a constant gravitational field.
Abbasi, Mohammad; Karami Mohammadi, Ardeshir
2015-05-01
A relationship based on a nonlocal elasticity theory is developed to investigate the torsional sensitivity and resonant frequency of an atomic force microscope (AFM) with assembled cantilever probe (ACP). This ACP comprises a horizontal cantilever and a vertical extension, and a tip located at the free end of the extension, which makes the AFM capable of topography at sidewalls of microstructures. First, the governing differential equations of motion and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of nonlocal elasticity theory and Hamilton's principle. Afterward, a closed-form expression for the sensitivity of vibration modes has been obtained using the relationship between the resonant frequency and contact stiffness of cantilever and sample. These analysis accounts for a better representation of the torsional behavior of an AFM with sidewall probe where the small-scale effect are significant. The results of the proposed model are compared with those of classical beam theory. The results show that the sensitivities and resonant frequencies of ACP predicted by the nonlocal elasticity theory are smaller than those obtained by the classical beam theory.
Quantum entanglement in non-local games, graph parameters and zero-error information theory
Scarpa, G.
2013-01-01
We study quantum entanglement and some of its applications in graph theory and zero-error information theory. In Chapter 1 we introduce entanglement and other fundamental concepts of quantum theory. In Chapter 2 we address the question of how much quantum correlations generated by entanglement can d
Kimura, Tetsuji; Noumi, Toshifumi; Yamaguchi, Masahide
2016-01-01
We construct $\\mathcal{N}=1$ supersymmetric nonlocal theories in four dimension. We discuss higher derivative extensions of chiral and vector superfields, and write down generic forms of K\\"ahler 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.
Chan, Poh Yin; Tong, Chi Ming; Durrant, Marcus C
2011-09-01
An empirical method for estimation of the boiling points of organic molecules based on density functional theory (DFT) calculations with polarized continuum model (PCM) solvent corrections has been developed. The boiling points are calculated as the sum of three contributions. The first term is calculated directly from the structural formula of the molecule, and is related to its effective surface area. The second is a measure of the electronic interactions between molecules, based on the DFT-PCM solvation energy, and the third is employed only for planar aromatic molecules. The method is applicable to a very diverse range of organic molecules, with normal boiling points in the range of -50 to 500 °C, and includes ten different elements (C, H, Br, Cl, F, N, O, P, S and Si). Plots of observed versus calculated boiling points gave R²=0.980 for a training set of 317 molecules, and R²=0.979 for a test set of 74 molecules. The role of intramolecular hydrogen bonding in lowering the boiling points of certain molecules is quantitatively discussed. Crown Copyright © 2011. Published by Elsevier Inc. All rights reserved.
Silbermann, C. B.; Ihlemann, J.
2016-03-01
Continuum Dislocation Theory (CDT) relates gradients of plastic deformation in crystals with the presence of geometrically necessary dislocations. Therefore, the dislocation tensor is introduced as an additional thermodynamic state variable which reflects tensorial properties of dislocation ensembles. Moreover, the CDT captures both the strain energy from the macroscopic deformation of the crystal and the elastic energy of the dislocation network, as well as the dissipation of energy due to dislocation motion. The present contribution deals with the geometrically linear CDT. More precise, the focus is on the role of dislocation kinematics for single and multi-slip and its consequences on the field equations. Thereby, the number of active slip systems plays a crucial role since it restricts the degrees of freedom of plastic deformation. Special attention is put on the definition of proper, well-defined invariants of the dislocation tensor in order to avoid any spurious dependence of the resulting field equations on the coordinate system. It is shown how a slip system based approach can be in accordance with the tensor nature of the involved quantities. At first, only dislocation glide in one active slip system of the crystal is allowed. Then, the special case of two orthogonal (interacting) slip systems is considered and the governing field equations are presented. In addition, the structure and symmetry of the backstress tensor is investigated from the viewpoint of thermodynamical consistency. The results will again be used in order to facilitate the set of field equations and to prepare for a robust numerical implementation.
Energy Technology Data Exchange (ETDEWEB)
Atabakhshian, V.; Shooshtari, A.; Karimi, M., E-mail: karimi_mh@yahoo.com
2015-01-01
In this study, nonlinear vibration and stability of a fluid-conveying nanotube (FCNT), elastically coupled to a smart piezoelectric polymeric beam (PPB) is investigated based on nonlocal elasticity theory, Euler–Bernoulli beam model and energy approach. In order to obtain an active instability control of FCNT, the PPB is longitudinally polarized as an actuator while in the absence of an imposed electric field it is also possible to be used as an alarm biosensor. Simulating the above smart coupled nanobeam system alike the double nanobeam systems (which are relatively developed by other authors) leads to obtain nonlinear differential equations of motion. The linear natural and damping frequencies are achieved by ignoring all the system nonlinearities which are then considered to obtain nonlinear frequencies using an iterative method. The effects of geometric nonlinearity, small scale parameter, coupled medium constants, Knudsen number, temperature change, aspect ratio and external applied voltage on critical flow velocity are studied in details. It is concluded that applying an electric voltage on PPB will increase the stability of FCNT. It is hoped that this research will provide a new approach to smart instability control of FCNTs which is no yet reported.
Atabakhshian, V.; Shooshtari, A.; Karimi, M.
2015-01-01
In this study, nonlinear vibration and stability of a fluid-conveying nanotube (FCNT), elastically coupled to a smart piezoelectric polymeric beam (PPB) is investigated based on nonlocal elasticity theory, Euler-Bernoulli beam model and energy approach. In order to obtain an active instability control of FCNT, the PPB is longitudinally polarized as an actuator while in the absence of an imposed electric field it is also possible to be used as an alarm biosensor. Simulating the above smart coupled nanobeam system alike the double nanobeam systems (which are relatively developed by other authors) leads to obtain nonlinear differential equations of motion. The linear natural and damping frequencies are achieved by ignoring all the system nonlinearities which are then considered to obtain nonlinear frequencies using an iterative method. The effects of geometric nonlinearity, small scale parameter, coupled medium constants, Knudsen number, temperature change, aspect ratio and external applied voltage on critical flow velocity are studied in details. It is concluded that applying an electric voltage on PPB will increase the stability of FCNT. It is hoped that this research will provide a new approach to smart instability control of FCNTs which is no yet reported.
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); Kolahchi, R.; Vossough, H. [Faculty of Mechanical Engineering, University of Kashan, Kashan (Iran, Islamic Republic of)
2012-11-15
This study presents an analytical approach for buckling analysis and smart control of a single layer graphene sheet (SLGS) using a coupled polyvinylidene fluoride (PVDF) nanoplate. The SLGS and PVDF nanoplate are considered to be coupled by an enclosing elastic medium which is simulated by the Pasternak foundation. The PVDF nanoplate is subjected to an applied voltage in the thickness direction which operates in control of critical load of the SLGS. In order to satisfy the Maxwell equation, electric potential distribution is assumed as a combination of a half-cosine and linear variation. The exact analysis is performed for the case when all four ends are simply supported and free electrical boundary condition. Adopting the nonlocal Mindlin plate theory, the governing equations are derived based on the energy method and Hamilton's principle. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, stiffness of the internal elastic medium, graphene length, mode number and external electric voltage on the buckling smart control of the SLGS. The results depict that the imposed external voltage is an effective controlling parameter for buckling of the SLGS. This study might be useful for the design and smart control of nano-devices.
Directory of Open Access Journals (Sweden)
Atangana Abdon
2016-01-01
Full Text Available In this manuscript we proposed a new fractional derivative with non-local and no-singular kernel. We presented some useful properties of the new derivative and applied it to solve the fractional heat transfer model.
A theory of nonlocal mixing-length convection. I - The moment formalism. [in stellar interior
Grossman, Scott A.; Narayan, Ramesh; Arnett, David
1993-01-01
A flexible and potentially powerful theory of convection, based on the mixing length picture, is developed to make unbiased self-consistent predictions about overshooting and other complicated phenomena in convection. The basic formalism is set up, and the method's power is demonstrated by showing that a simplified version of the theory reproduces all the standard results of local convection. The second-order equations of the theory are considered in the limit of a steady state and vanishing third moments, and it is shown that they reproduce all the standard results of local mixing-length convection. There is a particular value of the superadiabatic gradient, below which the only possible steady state of a fluid is nonconvecting. Above this critical value, a fluid is convectively unstable. Two distinct regimes of convection, which are identified as efficient and inefficient convection, are determined.
A theory of nonlocal mixing-length convection. I - The moment formalism. [in stellar interior
Grossman, Scott A.; Narayan, Ramesh; Arnett, David
1993-01-01
A flexible and potentially powerful theory of convection, based on the mixing length picture, is developed to make unbiased self-consistent predictions about overshooting and other complicated phenomena in convection. The basic formalism is set up, and the method's power is demonstrated by showing that a simplified version of the theory reproduces all the standard results of local convection. The second-order equations of the theory are considered in the limit of a steady state and vanishing third moments, and it is shown that they reproduce all the standard results of local mixing-length convection. There is a particular value of the superadiabatic gradient, below which the only possible steady state of a fluid is nonconvecting. Above this critical value, a fluid is convectively unstable. Two distinct regimes of convection, which are identified as efficient and inefficient convection, are determined.
Classical and Quantum Nonlocal Supergravity
Giaccari, Stefano
2016-01-01
We derive the N=1 supersymmetric extension for a class of weakly nonlocal four dimensional gravitational theories.The construction is explicitly done in the superspace and the tree-level perturbative unitarity is explicitly proved both in the superfield formalism and in field components. For the minimal nonlocal supergravity the spectrum is the same as in the local theory and in particular it is ghost-free. The supersymmetric extension of the super-renormalizable Starobinsky theory and of two alternative massive nonlocal supergravities are found as straightforward applications of the formalism. Power-counting arguments ensure super-renormalizability with milder requirement for the asymptotic behavior of form factors than in ordinary nonlocal gravity. The most noteworthy result, common to ordinary supergravity, is the absence of quantum corrections to the cosmological constant in any regularization procedure. We cannot exclude the usual one-loop quadratic divergences. However, local vertices in the superfields...
Post Buckling Behaviour of a Nanobeam considering both the surface and nonlocal effects
Maitra, Rajarshi; Bose, Supratik
2012-07-01
Nano-scale beams and plates have been the key components of the sensor and actuator in nanoelectromechnical (NEMS) systems with wide applications in environmental monitoring, medical diagnostics, food processing, mining, bioengineering and defence. Nonlocal and surface effects have been incorporated to find critical load of a nano beam subjected to a transverse loading. The Nonlocal theory, expresses the stress field at a point in an elastic continuum in terms of not only strains at that point but also the strains throughout the body. The governing equation of a normal beam has been modified to achieve the governing differential equation of a nano beam. The post buckling behaviour of a nano beam has been tried to be assessed. The results showed that the surface effects try to delay the buckling process whereas the nonlocal effects contribute to the instability.
Analytical Nonlocal Electrostatics Using Eigenfunction Expansions of Boundary-Integral Operators
Bardhan, Jaydeep P; Brune, Peter R
2012-01-01
In this paper, we present an analytical solution to 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 their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for analytical calculations in separable geometries, we rederive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion layer and then a dilute electrolyte (modeled with the linearized Poisson--Boltzmann equation). Our main result, however, is an analytical method for calculating the reaction potential in a protein embedded in a nonlocal-dielectric solvent, the Lorentz model studied by Dogonadze and Kornyshev. The analytical method enables biophysicists to study the new nonlocal theory in a simple, computationally fast way; an open-source MATLAB implementatio...
Directory of Open Access Journals (Sweden)
B. Amirian
2013-01-01
Full Text Available This study is concerned with the thermal vibration analysis of a short single-walled carbon nanotube embedded in an elastic medium based on nonlocal Timoshenko beam model. A Winkler- and Pasternak-type elastic foundation is employed to model the interaction of short carbon nanotubes and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, high temperature change, Winkler modulus parameter, Pasternak shear parameter, vibration mode and aspect ratio of short carbon nanotubes on the vibration frequency are analyzed and discussed. The present study shows that for high temperature changes, the effect of Winkler constant in different nonlocal parameters on nonlocal frequency is negligible. Furthermore, for all temperatures, the nonlocal frequencies are always smaller than the local frequencies in short carbon nanotubes. In addition, for high Pasternak modulus, by increasing the aspect ratio, the nonlocal frequency decreases. It is concluded that short carbon nanotubes have the higher frequencies as compared with long carbon nanotubes.
A generalized non-local optical response theory for plasmonic nanostructures
DEFF Research Database (Denmark)
Mortensen, N. Asger; Raza, Søren; Wubs, Martijn
2014-01-01
mechanism that even dominates the widely anticipated short circuiting by quantum tunnelling. We anticipate that our theory can be successfully applied in plasmonics to a wide class of conducting media, including doped semiconductors and low-dimensional materials such as graphene...
The wet solidus of silica: Predictions from the scaled particle theory and polarized continuum model
Energy Technology Data Exchange (ETDEWEB)
Ottonello, G., E-mail: giotto@dipteris.unige.it; Vetuschi Zuccolini, M. [DIPTERIS, Università di Genova, Corso Europa 26, 16132 Genoa (Italy); Richet, P. [Institut de Physique du Globe, Rue Jussieu 2, 75005 Paris (France)
2015-02-07
We present an application of the Scaling Particle Theory (SPT) coupled with an ab initio assessment of the electronic, dispersive, and repulsive energy terms based on the Polarized Continuum Model (PCM) aimed at reproducing the observed solubility behavior of OH{sub 2} over the entire compositional range from pure molten silica to pure water and wide pressure and temperature regimes. It is shown that the solution energy is dominated by cavitation terms, mainly entropic in nature, which cause a large negative solution entropy and a consequent marked increase of gas phase fugacity with increasing temperatures. Besides, the solution enthalpy is negative and dominated by electrostatic terms which depict a pseudopotential well whose minimum occurs at a low water fraction (X{sub H{sub 2O}}) of about 6 mol. %. The fine tuning of the solute-solvent interaction is achieved through very limited adjustments of the electrostatic scaling factor γ{sub el} which, in pure water, is slightly higher than the nominal value (i.e., γ{sub el} = 1.224 against 1.2), it attains its minimum at low H{sub 2}O content (γ{sub el} = 0.9958) and then rises again at infinite dilution (γ{sub el} = 1.0945). The complex solution behavior is interpreted as due to the formation of energetically efficient hydrogen bonding when OH functionals are in appropriate amount and relative positioning with respect to the discrete OH{sub 2} molecules, reinforcing in this way the nominal solute-solvent inductive interaction. The interaction energy derived from the SPT-PCM calculations is then recast in terms of a sub-regular Redlich-Kister expansion of appropriate order whereas the thermodynamic properties of the H{sub 2}O component at its standard state (1-molal solution referred to infinite dilution) are calculated from partial differentiation of the solution energy over the intensive variables.
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, the dynamic stress field near crack tips in the functionally graded materials subjected to the harmonic anti-plane shear stress waves was investi- gated by means of the non-local theory. The traditional concepts of the non-local theory were extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it was assumed that the material properties vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. The magnitude of the finite dynamic stress field depends on the crack length, the parameter describing the functionally graded materials, the circular frequency of the incident waves and the lattice parameter of materials.
Institute of Scientific and Technical Information of China (English)
ZHANG PeiWei; ZHOU ZhenGong; WU LinZhi
2007-01-01
In this paper, the dynamic stress field near crack tips in the functionally graded materials subjected to the harmonic anti-plane shear stress waves was investigated by means of the non-local theory. The traditional concepts of the non-local theory were extended to solve the fracture problem of functionally graded materials.To make the analysis tractable, it was assumed that the material properties vary exponentially with coordinate parallel to the crack. By use of the Fourier transform,the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. The magnitude of the finite dynamic stress field depends on the crack length, the parameter describing the functionally graded materials, the circular frequency of the incident waves and the lattice parameter of materials.
Rahmani, O.; Mohammadi Niaei, A.; Hosseini, S. A. H.; Shojaei, M.
2017-01-01
In the present study, free vibration model of a cantilever functionally graded (FG) nanobeam with an attached mass at tip and under various thermal loading and two types of material distribution is introduced. The vibration performance is considered using nonlocal Euler-Bernoulli beam theory. Two types of thermal loading, namely, uniform and nonlinear temperature rises through the thickness direction are considered. Thermo-mechanical properties of FG nano mass sensor are supposed to vary smoothly and continuously throughout the thickness based on power-law and Mori Tanaka distributions of material properties. Eringen non-local elasticity theory is exploited to describe the size dependency of FG nanobeam. The governing equations of the system with both axial and transverse displacements are derived based on Hamilton's principle and solved utilizing the differential transformation method (DTM) to find the non-dimensional natural frequencies. The results have good agreements with those discussing in the literature. After validation of the present model, the effect of various parameters such as mass and position of the attached nano particle, FG power-law exponent, thermal load type, material distribution type and nonlocal parameter on the frequency of nano sensor are studied. It is shown that the present model produces results of high accuracy, and it can be used as a benchmark in future studies of the free vibration of FG Nano-Mass Sensors.
Energy Technology Data Exchange (ETDEWEB)
Koutsoumaris, C. Chr.; Tsamasphyros, G. J. [School of Applied Mathematical and Physical Sciences National Technical University of Athens (NTUA) 5 Iroon Polytechniou Str., Zografou, Zografou Campus, Athens, GR-157 73 (Greece); Vogiatzis, G. G.; Theodorou, D. N. [School of Chemical Engineering National Technical University of Athens (NTUA) 5 Iroon Polytechniou Str., Zografou, Zografou Campus, Athens, GR-157 73 (Greece)
2015-12-31
The nonlocal theory of elasticity is employed for the study of the free vibrations of carbon nanotubes (CNT). For the first time, a bi-Helmholtz operator has been used instead of the standard Helmholtz operator in a nonlocal beam model. Alongside the continuum formulation and its numerical solution, atomistic Molecular Dynamics (MD) simulations have been conducted in order to directly evaluate the eigenfrequencies of vibrating CNTs with a minimum of adjustable parameters. Our results show that the bi-Helmholtz operator is the most appropriate one to fit MD simulation results. However, the estimation of vibration eigenfrequencies from molecular simulations still remains an open (albeit well-posed) problem.
Institute of Scientific and Technical Information of China (English)
周振功; 杜善义; 王彪
2003-01-01
In this paper, the non-local theory of elasticity is applied to obtain the behavior of a Griffith crack in the piezoelectric materials under anti-plane shear loading for permeable crack surface conditions. By means of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations with the unknown variable being the jump of the displacement across the crack surfaces. These equations are solved by the Schmidt method. Numerical examples are provided.Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularity is present at the crack tip. The non-local elastic solutions yield a finite hoop stress at the crack tip,thus allowing for a fracture criterion based on the maximum stress hypothesis. The finite hoop stress at the crack tip depends on the crack length and the lattice parameter of the materials, respectively.
Diffractive Interface Theory: Nonlocal polarizability approach to the optics of metasurfaces
Roberts, Christopher M; Podolskiy, Viktor A
2014-01-01
We present a formalism for understanding the elecromagnetism of metasurfaces, optically thin composite films with engineered diffraction. The technique, diffractive interface theory (DIT), takes explicit advantage of the small optical thickness of a metasurface, eliminating the need for solving for light propagation inside the film and providing a direct link between the spatial profile of a metasurface and its diffractive properties. Predictions of DIT are compared with full-wave numerical solutions of Maxwell's equations, demonstrating DIT's validity and computational advantages for optically thin structures. Applications of the DIT range from understanding of fundamentals of light-matter interaction in metasurfaces to efficient analysis of generalized refraction to metasurface optimization.
Diffractive interface theory: nonlocal susceptibility approach to the optics of metasurfaces.
Roberts, Christopher M; Inampudi, Sandeep; Podolskiy, Viktor A
2015-02-09
We present a formalism for understanding the electromagnetism of metasurfaces, optically thin composite films with engineered diffraction. The technique, diffractive interface theory (DIT), takes explicit advantage of the small optical thickness of a metasurface, eliminating the need for solving for light propagation inside the film and providing a direct link between the spatial profile of a metasurface and its diffractive properties. Predictions of DIT are compared with full-wave numerical solutions of Maxwell's equations, demonstrating DIT's validity and computational advantages for optically thin structures. Applications of the DIT range from understanding of fundamentals of light-matter interaction in metasurfaces to efficient analysis of generalized refraction to metasurface optimization.
Vera, R.
Non-local relativity NLR is a general theory based on optical physics and the equivalence principle according to which particles and standing waves obey the same inertial and gravitational G laws 1 2 3 The theoretical inertial and G properties of a particle model PM made up of standing waves correspond with all of them the Einstein s equivalence principle EEP special relativity quantum mechanics the conventional G tests and more critical ones presented here From NLR gravitation is a refraction phenomenon produced by a gradient of the relative refraction index of the space with respect to any observer at rest in the field During a free fall the relative mass-energy of a PM with respect to an observer at rest in the field is conserved After a stop the proportional changes of its basic relative properties are just equal to the proportional energy released i e to the change of GP Thus the relative changes occurring to bodies and observers after changes of velocity or of GP and universe expansion cannot be locally detected because they occur in common proportions To the contrary of current physics the cosmological red-shifts don t increase with the time The G energy comes not from the G field but from a fraction of the mass-energy of the body This is opposed to a the hypothesis in that the relative rest-mass of a body with respect to the observer is independent on the difference of GP between them b The Einstein s G field energy hypothesis In the conventional tests of GR such errors of opposite signs are compensated
Quasi-particle Continuum and Resonances in the Hartree-Fock-Bogoliubov Theory
Energy Technology Data Exchange (ETDEWEB)
Pei, J. C. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL); Kruppa, Andras Tibor [ORNL; Nazarewicz, Witold [ORNL
2011-01-01
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.
Quasiparticle continuum and resonances in the Hartree-Fock-Bogoliubov theory
Energy Technology Data Exchange (ETDEWEB)
Pei, Junchen [ORNL; Kruppa, A. T. [Joint Institute for Heavy Ion Research, Oak Ridge; Nazarewicz, W. [University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL)
2011-01-01
The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅳ)--SURFACE COUSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
戴天民
2003-01-01
The purpose is to reestablish rather complete surface conservation laws for micropolar thermomechanical continua from the translation and the rotation invariances of the general balance law. The generalized energy-momentum and energy-moment of momentum tensors are presented. The concrete forms of surface conservation laws for micropolar thermomechanical continua are derived. The existing related results are naturally derived as special cases from the results proposed in this paper. The incomplete degrees of the existing surface conservation laws are clearly seen from the process of the deduction.The surface conservation laws for nonlocal micropolar thermomechanical continua may be easily obtained via localization.
Nonlocal Gravity in the Solar System
Chicone, C
2015-01-01
The implications of the recent classical nonlocal generalization of Einstein's theory of gravitation for gravitational physics in the Solar System are investigated. In this theory, the nonlocal character of gravity simulates dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a_0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a_0 is determined.
Nonlocal gravity in the solar system
Chicone, C.; Mashhoon, B.
2016-04-01
The implications of the recent classical nonlocal generalization of Einstein’s theory of gravitation for gravitational physics in the solar system are investigated. In this theory, the nonlocal character of gravity appears to simulate dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a 0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a 0 is determined.
Causality, Non-Locality and Negative Refraction
Forcella, Davide; Carminati, Rémi
2016-01-01
The importance of spatial non-locality in the description of negative refraction in electromagnetic materials has been put forward recently. We develop a theory of negative refraction in homogeneous and isotropic media, based on first principles, and that includes non-locality in its full generality. The theory shows that both dissipation and spatial non-locality are necessary conditions for the existence of negative refraction. It also provides a sufficient condition in materials with weak spatial non-locality. These fundamental results should have broad implications in the theoretical and practical analyses of negative refraction of electromagnetic and other kinds of waves.
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.
Giddings, Steven B
2012-01-01
If quantum mechanics governs nature, black holes must evolve unitarily, providing a powerful constraint on the dynamics of quantum gravity. Such evolution apparently must in particular be nonlocal, when described from the usual semiclassical geometric picture, in order to transfer quantum information into the outgoing state. While such transfer from a disintegrating black hole has the dangerous potential to be violent to generic infalling observers, this paper proposes the existence of a more innocuous form of information transfer, to relatively soft modes in the black hole atmosphere. Simplified models for such nonlocal transfer are described and parameterized, within a possibly more basic framework of a Hilbert tensor network. Sufficiently sensitive measurements by infalling observers may detect departures from Hawking's predictions, and in generic models black holes decay more rapidly. Constraints of consistency -- internally and with known and expected features of physics -- restrict the form of informati...
Optimal measurements for nonlocal correlations
Schwarz, Sacha; Stefanov, André; Wolf, Stefan; Montina, Alberto
2016-08-01
A problem in quantum information theory is to find the experimental setup that maximizes the nonlocality of correlations with respect to some suitable measure such as the violation of Bell inequalities. There are however some complications with Bell inequalities. First and foremost it is unfeasible to determine the whole set of Bell inequalities already for a few measurements and thus unfeasible to find the experimental setup maximizing their violation. Second, the Bell violation suffers from an ambiguity stemming from the choice of the normalization of the Bell coefficients. An alternative measure of nonlocality with a direct information-theoretic interpretation is the minimal amount of classical communication required for simulating nonlocal correlations. In the case of many instances simulated in parallel, the minimal communication cost per instance is called nonlocal capacity, and its computation can be reduced to a convex-optimization problem. This quantity can be computed for a higher number of measurements and turns out to be useful for finding the optimal experimental setup. Focusing on the bipartite case, we present a simple method for maximizing the nonlocal capacity over a given configuration space and, in particular, over a set of possible measurements, yielding the corresponding optimal setup. Furthermore, we show that there is a functional relationship between Bell violation and nonlocal capacity. The method is illustrated with numerical tests and compared with the maximization of the violation of CGLMP-type Bell inequalities on the basis of entangled two-qubit as well as two-qutrit states. Remarkably, the anomaly of nonlocality displayed by qutrits turns out to be even stronger if the nonlocal capacity is employed as a measure of nonlocality.
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.
Modulation theory in PT-Symmetric Magnetic Metamaterial Arrays in the continuum limit
Wang, Danhua
2013-01-01
We present results on the dynamics of split-ring dimers having both gain and loss in one dimensional nonlinear parity-time- (PT-)symmetric magnetic metamaterials. For the longwave (continuum) limit approximation and in the weakly nonlinear limit, we show analytic results on the existence of gap soliton solutions and on symmetry breaking phenomenon at a critical value of the gain/loss term.
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES(Ⅶ)-INCREMENTAL RATE TYPE
Institute of Scientific and Technical Information of China (English)
戴安民
2003-01-01
The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between various stress and couple stress rate tensors are derived.Finally, the coupled equations of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as a special case.
Directory of Open Access Journals (Sweden)
M. Mohammadimehr
2013-12-01
Full Text Available In this article, the bending and free vibration analysis of functionally graded (FG nanocomposites Timoshenko beam model reinforced by single-walled boron nitride nanotube (SWBNNT using micro-mechanical approach embedded in an elastic medium is studied. The modified coupled stress (MCST and nonlocal elasticity theories are developed to take into account the size-dependent effect. The mechanical properties of FG boron nitride nanotube-reinforced composites are assumed to be graded in the thickness direction and estimated through the micro-mechanical approach. The governing equations of motion are obtained using Hamilton’s principle based on Timoshenko beam theory. The Navier's type solution is implemented to solve the equations that satisfy the simply supported boundary conditions. Furthermore, the influences of the slenderness ratio, length of nanocomposite beam, material length scale parameter, nonlocal parameter, power law index, axial wave number, and Winkler and Pasternak coefficients on the natural frequency of nanocomposite beam are investigated. Also, the effect of material length scale parameter on the dimensionless deflection of FG nanocomposite beam is studied.
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 defocusing nonlinearity the stability properties depend sensitively on the response function profile: for a smooth profile (e.g., a Gaussian) plane waves are always stable, but MI may occur for a rectangular response. We also find that the reduced model for a weak nonlocality predicts MI in defocusing media...... for arbitrary response profiles, as long as the intensity exceeds a certain critical value. However, it appears that this regime of MI is beyond the validity of the reduced model, if it is to represent the weakly nonlocal limit of a general nonlocal nonlinearity, as in optics and the theory of Bose...
Towards LHC physics with nonlocal Standard Model
Directory of Open Access Journals (Sweden)
Tirthabir Biswas
2015-09-01
Full Text Available 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.
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.
Virial Theorem in Nonlocal Newtonian Gravity
Mashhoon, B
2015-01-01
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.
Virial Theorem in Nonlocal Newtonian Gravity
Mashhoon, Bahram
2016-05-01
Nonlocal gravity is the recent classical nonlocal generalization of Einstein's theory of gravitation in which the past history of the gravitational field is taken into account. In this theory, nonlocality appears to simulate dark matter. The virial theorem for the Newtonian regime of nonlocal gravity theory is derived and its consequences for "isolated" astronomical systems in virial equilibrium at the present epoch are investigated. In particular, for a sufficiently isolated nearby galaxy in virial equilibrium, the galaxy's baryonic diameter---namely, the diameter of the smallest sphere that completely surrounds the baryonic system at the present time---is predicted to be larger than the effective dark matter fraction times a universal length that is the basic nonlocality length scale of about 3 kpc.
Continuum fusion: a theory of inference, with applications to hyperspectral detection.
Schaum, Alan
2010-04-12
A new theoretical framework is created for the class of detection problems traditionally addressed by the generalized likelihood ratio test. Absent prior knowledge that would permit implementation of the optimal detector, a family of optimal detectors is fused according to any one of a group of criteria. Geometrical solutions are presented to several specific problems motivated by hyperspectral signal processing. For the general case, a set of partial differential relations is derived. The generalized likelihood ratio test is shown to be equivalent to one of several flavors of continuum fusion detector.
Jansík, Branislav; Rizzo, Antonio; Frediani, Luca; Ruud, Kenneth; Coriani, Sonia
2006-12-01
The magnetic-field-induced axial birefringence (magnetochirality) of five closed-shell chiral molecules (three substituted oxiranes, carvone, and limonene) is studied at the density functional theory level using Becke's 3-parameter Lee-Yang-Parr functional and frequency-dependent quadratic response theory. The influence of the environment and the conformational distribution on the property is also studied. The environment effects are described by the polarizable continuum model in its integral-equation formulation. The effect of the conformational distribution is investigated by performing calculations on several conformers—for carvone and limonene—followed by Boltzmann averaging. The calculated values for the magnetochiral birefringence are compared to previous ab initio results and experimental data where available. The refined model presented here brings the ab initio values closer to experiment. Still, disagreements remain in some cases and it appears difficult to resolve these discrepancies.
Kirczenow, George
2015-09-01
Valley currents and nonlocal resistances of graphene nanostructures with broken inversion symmetry are considered theoretically in the linear response regime. Scattering state wave functions of electrons entering the nanostructure from the contacts represented by groups of ideal leads are calculated by solving the Lippmann-Schwinger equation and are projected onto the valley state subspaces to obtain the valley velocity fields and total valley currents in the nanostructures. In the tunneling regime when the Fermi energy is in the spectral gap around the Dirac point energy, inversion symmetry breaking is found to result in strong enhancement of the nonlocal four-terminal Büttiker-Landauer resistance and in valley currents several times stronger than the conventional electric current. These strong valley currents are the direct result of the injection of electrons from a contact into the graphene in the tunneling regime. They are chiral and occur near contacts from which electrons are injected into the nanostructure whether or not a net electric current flows through the contact. It is also pointed out that enhanced nonlocal resistances in the linear response regime are not a signature of valley currents arising from the combined effect of the electric field and Berry curvature on the velocities of electrons.
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.
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.
Totality of Subquantum Nonlocal Correlations
Khrennikov, Andrei
2011-01-01
In a series of previous papers we developed a purely field model of microphenomena, so called prequantum classical statistical field theory (PCSFT). This model not only reproduces important probabilistic predictions of QM including correlations for entangled systems, but it also gives a possibility to go beyond quantum mechanics (QM), i.e., to make predictions of phenomena which could be observed at the subquantum level. In this paper we discuss one of such predictions - existence of nonlocal correlations between prequantum random fields corresponding to {\\it 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 one hand, PCSFT demystifies quantum nonlocality by reducing it to nonlocal classical correlations based on the common random back...
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅹ)--MASTER BALANCE LAW
Institute of Scientific and Technical Information of China (English)
DAI Tian-min
2006-01-01
Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether's theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally,some existing results are reduced immediately as special cases.
A continuum theory for two-phase flows of particulate solids: application to Poiseuille flows
Monsorno, Davide; Varsakelis, Christos; Papalexandris, Miltiadis V.
2015-11-01
In the first part of this talk, we present a novel two-phase continuum model for incompressible fluid-saturated granular flows. The model accounts for both compaction and shear-induced dilatancy and accommodates correlations for the granular rheology in a thermodynamically consistent way. In the second part of this talk, we exercise this two-phase model in the numerical simulation of a fully-developed Poiseuille flow of a dense suspension. The numerical predictions are shown to compare favorably against experimental measurements and confirm that the model can capture the important characteristics of the flow field, such as segregation and formation of plug zones. Finally, results from parametric studies with respect to the initial concentration, the magnitude of the external forcing and the width of the channel are presented and the role of these physical parameters is quantified. Financial Support has been provided by SEDITRANS, an Initial Training Network of the European Commission's 7th Framework Programme
Hyperbolic metamaterial lens with hydrodynamic nonlocal response
DEFF Research Database (Denmark)
Yan, Wei; Mortensen, N. Asger; Wubs, Martijn
2013-01-01
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......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...
Hyperbolic metamaterial lens with hydrodynamic nonlocal response.
Yan, Wei; Mortensen, N Asger; Wubs, Martijn
2013-06-17
We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we propose to measure the near-field distribution of a hyperbolic metamaterial lens.
Durning, Steven J; Lubarsky, Stuart; Torre, Dario; Dory, Valérie; Holmboe, Eric
2015-01-01
The purpose of this article is to propose new approaches to assessment that are grounded in educational theory and the concept of "nonlinearity." The new approaches take into account related phenomena such as "uncertainty," "ambiguity," and "chaos." To illustrate these approaches, we will use the example of assessment of clinical reasoning, although the principles we outline may apply equally well to assessment of other constructs in medical education. Theoretical perspectives include a discussion of script theory, assimilation theory, self-regulated learning theory, and situated cognition. Assessment examples to include script concordance testing, concept maps, self-regulated learning microanalytic technique, and work-based assessment, which parallel the above-stated theories, respectively, are also highlighted. We conclude with some practical suggestions for approaching nonlinearity.
Origin of Dynamical Quantum Non-locality
Pachon, Cesar E.; Pachon, Leonardo A.
2014-03-01
Non-locality is one of the hallmarks of quantum mechanics and is responsible for paradigmatic features such as entanglement and the Aharonov-Bohm effect. Non-locality comes in two ``flavours'': a kinematic non-locality- arising from the structure of the Hilbert space- and a dynamical non-locality- arising from the quantum equations of motion-. Kinematic non-locality is unable to induce any change in the probability distributions, so that the ``action-at-a-distance'' cannot manifest. Conversely, dynamical non-locality does create explicit changes in probability, though in a ``causality-preserving'' manner. The origin of non-locality of quantum measurements and its relations to the fundamental postulates of quantum mechanics, such as the uncertainty principle, have been only recently elucidated. Here we trace the origin of dynamical non-locality to the superposition principle. This relation allows us to establish and identify how the uncertainty and the superposition principles determine the non-local character of the outcome of a quantum measurement. Being based on group theoretical and path integral formulations, our formulation admits immediate generalizations and extensions to to, e.g., quantum field theory. This work was supported by the Departamento Administrativo de Ciencia, Tecnologia e Innovacion -COLCIENCIAS- of Colombia under the grant number 111556934912.
Zhang, Lin-Feng; Xia, Xue-Wei
2016-05-01
The α-decay energies (Q α ) are systematically investigated with the nuclear masses for 10 ⩽ Z ⩽ 120 isotopes obtained by the relativistic continuum Hartree-Bogoliubov (RCHB) theory with the covariant density functional PC-PK1, and compared with available experimental values. It is found that the α-decay energies deduced from the RCHB results present a similar pattern to those from available experiments. Owing to the large predicted Q α values (⩾ 4 MeV), many undiscovered heavy nuclei in the proton-rich side and super-heavy nuclei may have large possibilities for α-decay. The influence of nuclear shell structure on α-decay energies is also analysed. Supported by Major State 973 Program of China (2013CB834400), National Natural Science Foundation of China (11175002, 11335002, 11375015, 11461141002), Research Fund for the Doctoral Program of Higher Education (20110001110087) and National Undergraduate Innovation Training Programs of Peking University.
A field theoretical approach to the quasi-continuum method
Iyer, Mrinal; Gavini, Vikram
2011-08-01
The quasi-continuum method has provided many insights into the behavior of lattice defects in the past decade. However, recent numerical analysis suggests that the approximations introduced in various formulations of the quasi-continuum method lead to inconsistencies—namely, appearance of ghost forces or residual forces, non-conservative nature of approximate forces, etc.—which affect the numerical accuracy and stability of the method. In this work, we identify the source of these errors to be the incompatibility of using quadrature rules, which is a local notion, on a non-local representation of energy. We eliminate these errors by first reformulating the extended interatomic interactions into a local variational problem that describes the energy of a system via potential fields. We subsequently introduce the quasi-continuum reduction of these potential fields using an adaptive finite-element discretization of the formulation. We demonstrate that the present formulation resolves the inconsistencies present in previous formulations of the quasi-continuum method, and show using numerical examples the remarkable improvement in the accuracy of solutions. Further, this field theoretic formulation of quasi-continuum method makes mathematical analysis of the method more amenable using functional analysis and homogenization theories.
A nonlocal discretization of fields
Campos, R G; Pimentel, L O; Campos, Rafael G.; Tututi, Eduardo S.
2001-01-01
A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion doubling or the breaking of chiral symmetry for the massless case, are absent in this method.
Bouhali, I.; Bezzaouia, S.; Telmini, M.; Jungen, Ch.
2016-08-01
Variational ab initio R -matrix theory combined with generalized multichannel quantum defect theory is used to calculate singly excited Rydberg states of the hydrohelium molecular ion, HeH+, for Σ,3+1,Π,31,Δ,31,Φ,31, and Γ,31 symmetry. Bound levels are calculated for n values up to n ≈10 , and continuum states up to ≈3 eV above the HeH2 + threshold. The calculations span the range of internuclear distances R from 1 to 5 bohrs. The present work follows a preliminary study on the Δ,31 states of HeH+ [Bouhali, Bezzaouia, Telmini, and Jungen, EPJ Web Conf. 84, 04004 (2015), 10.1051/epjconf/20158404004] which was also based on R -matrix theory. Further—although limited to rather small R values—the present work extends the recent ab initio computations of Jungen and Jungen [Mol. Phys. 113, 2333 (2015), 10.1080/00268976.2015.1040094] to higher excitation energies which are not accessible to standard quantum-chemical methods. Where a comparison with the calculations of Jungen and Jungen and other older results can be made, namely for n ≤5 , very good agreement with previous ab initio results is obtained.
Energy Technology Data Exchange (ETDEWEB)
Almeida, P. G. C.; Benilov, M. S. [Departamento de Física, CCCEE, Universidade da Madeira, Largo do Município, 9000 Funchal (Portugal)
2013-10-15
The work is aimed at advancing the multiple steady-state solutions that have been found recently in the theory of direct current (DC) glow discharges. It is shown that an account of detailed plasma chemistry and non-locality of electron transport and kinetic coefficients results in an increase of the number of multiple solutions but does not change their pattern. Multiple solutions are shown to exist for discharges in argon and helium provided that discharge pressure is high enough. This result indicates that self-organization in DC glow microdischarges can be observed not only in xenon, which has been the case until recently, but also in other plasma-producing gases; a conclusion that has been confirmed by recent experiments. Existence of secondary bifurcations can explain why patterns of spots grouped in concentric rings, observed in the experiment, possess in many cases higher number of spots in outer rings than in inner ones.
Dispersive shock waves with nonlocal nonlinearity
Barsi, Christopher; Sun, Can; Fleischer, Jason W
2007-01-01
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Computational Continuum Mechanics
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.
Nonlocal Measurements via Quantum Erasure.
Brodutch, Aharon; Cohen, Eliahu
2016-02-19
Nonlocal observables play an important role in quantum theory, from Bell inequalities and various postselection paradoxes to quantum error correction codes. Instantaneous measurement of these observables is known to be a difficult problem, especially when the measurements are projective. The standard von Neumann Hamiltonian used to model projective measurements cannot be implemented directly in a nonlocal scenario and can, in some cases, violate causality. We present a scheme for effectively generating the von Neumann Hamiltonian for nonlocal observables without the need to communicate and adapt. The protocol can be used to perform weak and strong (projective) measurements, as well as measurements at any intermediate strength. It can also be used in practical situations beyond nonlocal measurements. We show how the protocol can be used to probe a version of Hardy's paradox with both weak and strong measurements. The outcomes of these measurements provide a nonintuitive picture of the pre- and postselected system. Our results shed new light on the interplay between quantum measurements, uncertainty, nonlocality, causality, and determinism.
Yang, Yang; Zhang, Lixiang; Lim, C. W.
2011-04-01
This paper is concerned with the characteristics of wave propagation in double-walled carbon nanotubes (DWCNTs). The DWCNTs is simulated with a Timoshenko beam model based on the nonlocal continuum elasticity theory, referred to as an analytically nonlocal Timoshenko-beam (ANT) model. The governing equations of the DWCNTs beam consist of a set of four equations that are derived from the variational principle of the beam with high-order boundary conditions at the both ends, in which the effects of the nano-scale nonlocality and the van der Waals interaction between inner and outer tubes are inclusive. The characteristics of the wave propagation in the DWCNTs beam were analyzed with the new ANT model proposed and the comparisons with the partially nonlocal Timoshenko-beam (PNT) models in publication were made in details. The results show that the nonlocal effects of the ANT model proposed in the present study on the wave propagations are more significant because it is in stronger stiffness enhancement to the DWCNTs beam.
Teaching with Tupac: Building a Solid Grounding in Theory across the Social Work Education Continuum
Elkins, Jennifer; Miller, Shari; Briggs, Harold; Skinner, Sara
2015-01-01
This article describes a collaborative and emergent approach utilizing Tupac Shakur's "Brenda's Got a Baby" to leverage theory education. This song/video uses a fictionalized account of a pregnant 12-year-old African American girl to chronicle the ecological realities of life in the inner city (e.g., teen pregnancy, drug addiction and…
Voller, V. R.; Falcini, F.; Foufoula-Georgiou, E.; Ganti, V.; Paola, C.; Hill, K. M.; Swenson, J. B.; Longjas, A.
2013-12-01
The purpose of this work is to suggest how experiments might be constructed to provide data to test recently proposed phenomenological non-local model of depositional transport; formulated on the basis of morphological arguments but with limited data. A sound methodology for developing models of geological systems is to first collect significant data and then carefully identify an appropriate model form and parameters. An alternative approach is to construct what might be referred to as a phenomenological model, where limited observation of the system is used to suggest an appropriate mathematical form that matches the critical nature of the physical system behavior. By their nature, phenomenological models are often developed within a fairly narrow range of observations. In this way, interesting findings can occur when the models are modified and exercised across wider physical domains, in particular in domains where there is an absence of hard data to corroborate or invalidate the model predictions. Although this approach might be frown on my some, it is important to recognize the stellar and proven track record of phenomenological models, which despite the original scarcity of data, often pave the way to new perspectives and important findings. The poster child example is the Higgs boson. In the early 60's manipulation of the quantum field equations revealed a critical inconsistency related to the masses of fundamental particles that could only be mathematically resolved by assuming that they operated within a field that would exert drag; this conjecture took almost fifty years and the vast experimental operation of the Large Hadron Collider to physically confirm. In this work we examine a current phenomenological model used to describe non-local transport in fluvial sediment domains. This model has its genesis in attempting to describe the shapes of hill slope profiles, while acknowledging the fact that two points of the landscape with the same local slope are
Nonlocal Galileons and self-acceleration
Gabadadze, Gregory; Yu, Siqing
2017-05-01
A certain class of nonlocal theories eliminates an arbitrary cosmological constant (CC) from a universe that can be perceived as our world. Dark energy then cannot be explained by a CC; it could however be due to massive gravity. We calculate the new corrections, which originate from the nonlocal terms that eliminate the CC, to the decoupling limit Lagrangian of massive gravity. The new nonlocal terms also have internal field space Galilean symmetry and are referred here as ;nonlocal Galileons.; We then study a self-accelerated solution and show that the new nonlocal terms change the perturbative stability analysis. In particular, small fluctuations are now stable and non-superluminal for some simple parameter choices, whereas for the same choices the pure massive gravity fluctuations are unstable. We also study stable spherically symmetric solutions on this background.
Nonlocal Galileons and self-acceleration
Directory of Open Access Journals (Sweden)
Gregory Gabadadze
2017-05-01
Full Text Available 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.
Circumferential nonlocal effect on the buckling and vibration of nanotubes
Energy Technology Data Exchange (ETDEWEB)
Wang, Cheng Yuan, E-mail: cywang@ujs.edu.cn; Li, Xiao Hu; Luo, Ying
2016-04-01
The nonlocal beam theories are widely used to study the mechanics of cylindrical nanotubes (NTs). The one-dimensional models however are unable to account for the nonlocal effect in the circumferential direction, which may substantially affect the applicability of the nonlocal beam models. To address the issue this letter examines the circumferential nonlocal effect (CNE) on the buckling and vibration of the NTs. Here the CNE is characterized by the difference between the nonlocal beam model considering the axial nonlocal effect only and the nonlocal shell model with both axial and circumferential nonlocal effects. The aspect ratio and radius-dependence of the CNE are calculated for the singlewall carbon NTs selected as a typical example. The results show that the CNE is substantial for the buckling and vibration of the NTs with small radius (e.g., <1 nm) and aspect ratio (e.g., <15). It however decreases with the rising radius and the aspect ratio, and turns out to be small for relatively wide and long NTs. The nonlocal beam theories thus may overestimate the buckling load and vibration frequency for the thin and short NTs. - Highlights: • First revealed the substantial circumferential nonlocal effect (CNE) on nanotube buckling. • Achieved radius/aspect ratio-dependence of CNE on nanotube buckling and vibration. • Located the range of applicability of the nonlocal beam theory without CNE.
Jover, Julio; Galindo, Amparo; Jackson, George; Müller, Erich A.; Haslam, Andrew J.
2015-09-01
Using both theory and continuum simulation, we examine a system comprising a mixture of polymer chains formed from 100 hard-sphere (HS) segments and HS colloids with a diameter which is 20 times that of the polymer segments. According to Wertheim's first-order thermodynamic perturbation theory (TPT1) this athermal system is expected to phase separate into a colloid-rich and a polymer-rich phase. Using a previously developed continuous pseudo-HS potential [J. F. Jover, A. J. Haslam, A. Galindo, G. Jackson, and E. A. Muller, J. Chem. Phys. 137, 144505 (2012)], we simulate the system at a phase point indicated by the theory to be well within the two-phase binodal region. Molecular-dynamics simulations are performed from starting configurations corresponding to completely phase-separated and completely pre-mixed colloids and polymers. Clear evidence is seen of the stabilisation of two coexisting fluid phases in both cases. An analysis of the interfacial tension of the phase-separated regions is made; ultra-low tensions are observed in line with previous values determined with square-gradient theory and experiment for colloid-polymer systems. Further simulations are carried out to examine the nature of these coexisting phases, taking as input the densities and compositions calculated using TPT1 (and corresponding to the peaks in the probability distribution of the density profiles obtained in the simulations). The polymer chains are seen to be fully penetrable by other polymers. By contrast, from the point of view of the colloids, the polymers behave (on average) as almost-impenetrable spheres. It is demonstrated that, while the average interaction between the polymer molecules in the polymer-rich phase is (as expected) soft-repulsive in nature, the corresponding interaction in the colloid-rich phase is of an entirely different form, characterised by a region of effective intermolecular attraction.
RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅲ)-NOETHER'S THEOREM
Institute of Scientific and Technical Information of China (English)
戴天民
2003-01-01
The existing various couple stress theories have been carefully restudied. Thepurpose is to propose a coupled Noether's theorem and to reestablish rather completeconservation laws and balance equations for couple stress elastodynamics. The new concreteforms of various conservation laws of couple stress elasticity are derived. The precise natureof these conservation laws which result from the given invariance requirements areestablished. Various special cases are reduced and the results of micropolar continua may benaturally transited from the results presented in this paper.
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole; Wyller, John
2004-01-01
We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons.......We investigate the propagation of partially coherent beams in spatially nonlocal nonlinear media with a logarithmic type of nonlinearity. We derive analytical formulas for the evolution of the beam parameters and conditions for the formation of nonlocal incoherent solitons....
Free vibration analysis of microtubules based on the molecular mechanics and continuum beam theory.
Zhang, Jin; Wang, Chengyuan
2016-10-01
A molecular structural mechanics (MSM) method has been implemented to investigate the free vibration of microtubules (MTs). The emphasis is placed on the effects of the configuration and the imperfect boundaries of MTs. It is shown that the influence of protofilament number on the fundamental frequency is strong, while the effect of helix-start number is almost negligible. The fundamental frequency is also found to decrease as the number of the blocked filaments at boundaries decreases. Subsequently, the Euler-Bernoulli beam theory is employed to reveal the physics behind the simulation results. Fitting the Euler-Bernoulli beam into the MSM data leads to an explicit formula for the fundamental frequency of MTs with various configurations and identifies a possible correlation between the imperfect boundary conditions and the length-dependent bending stiffness of MTs reported in experiments.
Institute of Scientific and Technical Information of China (English)
戴天民
2003-01-01
The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity. The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle. The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case, respectively. Finally, the results of micropolar thermopiezoelectricity are directly given.
Can EPR non-locality be geometrical?
Energy Technology Data Exchange (ETDEWEB)
Ne`eman, Y. [Tel-Aviv Univ. (Israel). Raymond and Beverly Sackler Faculty of Exact Sciences]|[Univ. of Texas, Austin, TX (United States). Center for Particle Physics; Botero, A. [Texas Univ., Austin, TX (United States)
1995-10-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3.
Nims, Robert J; Durney, Krista M; Cigan, Alexander D; Dusséaux, Antoine; Hung, Clark T; Ateshian, Gerard A
2016-02-06
This study presents a damage mechanics framework that employs observable state variables to describe damage in isotropic or anisotropic fibrous tissues. In this mixture theory framework, damage is tracked by the mass fraction of bonds that have broken. Anisotropic damage is subsumed in the assumption that multiple bond species may coexist in a material, each having its own damage behaviour. This approach recovers the classical damage mechanics formulation for isotropic materials, but does not appeal to a tensorial damage measure for anisotropic materials. In contrast with the classical approach, the use of observable state variables for damage allows direct comparison of model predictions to experimental damage measures, such as biochemical assays or Raman spectroscopy. Investigations of damage in discrete fibre distributions demonstrate that the resilience to damage increases with the number of fibre bundles; idealizing fibrous tissues using continuous fibre distribution models precludes the modelling of damage. This damage framework was used to test and validate the hypothesis that growth of cartilage constructs can lead to damage of the synthesized collagen matrix due to excessive swelling caused by synthesized glycosaminoglycans. Therefore, alternative strategies must be implemented in tissue engineering studies to prevent collagen damage during the growth process.
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.
Wang, John T.; Pineda, Evan J.; Ranatunga, Vipul; Smeltzer, Stanley S.
2015-01-01
A simple continuum damage mechanics (CDM) based 3D progressive damage analysis (PDA) tool for laminated composites was developed and implemented as a user defined material subroutine to link with a commercially available explicit finite element code. This PDA tool uses linear lamina properties from standard tests, predicts damage initiation with an easy-to-implement Hashin-Rotem failure criteria, and in the damage evolution phase, evaluates the degradation of material properties based on the crack band theory and traction-separation cohesive laws. It follows Matzenmiller et al.'s formulation to incorporate the degrading material properties into the damaged stiffness matrix. Since nonlinear shear and matrix stress-strain relations are not implemented, correction factors are used for slowing the reduction of the damaged shear stiffness terms to reflect the effect of these nonlinearities on the laminate strength predictions. This CDM based PDA tool is implemented as a user defined material (VUMAT) to link with the Abaqus/Explicit code. Strength predictions obtained, using this VUMAT, are correlated with test data for a set of notched specimens under tension and compression loads.
Osmaston, Miles F.
My development of Continuum Theory rests importantly on two mathematical treatments and calculations which I wrote in 1994 and were published in 1998 as Appendices A and B to my PIRT V paper presented in London in 1996. In view of their continuing scientific relevance, this contribution to the V9 conference proceedings is a republication of those Appendices, subject to minimal re-editing. Appendix B, presented first, tackles our 1959 finding that the daylight sky brightness distribution at high altitude shows the presence of an additional contribution whose intensity and distribution which, on careful analysis, I identified as having come from a deflection scattering mechanism due to transmission by an (atmospheric) `particle-tied aether'. Appendix A shows that redshift is one of the consequences of such transmission. The parameters involved are then used to analyse the 1968 radio ground-wave caesium clock redshift observations of Sadeh et al and to extrapolate them to the intergalactic transmission paths pertinent to the cosmic redshift as a transmission effect, not a velocity. It finds this to be a reasonable evaluation within observational uncertainties, notably those of density and degree of ionization. In that case, there being no Big Bang, the temperature is precisely known from the CMBR, identified as synchrotron-type radiation from the randomly moving aether along the path, but slightly elevated where the path has traversed a heat-generating cluster.
Application of Nonlocal Elasticity Shell Model for Axial Buckling of Single-Walled Carbon Nanotubes
Directory of Open Access Journals (Sweden)
Farzad Khademolhosseini
2009-10-01
Full Text Available Recently, nano devices have been developed which use Carbon Nanotubes (CNTs as structural elements. To define the range of applicability of CNTs in such devices, it is important to investigate failure modes such as the axial buckling limit. Classical continuum models are inaccurate as they are unable to account for the size-effects in such devices. In this work, a modified nonlocal continuum shell model for the axial buckling of CNTs is proposed and compared with a nonlocal model for torsional buckling. This is done through modifying classical continuum models by incorporating basic concepts from nonlocal elasticity. Furthermore, molecular dynamics (MD simulations are performed on a range of nanotubes with different diameters. Compared to classical models, the modified nonlocal models provide a much better fit to MD simulation results. Using MD simulation results for axial buckling, values of the nonlocal constant and shell thickness are calculated.
Gainutdinov, A. M.; Read, N.; Saleur, H.; Vasseur, R.
2015-05-01
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 [1] [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.
Mujica-Parodi, L R
1998-01-01
I argue in the dissertation that there exists a fundamental contradiction between quantum theory and the special theory of relativity and that most of the well-known arguments to the contrary suffer from internal inconsistencies that render them ineffective in resolving the conflict...
Quantum nonlocality does not exist.
Tipler, Frank J
2014-08-05
Quantum nonlocality is shown to be an artifact of the Copenhagen interpretation, in which each observed quantity has exactly one value at any instant. In reality, all physical systems obey quantum mechanics, which obeys no such rule. Locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the many-worlds interpretation (MWI). Using the MWI, I show that the quantum side of Bell's inequality, generally believed nonlocal, is really due to a series of three measurements (not two as in the standard, oversimplified analysis), all three of which have only local effects. Thus, experiments confirming "nonlocality" are actually confirming the MWI. The mistaken interpretation of nonlocality experiments depends crucially on a question-begging version of the Born interpretation, which makes sense only in "collapse" versions of quantum theory, about the meaning of the modulus of the wave function, so I use the interpretation based on the MWI, namely that the wave function is a world density amplitude, not a probability amplitude. This view allows the Born interpretation to be derived directly from the Schrödinger equation, by applying the Schrödinger equation to both the observed and the observer.
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.
Natural discretization in noncommutative field theory
Energy Technology Data Exchange (ETDEWEB)
Acatrinei, Ciprian Sorin, E-mail: acatrine@theory.nipne.ro [Department of Theoretical Physics, Horia Hulubei National Institute for Nuclear Physics, Bucharest (Romania)
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
A Morphing framework to couple non-local and local anisotropic continua
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.
Diaz, Pablo; Walton, Mark
2016-01-01
With the aim of investigating the relation between gravity and non-locality at the classical level, we study a bilocal scalar field model. Bilocality introduces new (internal) degrees of freedom that can potentially reproduce gravity. We show that the equations of motion of the massless branch of the free bilocal model match those of linearized gravity. We also discuss higher orders of perturbation theory, where there is self-interaction in both gravity and the bilocal field sectors.
Gisin, Nicolas
2010-01-01
Observing the violation of Bell's inequality tells us something about all possible future theories: they must all predict nonlocal correlations. Hence Nature is nonlocal. After an elementary introduction to nonlocality and a brief review of some recent experiments, I argue that Nature's nonlocality together with the existence of free will is incompatible with the many-worlds view of quantum physics.
Tessarotto, Massimo
2016-01-01
This paper is motivated by the introduction of a new functional setting of General Relativity (GR) based on the adoption of suitable group non-local point transformations (NLPT). Unlike the customary local point transformatyion usually utilized in GR, these transformations map in each other intrinsically different curved space-times. In this paper the problem is posed of determining the tensor transformation laws holding for the $4-$% acceleration with respect to the group of general NLPT. Basic physical implications are considered. These concern in particular the identification of NLPT-acceleration effects, namely the relationship established via general NLPT between the $4-$accelerations existing in different curved-space times. As a further application the tensor character of the EM Faraday tensor.with respect to the NLPT-group is established.
Modesto, Leonardo
2013-01-01
We present a general covariant action for massive gravity merging together a class of "non-polynomial" and super-renormalizable or finite theories of gravity with the non-local theory of gravity recently proposed by Jaccard, Maggiore and Mitsou (arXiv:1305.3034 [hep-th]). Our diffeomorphism invariant action gives rise to the equations of motion appearing in non-local massive massive gravity plus quadratic curvature terms. Not only the massive graviton propagator reduces smoothly to the massless one without a vDVZ discontinuity, but also our finite theory of gravity is unitary at tree level around the Minkowski background. We also show that, as long as the graviton mass $m$ is much smaller the today's Hubble parameter $H_0$, a late-time cosmic acceleration can be realized without a dark energy component due to the growth of a scalar degree of freedom. In the presence of the cosmological constant $\\Lambda$, the dominance of the non-local mass term leads to a kind of "degravitation" for $\\Lambda$ at the late cos...
A Nonlocal Model for Carbon Nanotubes under Axial Loads
Directory of Open Access Journals (Sweden)
Raffaele Barretta
2013-01-01
Full Text Available Various beam theories are formulated in literature using the nonlocal differential constitutive relation proposed by Eringen. A new variational framework is derived in the present paper by following a consistent thermodynamic approach based on a nonlocal constitutive law of gradient-type. Contrary to the results obtained by Eringen, the new model exhibits the nonlocality effect also for constant axial load distributions. The treatment can be adopted to get new benchmarks for numerical analyses.
Nonlocal Infrared Modifications of Gravity. A Review
Maggiore, Michele
2016-01-01
We review an approach developed in the last few years by our group in which GR is modified in the infrared, at an effective level, by nonlocal terms associated to a mass scale. We begin by recalling the notion of quantum effective action and its associated nonlocalities, illustrating some of their features with the anomaly-induced effective actions in $D=2$ and $D=4$. We examine conceptual issues of nonlocal theories such as causality, degrees of freedoms and ghosts, stressing the importance of the fact that these nonlocalities only emerge at the effective level. We discuss a particular class of nonlocal theories where the nonlocal operator is associated to a mass scale, and we show that they perform very well in the comparison with cosmological observations, to the extent that they fit CMB, supernovae, BAO and structure formation data at a level fully competitive with $\\Lambda$CDM, with the same number of free parameters. We explore some extensions of these `minimal' models, and we finally discuss some direc...
Nonlocal Anomalous Hall Effect
Zhang, Steven S.-L.; Vignale, Giovanni
2016-04-01
The anomalous Hall (AH) effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator [yttrium iron garnet (YIG)], even when precautions are taken to ensure that there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin-Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect—the only difference being the spatial separation of the spin-orbit interaction and the magnetization. For this reason we name this effect the nonlocal anomalous Hall effect and predict that its sign will be determined by the sign of the spin-Hall angle in the metal. The AH conductivity that we calculate from our theory is in order of magnitude agreement with the measured values in Pt /YIG structures.
Nonlocal Anomalous Hall Effect.
Zhang, Steven S-L; Vignale, Giovanni
2016-04-01
The anomalous Hall (AH) effect is deemed to be a unique transport property of ferromagnetic metals, caused by the concerted action of spin polarization and spin-orbit coupling. Nevertheless, recent experiments have shown that the effect also occurs in a nonmagnetic metal (Pt) in contact with a magnetic insulator [yttrium iron garnet (YIG)], even when precautions are taken to ensure that there is no induced magnetization in the metal. We propose a theory of this effect based on the combined action of spin-dependent scattering from the magnetic interface and the spin-Hall effect in the bulk of the metal. At variance with previous theories, we predict the effect to be of first order in the spin-orbit coupling, just as the conventional anomalous Hall effect-the only difference being the spatial separation of the spin-orbit interaction and the magnetization. For this reason we name this effect the nonlocal anomalous Hall effect and predict that its sign will be determined by the sign of the spin-Hall angle in the metal. The AH conductivity that we calculate from our theory is in order of magnitude agreement with the measured values in Pt/YIG structures.
Classification of scalar and dyadic nonlocal optical response models.
Wubs, M
2015-11-30
Nonlocal optical response is one of the emerging effects on the nanoscale for particles made of metals or doped semiconductors. Here we classify and compare both scalar and tensorial nonlocal response models. In the latter case the nonlocality can stem from either the longitudinal response, the transverse response, or both. In phenomenological scalar models the nonlocal response is described as a smearing out of the commonly assumed infinitely localized response, as characterized by a distribution with a finite width. Here we calculate explicitly whether and how tensorial models, such as the hydrodynamic Drude model and generalized nonlocal optical response theory, follow this phenomenological description. We find considerable differences, for example that nonlocal response functions, in contrast to simple distributions, assume negative and complex values. Moreover, nonlocal response regularizes some but not all diverging optical near fields. We identify the scalar model that comes closest to the hydrodynamic model. Interestingly, for the hydrodynamic Drude model we find that actually only one third (1/3) of the free-electron response is smeared out nonlocally. In that sense, nonlocal response is stronger for transverse and scalar nonlocal response models, where the smeared-out fractions are 2/3 and 3/3, respectively. The latter two models seem to predict novel plasmonic resonances also below the plasma frequency, in contrast to the hydrodynamic model that predicts standing pressure waves only above the plasma frequency.
Lorentz Invariant CPT Violating Effects for a Class of Gauge-invariant Nonlocal Thirring Models
Patra, Pinaki
2013-01-01
CPT violation and Lorentz invariance can coexist in the framework of non-local field theory. Local gauge-invariance may not hold for the few non-local interaction terms. However, the gauge-invariance for the non-local interaction term can be formulated by the inclusion of Swinger non-integrable phase factor. In this article we have proposed a class of CPT violating Lorentz invariant Nonlocal Gauge-invariant models which can be termed as non-local gauge-invariant Thirring models. The inclusion of non-locality will modify the current conservation laws. Also, the possible particle antiparticle mass-splitting in this respect is discussed.
Modeling elastic tensile fractures in snow using nonlocal damage mechanics
Borstad, C. P.; McClung, D. M.
2011-12-01
The initiation and propagation of tensile fractures in snow and ice are fundamental to numerous important physical processes in the cryosphere, from iceberg calving to ice shelf rift propagation to slab avalanche release. The heterogeneous nature of snow and ice, their proximity to the melting temperature, and the varied governing timescales typically lead to nonlinear fracture behavior which does not follow the predictions of Linear Elastic Fracture Mechanics (LEFM). Furthermore, traditional fracture mechanics is formally inapplicable for predicting crack initiation in the absence of a pre-existing flaw or stress concentration. An alternative to fracture mechanics is continuum damage mechanics, which accounts for the material degradation associated with cracking in a numerically efficient framework. However, damage models which are formulated locally (e.g. stress and strain are defined as point properties) suffer from mesh-sensitive crack trajectories, spurious localization of damage and improper fracture energy dissipation with mesh refinement. Nonlocal formulations of damage, which smear the effects of the material heterogeneity over an intrinsic length scale related to the material microstructure, overcome these difficulties and lead to numerically efficient and mesh-objective simulations of the tensile failure of heterogeneous materials. We present the results of numerical simulations of tensile fracture initiation and propagation in cohesive snow using a nonlocal damage model. Seventeen beam bending experiments, both notched and unnotched, were conducted using blocks of cohesive dry snow extracted from an alpine snowpack. Material properties and fracture parameters were calculated from the experimental data using beam theory and quasi-brittle fracture mechanics. Using these parameters, a nonlocal isotropic damage model was applied to two-dimensional finite element meshes of the same scale as the experiments. The model was capable of simulating the propagation
Baez, John C
2016-01-01
Our assumption that spacetime is a continuum leads to many challenges in mathematical physics. Singularities, divergent integrals and the like threaten many of our favorite theories, from Newtonian gravity to classical electrodynamics, quantum electrodynamics and the Standard Model. In general relativity, singularities are intimately connected to some of the theory's most dramatic successful predictions. We survey these problems and the large amount of work that has gone into dealing with them.
Spencer, A J M
2004-01-01
The mechanics of fluids and the mechanics of solids represent the two major areas of physics and applied mathematics that meet in continuum mechanics, a field that forms the foundation of civil and mechanical engineering. This unified approach to the teaching of fluid and solid mechanics focuses on the general mechanical principles that apply to all materials. Students who have familiarized themselves with the basic principles can go on to specialize in any of the different branches of continuum mechanics. This text opens with introductory chapters on matrix algebra, vectors and Cartesian ten
Collins, Kim D
2012-06-01
Continuum electrostatics models for ions in water provide apparent long range electrostatic explanations for the forces on ions. However the electro-chemical free energy of solvation of ions resides largely in the first two water layers, which control the interfacial behavior of the ions and require explicit modeling to capture their distinctive behaviors. The resulting short range forces produce such surprising charge density-dependent behaviors as ion adsorption onto nonpolar surfaces, like charge aggregation of ions, and substantial ion pairing preferences, which arise largely from the affinity of specific ions for individual water molecules. Specific ion effects controlled by the local water affinity of the ion show a diagnostic change of sign between strongly hydrated Na(+) and weakly hydrated K(+) and between strongly hydrated F(-) and weakly hydrated Cl(-), in both cases marking the strength of water-water interactions in bulk solution, a critical benchmark missing from continuum electrostatics models.
Directory of Open Access Journals (Sweden)
M. W. Roberts
2010-01-01
Full Text Available Using a combination of continuum modeling, atomistic simulations, and numerical optimization, we estimate the flexural rigidity of a graphene sheet. We consider a rectangular sheet that is initially parallel to a rigid substrate. The sheet interacts with the substrate by van der Waals forces and deflects in response to loading on a pair of opposite edges. To estimate the flexural rigidity, we model the graphene sheet as a continuum and numerically solve an appropriate differential equation for the transverse deflection. This solution depends on the flexural rigidity. We then use an optimization procedure to find the value of the flexural rigidity that minimizes the difference between the numerical solutions and the deflections predicted by atomistic simulations. This procedure predicts a flexural rigidity of 0.26 nN nm=1.62 eV.
Matsumoto, Takuma; Ogata, Kazuyuki; Yahiro, Masanobu
2009-01-01
We present a practical way of smoothing discrete breakup S-matrix elements calculated by the continuum-discretized coupled-channel method (CDCC). This method makes the smoothing procedure much easier. The reliability of the smoothing method is confirmed for the three-body breakup reactions, 58Ni(d,pn) at 80 MeV and 12C(6He,4He2n) at 229.8 MeV.
Qi, Shuanhu; Behringer, Hans; Schmid, Friederike
2013-01-01
We develop a multiscale hybrid scheme for simulations of soft condensed matter systems, which allows one to treat the system at the particle level in selected regions of space, and at the continuum level elsewhere. It is derived systematically from an underlying particle-based model by field theoretic methods. Particles in different representation regions can switch representations on the fly, controlled by a spatially varying tuning function. As a test case, the hybrid scheme is applied to s...
DEFF Research Database (Denmark)
Sadrieva, Z. F.; Sinev, I. S.; Samusev, A. K.;
2016-01-01
In this work, we implement CMOS-compatible one-dimensional photonic structure based on silicon-on-insulator wafer supporting optical bound states in the continuum at telecommunication wavelengths — localized optical state with energy lying above the light line of the surrounding space. Such high-......-Q states are very promising for many potential applications ranging from on-chip photonics and optical communications to biological sensing and photovoltaics....
Nonlocality from Local Contextuality
Liu, Bi-Heng; Hu, Xiao-Min; Chen, Jiang-Shan; Huang, Yun-Feng; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can; Cabello, Adán
2016-11-01
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.
Nonlocality from Local Contextuality.
Liu, Bi-Heng; Hu, Xiao-Min; Chen, Jiang-Shan; Huang, Yun-Feng; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can; Cabello, Adán
2016-11-25
We experimentally show that nonlocality can be produced from single-particle contextuality by using two-particle correlations which do not violate any Bell inequality by themselves. This demonstrates that nonlocality can come from an a priori different simpler phenomenon, and connects contextuality and nonlocality, the two critical resources for, respectively, quantum computation and secure communication. From the perspective of quantum information, our experiment constitutes a proof of principle that quantum systems can be used simultaneously for both quantum computation and secure communication.
Energy Technology Data Exchange (ETDEWEB)
Firouz-Abadi, R. D.; Fotouhi, M. M.; Permoon, M. R.; Haddadpour, H. [Sharif University of Technology, Tehran (Iran, Islamic Republic of)
2012-02-15
The small-scale effect on the natural frequencies and buckling of pressurized nanotubes is investigated in this study. Based on the firstorder shear deformable shell theory, the nonlocal theory of elasticity is used to account for the small-scale effect and the governing equations of motion are obtained. Applying modal analysis technique and based on Galerkin's method a procedure is proposed to obtain natural frequencies of vibrations. For the case of nanotubes with simply supported boundary conditions, explicit expressions are obtained which establish the dependency of the natural frequencies and buckling loads of the nanotube on the small-scale parameter and natural frequencies obtained by local continuum mechanics. The obtained solutions generalize the results of nano-bar and -beam models and are verified by the literature. Based on several numerical studies some conclusions are drawn about the small-scale effect on the natural frequencies and buckling pressure of the nanotubes.
Wang, K. F.; Wang, B. L.; Kitamura, T.
2016-02-01
Analysis of the mechanical behavior of nanostructures has been very challenging. Surface energy and nonlocal elasticity of materials have been incorporated into the traditional continuum analysis to create modified continuum mechanics models. This paper reviews recent advancements in the applications of such modified continuum models in nanostructures such as nanotubes, nanowires, nanobeams, graphenes, and nanoplates. A variety of models for these nanostructures under static and dynamic loadings are mentioned and reviewed. Applications of surface energy and nonlocal elasticity in analysis of piezoelectric nanomaterials are also mentioned. This paper provides a comprehensive introduction of the development of this area and inspires further applications of modified continuum models in modeling nanomaterials and nanostructures.
Millen, James
2016-04-01
George Musser's book Spooky Action at a Distance focuses on one of quantum physics' more challenging concepts, nonlocality, and its multitude of implications, particularly its assault on space itself.
Liu, Da-Jiang; Evans, J. W.
2002-10-01
We present a comparison of the predictions of atomistic and continuum models for the sintering of pairs of near-square two-dimensional nanoclusters adsorbed on the (100) surface in fcc metal homoepitaxial systems. Mass transport underlying these processes is dominated by periphery diffusion (PD) of adatoms along the edge of the clusters. A Mullins-type continuum model for cluster evolution incorporates anisotropy in the step edge stiffness (reflecting the energetics and adsorption site lattice structure in the atomistic model), and can also account for anisotropy in the step edge mobility (reflecting details of the kinetics). In such continuum treatments, the characteristic time τeq for relaxation of clusters with linear size of order L satisfies τeq~L4. Deviations may generally be expected for small sizes L or low temperatures T. However, for the relaxation of dumbbell-shaped clusters (formed by corner-to-corner coalescence of square clusters), atomistic simulations for PD with no kink rounding barrier (δ=0) reveal that τeq~L4 always applies. In contrast, atomistic simulations with a large kink rounding barrier (δ>0) reveal distinct scaling with τeq~L3, for low T or small L, thus providing an effective way to test for δ>0. For the relaxation of faceted rectangular clusters (formed by side-to-side coalescence of square clusters), atomistic simulations for PD with δ=0 reveal that τeq~L2, for low T or small L. This is consistent with a recent proposal by Combe and Larralde. For large δ>0, τeq has an even weaker dependence on L. We elucidate scaling behavior and the effective activation barrier for relaxation in terms of the individual atomistic PD processes and their barriers.
Controllability of semilinear integrodifferential equations with nonlocal conditions
Directory of Open Access Journals (Sweden)
Rahima Atmania
2005-07-01
Full Text Available We establish sufficient conditions for the controllability of some semilinear integrodifferential systems with nonlocal condition in a Banach space. The results are obtained using the Schaefer fixed-point theorem and semigroup theory.
Compressive Sensing via Nonlocal Smoothed Rank Function.
Fan, Ya-Ru; Huang, Ting-Zhu; Liu, Jun; Zhao, Xi-Le
2016-01-01
Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction.
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....
Discrete model of dislocations in fractional nonlocal elasticity
Directory of Open Access Journals (Sweden)
Vasily E. Tarasov
2016-01-01
Full Text Available Discrete models of dislocations in fractional nonlocal materials are suggested. The proposed models are based on fractional-order differences instead of finite differences of integer orders that are usually used. The fractional differences allow us to describe long-range interactions in materials. In continuous limit the suggested discrete models give continuum models of dislocations in nonlocal continua. Fractional generalization of the Frenkel–Kontorova model by using long-range interactions is suggested. We also propose a fractional generalization of interacting atomic chains (IAC model of dislocations by considering long-range interacting chains.
Nonlocal and nonlinear electrostatics of a dipolar Coulomb fluid.
Sahin, Buyukdagli; Ralf, Blossey
2014-07-16
We study a model Coulomb fluid consisting of dipolar solvent molecules of finite extent which generalizes the point-like dipolar Poisson-Boltzmann model (DPB) previously introduced by Coalson and Duncan (1996 J. Phys. Chem. 100 2612) and Abrashkin et al (2007 Phys. Rev. Lett. 99 077801). We formulate a nonlocal Poisson-Boltzmann equation (NLPB) and study both linear and nonlinear dielectric response in this model for the case of a single plane geometry. Our results shed light on the relevance of nonlocal versus nonlinear effects in continuum models of material electrostatics.
Nonlocal dynamics of dissipative phononic fluids
Nemati, Navid; Lee, Yoonkyung E.; Lafarge, Denis; Duclos, Aroune; Fang, Nicholas
2017-06-01
We describe the nonlocal effective properties of a two-dimensional dissipative phononic crystal made by periodic arrays of rigid and motionless cylinders embedded in a viscothermal fluid such as air. The description is based on a nonlocal theory of sound propagation in stationary random fluid/rigid media that was proposed by Lafarge and Nemati [Wave Motion 50, 1016 (2013), 10.1016/j.wavemoti.2013.04.007]. This scheme arises from a deep analogy with electromagnetism and a set of physics-based postulates including, particularly, the action-response procedures, whereby the effective density and bulk modulus are determined. Here, we revisit this approach, and clarify further its founding physical principles through presenting it in a unified formulation together with the two-scale asymptotic homogenization theory that is interpreted as the local limit. Strong evidence is provided to show that the validity of the principles and postulates within the nonlocal theory extends to high-frequency bands, well beyond the long-wavelength regime. In particular, we demonstrate that up to the third Brillouin zone including the Bragg scattering, the complex and dispersive phase velocity of the least-attenuated wave in the phononic crystal which is generated by our nonlocal scheme agrees exactly with that reproduced by a direct approach based on the Bloch theorem and multiple scattering method. In high frequencies, the effective wave and its associated parameters are analyzed by treating the phononic crystal as a random medium.
Waldecker, S J
2016-01-01
The nonlocal dispersive optical model (NLDOM) nucleon potentials are used for the first time in the adiabatic analysis of a (d,p) reaction to generate distorted waves both in the entrance and exit channels. These potentials were designed and fitted by Mahzoon $et \\text{ } al.$ [Phys. Rev. Lett. 112, 162502 (2014)] to constrain relevant single-particle physics in a consistent way by imposing the fundamental properties, such as nonlocality, energy-dependence and dispersive relations, that follow from the complex nature of nuclei. However, the NLDOM prediction for the $^{40}$Ca(d,p)$^{41}$Ca cross sections at low energy, typical for some modern radioactive beam ISOL facilities, is about 70$\\%$ higher than the experimental data despite being reduced by the NLDOM spectroscopic factor of 0.73. This overestimation comes most likely either from insufficient absorption or due to constructive interference between ingoing and outgoing waves. This indicates strongly that additional physics arising from many-body effects ...
Origin and effect of nonlocality in a layered composite.
Energy Technology Data Exchange (ETDEWEB)
Silling, Stewart Andrew
2014-01-01
A simple demonstration of nonlocality in a heterogeneous material is presented. By analysis of the microscale deformation of a two-component layered medium, it is shown that nonlocal interactions necessarily appear in a homogenized model of the system. Explicit expressions for the nonlocal forces are determined. The way these nonlocal forces appear in various nonlocal elasticity theories is derived. The length scales that emerge involve the constituent material properties as well as their geometrical dimen- sions. A peridynamic material model for the smoothed displacement eld is derived. It is demonstrated by comparison with experimental data that the incorporation of non- locality in modeling dramatically improves the prediction of the stress concentration in an open hole tension test on a composite plate.
Origin and effect of nonlocality in a layered composite.
Energy Technology Data Exchange (ETDEWEB)
Silling, Stewart Andrew
2014-01-01
A simple demonstration of nonlocality in a heterogeneous material is presented. By analysis of the microscale deformation of a two-component layered medium, it is shown that nonlocal interactions necessarily appear in a homogenized model of the system. Explicit expressions for the nonlocal forces are determined. The way these nonlocal forces appear in various nonlocal elasticity theories is derived. The length scales that emerge involve the constituent material properties as well as their geometrical dimen- sions. A peridynamic material model for the smoothed displacement eld is derived. It is demonstrated by comparison with experimental data that the incorporation of non- locality in modeling dramatically improves the prediction of the stress concentration in an open hole tension test on a composite plate.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators.
Belenchia, Alessio; Benincasa, Dionigi M T; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-22
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Testing Quantum Gravity Induced Nonlocality via Optomechanical Quantum Oscillators
Belenchia, Alessio; Benincasa, Dionigi M. T.; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2016-04-01
Several quantum gravity scenarios lead to physics below the Planck scale characterized by nonlocal, Lorentz invariant equations of motion. We show that such nonlocal effective field theories lead to a modified Schrödinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of optomechanical quantum oscillators is characterized by a spontaneous periodic squeezing that cannot be generated by environmental effects. We discuss constraints on the nonlocality obtained by past experiments, and show how future experiments (already under construction) will either see such effects or otherwise cast severe bounds on the nonlocality scale (well beyond the current limits set by the Large Hadron Collider). This paves the way for table top, high precision experiments on massive quantum objects as a promising new avenue for testing some quantum gravity phenomenology.
Besse, Nicolas
2011-02-01
The aim of this paper is to study the existence of a classical solution for the waterbag model with a continuum of waterbags, which can been viewed as an infinite dimensional system of first-order conservation laws. The waterbag model, which constitutes a special class of exact weak solution of the Vlasov equation, is well known in plasma physics, and its applications in gyrokinetic theory and laser-plasma interaction are very promising. The proof of the existence of a continuum of regular waterbags relies on a generalized definition of hyperbolicity for an integrodifferential hyperbolic system of equations, some results in singular integral operators theory and harmonic analysis, Riemann-Hilbert boundary value problems and energy estimates.
Institute of Scientific and Technical Information of China (English)
DAI Tian-min
2005-01-01
Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Via total variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity &stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded.
Local orthogonality provides a tight upper bound for Hardy's nonlocality
Das, Subhadipa; Banik, Manik; Gazi, Md. Rajjak; Rai, Ashutosh; Kunkri, Samir
2013-12-01
The amount of nonlocality in quantum theory is limited compared to that allowed in generalized no-signaling theory [S. Popescu and D. Rohrlich, Found. Phys.FNDPA40015-901810.1007/BF02058098 24, 379 (1994)]. This feature, for example, gets manifested in the amount of Bell inequality violation as well as in the degree of success probability of Hardy's (Cabello's) nonlocality argument. Physical principles like information causality and macroscopic locality have been proposed for analyzing restricted nonlocality in quantum mechanics, viz. explaining the Cirel'son bound. However, these principles are not very successful in explaining the maximum success probability of Hardy's as well as Cabello's argument in quantum theory. Here we show that a recently proposed physical principle, namely local orthogonality, does better by providing a tighter upper bound on the success probability for Hardy's nonlocality. This bound is relatively closer to the corresponding quantum value compared to the bounds achieved from other principles.
Ansari, R.; Norouzzadeh, A.
2016-10-01
The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin-Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material properties vary in the thickness direction and are evaluated using the Mori-Tanaka homogenization scheme. The governing equations of buckled nanoplate are achieved by the minimum total potential energy principle. To perform the isogeometric analysis as a solution methodology, a novel matrix-vector form of formulation is presented. Numerical examples are given to study the effects of surface stress as well as other important parameters on the critical buckling loads of functionally graded nanoplates. It is found that the buckling configuration of nanoplates at small scales is significantly affected by the surface free energy.
Nonlocal effective medium analysis in symmetric metal-dielectric multilayer metamaterials
Sun, Lei; Luk, Ting S; Yang, Xiaodong; Gao, Jie
2015-01-01
The optical nonlocality in symmetric metal-dielectric multilayer metamaterials is theoretically and experimentally investigated with respect to transverse-magnetic-polarized incident light. A nonlocal effective medium theory is derived from the transfer-matrix method to determine the nonlocal effective permittivity depending on both the frequency and wave vector in a symmetric metal-dielectric multilayer stack. In contrast to the local effective medium theory, our proposed nonlocal effective medium theory can accurately predict measured incident angle-dependent reflection spectra from a fabricated multilayer stack and provide nonlocal dispersion relations. Moreover, the bulk plasmon polaritons with large wave vectors supported in the multilayer stack are also investigated with the nonlocal effective medium theory through the analysis of the dispersion relation and eigenmode.
Koutsoumaris, C. Chr.; Eptaimeros, K. G.; Zisis, T.; Tsamasphyros, G. J.
2016-12-01
The nonlocal theory of elasticity is widely employed to the study of nanoscale problems. The differential approach of Eringen's nonlocal beam theory has been widely used to solve problems whose size effect is substantial in structures. However, in the case of Euler-Bernoulli beam theory (EBBT), this approach reveals inconsistencies that do not allow for the energy functional formulation. To avoid these inconsistencies, an alternative route is to use the integral form of nonlocal elasticity. This study revolves around the nonlocal integral beam model for various attenuation functions with the intention to explore the static response of a beam (or a nanobeam) for different types of loadings and boundary conditions (BC).
Yan, Zhi; Jiang, Liying
2017-01-01
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. PMID:28336861
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.
Nonlocal diffusion and applications
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.
ON THE CONTINUUM MODELING OF CARBON NANOTUBES
Institute of Scientific and Technical Information of China (English)
张鹏; 黄永刚; Philippe H.Geubelle; 黄克智
2002-01-01
We have recently proposed a nanoscale continuum theory for carbonnanotubes. The theory links continuum analysis with atomistic modeling by incor-porating interatomic potentials and atomic structures of carbon nanotubes directlyinto the constitutive law. Here we address two main issues involved in setting upthe nanoscale continuum theory for carbon nanotubes, namely the multi-body in-teratomic potentials and the lack of centrosymmetry in the nanotube structure. Weexplain the key ideas behind these issues in establishing a nanoscale continuum theoryin terms of interatomic potentials and atomic structures.
Mennucci, Benedetta; Cappelli, Chiara; Guido, Ciro Achille; Cammi, Roberto; Tomasi, Jacopo
2009-04-02
This paper provides an overview of recent research activities concerning the quantum-mechanical description of structures and properties of electronically excited chromophores in solution. The focus of the paper is on a specific approach to include solvent effects, namely the polarizable continuum model (PCM). Such a method represents an efficient strategy if coupled to proper quantum-mechanical descriptions such as the time-dependent density functional theory (TDDFT). As a result, the description of molecules in the condensed phase can be extended to excited states still maintaining the computational efficiency and the physical reliability of the ground-state calculations. The most important theoretical and computational aspects of the coupling between PCM and TDDFT are presented and discussed together with an example of application to the study of the low-lying electronic excited states of push-pull chromophores in different solvents.
Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery
Energy Technology Data Exchange (ETDEWEB)
Mansfield, P. (Dept. of Mathematical Sciences, Univ. of Durham (United Kingdom))
1994-04-25
We solve Schroedinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero. (orig.)
A non-local evolution equation model of cell-cell adhesion in higher dimensional space.
Dyson, Janet; Gourley, Stephen A; Webb, Glenn F
2013-01-01
A model for cell-cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell-cell adhesion, J. Theor. Biol. 243 (2006), pp. 98-113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments.
Study on Risk Pre-control Continuum Theory in Coal Mine%煤矿风险预控连续统一体理论研究
Institute of Scientific and Technical Information of China (English)
孟现飞; 宋学锋; 张炎治
2011-01-01
In order to change passive safety management to active management in coal mine, risk pre-control continuum theory and gradient control framework of risk in coal mine are constructed by borrowing ideas from leadership continuum theory. Objects of risk pre-control are divided into four types which are stable safety system, unstable safety system, urgent condition of accident and accident. The different corresponding management modes form the risk pre-control continuum of coal mine. Gradient control measures should be enforced upon risks in coal mine which are comprised of prevention control, correction control, contingency control and accident control. The results show that the intrinsic safety of coal mine can be achieved only by making a better management of the risks in each period.%为了使煤矿被动式的安全管理模式真正转变为主动式预控管理模式,从而打造本质安全型矿井,借鉴领导方式连续统一体理论,提出煤矿风险预控连续统一体理论,建立煤矿风险梯度控制框架.将煤矿风险预控对象划分为4种类型,即稳定的安全系统、失稳的安全系统、事故紧急状态和事故,针对不同预控对象所实施的安全管理模式就构成风险预控的“连续统一体”.对煤矿风险应实施梯度控制,控制方案从高梯度到低梯度依次为预防控制、校正控制、应急控制和事故控制.研究表明:只有做好每一个风险阶段的安全管理工作,才能实现煤矿本质安全的目的.
Gouin, Henri
2011-01-01
A thermomechanical model of continuous fluid media based on second gradient theory is used to study motions in liquid-vapor interfaces. At equilibrium, the model is shown to be equivalent to mean-field molecular theories of capillarity. In such fluids, conservative motions verify first integrals that lead to Kelvin circulation theorems and potential equations. The dynamical surface tension of liquid-vapor interfaces is deduced from viscous fluid equations. The result provides and explains the Marangoni effect.
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
Stochastic waves in a Brusselator model with nonlocal interaction.
Biancalani, Tommaso; Galla, Tobias; McKane, Alan J
2011-08-01
We show that intrinsic noise can induce spatiotemporal phenomena such as Turing patterns and traveling waves in a Brusselator model with nonlocal interaction terms. In order to predict and to characterize these stochastic waves we analyze the nonlocal model using a system-size expansion. The resulting theory is used to calculate the power spectra of the stochastic waves analytically and the outcome is tested successfully against simulations. We discuss the possibility that nonlocal models in other areas, such as epidemic spread or social dynamics, may contain similar stochastically induced patterns.
Hertel, Peter
2012-01-01
This small book on the properties of continuously distributed matter covers a huge field. It sets out the governing principles of continuum physics and illustrates them by carefully chosen examples. These examples comprise structural mechanics and elasticity, fluid media, electricity and optics, thermoelectricity, fluctuation phenomena and more, from Archimedes' principle via Brownian motion to white dwarfs. Metamaterials, pattern formation by reaction-diffusion and surface plasmon polaritons are dealt with as well as classical topics such as Stokes' formula, beam bending and buckling, crystal optics and electro- and magnetooptic effects, dielectric waveguides, Ohm's law, surface acoustic waves, to mention just some. The set of balance equations for content, flow and production of particles, mass, charge, momentum, energy and entropy is augmented by material, or constitutive equations. They describe entire classes of materials, such as viscid fluids and gases, elastic media, dielectrics or electrical con...
Non-local plasticity effects on fracture toughness
DEFF Research Database (Denmark)
Niordson, Christian Frithiof
2002-01-01
The Mode I fracture strength in a nonlocal elastic-plastic material is analyzed under quasi-static steady crack growth. The plastic deformations are modelled using a constitutive model, where nonlocal plasticity effects are included in the instantaneous hardening moduli through a gradient measure...... of the effective plastic strain. Fracture is modelled by a cohesive zone criterion. Results on the numerically obtained stress fields are presented, as well as results on the steady-state fracture toughness. It is shown that the nonlocal theory predicts lower steady-state fracture toughness compared to predictions...... by conventional J2-flow theory, since higher normal stresses in front of the crack tip are predicted. Furthermore, the nonlocal material description increases the range of applicability of the cohesive zone model, since steady-state crack growth is possible for significantly larger values of the maximum stress...
Non-local plasticity effects on fracture toughness
DEFF Research Database (Denmark)
Niordson, Christian Frithiof
2002-01-01
The Mode I fracture strength in a nonlocal elastic-plastic material is analyzed under quasi-static steady crack growth. The plastic deformations are modelled using a constitutive model, where nonlocal plasticity effects are included in the instantaneous hardening moduli through a gradient measure...... of the effective plastic strain. Fracture is modelled by a cohesive zone criterion. Results on the numerically obtained stress fields are presented, as well as results on the steady-state fracture toughness. It is shown that the nonlocal theory predicts lower steady-state fracture toughness compared to predictions...... by conventional J2-flow theory, since higher normal stresses in front of the crack tip are predicted. Furthermore, the nonlocal material description increases the range of applicability of the cohesive zone model, since steady-state crack growth is possible for significantly larger values of the maximum stress...
Understanding quantum non-locality through pseudo-telepathy game
Kunkri, Samir
2006-11-01
Usually by quantum non-locality we mean that quantum mechanics can not be replaced by local realistic theory. On the other hand this nonlocal feature of quantum mechanics can not be used for instantaneous communication and hence it respect Einstein's special theory of relativity. But still it is not trivial as proved by various quantum information processing using entangled states. Recently there have been studies of hypothetical non-local system again respecting no-signalling which is beyond quantum mechanics. Here we study the power of such a hypothetical nonlocal box first suggested by Popescu et.al. in the context of recently suggested pseudo-telepathy game constructed from a Kochen-Specker set.
Hobson, Art
2012-01-01
Nonlocality arises from the unified "all or nothing" interactions of a spatially extended field quantum such as a photon or an electron. In the double-slit experiment with light, for example, each photon comes through both slits and arrives at the viewing screen as an extended but unified energy bundle or "field quantum." When the photon interacts…
Hobson, Art
2012-01-01
Nonlocality arises from the unified "all or nothing" interactions of a spatially extended field quantum such as a photon or an electron. In the double-slit experiment with light, for example, each photon comes through both slits and arrives at the viewing screen as an extended but unified energy bundle or "field quantum." When the photon interacts…
Indian Academy of Sciences (India)
Aurelien Drezet
2007-03-01
In a paper by Home and Agarwal [1], it is claimed that quantum nonlocality can be revealed in a simple interferometry experiment using only single particles. A critical analysis of the concept of hidden variable used by the authors of [1] shows that the reasoning is not correct.
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...
Ward, David B.; Wampler, Karen S.
2010-01-01
For years therapists have suggested that hope is an important catalyst in the process of change. This study takes a grounded theory approach to address the need for a clearer conceptualization of hope, and to place interventions that increase hope within a therapeutic context so that therapists know how and when to use those interventions. Fifteen…
Nonlocal correlations: Fair and Unfair Strategies in Bayesian Game
Roy, Arup; Mukherjee, Amit; Guha, Tamal; Ghosh, Sibasish; Bhattacharya, Some Sankar; Banik, Manik
2016-01-01
Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform classical equilibrium strategies in common interest Bayesian games and also in conflicting interest games. However, classical equilibrium strategies can be of two types, fair and unfair. Whereas in fair equilibrium payoffs of different players are same, in unfair case they ...
Nonlocal Problems for Fractional Differential Equations via Resolvent Operators
Directory of Open Access Journals (Sweden)
Zhenbin Fan
2013-01-01
Full Text Available We discuss the continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. An example is also given to illustrate our theory.
Carvalho, Nathalia F; Pliego, Josefredo R
2015-10-28
Absolute single-ion solvation free energy is a very useful property for understanding solution phase chemistry. The real solvation free energy of an ion depends on its interaction with the solvent molecules and on the net potential inside the solute cavity. The tetraphenyl arsonium-tetraphenyl borate (TATB) assumption as well as the cluster-continuum quasichemical theory (CC-QCT) approach for Li(+) solvation allows access to a solvation scale excluding the net potential. We have determined this free energy scale investigating the solvation of the lithium ion in water (H2O), acetonitrile (CH3CN) and dimethyl sulfoxide (DMSO) solvents via the CC-QCT approach. Our calculations at the MP2 and MP4 levels with basis sets up to the QZVPP+diff quality, and including solvation of the clusters and solvent molecules by the dielectric continuum SMD method, predict the solvation free energy of Li(+) as -116.1, -120.6 and -123.6 kcal mol(-1) in H2O, CH3CN and DMSO solvents, respectively (1 mol L(-1) standard state). These values are compatible with the solvation free energy of the proton of -253.4, -253.2 and -261.1 kcal mol(-1) in H2O, CH3CN and DMSO solvents, respectively. Deviations from the experimental TATB scale are only 1.3 kcal mol(-1) in H2O and 1.8 kcal mol(-1) in DMSO solvents. However, in the case of CH3CN, the deviation reaches a value of 9.2 kcal mol(-1). The present study suggests that the experimental TATB scale is inconsistent for CH3CN. A total of 125 values of the solvation free energy of ions in these three solvents were obtained. These new data should be useful for the development of theoretical solvation models.
Quantum Loops in Non-Local Gravity
Talaganis, Spyridon
2015-01-01
In this proceedings, I will consider quantum aspects of a non-local, infinite-derivative scalar field theory - a ${\\it toy \\, model}$ depiction of a covariant infinite-derivative, non-local extension of Einstein's general relativity which has previously been shown to be free from ghosts around the Minkowski background. The graviton propagator in this theory gets an exponential suppression making it ${\\it asymptotically \\, free}$, thus providing strong prospects of resolving various classical and quantum divergences. In particular, I will find that at $1$-loop, the $2$-point function is still divergent, but once this amplitude is renormalized by adding appropriate counter terms, the ultraviolet (UV) behavior of all other $1$-loop diagrams as well as the $2$-loop, $2$-point function remains well under control. I will go on to discuss how one may be able to generalize our computations and arguments to arbitrary loops.
Nonlocal neurology: beyond localization to holonomy.
Globus, G G; O'Carroll, C P
2010-11-01
The concept of local pathology has long served neurology admirably. Relevant models include self-organizing nonlinear brain dynamics, global workspace and dynamic core theories. However such models are inconsistent with certain clinical phenomena found in Charles Bonnet syndrome, disjunctive agnosia and schizophrenia, where there is disunity of content within the unity of consciousness. This is contrasted with the split-brain case where there is disunity of content and disunity of consciousnesses. The development of quantum brain theory with it nonlocal mechanisms under the law of the whole ("holonomy") offers new possibilities for explaining disintegration within unity. Dissipative quantum brain dynamics and its approach to the binding problem, memory and consciousness are presented. A nonlocal neurology armed with a holonomic understanding might see more deeply into what clinical neurology has always aspired to: the patient as a whole.
Uncertainty, non-locality and Bell's inequality
Pati, A K
1998-01-01
We derive a Bell-like inequality involving all correlations in local observables with uncertainty free states and show that the inequality is violated in quantum mechanics for EPR and GHZ states. If the uncertainties are allowed in local observables then the statistical predictions of hidden variable theory is well respected in quantum world. We argue that the uncertainties play a key role in understanding the non-locality issues in quantum world. Thus we can not rule out the possibility that a local, realistic hidden variable theory with statistical uncertainties in the observables might reproduce all the results of quantum theory.
Directory of Open Access Journals (Sweden)
O. Rahmani
2016-01-01
Full Text Available Nano structures such as nanowires, nanobeams and nanoplates have been investigated widely for their innovative properties. In this paper the buckling of nanowires surrounded in a Winkler - Pasternak elastic medium has been examined based on the nonlocal Euler-Bernoully model with considering the surface effects. In the following a parametric study that explores the influence of numerous physical and geometrical parameters on the buckling of nanowires is presented. It has been shown that by growing the ratio of surface area to bulk in nano-size structures, the effect of surface energy turn out to be important and should be taken into consideration. Moreover the results point out that surface elasticity and residual surface tension stimulus the buckling behavior of nanowires.
Homogenization of a Cauchy continuum towards a micromorphic continuum
Hütter, Geralf
2017-02-01
The micromorphic theory of Eringen and Mindlin, including special cases like strain gradient theory or Cosserat theory, is widely used to model size effects and localization phenomena. The heuristic construction of such theories based on thermodynamic considerations is well-established. However, the identification of corresponding constitutive laws and of the large number of respective constitutive parameters limits the practical application of such theories. In the present contribution, a closed procedure for the homogenization of a Cauchy continuum at the microscale towards a fully micromorphic continuum is derived including explicit definitions of all involved generalized macroscopic stress and deformation measures. The boundary value problem to be solved on the microscale is formulated either for using static or kinematic boundary conditions. The procedure is demonstrated with an example.
Doungmo Goufo, Emile Franc
2016-08-01
After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function Eα,β(z), z∈ℂ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα , β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα , β(z), certainly opening new doors to modeling with two-parameter derivatives.
Nonlocal transformation optics
Castaldi, Giuseppe; Alu', Andrea; Engheta, Nader
2011-01-01
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 equi-frequency 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.
Nonlocality of quantum correlations
Streltsov, A; Roga, W; Bruß, D; Illuminati, F
2012-01-01
We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. This type of nonlocality occurs also for states that do not violate a Bell inequality, such as, for instance, Werner states with a low degree of entanglement. We derive the exact relation between the global state change induced by local unitary evolutions and the amount of quantum correlations. We prove that the minimal change coincides with the geometric measure of discord, thus providing the latter with an operational interpretation in terms of the capability of a local unitary dynamics to modify a global state. We establish rigorously that Werner states are the maximally quantum correlated two-qubit states, and thus are the ones that maximize this novel type of nonlocality.
Entanglement without hidden nonlocality
Hirsch, Flavien; Túlio Quintino, Marco; Bowles, Joseph; Vértesi, Tamás; Brunner, Nicolas
2016-11-01
We consider Bell tests in which the distant observers can perform local filtering before testing a Bell inequality. Notably, in this setup, certain entangled states admitting a local hidden variable model in the standard Bell scenario can nevertheless violate a Bell inequality after filtering, displaying so-called hidden nonlocality. Here we ask whether all entangled states can violate a Bell inequality after well-chosen local filtering. We answer this question in the negative by showing that there exist entangled states without hidden nonlocality. Specifically, we prove that some two-qubit Werner states still admit a local hidden variable model after any possible local filtering on a single copy of the state.
Entanglement and nonlocality in multi-particle systems
Reid, M D; Drummond, P D
2011-01-01
Entanglement, the Einstein-Podolsky-Rosen (EPR) paradox and Bell's failure of local-hidden-variable (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.
Gilson, Ronan; Durrant, Marcus C
2009-12-14
The deprotonation energies of the water ligands in a set of 40 d-block metal complexes have been calculated using density functional theory with polarized continuum model solvent corrections. The complexes include 13 aqua ions [M(OH(2))(n)](2+/3+) and a variety of aqua complexes with organic co-ligands, whose experimental pK(a) values have been reported in the literature. For comparison, the deprotonation energies of a set of 60 organic and inorganic molecules with experimental pK(a) values ranging from -25 (HSbF(6)) to +52 (C(2)H(6)) have also been calculated. Three different classes of acids are identified as giving different slopes in plots of pK(a) versus deprotonation energies; namely non-hydroxy acids, hydroxy acids, and the metal complexes. The correlation coefficients for the straight lines obtained for these three classes are 0.96, 0.97 and 0.92 respectively. Better correlations are found for sub-sets of the complexes, such as the 31 first row complexes (correlation coefficient 0.95).For several of the complexes, comparison of the calculated and observed pK(a) values, together with changes in the geometry upon optimization, offer new insights into the possible solution structures. It is concluded that DFT calculations incorporating solvent corrections can be used to give reasonable estimates of pK(a) values for the aqua ligands in a range of complex types.
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.......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 inhomogeneous broadening in plasmonic nanoparticle ensembles
DEFF Research Database (Denmark)
Tserkezis, Christos; Maack, Johan Rosenkrantz; Liu, Z.
Nonclassical effects are increasingly more relevant in plasmonics as modern nanofabrication techniques rapidly approach the extreme nanoscale limits, for which departing from classical electrodynamics becomes important. One of the largest-scale necessary corrections towards this direction...... is to abandon the local response approximation (LRA) and take the nonlocal response of the metal into account, typically through the simple hydrodynamic Drude model (HDM), which predicts a sizedependent deviation of plasmon modes from the quasistatic (QS) limit. While this behaviour has been explored for simple...... averaging through both HDM and the recent Generalized Nonlocal Optical Response (GNOR) theory, which apart from the resonance frequency shifts accounts successfully for size-dependent damping as well. We examine NPs made of either ideal Drude-like metals [of plasmon frequency (wavelength) ωp (λp...
Non-local geometry inside Lifshitz horizon
Hu, Qi; Lee, Sung-Sik
2017-07-01
Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U( N ) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.
Near field radiative heat transfer between two nonlocal dielectrics
Singer, F; Joulain, Karl
2015-01-01
We explore in the present work the near-field radiative heat transfer between two semi-infinite parallel nonlocal dielectric planes by means of fluctuational electrodynamics. We use atheory for the nonlocal dielectric permittivityfunction proposed byHalevi and Fuchs. This theory has the advantage to includedifferent models performed in the literature. According to this theory, the nonlocal dielectric function is described by a Lorenz-Drude like single oscillator model, in which the spatial dispersion effects are represented by an additional term depending on the square of the total wavevector k. The theory takes into account the scattering of the electromagneticexcitation at the surface of the dielectric material, which leads to the need of additional boundary conditions in order to solve Maxwell's equations and treat the electromagnetic transmission problem. The additional boundary conditions appear as additional surface scattering parameters in the expressions of the surface impedances. It is shown that the...
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.)
Theory of Spin-State Selective Nonlocal Screening in Co 2p X-ray Photoemission Spectrum of LaCoO3
Hariki, Atsushi; Yamanaka, Akihiro; Uozumi, Takayuki
2015-07-01
The Co 2p X-ray photoemission spectrum (XPS) of LaCoO3 is investigated using a dp model simulating Co 3d and O 2p orbitals by means of a dynamical mean-field approach under the perovskite crystal structure. Across the spin-state transition from the low-spin to the high-spin state, the Co 2p3/2 main-line structure is substantially changed beyond expectation of a CoO6 cluster model calculation. In addition to the Coulombic multiplet effect, the origin of the spectral change is attributed to the nonlocal screening (NLS) from the correlated 3d band located on the top of the valence band to the core-excited Co site in the final state, where the NLS is practically active only for the high-spin state. The spin-state selectivity of the NLS is closely related to not only the spin state of the core-excited Co ion but also the spin and orbital character of the occupied Co 3d band in crystals. We emphasize that the Co 2p XPS can be an informative probe to investigate the spin state of Co ions in Co oxides, such as LaCoO3.
Nonlocal Crowd Dynamics Models for several Populations
Colombo, Rinaldo M
2011-01-01
This paper develops the basic analytical theory related to some recently introduced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of $\\reali^+$. The results on the stability with respect to the equations are improved. Moreover, here the case of several populations is considered, obtaining the well posedness of systems of multi-D non-local conservation laws. The basic analytical tools are provided by the classical Kruzkov theory of scalar conservation laws in several space dimensions.
NONLOCAL CROWD DYNAMICS MODELS FOR SEVERAL POPULATIONS
Institute of Scientific and Technical Information of China (English)
Rinaldo M. Colombo; Magali Lécureux-Mercier
2012-01-01
This paper develops the basic analytical theory related to some recently introduced crowd dynamics models.Where well posedness was known only locally in time,it is here extended to all of R+.The results on the stability with respect to the equations are improved.Moreover,here the case of several populations is considered,obtaining the well posedness of systems of multi-D non-local conservation laws.The basic analytical tools are provided by the classical Kru(z)kov theory of scalar conservation laws in several space dimensions.
Free vibrations analysis of carbon nanotubes resting on Winkler foundations based on nonlocal models
Energy Technology Data Exchange (ETDEWEB)
Rahmanian, M.; Torkaman-Asadi, M.A., E-mail: torkaman-asadi@ae.sharif.edu; Firouz-Abadi, R.D.; Kouchakzadeh, M.A.
2016-03-01
In the present study, free vibrations of single walled carbon nanotubes (SWCNT) on an elastic foundation is investigated by nonlocal theory of elasticity with both beam and shell models. The nonlocal boundary conditions are derived explicitly and effectiveness of nonlocal parameter appearing in nonlocal boundary conditions is studied. Also it is demonstrated that the beam model is comparatively incapable of capturing size effects while shell model captures size effects more precisely. Moreover, the effects of some parameters such as mechanical properties, foundation stiffness, length and radius ratios on the natural frequencies are studied and some conclusions are drawn.
Goos-Hänchen shifts of Helmholtz solitons at nonlocal nonlinear interfaces
Zhiwei, Shi; Jing, Xue; Jilong, Chen; Yang, Li; Huagang, Li
2015-02-01
We address the nonlinear Goos-Hänchen shift of Helmholtz solitons at a nonlocal nonlinear interface between a Kerr medium and a nonlocal nonlinear medium. Based on the framework of the Helmholtz theory, we have demonstrated that the Goos-Hänchen shift depends on the angle of the incidence, the linear and nonlinear refractive index mismatch at the interface, the nonparaxial parameter and the degree of nonlocality. Interestingly, internal and external refraction can be introduced when the nonlinear refractive index mismatch is greater than a threshold value. The total reflection will occur when the degree of nonlocality exceeds a value.
Senno, Gabriel; Bendersky, Ariel; Figueira, Santiago
2016-07-01
The concepts of randomness and non-locality are intimately intertwined outcomes of randomly chosen measurements over entangled systems exhibiting non-local correlations are, if we preclude instantaneous influence between distant measurement choices and outcomes, random. In this paper, we survey some recent advances in the knowledge of the interplay between these two important notions from a quantum information science perspective.
Quadratic solitons as nonlocal solitons
DEFF Research Database (Denmark)
Nikolov, Nikola Ivanov; Neshev, D.; Bang, Ole
2003-01-01
We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for analytical...
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.
Nonlocal modeling and buckling features of cracked nanobeams with von Karman nonlinearity
Akbarzadeh Khorshidi, Majid; Shaat, Mohamed; Abdelkefi, Abdessattar; Shariati, Mahmoud
2017-01-01
Buckling and postbuckling behaviors of cracked nanobeams made of single-crystalline nanomaterials are investigated. The nonlocal elasticity theory is used to model the nonlocal interatomic effects on the beam's performance accounting for the beam's axial stretching via von Karman nonlinear theory. The crack is then represented as torsional spring where the crack severity factor is derived accounting for the nonlocal features of the beam. By converting the beam into an equivalent infinite long plate with an edge crack subjected to a tensile stress at the far field, the crack energy release rate, intensity factor, and severity factor are derived according to the nonlocal elasticity theory. An analytical solution for the buckling and the postbuckling responses of cracked nonlocal nanobeams accounting for the beam axial stretching according to von Karman nonlinear theory of kinematics is derived. The impacts of the nonlocal parameter on the critical buckling loads and the static nonlinear postbuckling responses of cracked nonlocal nanobeams are studied. The results indicate that the buckling and postbuckling behaviors of cracked nanobeams are strongly affected by the crack location, crack depth, nonlocal parameter, and length-to-thickness ratio.
Weakly nonlocal non-equilibrium thermodynamics - variational principles and Second Law
Ván, P.
2009-01-01
A general, uniform, rigorous and constructive thermodynamic approach to weakly nonlocal non-equilibrium thermodynamics is reviewed. A method is given to construct and restrict the evolution equations of physical theories according to the Second Law of thermodynamics and considering weakly nonlocal constitutive state spaces. The evolution equations of internal variables, the classical irreversible thermodynamics and Korteweg fluids are treated.
A Systems-Theoretical Generalization of Non-Local Correlations
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.
Pion Form Factor in QCD Sum Rules with Nonlocal Condensates and in the Local-Duality Approach
Bakulev, Alexander P; Stefanis, N G
2009-01-01
We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the $O(\\alpha_s)$ approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold $s_0(Q^2)$ parameter is highly underestimated in the Local-Duality approach at $Q^2\\gtrsim 2$ GeV$^2$. Using our fit for this parameter, $s_0^\\text{LD}(Q^2)$, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the $O(\\alpha_s^2)$ contribution to the pion's form factor.
Lagrangian continuum dynamics in ALEGRA.
Energy Technology Data Exchange (ETDEWEB)
Wong, Michael K. W.; Love, Edward
2007-12-01
Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.
An operational framework for nonlocality
Gallego, Rodrigo; Acín, Antonio; Navascués, Miguel
2011-01-01
Due to the importance of entanglement for quantum information purposes, a framework has been developed for its characterization and quantification as a resource based on the following operational principle: entanglement among $N$ parties cannot be created by local operations and classical communication, even when $N-1$ parties collaborate. More recently, nonlocality has been identified as another resource, alternative to entanglement and necessary for device-independent quantum information protocols. We introduce an operational framework for nonlocality based on a similar principle: nonlocality among $N$ parties cannot be created by local operations and allowed classical communication even when $N-1$ parties collaborate. We then show that the standard definition of multipartite nonlocality, due to Svetlichny, is inconsistent with this operational approach: according to it, genuine tripartite nonlocality could be created by two collaborating parties. We finally discuss alternative definitions for which consist...
On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials
Directory of Open Access Journals (Sweden)
Luciano Feo
2016-01-01
Full Text Available Evaluation of size effects in functionally graded elastic nanobeams is carried out by making recourse to the nonlocal continuum mechanics. The Bernoulli-Euler kinematic assumption and the Eringen nonlocal constitutive law are assumed in the formulation of the elastic equilibrium problem. An innovative methodology, characterized by a lowering in the order of governing differential equation, is adopted in the present manuscript in order to solve the boundary value problem of a nanobeam under flexure. Unlike standard treatments, a second-order differential equation of nonlocal equilibrium elastic is integrated in terms of transverse displacements and equilibrated bending moments. Benchmark examples are developed, thus providing the nonlocality effect in nanocantilever and clampled-simply supported nanobeams for selected values of the Eringen scale parameter.
Institute of Scientific and Technical Information of China (English)
Ouyang Shi-Gen; Guo Qi; Lan Sheng; Wu Li-Jun
2007-01-01
The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schr(o)dinger equation for several types of nonlocal responses are calculated by Ritz's variational method.For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but difierent degrees of nonlocality are identical except for an amplitude factor.For a nonlocal case where the nonlocal response function decays in direct proportion to the ruth power of the distance near the source point,the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the(m+2)th power of its beam width.
Bell on Bell's theorem: The changing face of nonlocality
Brown, Harvey R
2015-01-01
Between 1964 and 1990, the notion of nonlocality in Bell's papers underwent a profound change as his nonlocality theorem gradually became detached from quantum mechanics, and referred to wider probabilistic theories involving correlations between separated beables. The proposition that standard quantum mechanics is itself nonlocal (more precisely, that it violates `local causality') became divorced from the Bell theorem per se from 1976 on, although this important point is widely overlooked in the literature. In 1990, the year of his death, Bell would express serious misgivings about the mathematical form of the local causality condition, and leave ill-defined the issue of the consistency between special relativity and violation of the Bell-type inequality. In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz-covariant version of quantum theory, free of action-at-a-distance, can be a...
Hyperbolic conservation laws in continuum physics
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...
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...
Solutions of Nonlocal -Laplacian Equations
Directory of Open Access Journals (Sweden)
Mustafa Avci
2013-01-01
Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.
Spontaneous Emission in Nonlocal Materials
Ginzburg, Pavel; Nasir, Mazhar E; Olvera, Paulina Segovia; Krasavin, Alexey V; Levitt, James; Hirvonen, Liisa M; Wells, Brian; Suhling, Klaus; Richards, David; Podolskiy, Viktor A; Zayats, Anatoly V
2016-01-01
Light-matter interactions can be dramatically modified by the surrounding environment. Here we report on the first experimental observation of molecular spontaneous emission inside a highly nonlocal metamaterial based on a plasmonic nanorod assembly. We show that the emission process is dominated not only by the topology of its local effective medium dispersion, but also by the nonlocal response of the composite, so that metamaterials with different geometric parameters but the same local effective medium properties exhibit different Purcell factors. A record-high enhancement of a decay rate is observed, in agreement with the developed quantitative description of the Purcell effect in a nonlocal medium. An engineered material nonlocality introduces an additional degree of freedom into quantum electrodynamics, enabling new applications in quantum information processing, photo-chemistry, imaging, and sensing.
Acceleration-induced nonlocality: kinetic memory versus dynamic memory
Chicone, C.; Mashhoon, B.
2001-01-01
The characteristics of the memory of accelerated motion in Minkowski spacetime are discussed within the framework of the nonlocal theory of accelerated observers. Two types of memory are distinguished: kinetic and dynamic. We show that only kinetic memory is acceptable, since dynamic memory leads to divergences for nonuniform accelerated motion.
A nonlocal parabolic system with application to a thermoelastic problem
Directory of Open Access Journals (Sweden)
Y. Lin
1999-01-01
problem is first transformed into an equivalent nonlocal parabolic systems using a transformation, and then the existence and uniqueness of the solutions are demonstrated via the theoretical potential representation theory of the parabolic equations. Finally some realistic situations in the applications are discussed using the results obtained in this paper.
Non-local common cause explanations for EPR
Egg, Matthias
2013-01-01
The paper argues that a causal explanation of the correlated outcomes of EPR-type experiments is desirable and possible. It shows how Bohmian mechanics and the GRW mass density theory offer such an explanation in terms of a non-local common cause.
Nonlocal Cauchy problem for nonlinear mixed integrodifferential equations
Directory of Open Access Journals (Sweden)
H.L. Tidke
2010-12-01
Full Text Available The present paper investigates the existence and uniqueness of mild and strong solutions of a nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition. The results obtained by using Schauder fixed point theorem and the theory of semigroups.
Inhomogeneous broadening in non-interacting nonlocal plasmonic ensembles
DEFF Research Database (Denmark)
Tserkezis, Christos; Maack, Johan Rosenkrantz; Liu, Z.
2016-01-01
important within the first-order correction to classical electrodynamics provided by the hydrodynamic Drude model, but turn out to be less prominent once additional single-particle size-dependent damping mechanisms are accounted for through the recently developed Generalized Nonlocal Optical Response theory....... Our work is therefore expected to provide insight and facilitate the design of nanoscale spectroscopy experiments....
ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.
Study of Nonlocal Optical Potential
Institute of Scientific and Technical Information of China (English)
TIAN; Yuan
2013-01-01
It is generally known that nuclear optical potentials are theoretically expected to be non-local.The non-locality arises from the exchange of particles between the projectile and target and from coupling tonon-elastic channels.This non-locality was first introduced by Frahn and Lemmer,and developed further by Perey and Buck(PB).The kernel is of the form
Ho, Gregory S.; Lignères, Vincent L.; Carter, Emily A.
2008-07-01
We derive an analytic form of the Wang-Govind-Carter (WGC) [Wang , Phys. Rev. B 60, 16350 (1999)] kinetic energy density functional (KEDF) with the density-dependent response kernel. A real-space aperiodic implementation of the WGC KEDF is then described and used in linear scaling orbital-free density functional theory (OF-DFT) calculations.
Nonlocal elasticity defined by Eringen's integral model: Introduction of a boundary layer method
National Research Council Canada - National Science Library
Abdollahi, R; Boroomand, B
2014-01-01
In this paper we consider a nonlocal elasticity theory defined by Eringen's integral model and introduce, for the first time, a boundary layer method by presenting the exponential basis functions (EBFs...
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.
Indian Academy of Sciences (India)
K Balachandran; K Uchiyama
2000-05-01
In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.
Nonlocal Classical Matter in Self-contained Machian Relativism
Bulyzhenkov-Widicker, I E
2007-01-01
The continuous elementary source in Einstein's gravitational theory is the r^{-4} radial distribution of the energy-momentum tensor density. The space energy integral of such an infinite (astro)source-particle is finite and determines its nonlocal gravitational charge for the energy-to-energy attraction of other (astro)particles. Non-empty flat space of the undivided material Universe is charged continuously by the world energy density of the global ensemble of overlapping radial particles. Nonlocal gravitational/inertial energy-charges incorporate Machian relativism quantitatively into Einstein's gravitation for self-contained GR-SR relations without references to Newton's mass-to-mass attraction.
Accelerating cosmologies from non-local higher-derivative gravity
Capozziello, Salvatore; Nojiri, Shin'ichi; Odintsov, Sergei D
2008-01-01
We study accelerating cosmological solutions of a general class of non-linear gravities which depend on Gauss-Bonnet and other higher derivative invariants. To achieve this goal a local formulation with auxiliary scalars for arbitrary higher-derivative non-local gravity is developed. It is demonstrated that non-local Gauss-Bonnet gravity can be reduced, in the local formulation, to a model of string-inspired scalar-Gauss-Bonnet gravity. A natural unification, in the theory here developed, of the early-time inflation epoch with a late-time acceleration stage can also be realized.
Accelerating cosmologies from non-local higher-derivative gravity
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' , INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli (Italy); Elizalde, Emilio [Consejo Superior de Investigaciones Cientificas ICE/CSIC-IEEC, Campus UAB, Facultat de Ciencies, Torre C5-Parell-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Nojiri, Shin' ichi [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan)], E-mail: nojiri@phys.nagoya-u.ac.jp; Odintsov, Sergei D. [Institucio Catalana de Recerca i Estudis Avancats (ICREA) and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra, Barcelona (Spain)
2009-01-12
We study accelerating cosmological solutions of a general class of non-linear gravities which depend on Gauss-Bonnet and other higher derivative invariants. To achieve this goal a local formulation with auxiliary scalars for arbitrary higher-derivative non-local gravity is developed. It is demonstrated that non-local Gauss-Bonnet gravity can be reduced, in the local formulation, to a model of string-inspired scalar-Gauss-Bonnet gravity. A natural unification, in the theory here developed, of the early-time inflation epoch with a late-time acceleration stage can also be realized.
Inhomogeneous broadening in non-interacting nonlocal plasmonic ensembles
DEFF Research Database (Denmark)
Tserkezis, Christos; Maack, Johan Rosenkrantz; Liu, Z.
2016-01-01
The importance of inhomogeneous broadening due to the size dependence of plasmon resonances in few-nm metallic particle ensembles is investigated through different models describing the nonlocal optical response of plasmonic nanospheres. Modal shifts and plasmon line broadening are shown to become...... important within the first-order correction to classical electrodynamics provided by the hydrodynamic Drude model, but turn out to be less prominent once additional single-particle size-dependent damping mechanisms are accounted for through the recently developed Generalized Nonlocal Optical Response theory...
Simple Explanation of the Quantum Limits of Genuine n-Body Nonlocality.
Cabello, Adán
2015-06-05
Quantum n-body correlations cannot be explained with (n-1)-body nonlocality. However, this genuine n-body nonlocality cannot surpass certain bounds. Here we address the problem of identifying the principles responsible for these bounds. We show that, for any n≥2, the exclusivity principle, as derived from axioms about sharp measurements, and a technical assumption give the exact bounds predicted by quantum theory. This provides a unified explanation of the bounds of single-body contextuality and n-body nonlocality, and connects two programs towards understanding quantum theory.
Torsional wave propagation in multiwalled carbon nanotubes using nonlocal elasticity
Arda, Mustafa; Aydogdu, Metin
2016-03-01
Torsional wave propagation in multiwalled carbon nanotubes is studied in the present work. Governing equation of motion of multiwalled carbon nanotube is obtained using Eringen's nonlocal elasticity theory. The effect of van der Waals interaction coefficient is considered between inner and outer nanotubes. Dispersion relations are obtained and discussed in detail. Effect of nonlocal parameter and van der Waals interaction to the torsional wave propagation behavior of multiwalled carbon nanotubes is investigated. It is obtained that torsional van der Waals interaction between adjacent tubes can change the rotational direction of multiwalled carbon nanotube as in-phase or anti-phase. The group and escape velocity of the waves converge to a limit value in the nonlocal elasticity approach.
A Caveat on Building Nonlocal Models of Cosmology
Tsamis, N C
2014-01-01
Nonlocal models of cosmology might derive from graviton loop corrections to the effective field equations from the epoch of primordial inflation. Although the Schwinger-Keldysh formalism would automatically produce causal and conserved effective field equations, the models so far proposed have been purely phenomenological. Two techniques have been employed to generate causal and conserved field equations: either varying an invariant nonlocal effective action and then enforcing causality by the ad hoc replacement of any advanced Green's function with its retarded counterpart, or else introducing causal nonlocality into a general ansatz for the field equations and then enforcing conservation. We point out here that the two techniques access very different classes of models, and that neither one of them may represent what would actually arise from fundamental theory.
Bound on Hardy's nonlocality from the principle of information causality
Ahanj, Ali; Kunkri, Samir; Rai, Ashutosh; Rahaman, Ramij; Joag, Pramod S.
2010-03-01
Recently, the principle of nonviolation of information causality [Nature 461, 1101 (2009)] has been proposed as one of the foundational properties of nature. We explore the Hardy’s nonlocality theorem for two-qubit systems, in the context of generalized probability theory, restricted by the principle of nonviolation of information causality. Applying a sufficient condition for information causality violation, we derive an upper bound on the maximum success probability of Hardy’s nonlocality argument. We find that the bound achieved here is higher than that allowed by quantum mechanics but still much less than what the no-signaling condition permits. We also study the Cabello type nonlocality argument (a generalization of Hardy’s argument) in this context.
Nonlocal dielectric effects in core-shell nanowires.
Energy Technology Data Exchange (ETDEWEB)
McMahon, J. M.; Gray, S. K.; Schatz, G. C. (Center for Nanoscale Materials); ( CSE); (Northwestern Univ.)
2010-01-01
We study the optical spectra and near fields of core-shell nanowires (nanoshells), using a recently developed finite-difference method that allows for a spatially nonlocal dielectric response. We first analyze the parameters of the nonlocal model by making comparisons with related experimental data and previous theoretical work. We then investigate how nonlocal effects are dependent on nanoshell features, such as shell thickness, overall size, and the ratio of core radius to shell radius. We demonstrate that the shell thickness along the longitudinal direction of the incident light is the primary controlling factor of nonlocal effects, which appear as anomalous absorption resonances and blueshifts in the localized surface plasmon resonance (LSPR) positions, relative to local theory. In addition, we show that the amount of blueshift depends on the order of the LSPR. The optical responses of nanoshells immersed in various refractive index (RI) environments are also studied. We show that the nonlocal anomalous absorption features are relatively insensitive to RI changes, but the blueshift of the dipolar LSPR varies nonlinearly.
Nonlocal Effects on D-branes in Plane-Wave Backgrounds
Ganor, O J; Ganor, Ori J.; Varadarajan, Uday
2002-01-01
We argue that the effective field theory on D3-branes in a plane-wave background with 3-form flux is a nonlocal deformation of Yang-Mills theory. In the case of NSNS flux, it is a dipole field theory with lightlike dipole vectors. For an RR 3-form flux the dipole theory is strongly coupled. We propose a weakly coupled S-dual description for it. The S-dual description is local at any finite order in string perturbation theory but becomes nonlocal when all perturbation theory orders are summed together.
Nonlocal optical response in metallic nanostructures.
Raza, Søren; Bozhevolnyi, Sergey I; Wubs, Martijn; Asger Mortensen, N
2015-05-13
This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response.
Nonlocal optical response in metallic nanostructures
DEFF Research Database (Denmark)
Raza, Søren; Bozhevolnyi, Sergey I.; Wubs, Martijn
2015-01-01
This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response...... on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response....
The General Theory of Homogenization A Personalized Introduction
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,
Robustness of the far-field response of nonlocal plasmonic ensembles
DEFF Research Database (Denmark)
Tserkezis, Christos; Maack, Johan Rosenkrantz; Liu, Zhaowei
2016-01-01
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......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...
Tests of Quantum Gravity induced non-locality via opto-mechanical quantum oscillators
Belenchia, Alessio; Liberati, Stefano; Marin, Francesco; Marino, Francesco; Ortolan, Antonello
2015-01-01
Several quantum gravity scenarios lead to physics below the Planck scale characterised by nonlocal, Lorentz invariant equations of motion. We show that such non-local effective field theories lead to a modified Schr\\"odinger evolution in the nonrelativistic limit. In particular, the nonlocal evolution of opto-mechanical quantum oscillators is characterised 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 non-locality 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.
Continuum mechanics of single-substance bodies
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
Lan, Tran Nguyen; Zgid, Dominika
2016-01-01
We present a detailed discussion of self-energy embedding theory (SEET) which is a quantum embedding scheme allowing us to describe a chosen subsystem very accurately while keeping the description of the environment at a lower cost. We apply SEET to molecular examples where commonly our chosen subsystem is made out of a set of strongly correlated orbitals while the weakly correlated orbitals constitute an environment. Such a self-energy separation is very general and to make this procedure applicable to multiple systems a detailed and practical procedure for the evaluation of the system and environment self-energy is necessary. We list all the intricacies for one of the possible procedures while focusing our discussion on many practical implementation aspects such as the choice of best orbital basis, impurity solver, and many steps necessary to reach chemical accuracy. Finally, on a set of carefully chosen molecular examples, we demonstrate that SEET which is a controlled, systematically improvable Green's fu...
Bieberich, E
1999-01-01
Current quantum theories of consciousness suggest a configuration space of an entangled ensemble state as global work space for conscious experience. This study will describe a procedure for adjustment of the singlet evolution of a quantum computation to a classical signal input by action potentials. The computational output of an entangled state in a single neuron will be selected in a network environment by "survival of the fittest" coupling with other neurons. Darwinian evolution of this coupling will result in a binding of action potentials to a convoluted orbit of phase-locked oscillations with harmonic, m-adic, or fractal periodicity. Progressive integration of signal inputs will evolve a present memory space independent from the history of construction. Implications for mental processes, e.g., associative memory, creativity, and consciousness will be discussed. A model for the generation of quantum coherence in a single neuron will be suggested.
Application of nonlocal models to nano beams. Part I: Axial length scale effect.
Kim, Jun-Sik
2014-10-01
Applicability of nonlocal models to nano-beams is discussed in terms of physical implications via the similarity between a nonlocal Euler-Bernoulli (EB) beam theory and a classical Rankine-Timoshenko (RT) beam theory. The nonlocal EB beam model, Eringen's model, is briefly reviewed and the classical RT beam theory is recast by the primary variables of the EB model. A careful comparison of these two models reveals that the scale parameter used to the Eringen's model has a strike resemblance to the shear flexibility in the RT model. This implies that the nonlocal model employed in literature consider the axial length scale effect only. In addition, the paradox for a cantilevered nano-beam subjected to tip shear force is clearly explained by finding appropriate displacement prescribed boundary conditions.
Effective field theories for QCD with rooted staggered fermions
Bernard, Claude; Shamir, Yigal
2007-01-01
Even highly improved variants of lattice QCD with staggered fermions show significant violations of taste symmetry at currently accessible lattice spacings. In addition, the "rooting trick" is used in order to simulate with the correct number of light sea quarks, and this makes the lattice theory nonlocal, even though there is good reason to believe that the continuum limit is in the correct universality class. In order to understand scaling violations, it is thus necessary to extend the construction of the Symanzik effective theory to include rooted staggered fermions. We show how this can be done, starting from a generalization of the renormalization-group approach to rooted staggered fermions recently developed by one of us. We then explain how the chiral effective theory follows from the Symanzik action, and show that it leads to "rooted" staggered chiral perturbation theory as the correct chiral theory for QCD with rooted staggered fermions. We thus establish a direct link between the renormalization-gro...
Nonlocal optical response in metallic nanostructures
Raza, Søren; Bozhevolnyi, Sergey I.; Wubs, Martijn; Mortensen, N. Asger
2014-01-01
This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future w...
Nonlocal higher order evolution equations
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.
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...
Anderson Localization in Nonlocal Nonlinear Media
Folli, Viola; 10.1364/OL.37.000332
2012-01-01
The effect of focusing and defocusing nonlinearities on Anderson localization in highly nonlocal media is theoretically and numerically investigated. A perturbative approach is developed to solve the nonlocal nonlinear Schroedinger equation in the presence of a random potential, showing that nonlocality stabilizes Anderson states.
Solitons in nonlocal nonlinear media: Exact solutions
DEFF Research Database (Denmark)
Krolikowski, Wieslaw; Bang, Ole
2001-01-01
We investigate the propagation of one-dimensional bright and dark spatial solitons in a nonlocal Kerr-like media, in which the nonlocality is of general form. We find an exact analytical solution to the nonlinear propagation equation in the case of weak nonlocality. We study the properties...
Nonlocally Centralized Simultaneous Sparse Coding
Institute of Scientific and Technical Information of China (English)
雷阳; 宋占杰
2016-01-01
The concept of structured sparse coding noise is introduced to exploit the spatial correlations and nonlo-cal constraint of the local structure. Then the model of nonlocally centralized simultaneous sparse coding(NC-SSC)is proposed for reconstructing the original image, and an algorithm is proposed to transform the simultaneous sparse coding into reweighted low-rank approximation. Experimental results on image denoisng, deblurring and super-resolution demonstrate the advantage of the proposed NC-SSC method over the state-of-the-art image resto-ration methods.
Energy Technology Data Exchange (ETDEWEB)
Maccari, A. [Istituto Tecnico `G. Cardano`, Monterotondo, Rome (Italy)
1996-08-01
The most important characteristics of the non-local oscillator, an oscillator subjected to an additional non-local force, are extensively studied by means of a new asymptotic perturbation method that is able to furnish an approximate solution of weakly non-linear differential equations. The resulting motion is doubly periodic, because a second little frequency appears, in addition to the fundamental harmonic frequency. Comparison with the numerical solution obtained by the Runge-Kitta method confirms the validity of the asymptotic perturbation method and its importance for the study of non-linear dynamical systems.
Retarded versus time-nonlocal quantum kinetic equations
Energy Technology Data Exchange (ETDEWEB)
Morawetz, K. [Grand Accelerateur National d' Ions Lourds (GANIL), 14 - Caen (France); Spicka, V.; Lipavsky, P. [Institute of Physics, Academy of Sciences, Praha (Czech Republic)
2000-07-01
The finite duration of the collisions in Fermionic systems as expressed by the retardation time in the non-Markovian Levinson equation is discussed in the quasiclassical limit. The separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates and (iii) of the single-particle energy, (iv) collision delay and (v) related non-local corrections to the scattering integral. In this way we transform the Levison equation into the Landau-Silin equation extended by the non-local corrections known from the theory of dense gases. The derived kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other. (authors)
The charge-asymmetric nonlocally-determined local-electric (CANDLE) solvation model
Sundararaman, Ravishankar
2014-01-01
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 only three parameters per solvent, this `CANDLE' model simultaneously reproduce...
Let's call it Nonlocal Quantum Physics
Requardt, M
2000-01-01
In the following we undertake to derive quantum theory as a stochastic low-energy and coarse-grained theory from a more primordial discrete and basically geometric theory living on the Planck scale and which (as we argue) possibly underlies also \\tit{string theory}. We isolate the so-called \\tit{ideal elements} which represent at the same time the cornerstones of the framework of ordinary quantum theory and show how and why they encode the \\tit{non-local} aspects, being ubiquituous in the quantum realm, in a, on the surface, local way. We show that the quantum non-locality emerges in our approach as a natural consequence of the underlying \\tit{two-storey} nature of space-time or the physical vacuum, that is, quantum theory turns out to be a residual effect of the geometric depth structure of space-time on the Planck scale. We indicate how the \\tit{measurement problem} and the emergence of the \\tit{macroscopic sub-regime} can be understood in this framework.
Causality for nonlocal phenomena
Eckstein, Michał
2015-01-01
Drawing from the theory of optimal transport we propose a rigorous notion of a causal relation for Borel probability measures on a given spacetime. To prepare the ground, we explore the borderland between causality, topology and measure theory. We provide various characterisations of the proposed causal relation, which turn out to be equivalent if the underlying spacetime has a sufficiently robust causal structure. We also present the notion of the 'Lorentz-Wasserstein distance' and study its basic properties. Finally, we discuss how various results on causality in quantum theory, aggregated around Hegerfeldt's theorem, fit into our framework.
Energy Technology Data Exchange (ETDEWEB)
Kolenda, Stefan; Wolf, Michael J.; Beckmann, Detlef [Institut fuer Nanotechnologie, KIT, 76021 Karlsruhe (Germany)
2013-07-01
In normalmetal/superconductor hybrid structures nonlocal conductance is determined by crossed Andreev reflection (CAR) and elastic cotunneling (EC). This was investigated recently both experimentally and theoretically. Dynamical Coulomb blockade of EC and CAR was predicted theoretically. Here we report on experimental investigations of these effects. We found signatures of dynamical Coulomb blockade in local and nonlocal conductance in the normal state. In the superconducting state, we find s-shaped nonlocal differential conductance curves as a function of bias applied on both contacts. These curves were observed for bias voltages both below and above the gap. We compare our results to theory.
Hashiguchi, Koichi
2009-01-01
This book details the mathematics and continuum mechanics necessary as a foundation of elastoplasticity theory. It explains physical backgrounds with illustrations and provides descriptions of detailed derivation processes..
Nonlocal Response in Plasmonic Nanostructures
DEFF Research Database (Denmark)
Wubs, Martijn; Mortensen, N. Asger
2016-01-01
After a brief overview of nanoplasmonics experiments that defy explanation with classical electrodynamics, we introduce nonlocal response as a main reason for non-classical effects. This concept is first introduced phenomenologically, and afterwards based on the semi-classical hydrodynamic Drude ...
Learning Non-Local Dependencies
Kuhn, Gustav; Dienes, Zoltan
2008-01-01
This paper addresses the nature of the temporary storage buffer used in implicit or statistical learning. Kuhn and Dienes [Kuhn, G., & Dienes, Z. (2005). Implicit learning of nonlocal musical rules: implicitly learning more than chunks. "Journal of Experimental Psychology-Learning Memory and Cognition," 31(6) 1417-1432] showed that people could…
Learning Non-Local Dependencies
Kuhn, Gustav; Dienes, Zoltan
2008-01-01
This paper addresses the nature of the temporary storage buffer used in implicit or statistical learning. Kuhn and Dienes [Kuhn, G., & Dienes, Z. (2005). Implicit learning of nonlocal musical rules: implicitly learning more than chunks. "Journal of Experimental Psychology-Learning Memory and Cognition," 31(6) 1417-1432] showed that people could…
A non-local, ordinary-state-based viscoelasticity model for peridynamics.
Energy Technology Data Exchange (ETDEWEB)
Mitchell, John Anthony
2011-10-01
A non-local, ordinary-state-based, peridynamics viscoelasticity model is developed. In this model, viscous effects are added to deviatoric deformations and the bulk response remains elastic. The model uses internal state variables and is conceptually similar to linearized isotropic viscolelasticity in the local theory. The modulus state, which is used to form the Jacobian matrix in Newton-Raphson algorithms, is presented. The model is shown to satisfy the 2nd law of thermodynamics and is applicable to problems in solid continuum mechanics where fracture and rate effects are important; it inherits all the advantages for modeling fracture associated with peridynamics. By combining this work with the previously published ordinary-state-based plasticity model, the model may be amenable to viscoplasticity problems where plasticity and rate effects are simultaneously important. Also, the model may be extended to include viscous effects for spherical deformations as well. The later two extensions are not presented and may be the subject of further work.
Collapse arrest and soliton stabilization in nonlocal nonlinear media
DEFF Research Database (Denmark)
Bang, Ole; Krolikowski, Wieslaw; Wyller, John
2002-01-01
We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian that nonloc......We investigate the properties of localized waves in cubic nonlinear materials with a symmetric nonlocal nonlinear response of arbitrary shape and degree of nonlocality, described by a general nonlocal nonlinear Schrodinger type equation. We prove rigorously by bounding the Hamiltonian...
Continuum representations of cellular solids
Energy Technology Data Exchange (ETDEWEB)
Neilsen, M.K.
1993-09-01
Cellular materials consist of interconnected struts or plates which form cells. The struts or plates are constructed from a variety of metals, polymers, ceramics and wood products. Cellular materials are often used in impact limiters for shipping containers to protect the contents from accidental impact events. These materials exhibit a variety of complex behavior when subjected to crushing loads. This research focuses on the development of continuum representations of cellular solids that can be used in the finite element analysis of shipping container accidents. A significant portion of this work is the development of a new methodology to relate localized deformations to appropriate constitutive descriptions. This methodology provides the insight needed to select constitutive descriptions for cellular solids that capture the localized deformations that are observed experimentally. Constitutive relations are developed for two different cellular materials, aluminum honeycomb and polyurethane foam. These constitutive relations are based on plasticity and continuum damage theories. Plasticity is used to describe the permanent deformation exhibited by both aluminum honeycomb and polyurethane foam. Continuum damage is needed to capture the change in elastic parameters due to cracking of the polyurethane cell wall materials. The new constitutive description of polyurethane foam is implemented in both static and dynamic finite element codes, and analytical and numerical predictions are compared with available experimental data.
Chaves, Eduardo W V
2013-01-01
This publication is aimed at students, teachers, and researchers of Continuum Mechanics and focused extensively on stating and developing Initial Boundary Value equations used to solve physical problems. With respect to notation, the tensorial, indicial and Voigt notations have been used indiscriminately. The book is divided into twelve chapters with the following topics: Tensors, Continuum Kinematics, Stress, The Objectivity of Tensors, The Fundamental Equations of Continuum Mechanics, An Introduction to Constitutive Equations, Linear Elasticity, Hyperelasticity, Plasticity (small and large deformations), Thermoelasticity (small and large deformations), Damage Mechanics (small and large deformations), and An Introduction to Fluids. Moreover, the text is supplemented with over 280 figures, over 100 solved problems, and 130 references.
EXACT NULL CONTROLLABILITY OF NON-AUTONOMOUS FUNCTIONAL EVOLUTION SYSTEMS WITH NONLOCAL CONDITIONS
Institute of Scientific and Technical Information of China (English)
Xianlong FU; Yu ZHANG
2013-01-01
In this article,by using theory of linear evolution system and Schauder fixed point theorem,we establish a sufficient result of exact null controllability for a non-autonomous functional evolution system with nonlocal conditions.In particular,the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here.An example is also provided to show an application of the obtained result.
Heikkinen, M O J; Kim, D-H; Troyer, M; Törmä, P
2014-10-31
We study fermionic superfluidity in strongly anisotropic optical lattices with attractive interactions utilizing the cluster dynamical mean-field theory method, and focusing in particular on the role of nonlocal quantum fluctuations. We show that nonlocal quantum fluctuations impact the BCS superfluid transition dramatically. Moreover, we show that exotic superfluid states with a delicate order parameter structure, such as the Fulde-Ferrell-Larkin-Ovchinnikov phase driven by spin population imbalance, can emerge even in the presence of such strong fluctuations.
Elementary Continuum Mechanics for Everyone
DEFF Research Database (Denmark)
Byskov, Esben
•The principle of virtual work is used to establish consistent theories of kinematic nonlinearity and linearity for other kinds of bodies, such as beams and plates •An in-depth treatment of structural instability as many structures fail due to this phenomenon •An introduction to the most versatile...... numerical method, the finite element method, including means of mending inherent problems •An informal, yet precise exposition that emphasizes not just how a topic is treated, but discusses why a particular choice is made The book opens with a derivation of kinematically nonlinear 3-D continuum mechanics...... for solids. Then the principle of virtual work is utilized to derive the simpler, kinematically linear 3-D theory and to provide the foundation for developing consistent theories of kinematic nonlinearity and linearity for specialized continua, such as beams and plates, and finite element methods...
Continuum modeling of myxobacteria clustering
Harvey, Cameron W.; Alber, Mark; Tsimring, Lev S.; Aranson, Igor S.
2013-03-01
In this paper we develop a continuum theory of clustering in ensembles of self-propelled inelastically colliding rods with applications to collective dynamics of common gliding bacteria Myxococcus xanthus. A multi-phase hydrodynamic model that couples densities of oriented and isotropic phases is described. This model is used for the analysis of an instability that leads to spontaneous formation of directionally moving dense clusters within initially dilute isotropic ‘gas’ of myxobacteria. Numerical simulations of this model confirm the existence of stationary dense moving clusters and also elucidate the properties of their collisions. The results are shown to be in a qualitative agreement with experiments.
Nonlocal correlations: Fair and unfair strategies in Bayesian games
Roy, Arup; Mukherjee, Amit; Guha, Tamal; Ghosh, Sibasish; Bhattacharya, Some Sankar; Banik, Manik
2016-09-01
An interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform classical equilibrium strategies in common-interest Bayesian games and also in conflicting-interest Bayesian games. Classical equilibrium strategies can be of two types, fair and unfair. Whereas in fair equilibrium payoffs of different players are equal, in the unfair case they differ. An advantage of nonlocal correlation has been demonstrated over fair strategies only. We show that quantum strategies can outperform even the unfair classical equilibrium strategies. For this purpose we consider a class of two-player Bayesian games. It becomes that such games can have only fair equilibria, both fair and unfair equilibria, or only unfair ones. We provide a simple analytic method to characterize the nonlocal correlations that are advantageous over the classical equilibrium strategies in these games. We also show that quantum advice provides a better social optimality solution (a relevant notion of equilibrium for the unfair case) over the classical one.
Theoretical Foundations of Incorporating Local Boundary Conditions into Nonlocal Problems
Aksoylu, Burak; Beyer, Horst Reinhard; Celiker, Fatih
2017-08-01
We study nonlocal equations from the area of peridynamics on bounded domains. We present four main results. In our recent paper, we have discovered that, on R, the governing operator in peridynamics, which involves a convolution, is a bounded function of the classical (local) governing operator. Building on this, as main result 1, we construct an abstract convolution operator on bounded domains which is a generalization of the standard convolution based on integrals. The abstract convolution operator is a function of the classical operator, defined by a Hilbert basis available due to the purely discrete spectrum of the latter. As governing operator of the nonlocal equation we use a function of the classical operator, this allows us to incorporate local boundary conditions into nonlocal theories. As main result 2, we prove that the solution operator can be uniquely decomposed into a Hilbert-Schmidt operator and a multiple of the identity operator. As main result 3, we prove that Hilbert-Schmidt operators provide a smoothing of the input data in the sense a square integrable function is mapped into a function that is smooth up to boundary of the domain. As main result 4, for the homogeneous nonlocal wave equation, we prove that continuity is preserved by time evolution. Namely, the solution is discontinuous if and only if the initial data is discontinuous. As a consequence, discontinuities remain stationary.
Nonlocal effect in surface plasmon polariton of ultrathin metal films
Energy Technology Data Exchange (ETDEWEB)
Xue, Hong-jie; Yu, Yabin, E-mail: apybyu@hnu.edu.cn; Wu, Reng-lai; Yu, Yan-qin; Wang, Ya-xin
2015-09-01
Using the nonlocal conductivity based on quantum response theory, we study the optical properties of p-polarized wave in quartz–metal–film–air structures, especially the influence of nonlocal effect on the surface plasmon polaritons (SPPs) resonance. In absorption spectrum, the resonant peak of SPP is found, and the dependence of the resonant peak on film thickness shows that nonlocal effect in the SPP resonance is enhanced significantly with the decrease of film-thickness, especially in the less than 20 nm metal film. We calculate the surface charge density as a function of frequency, and find that the frequencies at the charge and absorption peaks are the same. This clearly confirms that the absorption peak stems from SPP resonance excitation, and SPPs absorb the energy of the electromagnetic wave via charge oscillations. In the case of SPP resonance, the charge and electric field on the down-surface of thin film are always greater than that on the up-surface; however, the situation is just opposite in the case of no SPP resonance. This implies that the SPP resonance occurs near the down-surface of the film. Moreover, due to the nonlocal response of electric current to the electric field, the energy flow and electric current show anomalous oscillations, and with the increase of film thickness the anomalous oscillations exhibit obvious attenuation.
Nonlocal Theory for Fracturing of Quasibrittle Materials.
1994-03-01
fracture behavior and its impact on design code, ACI Fall Con- vention, San Juan, Puerto Rico, October 29, 1992. 1621 Discrete element modeling of...eaeieengf’em Mi.Heweitser Uxirenris^ His research mieieests i’clairt faitie andfract applicatioms to htictcura destga. p Fiv. 2- TesI etrup ’eIr
The quantum handshake entanglement, nonlocality and transactions
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.
Frediani, Luca; Ågren, Hans; Ferrighi, Lara; Ruud, Kenneth
2005-10-01
We present the first implementation of the quadratic response function for multiconfigurational self-consistent-field wave functions of solvated molecules described by a polarizable continuum model employing a molecule-shaped cavity. We apply the methodology to the first hyperpolarizability β and, in particular, the second-harmonic generation process for a series of conjugated push-pull oligomers, as well as for para-nitroaniline. The effect of solvation on the dispersion of the hyperpolarizability and the change in the hyperpolarizability for increasing chain length of the oligomers in vacuum and in solution is considered. The effect of a correlated description is analyzed by comparing the Hartree-Fock hyperpolarizabilities to the multiconfigurational self-consistent-field hyperpolarizabilities. The effect of geometry relaxation in the solvent on the properties of the solvated molecules are also investigated.
Frediani, Luca; Agren, Hans; Ferrighi, Lara; Ruud, Kenneth
2005-10-08
We present the first implementation of the quadratic response function for multiconfigurational self-consistent-field wave functions of solvated molecules described by a polarizable continuum model employing a molecule-shaped cavity. We apply the methodology to the first hyperpolarizability beta and, in particular, the second-harmonic generation process for a series of conjugated push-pull oligomers, as well as for para-nitroaniline. The effect of solvation on the dispersion of the hyperpolarizability and the change in the hyperpolarizability for increasing chain length of the oligomers in vacuum and in solution is considered. The effect of a correlated description is analyzed by comparing the Hartree-Fock hyperpolarizabilities to the multiconfigurational self-consistent-field hyperpolarizabilities. The effect of geometry relaxation in the solvent on the properties of the solvated molecules are also investigated.
A histories perspective on characterising quantum non-locality
Dowker, Fay; Wallden, Petros
2013-01-01
We introduce a framework for studying non-locality and contextuality inspired by the path integral formulation of quantum theory. We prove that the existence of a strongly positive joint quantum measure -- the quantum analogue of a joint probability measure -- on a set of experimental probabilities implies the Navascues-Pironio-Acin (NPA) condition $Q^1$ and is implied by the stronger NPA condition $Q^{1+AB}$. A related condition is shown to be equivalent to $Q^{1+AB}$.
Combinatorics and quantum nonlocality.
Buhrman, Harry; Høyer, Peter; Massar, Serge; Röhrig, Hein
2003-07-25
We use techniques for lower bounds on communication to derive necessary conditions (in terms of detector efficiency or amount of superluminal communication) for being able to reproduce the quantum correlations occurring in Einstein-Podolsky-Rosen-type experiments with classical local hidden-variable theories. As an application, we consider n parties sharing a Greenberger-Horne-Zeilinger-type state and show that the amount of superluminal classical communication required to reproduce the correlations is at least n(log((2)n-3) bits and the maximum detector efficiency eta(*) for which the resulting correlations can still be reproduced by a local hidden-variable theory is upper bounded by eta(*)
Positive cosmological constant, non-local gravity and horizon entropy
Energy Technology Data Exchange (ETDEWEB)
Solodukhin, Sergey N., E-mail: Sergey.Solodukhin@lmpt.univ-tours.fr [Laboratoire de Mathematiques et Physique Theorique, Universite Francois-Rabelais Tours, Federation Denis Poisson - CNRS, Parc de Grandmont, 37200 Tours (France)
2012-08-21
We discuss a class of (local and non-local) theories of gravity that share same properties: (i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; (ii) the on-shell action of such a theory vanishes and (iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant {Lambda}>0 and with zero {Lambda}. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive {Lambda}, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.
Positive cosmological constant, non-local gravity and horizon entropy
Solodukhin, Sergey N.
2012-08-01
We discuss a class of (local and non-local) theories of gravity that share same properties: (i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; (ii) the on-shell action of such a theory vanishes and (iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant Λ>0 and with zero Λ. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive Λ, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entropy proportional to the area. We conclude that, somewhat surprisingly, the presence of any, even extremely tiny, positive cosmological constant should be important for the proper resolution of the entropy problem and, possibly, the information puzzle.
Positive cosmological constant, non-local gravity and horizon entropy
Solodukhin, Sergey N
2012-01-01
We discuss a class of (local and non-local) theories of gravity that share same properties: i) they admit the Einstein spacetime with arbitrary cosmological constant as a solution; ii) the on-shell action of such a theory vanishes and iii) any (cosmological or black hole) horizon in the Einstein spacetime with a positive cosmological constant does not have a non-trivial entropy. The main focus is made on a recently proposed non-local model. This model has two phases: with a positive cosmological constant $\\Lambda>0$ and with zero $\\Lambda$. The effective gravitational coupling differs essentially in these two phases. Generalizing the previous result of Barvinsky we show that the non-local theory in question is free of ghosts on the background of any Einstein spacetime and that it propagates a standard spin-2 particle. Contrary to the phase with a positive $\\Lambda$, where the entropy vanishes for any type of horizon, in an Einstein spacetime with zero cosmological constant the horizons have the ordinary entro...
Conformal symmetry and nonlinear extensions of nonlocal gravity
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...
Cassini observation of Jovian anomalous continuum radiation
Ye, Sheng-Yi; Gurnett, D. A.; Menietti, J. D.; Kurth, W. S.; Fischer, G.; Schippers, P.; Hospodarsky, G. B.
2012-04-01
Jovian anomalous continuum is a narrowband electromagnetic radiation near 10 kHz that can escape from Jupiter's magnetosphere to interplanetary space. One possible source mechanism is the magnetosheath re-radiation of the Jovian low frequency radio emissions such as the quasiperiodic (QP) radio emissions, broadband kilometric radiation (bKOM) and non-thermal continuum. Jovian anomalous continuum was consistently observed by the Cassini Radio and Plasma Wave Science instrument from 2000 to 2004, right before the Saturn orbit insertion, which means the radiation can be detected as far as 8 AU away from Jupiter. An analysis of intensity versus radial distance shows that the Jovian anomalous continuum has a line source rather than a point source, consistent with the theory that the emission is radiated by the whole length of the magnetotail. The emissions are modulated at the system III period of Jupiter and are unpolarized. Since the lower cutoff frequency of the anomalous continuum is related to the plasma frequency in the magnetosheath of Jupiter, which is a function of solar wind density, the recurrent variations of the lower cutoff frequency can be used as a remote diagnostic of the solar wind condition at Jupiter. We propose that the frequency dispersion, a unique characteristic of the anomalous continuum, is likely a comprehensive effect of both the slow group velocity near the local plasma frequency and the refraction/scattering of the waves by density structures as they propagate in the magnetosheath.
Ebrahimi, Farzad; Barati, Mohammad Reza
2016-09-01
In this article, combined effect of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is investigated by developing various refined beam theories which capture shear deformation influences needless of any shear correction factor. The material properties of FG nanobeam are temperature dependent and change gradually along the thickness through the power-law model. Size-dependent description of the nanobeam is performed applying nonlocal elasticity theory of Eringen. Nonlocal governing equations of embedded FG nanobeam in hygro-thermal environment obtained from Hamilton's principle are solved analytically. To verify the validity of the developed theories, the results of the present work are compared with those available in the literature. The effects of various hygro-thermal loadings, elastic foundation, gradient index, nonlocal parameter, and slenderness ratio on the vibrational behavior of FG nanobeams modeled via various beam theories are explored.
Chaudhury, Kunal N; Singer, Amit
2012-11-01
In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.
Extreme nonlocality with one photon
Heaney, Libby; Santos, Marcelo F; Vedral, Vlatko
2009-01-01
The bizarre concept of nonlocality appears in quantum mechanics because the properties of two or more particles may be assigned globally and are not always pinned to each particle individually. Experiments using two, three, or more of these entangled particles have strongly rejected a local realist interpretation of nature. Nonlocality is also argued to be an intrinsic property of a quantum field, implying that just one excitation, a photon for instance, could also by itself violate local realism. Here we show that one photon superposed symmetrically over many distant sites (which in quantum information terms is a W-state) can give a stunning all-versus-nothing demolition of local realism in an identical manner to the GHZ class of states. The elegance of this result is that it is due solely to the wave-particle duality of light and matter. We present experimental implementations capable of testing our predictions.
Percolation transitions with nonlocal constraint.
Shim, Pyoung-Seop; Lee, Hyun Keun; Noh, Jae Dong
2012-09-01
We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose r-neighbors share any exclusive pair. The r-neighbor of a node x is defined as a set of at most N(r) neighbors of x, where N is the total number of nodes. The parameter r controls the strength of a nonlocal effect. The system is found to undergo a percolation transition belonging to the mean-field universality class for r1/2, the system undergoes a peculiar phase transition from a nonpercolating phase to a quasicritical phase where the largest cluster size G scales as G~N(α) with α=0.74(1). In the marginal case with r=1/2, the model displays a percolation transition that does not belong to the mean-field universality class.
Horikis, Theodoros P
2016-01-01
The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the contrary, a parameter regime is identified where the instability is suppressed but nevertheless the number and amplitude of the rogue events increase, as compared to the standard NLS (which is a limit of the nonlocal system). Furthermore, the nature of these waves is investigated; while no analytical solutions are known to model these events, numerically it is shown that they differ significantly from either the rational (Peregrine) or soliton solution of the limiting NLS equation. As such, these findings may also help in rogue wave realization experimentally in these media.
Nonlocal Quantum Effects in Cosmology
Dumin, Yurii V
2014-01-01
Since it is commonly believed that the observed large-scale structure of the Universe is an imprint of quantum fluctuations existing at the very early stage of its evolution, it is reasonable to pose the question: Do the effects of quantum nonlocality, which are well established now by the laboratory studies, manifest themselves also in the early Universe? We try to answer this question by utilizing the results of a few experiments, namely, with the superconducting multi-Josephson-junction loops and the ultracold gases in periodic potentials. Employing a close analogy between the above-mentioned setups and the simplest one-dimensional Friedmann-Robertson-Walker cosmological model, we show that the specific nonlocal correlations revealed in the laboratory studies might be of considerable importance also in treating the strongly-nonequilibrium phase transitions of Higgs fields in the early Universe. Particularly, they should substantially reduce the number of topological defects (e.g., domain walls) expected du...
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 ar...... 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.......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...... 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 electronâ€“hole pairs near...
Nonlocal reflection by photonic barriers
Vetter, R. -M.; A. Haibel; Nimtz, G.
2001-01-01
The time behaviour of microwaves undergoing partial reflection by photonic barriers was measured in the time and in the frequency domain. It was observed that unlike the duration of partial reflection by dielectric layers, the measured reflection duration of barriers is independent of their length. The experimental results point to a nonlocal behaviour of evanescent modes at least over a distance of some ten wavelengths. Evanescent modes correspond to photonic tunnelling in quantum mechanics.
Boundary fluxes for nonlocal diffusion
Cortazar, Carmen; Elgueta, Manuel; Rossi, Julio D.; Wolanski, Noemi
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence, uniqueness and a comparison principle. Next, we study the behavior of solutions for some prescribed boundary data including blowing up ones. Finally, we look at a nonlinear flux boundary condition.
Katanin, A. A.; Belozerov, A. S.; Anisimov, V. I.
2016-01-01
We consider nonlocal correlations in iron in the vicinity of the $\\alpha$-$\\gamma$ phase transition within the spin-rotationally-invariant dynamical mean-field theory (DMFT) approach, combined with the recently proposed spin-fermion model of iron. The obtained nonlocal corrections to DMFT yield a decrease of the Curie temperature of the $\\alpha$ phase, leading to an agreement with its experimental value. We show that the corresponding nonlocal corrections to the energy of the $\\alpha$ phase a...
Natarajan, S; Bordas, S; Mahapatra, D Roy
2012-01-01
In this paper, the axial vibration of cracked beams, the free flexural vibrations of nanobeams and plates based on Timoshenko beam theory and first-order shear deformable plate theory, respectively, using Eringen's nonlocal elasticity theory is numerically studied. The field variable is approximated by Lagrange polynomials and non-uniform rational B-splines. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the natural frequency is numerically studied. The influence of a crack on axial vibration is also studied. The results obtained from this study are found to be in good agreement with those reported in the literature.
Nonlocal description of sound propagation through an array of Helmholtz resonators
Nemati, Navid; Lafarge, Denis; Fang, Nicholas X
2015-01-01
A generalized macroscopic nonlocal theory of sound propagation in rigid-framed porous media saturated with a viscothermal fluid has been recently proposed, which takes into account both temporal and spatial dispersion. Here, we consider applying this theory capable to describe resonance effects, to the case of sound propagation through an array of Helmholtz resonators whose unusual metamaterial properties such as negative bulk moduli, have been experimentally demonstrated. Three different calculations are performed, validating the results of the nonlocal theory, relating to the frequency-dependent Bloch wavenumber and bulk modulus of the first normal mode, for 1D propagation in 2D or 3D periodic structures.
Nonlocal transport in superconducting oxide nanostructures
Veazey, Joshua; Cheng, Guanglei; Lu, Shicheng; Tomczyk, Michelle; Irvin, Patrick; Huang, Mengchen; Wung Bark, Chung; Ryu, Sangwoo; Eom, Chang-Beom; Levy, Jeremy
2013-03-01
We report nonlocal transport signatures in the superconducting state of nanostructures formed[2] at the LaAlO3/SrTiO3 interface using conductive AFM lithography. Nonlocal resistances (nonlocal voltage divided by current) are as large as 200 Ω when 2-10 μm separate the current-carrying segments from the voltage-sensing leads. The nonlocal resistance reverses sign at the local critical current of the superconducting state. Features observed in the nonlocal V-I curves evolve with back gate voltage and magnetic field, and are correlated with the local four-terminal V-I curves. We discuss how nonlocal and local transport effects in LaAlO3/SrTiO3 nanostructures may result from the electronic phase separation and superconducting inhomogeneity reported by others in planar structures[3]. This work is supported by AFOSR (FA9550-10-1-0524) and NSF DMR-0906443
Detrimental nonlocality in luminescence measurements
Pluska, Mariusz; Czerwinski, Andrzej
2017-08-01
Luminescence studies are used to investigate the local properties of various light-emitting materials. A critical issue of these studies is presented that the signals often lack all advantages of luminescence-studies of high locality, and may originate from an extended spatial region of even a few millimeters in size or the whole sample, i.e., places other than intended for investigation. This is a key problem for research and development in photonics. Due to this nonlocality, information indicating defects, irregularities, nonuniformities and inhomogeneities is lost. The issue refers to typical structures with a strong built-in electric field. Such fields exist intentionally in most photonic structures and occur unintentionally in many other materials investigated by applied physics. We reveal [using test samples prepared with focused ion beam (FIB) on an AlGaAs/GaAs laser heterostructure with an InGaAs quantum well (QW)] that nonlocality increases at low temperatures. This is contrary to the widely expected outcome, as low-temperature luminescence measurements are usually assumed to be free from disturbances. We explain many effects observed due to nonlocality in luminescence studies and prove that separation of the investigated area by focused ion beam milling is a practical solution enabling truly local luminescence measurements. All conclusions drawn using the example of cathodoluminescence are useful for other luminescence techniques.
Nonlocal response of hyperbolic metasurfaces.
Correas-Serrano, D; Gomez-Diaz, J S; Tymchenko, M; Alù, A
2015-11-16
We analyze and model the nonlocal response of ultrathin hyperbolic metasurfaces (HMTSs) by applying an effective medium approach. We show that the intrinsic spatial dispersion in the materials employed to realize the metasurfaces imposes a wavenumber cutoff on the hyperbolic isofrequency contour, inversely proportional to the Fermi velocity, and we compare it with the cutoff arising from the structure granularity. In the particular case of HTMSs implemented by an array of graphene nanostrips, we find that graphene nonlocality can become the dominant mechanism that closes the hyperbolic contour - imposing a wavenumber cutoff at around 300k(0) - in realistic configurations with periodicity Lnonlocal response is mainly relevant in hyperbolic metasurfaces and metamaterials with periodicity below a few nm, being very weak in practical scenarios. In addition, we investigate how spatial dispersion affects the spontaneous emission rate of emitters located close to HMTSs. Our results establish an upper bound set by nonlocality to the maximum field confinement and light-matter interactions achievable in practical HMTSs, and may find application in the practical development of hyperlenses, sensors and on-chip networks.
Searching for a Continuum Limit in CDT Quantum Gravity
Ambjorn, Jan; Gizbert-Studnicki, Jakub; Jurkiewicz, Jerzy
2016-01-01
We search for a continuum limit in the causal dynamical triangulation (CDT) approach to quantum gravity by determining the change in lattice spacing using two independent methods. The two methods yield similar results that may indicate how to tune the relevant couplings in the theory in order to take a continuum limit.
The Elastic Continuum Limit of the Tight Binding Model
Institute of Scientific and Technical Information of China (English)
Weinan E; Jianfeng LU
2007-01-01
The authors consider the simplest quantum mechanics model of solids, the tight binding model, and prove that in the continuum limit, the energy of tight binding model converges to that of the continuum elasticity model obtained using Cauchy-Born rule. Thet echnique in this paper is based mainly on spectral perturbation theory for large matrices.
Making nonlocal reality compatible with relativity
Nikolic, H.
2010-01-01
It is often argued that hypothetic nonlocal reality responsible for nonlocal quantum correlations between entangled particles cannot be consistent with relativity. I review the most frequent arguments of that sort, explain how they can all be circumvented, and present an explicit Bohmian model of nonlocal reality (compatible with quantum phenomena) that fully obeys the principle of relativistic covariance and does not involve a preferred Lorentz frame.
Wavefunction Collapse via a Nonlocal Relativistic Variational Principle
Energy Technology Data Exchange (ETDEWEB)
Harrison, Alan K. [Los Alamos National Laboratory
2012-06-18
Since the origin of quantum theory in the 1920's, some of its practitioners (and founders) have been troubled by some of its features, including indeterminacy, nonlocality and entanglement. The 'collapse' process described in the Copenhagen Interpretation is suspect for several reasons, and the act of 'measurement,' which is supposed to delimit its regime of validity, has never been unambiguously defined. In recent decades, nonlocality and entanglement have been studied energetically, both theoretically and experimentally, and the theory has been reinterpreted in imaginative ways, but many mysteries remain. We propose that it is necessary to replace the theory by one that is explicitly nonlinear and nonlocal, and does not distinguish between measurement and non-measurement regimes. We have constructed such a theory, for which the phase of the wavefunction plays the role of a hidden variable via the process of zitterbewegung. To capture this effect, the theory must be relativistic, even when describing nonrelativistic phenomena. It is formulated as a variational principle, in which Nature attempts to minimize the sum of two spacetime integrals. The first integral tends to drive the solution toward a solution of the standard quantum mechanical wave equation, and also enforces the Born rule of outcome probabilities. The second integral drives the collapse process. We demonstrate that the new theory correctly predicts the possible outcomes of the electron two-slit experiment, including the infamous 'delayed-choice' variant. We observe that it appears to resolve some long-standing mysteries, but introduces new ones, including possible retrocausality (a cause later than its effect). It is not clear whether the new theory is deterministic.
3D real-space calculations of continuum response
Nakatsukasa, T; Nakatsukasa, Takashi; Yabana, Kazuhiro
2001-01-01
We present linear response theories in the continuum capable of describing continuum spectra and dynamical correlations of finite systems with no spatial symmetry. Our formulation is essentially the same as the continuum random-phase approximation (RPA) but suitable for uniform grid representation in the three-dimensional (3D) Cartesian coordinate. Effects of the continuum are taken into account by solving equations iteratively with a retarded Green's function. The method is applied to photoabsorption spectra in small molecules (acetylene and ethylene) and inelastic electron scattering from a deformed nucleus 12C.
Perturbative loop corrections and nonlocal gravity
Maggiore, Michele
2016-01-01
Nonlocal gravity has been shown to provide a phenomenologically viable infrared modification of GR. A natural question is whether the required nonlocality can emerge from perturbative quantum loop corrections due to light particles. We show that this is not the case. For the value of the mass scale of the non-local models required by cosmology, the perturbative form factors obtained from the loop corrections, in the present cosmological epoch, are in the regime where they are local. The mechanism behind the generation of the required nonlocality must be more complex, possibly related to strong infrared effects and non-perturbative mass generation for the conformal mode.
Local and Nonlocal Regularization to Image Interpolation
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Yi Zhan
2014-01-01
Full Text Available This paper presents an image interpolation model with local and nonlocal regularization. A nonlocal bounded variation (BV regularizer is formulated by an exponential function including gradient. It acts as the Perona-Malik equation. Thus our nonlocal BV regularizer possesses the properties of the anisotropic diffusion equation and nonlocal functional. The local total variation (TV regularizer dissipates image energy along the orthogonal direction to the gradient to avoid blurring image edges. The derived model efficiently reconstructs the real image, leading to a natural interpolation which reduces blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.