Flach, S
1998-01-01
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattic...
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.
Discrete breathers in crystals
Dmitriev, S. V.; Korznikova, E. A.; Baimova, Yu A.; Velarde, M. G.
2016-05-01
It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite
Linearity stabilizes discrete breathers
T R Krishna Mohan; Surajit Sen
2011-11-01
The study of the dynamics of 1D chains with both harmonic and nonlinear interactions, as in the Fermi–Pasta–Ulam (FPU) and related problems, has played a central role in efforts to identify the broad consequences of nonlinearity in these systems. Here we study the dynamics of highly localized excitations, or discrete breathers, which are known to be initiated by the quasistatic stretching of bonds between adjacent particles. We show via dynamical simulations that acoustic waves introduced by the harmonic term stabilize the discrete breather by suppressing the breather’s tendency to delocalize and disperse. We conclude that the harmonic term, and hence acoustic waves, are essential for the existence of localized breathers in these systems.
Discrete breathers in Josephson ladders
Trias, E.; Mazo, J.J.; Brinkman, A.; Orlando, T.P.
2001-01-01
We present a study of nonlinear localized excitations called discrete breathers in a superconducting array. These localized solutions were recently observed in Josephson-junction ladder arrays by two different experimental groups [Phys. Rev. Lett. 84 (2000) 741; Phys. Rev. Lett. 84 (2000) 745; Phys.
Discrete breathers in hexagonal dusty plasma lattices.
Koukouloyannis, V; Kourakis, I
2009-08-01
The occurrence of single-site or multisite localized vibrational modes, also called discrete breathers, in two-dimensional hexagonal dusty plasma lattices is investigated. The system is described by a Klein-Gordon hexagonal lattice characterized by a negative coupling parameter epsilon in account of its inverse dispersive behavior. A theoretical analysis is performed in order to establish the possibility of existence of single as well as three-site discrete breathers in such systems. The study is complemented by a numerical investigation based on experimentally provided potential forms. This investigation shows that a dusty plasma lattice can support single-site discrete breathers, while three-site in phase breathers could exist if specific conditions, about the intergrain interaction strength, would hold. On the other hand, out of phase and vortex three-site breathers cannot be supported since they are highly unstable.
Compact-like discrete breather and its stability in a discrete monatomic Klein-Gordon chain
Xu Quan; Tian Qiang
2008-01-01
This paper studies a discrete one-dimensional monatomie Klein-Gordon chain with only quartic nearest-neighbour interactions, in which the compact-like discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. Introducing the trying method, it proves that compact-like discrete breathers exist in this nonlinear system. It also discusses the linear stability of the compact-like discrete breathers, when the coefficient (β)of quartic on-site potential and the coupling constant (K4) of quartic interactive potential satisfy the given conditions,they are linearly stable.
Localization in finite vibroimpact chains: Discrete breathers and multibreathers
Grinberg, Itay; Gendelman, Oleg V.
2016-09-01
We explore the dynamics of strongly localized periodic solutions (discrete solitons or discrete breathers) in a finite one-dimensional chain of oscillators. Localization patterns with both single and multiple localization sites (breathers and multibreathers) are considered. The model involves parabolic on-site potential with rigid constraints (the displacement domain of each particle is finite) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an inelastic impact according to Newton's impact model. The rigid nonideal impact constraints are the only source of nonlinearity and damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the breathers and multibreathers with an arbitrary set of localization sites, both in conservative and in forced-damped settings. Periodic boundary conditions are considered; exact solutions for other types of boundary conditions are also available. Local character of the nonlinearity permits explicit derivation of a monodromy matrix for the breather solutions. Consequently, the stability of the derived breather and multibreather solutions can be efficiently studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. One reveals that that the finiteness of the chain fragment and possible proximity of the localization sites strongly affect both the existence and the stability patterns of these localized solutions.
Localization in finite vibroimpact chains: Discrete breathers and multibreathers.
Grinberg, Itay; Gendelman, Oleg V
2016-09-01
We explore the dynamics of strongly localized periodic solutions (discrete solitons or discrete breathers) in a finite one-dimensional chain of oscillators. Localization patterns with both single and multiple localization sites (breathers and multibreathers) are considered. The model involves parabolic on-site potential with rigid constraints (the displacement domain of each particle is finite) and a linear nearest-neighbor coupling. When the particle approaches the constraint, it undergoes an inelastic impact according to Newton's impact model. The rigid nonideal impact constraints are the only source of nonlinearity and damping in the system. We demonstrate that this vibro-impact model allows derivation of exact analytic solutions for the breathers and multibreathers with an arbitrary set of localization sites, both in conservative and in forced-damped settings. Periodic boundary conditions are considered; exact solutions for other types of boundary conditions are also available. Local character of the nonlinearity permits explicit derivation of a monodromy matrix for the breather solutions. Consequently, the stability of the derived breather and multibreather solutions can be efficiently studied in the framework of simple methods of linear algebra, and with rather moderate computational efforts. One reveals that that the finiteness of the chain fragment and possible proximity of the localization sites strongly affect both the existence and the stability patterns of these localized solutions.
Energy Criterion for the Spectral Stability of Discrete Breathers
Kevrekidis, Panayotis G.; Cuevas-Maraver, Jesús; Pelinovsky, Dmitry E.
2016-08-01
Discrete breathers are ubiquitous structures in nonlinear anharmonic models ranging from the prototypical example of the Fermi-Pasta-Ulam model to Klein-Gordon nonlinear lattices, among many others. We propose a general criterion for the emergence of instabilities of discrete breathers analogous to the well-established Vakhitov-Kolokolov criterion for solitary waves. The criterion involves the change of monotonicity of the discrete breather's energy as a function of the breather frequency. Our analysis suggests and numerical results corroborate that breathers with increasing (decreasing) energy-frequency dependence are generically unstable in soft (hard) nonlinear potentials.
XU Quan; TIAN Qiang; LUO Jun
2009-01-01
@@ We study a two-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the two-dimensional Klein-Gordon lattice with hard on-site potential. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.
Feigenbaum Cascade of Discrete Breathers in a Model of DNA
Maniadis, P; Bishop, A R; Rasmussen, K \\O
2010-01-01
We demonstrate that period-doubled discrete breathers appear from the anti-continuum limit of the driven Peyrard-Bishop-Dauxois model of DNA. These novel breathers result from a stability overlap between sub-harmonic solutions of the driven Morse oscillator. Sub-harmonic breathers exist whenever a stability overlap is present within the Feigenbaum cascade to chaos and therefore an entire cascade of such breathers exists. This phenomenon is present in any driven lattice where the on-site potential admits sub-harmonic solutions. In DNA these breathers may have ramifications for cellular gene expression.
XU Quan; TIAN Qiang
2009-01-01
We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for twodimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry's linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete twodimensional monatomic β-FPU lattice.
Xu Quan; Tian Qiang
2009-01-01
We study a two-dimensional (2D) diatomic lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DBs) can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein-Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers (QDBs) and chaotic discrete breathers (CDBs) by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.
XU Quan; TIAN Qiang
2007-01-01
@@ Compact-like discrete breathers in discrete one-dimensional monatomic chains are investigated by discussing a generalized discrete one-dimensional monatomic model. It is proven that compact-like discrete breathers exist not only in soft φ4 potential but also in hard φ4 potential and K4 chains. The measurements of compact-like discrete breathers' core in soft and hard φ4 potential are determined by coupling parameter K4, while the measurements of compact-like discrete breathers' core in K4 chains are not related to coupling parameter K4. The stabilities of compact-like discrete breathers correlate closely to coupling parameter K4 and the boundary condition of lattice.
Oscillations of a highly discrete breather with a critical regime
Coquet; Remoissenet; Dinda
2000-10-01
We analyze carefully the essential features of the dynamics of a stationary discrete breather in the ultimate degree of energy localization in a nonlinear Klein-Gordon lattice with an on-site double-well potential. We demonstrate the existence of three different regimes of oscillatory motion in the breather dynamics, which are closely related to the motion of the central particle in an effective potential having two nondegenerate wells. In given parameter regions, we observe an untrapped regime, in which the central particle executes large-amplitude oscillations from one to the other side of the potential barrier. In other parameter regions, we find the trapped regime, in which the central particle oscillates in one of the two wells of the effective potential. Between these two regimes we find a critical regime in which the central particle undergoes several temporary trappings within an untrapped regime. Importantly, our study reveals that in the presence of purely anharmonic coupling forces, the breather compactifies, i.e., the energy becomes abruptly localized within the breather.
Multi-site Compact-Like Discrete Breather in Discrete One-Dimensional Monatomic Chains
XU Quan; TIAN Qiang
2007-01-01
Multi-site compact-like discrete breathers in djscrete one-dimensional monatomic chains are irIvestigated by discussing a generalized discrete one-dimensional monatomic model.We obtain that the two-site compact-like discrete breathers with codes σ={0,…,0,1,1,0…,0}and codes σ={0,…,0,1,-1,0…,0}can exist in discrete one-dimensional monatomic chain with quartic on-site and inter-site potentials.However,the former can only exist in hard quartic on-site potential and cannot exist in soft quartic on-site potential,whereas the latter is just reversed.All of the two-site Compact-like discrete breathers with codes σ={0,…,0,1,1,0,…,0}and σ={0,…,0,1,-1,0…,0}cannot exist in a pure K4 chain.
Discrete Nonlinear Schrödinger Breathers in a Phonon Bath
Rasmussen, K O; Bishop, A R; Tsironis, G P
1999-01-01
The dynamics of the discrete nonlinear Schr{ö}dinger lattice initialized in a non-extensive mode is studied. The non-extensivity causes the system to remain out of thermal equilibrium for a very long transitory period of time in which standard Boltzmann statistics is insufficient. Alternative statistics based on non standard entropy concepts should be applied. Our study of the nonlinear system locked in this meta-thermodynamic state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). Due to the non-extensivity of the system, it is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete bre...
Energy thresholds for discrete breathers in one-, two- and three-dimensional lattices
Flach, S; MacKay, R S
1997-01-01
Discrete breathers are time-periodic, spatially localized solutions of equations of motion for classical degrees of freedom interacting on a lattice. They come in one-parameter families. We report on studies of energy properties of breather families in one-, two- and three-dimensional lattices. We show that breather energies have a positive lower bound if the lattice dimension of a given nonlinear lattice is greater than or equal to a certain critical value. These findings could be important for the experimental detection of discrete breathers.
XU Quan; TIAN Qiang
2007-01-01
Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generafized discrete two-dimensional monatomic model.It is proven that the twodimensional compact-like discrete breathers exist not only in two-dimensional soft Ф4 potentials but also in hard two-dimensional Ф4 potentials and pure two-dimensional K4 lattices.The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Ф4 potential are determined by coupling parameter K4,while those in pure two-dimensional K4 lattices have no coupling with parameter K4.The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices.
Discrete breathers in a mass-in-mass chain with Hertzian local resonators
Wallen, S. P.; Lee, J.; Mei, D.; Chong, C.; Kevrekidis, P. G.; Boechler, N.
2017-02-01
We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear, precompressed Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the existence of discrete breathers in the continuum and anticontinuum limits of intersite coupling, we use numerical continuation to compute a family of breathers interpolating between the two regimes in a finite chain, where the displacement profiles of the breathers are localized around one lattice site. We then analyze the frequency-amplitude dependence of the breathers by performing numerical continuation on a linear eigenmode (vanishing amplitude) solution of the system near the upper band gap edge. Finally, we use direct numerical integration of the equations of motion to demonstrate the formation and evolution of the identified localized modes in energy-conserving and dissipative scenarios, including within settings that may be relevant to future experimental studies.
Exact analysis of discrete data
Hirji, Karim F
2005-01-01
Researchers in fields ranging from biology and medicine to the social sciences, law, and economics regularly encounter variables that are discrete or categorical in nature. While there is no dearth of books on the analysis and interpretation of such data, these generally focus on large sample methods. When sample sizes are not large or the data are otherwise sparse, exact methods--methods not based on asymptotic theory--are more accurate and therefore preferable.This book introduces the statistical theory, analysis methods, and computation techniques for exact analysis of discrete data. After reviewing the relevant discrete distributions, the author develops the exact methods from the ground up in a conceptually integrated manner. The topics covered range from univariate discrete data analysis, a single and several 2 x 2 tables, a single and several 2 x K tables, incidence density and inverse sampling designs, unmatched and matched case -control studies, paired binary and trinomial response models, and Markov...
Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice
XU Quan; QIANG Tian
2009-01-01
We study the existence and stability of two-dimensional discrete breathers in a two-dimensional discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling.Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential (soft or hard), the interaction potential (attractive or repulsive)and the center of the two-dimensional gap breather (on a light or a heavy atom).
Signatures of discrete breathers in coherent state quantum dynamics.
Igumenshchev, Kirill; Ovchinnikov, Misha; Maniadis, Panagiotis; Prezhdo, Oleg
2013-02-07
In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that
Xu Quan; Tian Qiang
2013-01-01
Using numerical method,we investigate whether periodic,quasiperiodic,and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam (FPU) lattice with linear dispersion term.The spatial profile and time evolution of the two-dimensional discrete β-FPU lattice are segregated by the method of separation of variables,and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system.By introducing a periodic interaction into the linear interaction between the atoms,we achieve the coupling of two incommensurate frequencies for a single DB,and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system,too.
Breather Solutions of the Discrete p-Schrödinger Equation
James, Guillaume; Starosvetsky, Yuli
We consider the discrete p-Schrödinger (DpS) equation, which approximates small amplitude oscillations in chains of oscillators with fully-nonlinear nearest-neighbors interactions of order α = p - 1> 1 . Using a mapping approach, we prove the existence of breather solutions of the DpS equation with even- or odd-parity reflectional symmetries. We derive in addition analytical approximations for the breather profiles and the corresponding intersecting stable and unstable manifolds, valid on a whole range of nonlinearity orders α. In the limit of weak nonlinearity (α → 1+), we introduce a continuum limit connecting the stationary DpS and logarithmic nonlinear Schrödinger equations. In this limit, breathers correspond asymptotically to Gaussian homoclinic solutions. We numerically analyze the stability properties of breather solutions depending on their even- or odd-parity symmetry. A perturbation of an unstable breather generally results in a translational motion (traveling breather) when α is close to unity, whereas pinning becomes predominant for larger values of α.
Johansson; Aubry
2000-05-01
We investigate the long-time evolution of weakly perturbed single-site breathers (localized stationary states) in the discrete nonlinear Schrodinger equation. The perturbations we consider correspond to time-periodic solutions of the linearized equations around the breather, and can be either (i) spatially localized or (ii) spatially extended. For case (i), which corresponds to the excitation of an internal mode of the breather, we find that the nonlinear interaction between the breather and its internal mode always leads to a slow growth of the breather amplitude and frequency. In case (ii), corresponding to interaction between the breather and a standing-wave phonon, the breather will grow provided that the wave vector of the phonon is such that the generation of radiating higher harmonics at the breather is possible. In other cases, breather decay is observed. This condition yields a limit value for the breather frequency above which no further growth is possible. We also discuss another mechanism for breather growth and destruction which becomes important when the amplitude of the perturbation is non-negligible, and which originates from the oscillatory instabilities of the nonlinear standing-wave phonons.
Campbell, Russell; Oppo, Gian-Luca; Borkowski, Mateusz
2015-01-01
The dynamics of static and traveling breathers in two-species Bose-Einstein condensates in a one-dimensional optical lattice is modelled within the tight-binding approximation. Two coupled discrete nonlinear Schrödinger equations describe the interaction of the condensates in two cases of relevance: a mixture of two ytterbium isotopes and a mixture of 87Rb and 41K. Depending on their initial separation, interaction between static breathers of different species can lead to the formation of symbiotic structures and transform one of the breathers from a static into a traveling one. Collisions between traveling and static discrete breathers composed of different species are separated into four distinct regimes ranging from totally elastic when the interspecies interaction is highly attractive to mutual destruction when the interaction is sufficiently large and repulsive. We provide an explanation of the collision features in terms of the interspecies coupling and the negative effective mass of the discrete breathers.
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-03-28
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reproduces all the known Hamiltonians whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. Several new exactly and QES Hamiltonians are constructed. The sinusoidal coordinate plays an essential role.
Exactly and quasi-exactly solvable 'discrete' quantum mechanics.
Sasaki, Ryu
2011-01-01
A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly solvable (QES) Hamiltonians in one-dimensional 'discrete' quantum mechanics is presented. It reprod...
Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice
Kavitha, L., E-mail: louiskavitha@yahoo.co.in [Department of Physics, School of Basic and Applied Sciences, Central University of Tamil Nadu (CUTN), Thiruvarur 610 101, Tamil Nadu (India); Max-Planck Institute for the Physics of Complex Systems, Dresden (Germany); The Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Parasuraman, E. [Department of Physics, Periyar University, Salem 636 011, Tamil Nadu (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamil Nadu (India); Gopi, D. [Department of Chemistry, Periyar University, Salem 636 011, Tamil Nadu (India); Center for Nanoscience and Nanotechnology, Periyar University, Salem 636 011, Tamil Nadu (India); Prabhu, A. [Department of Physics, Periyar University, Salem 636 011, Tamil Nadu (India); Vicencio, Rodrigo A. [Departamento de Física and MSI-Nucleus on Advanced Optics, Center for Optics and Photonics (CEFOP), Facultad de Ciencias, Universidad de Chile, Santiago 7800003 (Chile); Max-Planck Institute for the Physics of Complex Systems, Dresden (Germany)
2016-03-01
We investigate the propagation dynamics of highly localized discrete breather modes in a weak ferromagnetic spin lattice with on-site easy axis anisotropy due to crystal field effect. We derive the discrete nonlinear equation of motion by employing boson mappings and p-representation. We explore the onset of modulational instability both analytically in the framework of linear stability analysis and numerically by means of molecular dynamics (MD) simulations, and a perfect agreement was demonstrated. It is also explored that how the antisymmetric nature of the canted ferromagnetic lattice supports highly localized discrete breather (DBs) modes as shown in the stability/instability windows. The energy exchange between low amplitude discrete breathers favours the growth of higher amplitude DBs, resulting eventually in the formation of few long-lived high amplitude DBs. - Highlights: • The effects of DM and anisotropy interaction on the DB modes are studied. • The antisymmetric nature of the canted ferromagnetic medium supports the DB modes. • Dynamics of ferromagnetic chain is governed by boson mappings and p-representation.
Dynamics of breathers in discrete nonlinear Schrodinger models
Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge
1998-01-01
We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...
Breathers in ferrimagnetic systems
Tarashankar Nag; Swapan Kumar Das; Ajoy Chowdhury
2006-09-01
Breathers in discrete nonlinear ferrimagnetic spin lattices are investigated for both easy-axis and easy-plane configurations. The region in frequency space of the formation of breathers is determined and the anticontinuum limit discussed. The mono-chromatic and the coloured breathers are found out numerically for different parameters and different conditions of excitations.
Johansson, Magnus; Derevyanko, Stanislav A
2013-01-01
We investigate the mobility of nonlinear localized modes in a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping, described by a generalized discrete Ginzburg-Landau type model. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present in the corresponding conservative system, by self-induced time-periodic oscillations of its power (norm) and energy (Hamiltonian), yielding exponential decays to zero with different rates in the forward and backward directions. In certain parameter windows, bistability appears between fast modes with small oscillations, and slower, large-oscillation modes. The velocities and the oscillation periods are typically related...
Bulk and surface magnetoinductive breathers in binary metamaterials.
Molina, M I; Lazarides, N; Tsironis, G P
2009-10-01
We investigate theoretically the existence of bulk and surface discrete breathers in a one-dimensional magnetic metamaterial comprised of a periodic binary array of split-ring resonators; the two types of resonators used have different resonant frequencies caused by unequal slit sizes. We use the rotating-wave approximation and construct several types of breather excitations both for the energy-conserving as well as dissipative-driven case; we corroborate these approximate results trough numerically exact computations. We demonstrate that discrete breathers can appear spontaneously in the dissipative-driven system as a result of a fundamental instability.
Bai, Xiao-Dong; Malomed, Boris A.; Deng, Fu-Guo
2016-09-01
We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while in the absence of the TDB, the same lattice admits bidirectional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.
Breathers in a locally resonant granular chain with precompression
Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; Vainchtein, Anna
2016-09-01
We study a locally resonant granular material in the form of a precompressed Hertzian chain with linear internal resonators. Using an asymptotic reduction, we derive an effective nonlinear Schrödinger (NLS) modulation equation. This, in turn, leads us to provide analytical evidence, subsequently corroborated numerically, for the existence of two distinct types of discrete breathers related to acoustic or optical modes: (a) traveling bright breathers with a strain profile exponentially vanishing at infinity and (b) stationary and traveling dark breathers, exponentially localized, time-periodic states mounted on top of a non-vanishing background. The stability and bifurcation structure of numerically computed exact stationary dark breathers is also examined. Stationary bright breathers cannot be identified using the NLS equation, which is defocusing at the upper edges of the phonon bands and becomes linear at the lower edge of the optical band.
Discrete gap breathers in a diatomic Klein-Gordon chain: stability and mobility.
Gorbach, Andrey V; Johansson, Magnus
2003-06-01
A one-dimensional diatomic chain with harmonic intersite potential and nonlinear external potential is considered (the Klein-Gordon model). Localized solutions of the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum--"gap breathers"--are studied numerically. The linear stability analysis for these solutions is performed while changing the system parameters from the anticontinuous to the continuous limit. Two different types of solutions are considered: symmetric centered at a heavy atom and antisymmetric centered at a light atom, respectively. Different mechanisms of instability, oscillatory as well as nonoscillatory, of the gap breathers are studied, and the influence of the instabilities on the breather solutions is investigated in the dynamics simulations. In particular, the presence of an "inversion of stability" regime, with simultaneous nonoscillatory instabilities of symmetric and antisymmetric solutions with respect to antisymmetric perturbations, is found, yielding practically radiationless mobility.
Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations
Vasily E. Tarasov
2016-06-01
Full Text Available An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are represented by infinite series. This new mathematical tool allows us to build sensible discrete quantum mechanics based on the suggested differences and includes the correct canonical commutation and uncertainty relations.
Quantized Hamilton dynamics describes quantum discrete breathers in a simple way.
Igumenshchev, Kirill; Prezhdo, Oleg
2011-08-01
We study the localization of energy in a nonlinear coupled system, exhibiting so-called breather modes, using quantized Hamilton dynamics (QHD). Already at the lowest order, which is only twice as complex as classical mechanics, this simple semiclassical method incorporates quantum-mechanical effects. The transition between the localized and delocalized regimes is instantaneous in classical mechanics, while it is gradual due to tunneling in both quantum mechanics and QHD. In contrast to classical mechanics, which predicts an abrupt appearance of breathers, quantum mechanics and QHD show an alternation of localized and delocalized behavior in the transient region. QHD includes zero-point energy that is reflected in a shifted energy asymptote for the localized states, providing another improvement on the classical perspective. By detailed analysis of the distribution and transfer of energy within classical mechanics, QHD, and quantum dynamics, we conclude that QHD is an efficient approach that accounts for moderate quantum effects and can be used to identify quantum breathers in large nonlinear systems.
Quantum signatures of breather-breather interactions
Dorignac, J; Salerno, M; Scott, A C
2003-01-01
The spectrum of the Quantum Discrete Nonlinear Schr\\"odinger equation on a periodic 1D lattice shows some interesting detailed band structure which may be interpreted as the quantum signature of a two-breather interaction in the classical case. We show that this fine structure can be interpreted using degenerate perturbation theory.
Exact discrete soliton solutions of quintic discrete nonlinear Schr(o)dinger equation
Li Hua-Mei; Wu Feng-Min
2005-01-01
By using the extended hyperbolic function approach, we have studied a quintic discrete nonlinear Schrodinger equation and obtained new exact localized solutions, including the discrete bright soliton solution, dark soliton solution,alternating phase bright soliton solution and alternating phase dark soliton solution, if a special constraint is imposed on the coefficients of the equation.
Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao
2017-09-01
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.
Breathers on Quantized Superfluid Vortices
Salman, Hayder
2013-01-01
We consider the propagation of breathers along a quantised superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schr\\"odinger equation, we identify a set of initial conditions corresponding to breather solutions of vortex motion governed by the LIA. These initial conditions, which give rise to a long-wavelength modulational instability, result in the emergence of large amplitude perturbations that are localised in both space and time. The emergent structures on the vortex filament are analogous to loop solitons. Although the breather solutions we study are exact solutions of the LIA equations, we demonstrate through full numerical simulations that their key emergent attributes carry over to vortex dynamics governed by the Biot-Savart law and to quantized vortices described by the Gross-Pitaevskii equation. The breather excitations can lead to self-reconnections, a mechanism that can play an important role within the cross-over range of scales in superfl...
Probabilistic methods for discrete nonlinear Schr\\"odinger equations
Chatterjee, Sourav
2010-01-01
Using techniques from probability theory, we show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation (NLS) are exactly solvable in dimensions three and higher. A number of explicit formulas are derived. The probabilistic results, combined with dynamical information, prove the existence and typicality of solutions to the discrete NLS with highly stable localized modes that are sometimes called discrete breathers.
Constructing exact solutions to discrete systems with the trial function method
Taogetusang Sirendaoerji
2008-01-01
Based on the homogenous balance method and the trial function method, several trial function methods composed of exponential functions are proposed and applied to nonlinear discrete systems. With the help of symbolic computation system, the new exact solitary wave solutions to discrete nonlinear mKdV lattice equation, discrete nonlinear (2+1) dimensional Toda lattice equation, Ablowitz-Ladik-lattice system are constructed.The method is of significance to seek exact solitary wave solutions to other nonlinear discrete systems.
Breathers in strongly anharmonic lattices.
Rosenau, Philip; Pikovsky, Arkady
2014-02-01
We present and study a family of finite amplitude breathers on a genuinely anharmonic Klein-Gordon lattice embedded in a nonlinear site potential. The direct numerical simulations are supported by a quasilinear Schrodinger equation (QLS) derived by averaging out the fast oscillations assuming small, albeit finite, amplitude vibrations. The genuinely anharmonic interlattice forces induce breathers which are strongly localized with tails evanescing at a doubly exponential rate and are either close to a continuum, with discrete effects being suppressed, or close to an anticontinuum state, with discrete effects being enhanced. Whereas the D-QLS breathers appear to be always stable, in general there is a stability threshold which improves with spareness of the lattice.
Mixed continuous/discrete time modelling with exact time adjustments
Rovers, K.C.; Kuper, Jan; van de Burgwal, M.D.; Kokkeler, Andre B.J.; Smit, Gerardus Johannes Maria
2011-01-01
Many systems interact with their physical environment. Design of such systems need a modelling and simulation tool which can deal with both the continuous and discrete aspects. However, most current tools are not adequately able to do so, as they implement both continuous and discrete time signals
Exact Solutions of Discrete Complex Cubic Ginzburg-Landau Equation and Their Linear Stability
张金良; 刘治国
2011-01-01
The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schr(o)dinger Equation
YANG Qin; DAI Chao-Qing; ZHANG Jie-Fang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schrodinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differentialdifferent models.
Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit
Matsuya, Keisuke; Kanai, Masahiro
2015-01-01
We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum limit, we recover the delay differential equation for this model and the exact solutions as well. We then work in the ultra-discrete limit, obtaining a delay cellular-automaton model, which successfully inherits the solutions. Also the dispersion relation ...
Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach
DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.
Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities
Khare, A.; Rasmussen, Kim Ø; Salerno, M.
2006-01-01
A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowi......-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated....
Exactly solvable potentials with finitely many discrete eigenvalues of arbitrary choice
Sasaki, Ryu
2014-01-01
We address the problem of possible deformations of exactly solvable potentials having finitely many discrete eigenvalues of arbitrary choice. As Kay and Moses showed in 1956, reflectionless potentials in one dimensional quantum mechanics are exactly solvable. With an additional time dependence these potentials are identified as the soliton solutions of the KdV hierarchy. An $N$-soliton potential has the time $t$ and $2N$ positive parameters, $k_1<...
Quantum breathers in lithium tantalate ferroelectrics
Biswas, Arindam; Adhikar, Sutapa; Choudhary, Kamal; Basu, Reshmi; Bandyopadhyay, A. K.; Bhattacharjee, A. K.; Mandal, D.
2013-08-01
Lithium tantalate is technologically one of the most important ferroelectric materials with a low poling field that has several applications in the field of photonics and memory switching devices. In a Hamiltonian system, such as dipolar system, the polarization behavior of such ferroelectrics can be well-modeled by Klein-Gordon (K-G) equation. Due to strong localization coupled with discreteness in a nonlinear K-G lattice, there is a formation of breathers and multi-breathers that manifest in the localization peaks across the domains in polarization-space-time plot. Due to the presence of nonlinearity and also impurities (as antisite tantalum defects) in the structure, dissipative effects are observed and hence dissipative breathers are studied here. To probe the quantum states related to discrete breathers, the same K-G lattice is quantized to give rise to quantum breathers (QBs) that are explained by a periodic boundary condition. The gap between the localized and delocalized phonon-band is a function of impurity content that is again related to the effect of pinning of domains due to antisite tantalum defects in the system, i.e., a point of easier switching within the limited amount of data on poling field, which is related to Landau coefficient (read, nonlinearity). Secondly, in a non-periodic boundary condition, the temporal evolution of quanta shows interesting behavior in terms of `critical' time of redistribution of quanta that is proportional to QB's lifetime in femtosecond having a possibility for THz applications. Hence, the importance of both the methods for characterizing quantum breathers is shown in these perspectives.
Breathers in Josephson junction ladders: Resonances and electromagnetic wave spectroscopy
Miroshnichenko, A. E.; Flach, S.; Fistul, M.
2001-01-01
We present a theoretical study of the resonant interaction between dynamical localized states (discrete breathers) and linear electromagnetic excitations (EE's) in Josephson junction ladders. By making use of direct numerical simulations we find that such an interaction manifests itself by resonant...... steps and various sharp switchings (voltage jumps) in the current-voltage characteristics. Moreover, the power of ac oscillations away from the breather center (the breather tail) displays singularities as the externally applied dc bias decreases. All these features may be mapped to the spectrum of EE...
Elegant Ince-Gaussian breathers in strongly nonlocal nonlinear media
Bai Zhi-Yong; Deng Dong-Mei; Guo Qi
2012-01-01
A novel class of optical breathers,called elegant Ince-Gaussian breathers,are presented in this paper.They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system,and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function.We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schr(o)dinger equation.
Breathers in oscillator chains with Hertzian interactions
James, Guillaume; Cuevas, Jesus
2011-01-01
We prove nonexistence of breathers (spatially localized and time-periodic oscillations) for a class of Fermi-Pasta-Ulam lattices representing an uncompressed chain of beads interacting via Hertz's contact forces. We then consider the setting in which an additional on-site potential is present, motivated by the Newton's cradle under the effect of gravity. Using both direct numerical computations and a simplified asymptotic model of the oscillator chain, the so-called discrete p-Schr\\"odinger (DpS) equation, we show the existence of discrete breathers and study their spectral properties and mobility. Due to the fully nonlinear character of Hertzian interactions, breathers are found to be much more localized than in classical nonlinear lattices and their motion occurs with less dispersion. In addition, we study numerically the excitation of a traveling breather after an impact at one end of a semi-infinite chain. This case is well described by the DpS equation when local oscillations are faster than binary colli...
Discretization error estimation and exact solution generation using the method of nearby problems.
Sinclair, Andrew J. (Auburn University Auburn, AL); Raju, Anil (Auburn University Auburn, AL); Kurzen, Matthew J. (Virginia Tech Blacksburg, VA); Roy, Christopher John (Virginia Tech Blacksburg, VA); Phillips, Tyrone S. (Virginia Tech Blacksburg, VA)
2011-10-01
The Method of Nearby Problems (MNP), a form of defect correction, is examined as a method for generating exact solutions to partial differential equations and as a discretization error estimator. For generating exact solutions, four-dimensional spline fitting procedures were developed and implemented into a MATLAB code for generating spline fits on structured domains with arbitrary levels of continuity between spline zones. For discretization error estimation, MNP/defect correction only requires a single additional numerical solution on the same grid (as compared to Richardson extrapolation which requires additional numerical solutions on systematically-refined grids). When used for error estimation, it was found that continuity between spline zones was not required. A number of cases were examined including 1D and 2D Burgers equation, the 2D compressible Euler equations, and the 2D incompressible Navier-Stokes equations. The discretization error estimation results compared favorably to Richardson extrapolation and had the advantage of only requiring a single grid to be generated.
Breather trapping and breather transmission in a DNA model with an interface
Alvarez, A.; Romero, F.R.; Archilla, J.F.R.
2006-01-01
We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian...
Discrete supersymmetries of the Schrodinger equation and non-local exactly solvable potentials
Samsonov, B F; Samsonov, Boris F.
2002-01-01
Using an isomorphism between Hilbert spaces $L^2$ and $\\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term difference equation. Technique of intertwining operators is applied to creating new families of exactly solvable Jacobi matrices. It is shown that any thus obtained Jacobi matrix gives rise to a new exactly solvable non-local potential of the Schroedinger equation. We also show that the algebraic structure underlying our approach corresponds to supersymmetry. Supercharge operators acting in the space $\\ell^{2}\\times \\ell^{2} $ are introduced which together with a matrix form of the superhamiltonian close the simplest superalgebra.
New exact solutions for the discrete fourth Painlevé equation
Bassom, A P
1994-01-01
In this paper we derive a number of exact solutions of the discrete equation x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})= {-2z_nx_n^3+(\\eta-3\\delta^{-2}-z_n^2)x_n^2+\\mu^2\\over (x_n+z_n+\\gamma)(x_n+z_n-\\gamma)},\\eqno(1) where z_n=n\\delta and \\eta, \\delta, \\mu and \\gamma are constants. In an appropriate limit (1) reduces to the fourth \\p\\ (PIV) equation {\\d^2w\\over\\d z^2} = {1\\over2w}\\left({\\d w\\over\\d z}\\right)^2+\\tfr32w^3 + 4zw^2 + 2(z^2-\\alpha)w +{\\beta\\over w},\\eqno(2) where \\alpha and \\beta are constants and (1) is commonly referred to as the discretised fourth Painlev\\'e equation. A suitable factorisation of (1) facilitates the identification of a number of solutions which take the form of ratios of two polynomials in the variable z_n. Limits of these solutions yield rational solutions of PIV (2). It is also known that there exist exact solutions of PIV (2) that are expressible in terms of the complementary error function and in this article we show that a discrete analogue of this function can be obtained by ana...
Multi-site breathers in Klein--Gordon lattices: stability, resonances, and bifurcations
Pelinovsky, Dmitry
2011-01-01
We prove the most general theorem about spectral stability of multi-site breathers in the discrete Klein--Gordon equation with a small coupling constant. In the anti-continuum limit, multi-site breathers represent excited oscillations at different sites of the lattice separated by a number of "holes" (sites at rest). The theorem describes how the stability or instability of a multi-site breather depends on the phase difference and distance between the excited oscillators. Previously, only multi-site breathers with adjacent excited sites were considered within the first-order perturbation theory. We show that the stability of multi-site breathers with one-site holes change for large-amplitude oscillations in soft nonlinear potentials. We also discover and study a symmetry-breaking (pitchfork) bifurcation of one-site and multi-site breathers in soft quartic potentials near the points of 1:3 resonance.
许涛
2004-01-01
M r.Sm ith liked to be exact. O ne day when he was w alking in thestreet a m an cam e over and asked him E xcuse m e but w here's the , : “ ,nearest bookshop ?” The nearest bookshop Y ou have to cross a bridge and then turn “ ?to the right. ” A nd is the bridge long “ ?” Thirty m eters. “ ” The m an thanked him and went towards the bridge. Suddenly heheard som eone running after him . Stop M r.Sm ith w as shouting. I'm sorry. I just rem em bered ...
Tracking breather dynamics in irregular sea state conditions
Chabchoub, A
2016-01-01
Breather solutions of the nonlinear Schr\\"odinger equation (NLSE) are known to be considered as backbone models for extreme events in the ocean as well as in Kerr media. These exact determinisitic rogue wave (RW) prototypes on a regular background describe a wide-range of modulation instability configurations. Alternatively, oceanic or electromagnetic wave fields can be of chaotic nature and it is known that RWs may develop in such conditions as well. We report an experimental study confirming that extreme localizations in an irregular oceanic JONSWAP wave field can be tracked back to originate from exact NLSE breather solutions, such as the Peregrine breather. Numerical NLSE as well as modified NLSE simulations are both in good agreement with laboratory experiments and highlight the significance of universal weakly nonlinear evolution equations in the emergence as well as prediction of extreme events in nonlinear dispersive media.
Hu, Xiao-Bing; Wang, Ming; Di Paolo, Ezequiel
2013-06-01
Searching the Pareto front for multiobjective optimization problems usually involves the use of a population-based search algorithm or of a deterministic method with a set of different single aggregate objective functions. The results are, in fact, only approximations of the real Pareto front. In this paper, we propose a new deterministic approach capable of fully determining the real Pareto front for those discrete problems for which it is possible to construct optimization algorithms to find the k best solutions to each of the single-objective problems. To this end, two theoretical conditions are given to guarantee the finding of the actual Pareto front rather than its approximation. Then, a general methodology for designing a deterministic search procedure is proposed. A case study is conducted, where by following the general methodology, a ripple-spreading algorithm is designed to calculate the complete exact Pareto front for multiobjective route optimization. When compared with traditional Pareto front search methods, the obvious advantage of the proposed approach is its unique capability of finding the complete Pareto front. This is illustrated by the simulation results in terms of both solution quality and computational efficiency.
Numerical computation of travelling breathers in Klein Gordon chains
Sire, Yannick; James, Guillaume
2005-05-01
We numerically study the existence of travelling breathers in Klein-Gordon chains, which consist of one-dimensional networks of nonlinear oscillators in an anharmonic on-site potential, linearly coupled to their nearest neighbors. Travelling breathers are spatially localized solutions having the property of being exactly translated by p sites along the chain after a fixed propagation time T (these solutions generalize the concept of solitary waves for which p=1). In the case of even on-site potentials, the existence of small amplitude travelling breathers superposed on a small oscillatory tail has been proved recently [G. James, Y. Sire, Travelling breathers with exponentially small tails in a chain of nonlinear oscillators, Commun. Math. Phys., 2005, in press (available online at http://www.springerlink.com)], the tail being exponentially small with respect to the central oscillation size. In this paper, we compute these solutions numerically and continue them into the large amplitude regime for different types of even potentials. We find that Klein-Gordon chains can support highly localized travelling breather solutions superposed on an oscillatory tail. We provide examples where the tail can be made very small and is difficult to detect at the scale of central oscillations. In addition, we numerically observe the existence of these solutions in the case of non-even potentials.
Johansson, Magnus
2006-04-01
We analyze certain aspects of the classical dynamics of a one-dimensional discrete nonlinear Schrödinger model with inter-site as well as on-site nonlinearities. The equation is derived from a mixed Klein-Gordon/Fermi-Pasta-Ulam chain of anharmonic oscillators coupled with anharmonic inter-site potentials, and approximates the slow dynamics of the fundamental harmonic of discrete small-amplitude modulational waves. We give explicit analytical conditions for modulational instability of travelling plane waves, and find in particular that sufficiently strong inter-site nonlinearities may change the nature of the instabilities from long-wavelength to short-wavelength perturbations. Further, we describe thermodynamic properties of the model using the grand-canonical ensemble to account for two conserved quantities: norm and Hamiltonian. The available phase space is divided into two separated parts with qualitatively different properties in thermal equilibrium: one part corresponding to a normal thermalized state with exponentially small probabilities for large-amplitude excitations, and another part typically associated with the formation of high-amplitude localized excitations, interacting with an infinite-temperature phonon bath. A modulationally unstable travelling wave may exhibit a transition from one region to the other as its amplitude is varied, and thus modulational instability is not a sufficient criterion for the creation of persistent localized modes in thermal equilibrium. For pure on-site nonlinearities the created localized excitations are typically pinned to particular lattice sites, while for significant inter-site nonlinearities they become mobile, in agreement with well-known properties of localized excitations in Fermi-Pasta-Ulam-type chains.
TAO Liang; LUO Bin
2005-01-01
An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.
Eugenia BABILONI
2012-01-01
Full Text Available The fill rate is usually computed by using the traditional approach, which calculates it as the complement of the quotient between the expected unfulfilled demand and the expected demand per replenishment cycle, instead of directly the expected fraction of fulfilled demand. Furthermore the available methods to estimate the fill rate apply only under specific demand conditions. This paper shows the research gap regarding the estimation procedures to compute the fill rate and suggests: (i a new exact procedure to compute the traditional approximation for any discrete demand distribution; and (ii a new method to compute the fill rate directly as the fraction of fulfilled demand for any discrete demand distribution. Simulation results show that the latter methods outperform the traditional approach, which underestimates the simulated fill rate, over different demand patterns. This paper focuses on the traditional periodic review, base stock system when backlogged demands are allowed.
Zha Qi-Lao; Sirendaoreji
2006-01-01
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach.This approach can also be applied to other nonlinear differential-difference equations.
Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm
2010-01-01
We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e......We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show...
Khare, Avinash; Samuelsen, Mogens R; Saxena, Avadh; 10.1088/1751-8113/43/37/375209
2010-01-01
We show that the two-dimensional, nonlinear Schr\\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.
Reflection of sine-Gordon breathers
Olsen, O. H.; Samuelsen, Mogens Rugholm
1981-01-01
The influence of a boundary on a breather traveling in a Josephson line cavity is examined by means of numerical computations. For a passive termination the breather is reflected into a breather of less energy; when the characteristic impedance of the line equals the external load resistor the br...
Clarkson, P A
1994-01-01
In this paper we describe B\\"acklund transformations and hierarchies of exact solutions for the fourth Painlev\\'e equation (PIV) {\\d^2 w\\over\\d z^2}={1\\over2w}\\left(\\d w\\over\\d z\\right)^2 + {{3\\over2}}w^3 + 4zw^2 + 2(z^2-\\alpha)w+{\\beta\\over w},\\eqno(1){\\hbox to 16pt{\\hfill}} with \\alpha, \\beta constants. Specifically, a nonlinear superposition principle for PIV, hierarchies of solutions expressible in terms of complementary error or parabolic cylinder functions as well as rational solutions will be derived. Included amongst these hierarchies are solutions of (1) for which \\alpha=\\pm\\tfr12n and \\beta=-\\tfr12n^2, with n an integer. These particular forms arise in quantum gravity and also satisfy a discrete analogue of the first Painlev\\'e equation. We also obtain a number of exact solutions of the discrete fourth Painlev\\'e equation x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})= {-2z_nx_n^3+(\\eta-3\\delta^{-2}-z_n^2)x_n^2+\\mu^2\\over (x_n+z_n+\\gamma)(x_n+z_n-\\gamma)},\\eqno(2){\\hbox to 16pt{\\hfill}}}% {\
Breathers and rogue waves: Demonstration with coupled nonlinear Schrödinger family of equations
N Vishnu Priya; M Senthilvelan; M Lakshmanan
2015-03-01
Different types of breathers and rogue waves (RWs) are some of the important coherent structures which have been recently realized in several physical phenomena in hydrodynamics, nonlinear optics, Bose–Einstein condensates, etc. Mathematically, they have been deduced in non-linear Schrödinger (NLS) equations. Here we show the existence of general breathers, Akhmediev breathers, Ma soliton and rogue wave solutions in coupled Manakov-type NLS equations and coupled generalized NLS equations representing four-wave mixing. We deduce their explicit forms using Hirota bilinearization procedure and bring out their exact structures and important properties. We also show the method to deduce the various breather solutions from rogue wave solutions using factorization form and the so-called imbricate series.
Breather soliton dynamics in microresonators
Yu, Mengjie; Okawachi, Yoshitomo; Griffith, Austin G; Luke, Kevin; Miller, Steven A; Ji, Xingchen; Lipson, Michal; Gaeta, Alexander L
2016-01-01
The generation of temporal cavity solitons in microresonators results in low-noise optical frequency combs which are critical for applications in spectroscopy, astronomy, navigation or telecommunications. Breather solitons also form an important part of many different classes of nonlinear wave systems with a localized temporal structure that exhibits oscillatory behavior. To date, the dynamics of breather solitons in microresonators remains largely unexplored, and its experimental characterization is challenging. Here, we demonstrate the excitation of breather solitons in two different microresonator platforms based on silicon nitride and on silicon. We investigate the dependence of the breathing frequency on pump detuning and observe the transition from period-1 to period-2 oscillation in good agreement with the numerical simulations. Our study presents experimental confirmation of the stability diagram of dissipative cavity solitons predicted by the Lugiato-Lefever equation and is importance to understandin...
The role of superregular breathers in the development of modulation instability
Gelash, Andrey
2016-04-01
The integrable model of modulation instability (MI) - the one-dimensional nonlinear Schrodinger equation (NLSE) is in the focus of research for many years. Recently a significant progress has been made in the understanding of MI long time consequences (nonlinear stage of MI). Namely, the role of continuous spectrum was studied in the work [1], another two works are devoted to integrable turbulence formation [2] and to the Fermi-Pasta-Ulam recurrence [3]. We proposed so-called superregular breathers scenario of MI in [4]. In this scenario instability evolves from small localized perturbations of the condensate to N pairs of breathers which moves in opposite directions leaving a nonperturbed condensate with changed phase behind them. Recently we observed superregular breathers in hydrodynamics and optics experiments [5]. Here we discuss the role of superregular breathers in general scenario of MI. Furthermore we study another important question - the formation of freak waves from the perturbed condensate. To date two possible scenarios in the frame of NLSE have been described: 1) the collisions of Akhmediev breathers and 2) the rational solutions, such as Peregrine breather. In the first case the initial conditions usually include breathers of quite large amplitude. In the case of rational scenario the solution is pure homoclinic, i.e. completely returns to initial unperturbed condensate. Meanwhile, results of numerical modeling of freak waves formation in more exact models like Euler equation and NLSE with higher nonlinearities demonstrate formation of breathers. We present a new model of freak waves formation caused by particular collisions of superregular breathers. In the frame of this scenario extreme waves appear from small perturbations of the condensate and leave breathers, which never disappear. We study special two-pair superregular breathers scenario as well as randomly distributed N pairs solution. The latter case can be considered as a kind of integrable
Pinto Rengifo, Ricardo Alberto
2008-02-15
We address the excitation of quantum breathers in small nonlinear networks of two and three degrees of freedom, in order to study their properties. The invariance under permutation of two sites of these networks substitutes the translation invariance that is present in nonlinear lattices, where (classical) discrete breathers are time periodic space localized solutions of the underlying classical equations of motion. We do a systematic analysis of the spectrum and eigenstates of such small systems, characterizing quantum breather states by their tunneling rate (energy splitting), site correlations, fluctuations of the number of quanta, and entanglement. We observe how these properties are reflected in the time evolution of initially localized excitations. Quantum breathers manifest as pairs of nearly degenerate eigenstates that show strong site correlation of quanta, and are characterized by a strong excitation of quanta on one site of the network which perform slow coherent tunneling motion from one site to another. They enhance the fluctuations of quanta, and are the least entangled states among the group of eigenstates in the same range of the energy spectrum. We use our analysis methods to consider the excitation of quantum breathers in a cell of two coupled Josephson junctions, and study their properties as compared with those in the previous cases. We describe how quantum breathers could be experimentally observed by employing the already developed techniques for quantum information processing with Josephson junctions. (orig.)
On the nonlinear stability of mKdV breathers
Alejo Plana, Miguel Angel; Muñoz, Claudio
2012-01-01
Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under...
Costa-Cabral, M.C. [GKSS-Forschungszentrum Geesthacht GmbH (Germany). Inst. fuer Hydrophysik
1999-07-01
Current Lagrangian models for simulating advective transport of trace species in a discretized two-dimensional flow field use simplified descriptions of tracer sources, receptors and flow paths. When 'forward trajectories' are used, a diffuse source spread over a two-dimensional grid cell is treated as a single point source located at the cell's center, and its flow is projected in the downflow direction by a line. When 'backward trajectories' are used, each cell is treated as a point receptor and flow is projected back in time in the upflow direction by a line. In both cases, two-dimensional sources or receptors are treated as zero dimensional, and two-dimensional flow tubes are replaced by one-dimensional lines. While these simplifications may be acceptable in some cases, they can generate large errors when the flow field contains regions of considerable divergence of flow directions, or when fine scales are used. A new algorithm is introduced, called TUBES, which provides an exact solution to advective transport in a discretized two-dimensional flow field. TUBES uses two-dimensional flow tubes whose width expands and contracts over directionally divergent and convergent regions of the flow field, respectively. TUBES has applications in a wide variety of the earth sciences, including atmospheric science, oceanography, and surface and groundwater hydrology. (orig.) [German] Gegenwaertige Lagrange-Modelle zur Simulation advektiver Transporte von Tracern in einem diskretisierten zweidimensionalen Stroemungsfeld verwenden vereinfachte Beschreibungen der Quellen, Rezeptoren und Transportwege. Bei der Verwendung vorwaerts gerichteter Trajektorien ('forward trajectories') werden diffusive Quellen, die ueber eine zweidimensionale Gitterzelle verteilt sind, als Punktquelle behandelt, und der Transport mit der Stroemung erfolgt entlang einer Linie. Bei der Verwendung rueckwaerts gerichteter Trajektorien ('backward trajectories
Relaxation and coarsening of weakly-interacting breathers in a simplified DNLS chain
Iubini, Stefano; Politi, Antonio; Politi, Paolo
2017-07-01
The discrete nonlinear Schrödinger (DNLS) equation displays a parameter region characterized by the presence of localized excitations (breathers). While their formation is well understood and it is expected that the asymptotic configuration comprises a single breather on top of a background, it is not clear why the dynamics of a multi-breather configuration is essentially frozen. In order to investigate this question, we introduce simple stochastic models, characterized by suitable conservation laws. We focus on the role of the coupling strength between localized excitations and background. In the DNLS model, higher breathers interact more weakly, as a result of their faster rotation. In our stochastic models, the strength of the coupling is controlled directly by an amplitude-dependent parameter. In the case of a power-law decrease, the associated coarsening process undergoes a slowing down if the decay rate is larger than a critical value. In the case of an exponential decrease, a freezing effect is observed that is reminiscent of the scenario observed in the DNLS. This last regime arises spontaneously when direct energy diffusion between breathers and background is blocked below a certain threshold.
Breather-to-soliton transformation rules in the hierarchy of nonlinear Schrödinger equations
Chowdury, Amdad; Krolikowski, Wieslaw
2017-06-01
We study the exact first-order soliton and breather solutions of the integrable nonlinear Schrödinger equations hierarchy up to fifth order. We reveal the underlying physical mechanism which transforms a breather into a soliton. Furthermore, we show how the dynamics of the Akhmediev breathers which exist on a constant background as a result of modulation instability, is connected with solitons on a zero background. We also demonstrate that, while a first-order rogue wave can be directly transformed into a soliton, higher-order rogue wave solutions become rational two-soliton solutions with complex collisional structure on a background. Our results will have practical implications in supercontinuum generation, turbulence, and similar other complex nonlinear scenarios.
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A.
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
Aslan, İsmail, E-mail: ismailaslan@iyte.edu.tr [Department of Mathematics, Izmir Institute of Technology, Urla, İzmir 35430 (Turkey)
2011-11-14
We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G{sup ′}/G)-expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are constructed; hyperbolic, trigonometric, and rational which have not been explicitly computed before. -- Highlights: ► Discrete nonlinear Schrödinger equation with a saturable nonlinearity. ► We confirm that the model supports three types of solutions with arbitrary parameters. ► A new application of the (G{sup ′}/G)-expansion method presented.
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
Ion-acoustic rogue waves and breathers in relativistically degenerate electron-positron plasmas
Abdikian, A.; Ismaeel, S.
2017-08-01
In this paper, we employ a weakly relativistic fluid model to study the nonlinear amplitude modulation of electrostatic waves in an unmagnetized electron-positron-ion plasma. It is assumed that the degeneracy pressure law for electrons and positrons follows the Chandrasekhar limit of state whereas ions are warm and classical. The hydrodynamic approach along with the perturbation method have been applied to obtain the corresponding nonlinear Schrödinger equation (NLSE) in which nonlinearity is in balance with the dispersive terms. Using the NLSE, we could evaluate the modulational instability to show that various types of localized ion acoustic excitations exist in the form of either bright-type envelope solitons or dark-type envelope solitons. The regions of the stable and unstable envelope wave have been confined punctually for various regimes. Furthermore, it is proposed that the exact solutions of the NLSE for breather waves are the rogue waves (RWs), Akhmediev breather (AB), and Kuznetsov-Ma breather (KM) soliton. In order to show that the characteristics of breather structures is influenced by the plasma parameters (namely, relativistic parameter, positron concentration, and ionic temperature), the relevant numerical analysis of the NLSE is examined. In particular, it is observed that by increasing the values of the mentioned plasma parameters, the amplitude of the RWs will be decreased. Our results help researchers to explain the formation and dynamics of nonlinear electrostatic excitations in super dense astrophysical regimes.
Chin, Alex W; Huelga, Susana F; Plenio, Martin B
2010-01-01
By using the properties of orthogonal polynomials, we present an exact unitary transformation that maps the Hamiltonian of a quantum system coupled linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that describes a one-dimensional chain with only nearest-neighbour interactions. This analytical transformation predicts a simple set of relations between the parameters of the chain and the recurrence coefficients of the orthogonal polynomials used in the transformation, and allows the chain parameters to be computed using numerically stable algorithms that have been developed to compute recurrence coefficients. We then prove some general properties of this chain system for a wide range of spectral functions, and give examples drawn from physical systems where exact analytic expressions for the chain properties can be obtained. Crucially, the short range interactions of the effective chain system permits these open quantum systems to be efficiently simulated by the density matrix renormalizati...
Pascual-Marqui, Roberto D
2007-01-01
This paper deals with the EEG/MEG neuroimaging problem: given measurements of scalp electric potential differences (EEG: electroencephalogram) and extracranial magnetic fields (MEG: magnetoencephalogram), find the 3D distribution of the generating electric neuronal activity. This problem has no unique solution. Only particular solutions with "good" localization properties are of interest, since neuroimaging is concerned with the localization of brain function. In this paper, a general family of linear imaging methods with exact, zero error localization to point-test sources is presented. One particular member of this family is sLORETA (standardized low resolution brain electromagnetic tomography; Pascual-Marqui, Methods Find. Exp. Clin. Pharmacol. 2002, 24D:5-12; http://www.unizh.ch/keyinst/NewLORETA/sLORETA/sLORETA-Math01.pdf). It is shown here that sLORETA has no localization bias in the presence of measurement and biological noise. Another member of this family, denoted as eLORETA (exact low resolution bra...
Xu Quan; Tian Qiang
2009-01-01
This paper discusses the two-dimensional discrete monatomic Fermi-Pasta-Ulam lattice, by using the method of multiple-scale and the quasi-discreteness approach. By taking into account the interaction between the atoms in the lattice and their nearest neighbours, it obtains some classes of two-dimensional local models as follows: two-dimensional bright and dark discrete soliton trains, two-dimensional bright and dark line discrete breathers, and two-dimensional bright and dark discrete breather.
Nonlinear Stability of MKdV Breathers
Alejo Plana, Miguel Angel; Muñoz, Claudio
2013-01-01
Breather solutions of the modified Korteweg-de Vries equation are shown to be globally stable in a natural H 2 topology. Our proof introduces a new Lyapunov functional, at the H 2 level, which allows to describe the dynamics of small perturbations, including oscillations induced by the periodicit...
Gridnev, Dmitry K.
2014-12-01
We consider the system of three nonrelativistic spinless fermions in two dimensions, which interact through spherically-symmetric pair interactions. Recently, a claim has been made by Nishida et al for the existence of the so-called super Efimov effect by Nishida et al (2013 Phys. Rev. Lett. 110 235301). Namely, if the interactions in the system are fine-tuned to a p-wave resonance, an infinite number of bound states appears, whose negative energies are scaled according to the double exponential law. We present the mathematical proof that such a system indeed has an infinite number of bound levels. We also prove that {{lim }E\\to 0}| ln | ln E |{{|}-1}N(E)=8/(3π ), where N(E) is the number of bound states with the energy less than -E\\lt 0. The value of this limit is exactly equal to the value derived in Nishida et al using the renormalization group approach. Our proof resolves a recent controversy about the validity of results in Nishida et al (2013 Phys. Rev. Lett. 110 235301).
Dean, David S.; Hammant, Thomas C.; Horgan, Ronald R.; Naji, Ali; Podgornik, Rudolf
2012-10-01
The wrapping equilibria of one and two adsorbing cylinders are studied along a semi-flexible filament (polymer) due to the interplay between elastic rigidity and short-range adhesive energy between the cylinder and the filament. We show that statistical mechanics of the system can be solved exactly using a path integral formalism which gives access to the full effect of thermal fluctuations, going thus beyond the usual Gaussian approximations which take into account only the contributions from the minimal energy configuration and small fluctuations about this minimal energy solution. We obtain the free energy of the wrapping-unwrapping transition of the filament around the cylinders as well as the effective interaction between two wrapped cylinders due to thermal fluctuations of the elastic filament. A change of entropy due to wrapping of the filament around the adsorbing cylinders as they move closer together is identified as an additional source of interactions between them. Such entropic wrapping effects should be distinguished from the usual entropic configuration effects in semi-flexible polymers. Our results may be relevant to the problem of adsorption of oriented nano-rods on semi-flexible polymers.
Breather statics and dynamics in Klein-Gordon chains with a bend.
Cuevas, J; Kevrekidis, P G
2004-05-01
In this paper, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effects. We focus on both the bifurcation and stability analysis of the modes that emerge as a function of the strength of the bend angle, but we also examine dynamical effects including the scattering of mobile localized modes (discrete breathers) off of such a geometric structure. The potential outcomes of such numerical experiments (including transmission, trapping within the bend as well as reflection) are highlighted and qualitatively explained. Such models are of interest both theoretically in understanding the interplay of breathers with curvature, but also practically in simple models of photonic crystals or of bent chains of DNA.
Nonlinear dynamics of breathers in the spiral structures of magnets
Kiselev, V. V., E-mail: kiselev@imp.uran.ru; Raskovalov, A. A. [Russian Academy of Sciences, Mikheev Institute of Metal Physics, Ural Branch (Russian Federation)
2016-06-15
The structure and properties of pulsating solitons (breathers) in the spiral structures of magnets are analyzed within the sine-Gordon model. The breather core pulsations are shown to be accompanied by local shifts and oscillations of the spiral structure with the formation of “precursors” and “tails” in the moving soliton. The possibilities for the observation and excitation of breathers in the spiral structures of magnets and multiferroics are discussed.
Farhad A. Namin
2016-08-01
Full Text Available A rigorous method for obtaining the diffraction patterns of quasicrystals is presented. Diffraction patterns are an essential analytical tool in the study of quasicrystals, since they can be used to determine their photonic resonances. Previous methods for approximating the diffraction patterns of quasicrystals have relied on evaluating the Fourier transform of finite-sized super-lattices. Our approach, on the other hand, is exact in the sense that it is based on a technique that embeds quasicrystals into higher dimensional periodic hyper-lattices, thereby completely capturing the properties of the infinite structure. The periodicity of the unit cell in the higher dimensional space can be exploited to obtain the Fourier series expansion in closed-form of the corresponding atomic surfaces. The utility of the method is demonstrated by applying it to one-dimensional Fibonacci and two-dimensional Penrose quasicrystals. The results are verified by comparing them to those obtained by using the conventional super-lattice method. It is shown that the conventional super-cell approach can lead to inaccurate results due to the continuous nature of the Fourier transform, since quasicrystals have a discrete spectrum, whereas the approach introduced in this paper generates discrete Fourier harmonics. Furthermore, the conventional approach requires very large super-cells and high-resolution sampling of the reciprocal space in order to produce accurate results leading to a very large computational burden, whereas the proposed method generates accurate results with a relatively small number of terms. Finally, we propose how this approach can be generalized from the vertex model, which assumes identical particles at all vertices, to a more realistic case where the quasicrystal is composed of different atoms.
Existence and stability of multisite breathers in honeycomb and hexagonal lattices
Koukouloyannis, V [Department of Physics, Section of Astrophysics, Astronomy and Mechanics, Aristotle University of Thessaloniki, 54124 Thessaloniki (Greece); Kevrekidis, P G; Law, K J H [Department of Mathematics and Statistics, University of Massachusetts, Amherst MA 01003-4515 (United States); Kourakis, I [Centre for Plasma Physics, Queen' s University Belfast, BT7 1 NN (United Kingdom); Frantzeskakis, D J, E-mail: vkouk@physics.auth.g [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
2010-06-11
We study the existence and stability of multisite discrete breathers in two prototypical non-square Klein-Gordon lattices, namely a honeycomb and a hexagonal one. In the honeycomb case we consider six-site configurations and find that for soft potential and positive coupling the out-of-phase breather configuration and the charge-two vortex breather are linearly stable, while the in-phase and charge-one vortex states are unstable. In the hexagonal lattice, we first consider three-site configurations. In the case of soft potential and positive coupling, the in-phase configuration is unstable and the charge-one vortex is linearly stable. The out-of-phase configuration here is found to always be linearly unstable. We then turn to six-site configurations in the hexagonal lattice. The stability results in this case are the same as in the six-site configurations in the honeycomb lattice. For all configurations in both lattices, the stability results are reversed in the setting of either hard potential or negative coupling. The study is complemented by numerical simulations which are in very good agreement with the theoretical predictions. Since neither the form of the on-site potential nor the sign of the coupling parameter involved have been prescribed, this description can accommodate inverse-dispersive systems (e.g. supporting backward waves) such as transverse dust-lattice oscillations in dusty plasma (Debye) crystals or analogous modes in molecular chains.
Breather compactons in nonlinear Klein-Gordon systems.
Dinda, P T; Remoissenet, M
1999-11-01
We demonstrate the existence of a localized breathing mode with a compact support, i.e., a stationary breather compacton, in a nonlinear Klein-Gordon system. This breather compacton results from a delicate balance between the harmonicity of the substrate potential and the total nonlinearity induced by the substrate potential and the coupling forces between adjacent lattice sites.
Scalar field breathers on anti-de Sitter background
Fodor, Gyula; Grandclément, Philippe
2013-01-01
We study spatially localized, time-periodic solutions (breathers) of scalar field theories with various self-interacting potentials on Anti-de Sitter (AdS) spacetimes in $D$ dimensions. A detailed numerical study of spherically symmetric configurations in $D=3$ dimensions is carried out, revealing a rich and complex structure of the phase-space (bifurcations, resonances). Scalar breather solutions form one-parameter families parametrized by their amplitude, $\\varepsilon$, while their frequency, $\\omega=\\omega(\\varepsilon)$, is a function of the amplitude. The scalar breathers on AdS we find have a small amplitude limit, tending to the eigenfunctions of the linear Klein-Gordon operator on AdS. Importantly most of these breathers appear to be generically stable under time evolution.
Hamiltonian dynamics of breathers with third-order dispersion
Mookherjea, Shayan; Yariv, Amnon
2001-01-01
We present a nonperturbative analysis of certain dynamical aspects of breathers (dispersion-managed solitons) including the effects of third-order dispersion. The analysis highlights the similarities to and differences from the well-known analogous procedures for second-order dispersion. We discuss in detail the phase-space evolution of breathers in dispersion-managed systems in the presence of third-order dispersion.
Discrete Wigner function dynamics
Klimov, A B; Munoz, C [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44410, Guadalajara, Jalisco (Mexico)
2005-12-01
We study the evolution of the discrete Wigner function for prime and the power of prime dimensions using the discrete version of the star-product operation. Exact and semiclassical dynamics in the limit of large dimensions are considered.
Chin, Siu A; Nikolic, Stanko N; Belic, Milivoj R
2016-01-01
It is well known that Akhmediev breathers of the nonlinear cubic Schrodinger equation can be superposed nonlinearly via the Darboux transformation to yield breathers of higher order. Surprisingly, we find that the peak height of each Akhmediev breather only adds {\\it linearly} to form the peak height of the final breather. Using this new peak-height formula, we show that at any given periodicity, there exist a unique high-order breather of maximal intensity. Moreover, these high-order breathers form a continuous hierarchy, growing in intensity with increasing periodicity. For any such higher-order breather, a simple initial wave function can be extracted from the Darboux transformation to dynamically generate that breather from the nonlinear Schrodinger equation.
Breather kink-antikink-pair conversion in the driven sine-Gordon system
Lomdahl, P. S.; Olsen, O. H.; Samuelsen, Mogens Rugholm
1984-01-01
Breather excitations in the sine-Gordon equation influenced by constant driving forces are investigated—large driving forces cause the breather to split into a kk― (2π kink-2π antikink) pair while for small driving forces the breather excitations enter stationary modes. A perturbation method...
Periodic and Chaotic Breathers in the Nonlinear Schr(o)dinger Equation
LIU Xue-Shen; QI Yue-Ying; DING Pei-Zhu
2004-01-01
@@ The breathers in the cubic nonlinear Schrodinger equation are investigated numerically by using the symplectic method. We show that the solitonlike wave, the periodic, quasiperiodic and chaotic breathers can be observed with the increase of cubic nonlinear perturbation. Finally, we discuss the breathers in the cubic-quintic nonlinear Schrodinger equation with the increase of quintic nonlinear perturbation.
Localized solutions for a nonlocal discrete NLS equation
Ben, Roberto I. [Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, 1613 Los Polvorines (Argentina); Cisneros Ake, Luís [Department of Mathematics, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 México D.F. (Mexico); Minzoni, A.A. [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico); Panayotaros, Panayotis, E-mail: panos@mym.iimas.unam.mx [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico)
2015-09-04
We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces.
Parametrically excited internal wave breathers and kinks in liquids
陈伟中; 魏荣爵; 王本仁
1996-01-01
In parametrically excited Faraday experiment the non-propagating solitons-breathers, kinksand breather pairs-have been observed at the interface of two insoluble liquids with different densities.Phenomena observed at the interface are similar to those on the surface, except that the eigenfrequencies are remarkably red-shifted, and the wave forms are flatter and less stable due to the presence of the upper liquid. A nonlinear Schrodinger equation with damping and drive terms has been derived to explain the new observations. Both experiment and theory show that the free surface wave is a special case of the interface wave.
On exactly conservative integrators
Bowman, J.C. [Max-Planck-Inst. fuer Plasmaphysik, Garching (Germany); Shadwick, B.A. [Univ. of California, Berkeley, CA (United States). Dept. of Physics; Morrison, P.J. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1997-06-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of nonlinear invariants. These algorithms are based on polynomial functions of the time step. The authors discuss a general approach for developing explicit algorithms that conserve such invariants exactly. They illustrate the method by applying it to the truncated two-dimensional Euler equations.
On exactly conservative integrators
Bowman, J.C. [Max-Planck-Inst. fuer Plasmaphysik, Garching (Germany); Shadwick, B.A. [Univ. of California, Berkeley, CA (United States). Dept. of Physics; Morrison, P.J. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1997-06-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of nonlinear invariants. These algorithms are based on polynomial functions of the time step. The authors discuss a general approach for developing explicit algorithms that conserve such invariants exactly. They illustrate the method by applying it to the truncated two-dimensional Euler equations.
Ve Koon, K Tse; Leon, J; Marquié, P; Tchofo-Dinda, P
2007-06-01
A discrete nonlinear system driven at one end by a periodic excitation of frequency above the upper band edge (the discreteness induced cutoff) is shown to be a means to (1) generate propagating breather excitations in a long chain and (2) reveal the bistable property of a short chain. After detailed numerical verifications, the bistability prediction is demonstrated experimentally on an electrical transmission line made of 18 inductance-capacitance (LC) cells. The numerical simulations of the LC -line model allow us also to verify the breather generation prediction with a striking accuracy.
Changes in pharyngeal aerobic microflora in oral breathers after palatal rapid expansion
Ripa Antonio
2006-01-01
Full Text Available Abstract Background The purpose of this study was to investigate in oral breathing children the qualitative and quantitative effects on aerobic and facultatively anaerobic oropharyngeal microflora of respiratory function improved by rapid palatal expansion (RPE. Methods In an open clinical trial, we studied 50 oral breathers, aged 8 to 14 years and suffering from both maxillary constriction and posterior cross-bite. At baseline, patients were examined by a single otorhinolaryngologist (ENT, confirming nasal obstruction in all subjects by posterior rhino-manometric test. Patients were evaluated three times by oropharyngeal swabs:1 at baseline (T = 0; 2 after palatal spreading out (T = 1; and 3 at the end of RPE treatment (T = 2. With regard to the microbiological aspect, the most common and potentially pathogenic oral microrganisms (i.e. Streptococcus pyogenes, Diplococcus pneumoniae, Staphylococcus aureus, Haemophilus spp, Branhamella catarrhalis, Klebsiella pneumoniae, Candida albicans were specifically detected in proper culture plates, isolated colonies were identified by means of biochemical tests and counted by calibrated loop. The data were analyzed by means of the following tests: Chi-square test, Fisher's exact test and Wilcoxon's test. Results After the use of RME there was a statistically significant decrease of Staphylococcus aureus stock at CFU/mLat T1(P = 0.0005; Z = -3,455 by Wilcoxon Rank test and T2 (P Conclusion Our data suggest that RPE therapy in oral breathers may strongly reduce the pathogenic aerobic and facultatively anaerobic microflora in the oral pharynx after a normalization of the upper airways function, and may reduce the risk of respiratory infections.
Breather Dynamics of the Sine-Gordon Equation
Stephen Johnson; Anjan Biswas
2013-01-01
This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation.The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity.Time-dependent functions arise and their properties are studied.These functions are found to be bounded and periodic and affect the soliton velocity.The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.
Breather mobility and the PN potential: Brief review and recent progress
Johansson, Magnus
2014-01-01
The question whether a nonlinear localized mode (discrete soliton/breather) can be mobile in a lattice has a standard interpretation in terms of the Peierls-Nabarro (PN) potential barrier. For the most commonly studied cases, the PN barrier for strongly localized solutions becomes large, rendering these essentially immobile. Several ways to improve the mobility by reducing the PN-barrier have been proposed during the last decade, and the first part gives a brief review of such scenarios in 1D and 2D. We then proceed to discuss two recently discovered novel mobility scenarios. The first example is the 2D Kagome lattice, where the existence of a highly degenerate, flat linear band allows for a very small PN-barrier and mobility of highly localized modes in a small-power regime. The second example is a 1D waveguide array in an active medium with intrinsic (saturable) gain and damping, where exponentially localized, travelling discrete dissipative solitons may exist as stable attractors. Finally, using the framew...
Breather-like solitons extracted from the Peregrine rogue wave
Yang, Guangye; Qin, Zhenyun; Malomed, Boris A; Mihalache, Dumitru; Li, Lu
2014-01-01
Based on the Peregrine solution (PS) of the nonlinear Schr\\"odinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breather-like solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too.
Exactly conservation integrators
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J. [Univ. of Texas, Austin, TX (United States)
1999-03-01
Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts of any nonlinear invariants. In this work the authors present a general approach for developing explicit nontraditional algorithms that conserve such invariants exactly. They illustrate the method by applying it to the three-wave truncation of the Euler equations, the Lotka-Volterra predator-prey model, and the Kepler problem. The ideas are discussed in the context of symplectic (phase-space-conserving) integration methods as well as nonsymplectic conservative methods. They comment on the application of the method to general conservative systems.
Exactly conservative integrators
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J.
1995-07-19
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves invariants. We illustrate the general method by applying it to the Three-Wave truncation of the Euler equations, the Volterra-Lotka predator-prey model, and the Kepler problem. We discuss our method in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Exactly conservative integrators
Shadwick, B A; Morrison, P J; Bowman, John C
1995-01-01
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves these invariants. We illustrate the general method by applying it to the three-wave truncation of the Euler equations, the Lotka--Volterra predator--prey model, and the Kepler problem. This method is discussed in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Exactly conservative integrators
Shadwick, B.A.; Bowman, J.C.; Morrison, P.J.
1995-07-19
Traditional numerical discretizations of conservative systems generically yield an artificial secular drift of any nonlinear invariants. In this work we present an explicit nontraditional algorithm that exactly conserves invariants. We illustrate the general method by applying it to the Three-Wave truncation of the Euler equations, the Volterra-Lotka predator-prey model, and the Kepler problem. We discuss our method in the context of symplectic (phase space conserving) integration methods as well as nonsymplectic conservative methods. We comment on the application of our method to general conservative systems.
Inclined periodic homoclinic breather and rogue waves for the (1+1)-dimensional Boussinesq equation
Zhengde Dai; Chuanjian Wang; Jun Liu
2014-10-01
A new method, homoclinic (heteroclinic) breather limit method (HBLM), for seeking rogue wave solution to nonlinear evolution equation (NEE) is proposed. (1+1)-dimensional Boussinesq equation is used as an example to illustrate the effectiveness of the suggested method. Rational homoclinic wave solution, a new family of two-wave solution, is obtained by inclined periodic homoclinic breather wave solution and is just a rogue wave solution. This result shows that rogue wave originates by the extreme behaviour of homoclinic breather wave in (1+1)-dimensional nonlinear wave fields.
Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.
Interactions between impurities and breather-pairs in a nonlinear lattice
Lin, Han; Chen, Weizhong; Lu, Lei; Wei, Rongjue
2003-09-01
Based on the Frenkel-Kontorova (FK) model with a δ-impurity, this Letter investigates the interactions between impurities and breather-pairs in a nonlinear pendulum chain driven by a vertical vibration. The numerical results show that a long impurity in pendulum length can absorb more energy into the chain and upgrade the energy level of the breather-pair, when the driving frequency is slight lower than that of parametric resonance of the perfect pendulums, while a short one plays a counteractive role. As the chain is driven at a higher frequency, the effect of impurities turns reverse, which shows a clear symmetry and equivalency between long and short impurities. The main results including the effect and the symmetry of impurities generalize the conclusion on the single breather to the breather-pair.
Interactions between impurities and breather-pairs in a nonlinear lattice
Lin Han; Chen Weizhong; Lu Lei; Wei Rongjue
2003-09-15
Based on the Frenkel-Kontorova (FK) model with a {delta}-impurity, this Letter investigates the interactions between impurities and breather-pairs in a nonlinear pendulum chain driven by a vertical vibration. The numerical results show that a long impurity in pendulum length can absorb more energy into the chain and upgrade the energy level of the breather-pair, when the driving frequency is slight lower than that of parametric resonance of the perfect pendulums, while a short one plays a counteractive role. As the chain is driven at a higher frequency, the effect of impurities turns reverse, which shows a clear symmetry and equivalency between long and short impurities. The main results including the effect and the symmetry of impurities generalize the conclusion on the single breather to the breather-pair.
The breakdown of breathers in the Fermi-Pasta-Ulam-Tsingou system
Westley, Alexandra; Kashyap, Rahul; Sen, Surajit
It is well known that in many nonlinear lattices, remarkably stable and localized disturbances known as breathers may form. Here we discuss in short the properties of these objects in the context of the Fermi-Pasta-Ulam-Tsingou (FPUT) system which consists of a mass-spring chain, with spring potentials containing both quadratic and quartic terms. These breathers, though long-lasting, inevitably decay and eventually break apart with sudden violence. This talk in particular will focus on recent numerical work studying the lead-up to the breakdown in which the breather emits at (seemingly) random intervals solitary and anti-solitary waves in the highly nonlinear limit. Furthermore, a possible method to predict the times at which these waves are emitted by examing the frequency structure of the breather will be discussed. Partially supported by US Army Research Office.
Quantum breathers in Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction.
Tang, Bing; Li, De-Jun; Tang, Yi
2014-06-01
We present an analytical study on quantum breathers in one-dimensional ferromagnetic XXZ chains with Dzyaloshinsky-Moriya interaction by means of the time-dependent Hartree approximation and the semidiscrete multiple-scale method. The stationary localized single-boson wave functions are obtained and these analytical solutions are checked by numerical simulations. With such stationary localized single-boson wave functions, we construct quantum breather states. Furthermore, the role of the Dzyaloshinsky-Moriya interaction is discussed.
Quantum breathers in Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction
Tang, Bing; Tang, Yi, E-mail: tangyii@hotmail.com [Department of Physics, Xiangtan University, Xiangtan 411105 (China); Li, De-Jun [College of Physics, Mechanical and Electrical Engineering, Jishou University, Jishou 416000 (China)
2014-06-15
We present an analytical study on quantum breathers in one-dimensional ferromagnetic XXZ chains with Dzyaloshinsky-Moriya interaction by means of the time-dependent Hartree approximation and the semidiscrete multiple-scale method. The stationary localized single-boson wave functions are obtained and these analytical solutions are checked by numerical simulations. With such stationary localized single-boson wave functions, we construct quantum breather states. Furthermore, the role of the Dzyaloshinsky-Moriya interaction is discussed.
The Discrete Wavelet Transform
1991-06-01
focuses on bringing together two separately motivated implementations of the wavelet transform , the algorithm a trous and Mallat’s multiresolution...decomposition. These algorithms are special cases of a single filter bank structure, the discrete wavelet transform , the behavior of which is governed by...nonorthogonal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, we show that the commonly used Lagrange a trous
Evaluation of Respiratory Muscle Strength in Mouth Breathers: Clinical Evidences
Cunha, Renata Andrade da
2014-01-01
Full Text Available Introduction The child who chronically breathes through the mouth may develop a weakness of the respiratory muscles. Researchers and clinical are seeking for methods of instrumental evaluation to gather complementary data to clinical evaluations. With this in mind, it is important to evaluate breathing muscles in the child with Mouth Breathing. Objective To develop a review to investigate studies that used evaluation methods of respiratory muscle strength in mouth breathers. Data Synthesis The authors were unanimous in relation to manovacuometry method as a way to evaluate respiratory pressures in Mouth Breathing children. Two of them performed with an analog manovacuometer and the other one, digital. The studies were not evaluated with regard to the method efficacy neither the used instruments. Conclusion There are few studies evaluating respiratory muscle strength in Mouth Breathing people through manovacuometry and the low methodological rigor of the analyzed studies hindered a reliable result to support or refuse the use of this technique.
Aydin, Alhun; Sisman, Altug
2016-03-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic.
Fiol, Bartomeu; Torrents, Genis
2014-01-01
We compute the exact vacuum expectation value of circular Wilson loops for Euclidean ${\\cal N}=4$ super Yang-Mills with $G=SO(N),Sp(N)$, in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on $AdS_5\\times {\\mathbb R} {\\mathbb P}^5$ plus certain choices of discrete torsion, and we use our results to probe this holographic duality. We first revisit the LLM-type geometries having $AdS_5\\times {\\mathbb R} {\\mathbb P}^5$ as ground state. Our results clarify and refine the identification of these LLM-type geometries as bubbling geometries arising from fermions on a half harmonic oscillator. We furthermore identify the presence of discrete torsion with the one-fermion Wigner distribution becoming negative at the origin of phase space. We then turn to the string world-sheet interpretation of our results and argue that for the quantities considered they imply two features: first, the contribution coming from world-sheets with a single crosscap is closely ...
Calini, A.; Schober, C. M.
2013-09-01
In this article we present the results of a broad numerical investigation on the stability of breather-type solutions of the nonlinear Schrödinger (NLS) equation, specifically the one- and two-mode breathers for an unstable plane wave, which are frequently used to model rogue waves. The numerical experiments involve large ensembles of perturbed initial data for six typical random perturbations. Ensemble estimates of the "closeness", Calligraphy">A(t), of the perturbed solution to an element of the respective unperturbed family indicate that the only neutrally stable breathers are the ones of maximal dimension, that is: given an unstable background with N unstable modes, the only neutrally stable breathers are the N-dimensional ones (obtained as a superimposition of N simple breathers via iterated Backlund transformations). Conversely, breathers which are not fully saturated are sensitive to noisy environments and are unstable. Interestingly, Calligraphy">A(t) is smallest for the coalesced two-mode breather indicating the coalesced case may be the most robust two-mode breather in a laboratory setting. The numerical simulations confirm and provide a realistic realization of the stability behavior established analytically by the authors.
Liu, Junyang; Hang, Chao; Huang, Guoxiang
2016-06-01
We propose a scheme to demonstrate the existence of optical Peregrine rogue waves and Akhmediev and Kuznetsov-Ma breathers and realize their active control via electromagnetically induced transparency (EIT). The system we suggest is a cold, Λ -type three-level atomic gas interacting with a probe and a control laser fields and working under EIT condition. We show that, based on EIT with an incoherent optical pumping, which can be used to cancel optical absorption, (1+1)-dimensional optical Peregrine rogue waves, Akhmediev breathers, and Kuznetsov-Ma breathers can be generated with very low light power. In addition, we demonstrate that the Akhmediev and Kuznetsov-Ma breathers in (2+1)-dimensions obtained can be actively manipulated by using an external magnetic field. As a result, these breathers can display trajectory deflections and bypass obstacles during propagation.
Interactions of breathers and solitons of the extended Korteweg de Vries equation
Shek, C. M.; Grimshaw, R. H. J.; Ding, E.
2005-11-01
A popular model for the evolution of weakly nonlinear, weakly dispersive waves in the ocean is the extended Korteweg -- de Vries equation (eKdV), which incorporates both quadratic and cubic nonlinearities. The case of positive cubic nonlinearity allows for both solitons of elevation and depression, as well as breathers (pulsating modes). Multi-soliton solutions are computed analytically, and will yield expressions for breather-soliton interactions. Both the soliton and breather will retain their identities after interactions, but suffer phase shifts. However, the details of the interaction process will depend on the polarity of the interacting soliton, and have been investigated by a computer algebra software. This highly time dependent motion during the interaction process is important in nonlinear science and physical oceanography. As the dynamics of the current and an evolving internal oceanic tide can be modeled by eKdV, this knowledge is relevant to the temporal and spatial variability observed in the oceanic internal soliton fields.
Exogenous lipoid pneumonia caused by paraffin in an amateur fire breather.
Weinberg, I; Fridlender, Z G
2010-05-01
Paraffin has characteristics that make it popular among fire breathers. To describe a case of paraffin-induced lipoid pneumonia in a fire breather. The patient was evaluated clinically in relation to his occupational history. A 32-year-old man presented with dyspnoea, tachypnoea and non-productive cough of 2 h duration that started immediately following an attempt to blow fire using paraffin as the volatile substance. He was discharged from the emergency ward but returned the next day presenting again with dyspnoea accompanied by mid-sternal pain, fever (38.1 degrees C) and leucocytosis. Chest radiography showed perihilar punctuate infiltrations. A diagnosis of exogenous lipoid pneumonia caused by paraffin was made, and the patient was treated, with full recovery within a week. Fire breathers must be viewed as a population at risk of paraffin-induced lipoid pneumonia.
Nonlinear wave collapse, shock, and breather formation in an electron magnetohydrodynamic plasma.
Ghosh, Samiran; Chakrabarti, Nikhil
2014-12-01
Low-frequency nonlinear wave dynamics is investigated in a two-dimensional inhomogeneous electron magnetohydrodynamic (EMHD) plasma in the presence of electron viscosity. In the long-wavelength limit, the dynamics of the wave is found to be governed by a novel nonlinear equation. The result of the moving-frame nonlinear analysis is noteworthy, which shows that this nonlinear equation does have a breather solution and electron viscosity is responsible for the breather. A breather is a nonlinear wave in which energy accumulates in a localized and oscillatory manner. Analytical solution and time-dependent numerical simulation of this novel equation reveal the collapse of a soliton (localized pulse) into a weak noise shelf and formation of shocklike structures.
Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect
Saadatmand, Danial; Dmitriev, Sergey V.; Borisov, Denis I.; Kevrekidis, Panayotis G.
2014-11-01
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible.
Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation
Hai-Feng Zhang
2013-01-01
Full Text Available A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle of x-axis and t-axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.
2017-05-23
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy otherwise. The mimetic character of many of the DEC operators provides exact conservation of both mass and vorticity, in addition to superior kinetic energy conservation. The employment of barycentric Hodge star allows the discretization to admit arbitrary simplicial meshes. The discretization scheme is presented along with various numerical test cases demonstrating its main characteristics.
Lohmann, E.R.M.A.; Borm, P.E.M.; Herings, P.J.J.
2011-01-01
To verify whether a transferable utility game is exact, one has to check a linear inequality for each exact balanced collection of coalitions. This paper studies the structure and properties of the class of exact balanced collections. Comparing the definition of exact balanced collections with the
Hill, Pamela
This student manual on servicing the crankcase breather is the third of three in an instructional package on the lubrication system in the Small Engine Repair Series for handicapped students. The stated purpose for the booklet is to help students learn what tools and equipment to use and all the steps of the job. Informative material and…
Stabilization of breathers in a parametrically driven sine-Gordon system with loss
Grønbech-Jensen, N.; Kivshar, Yu. S.; Samuelsen, Mogens Rugholm
1991-01-01
We demonstrate that in a parametrically driven sine-Gordon system with loss, a breather, if driven, can be maintained in a steady state at half the external frequency. In the small-amplitude limit the system is described by the effective perturbed nonlinear Schrödinger equation. For an arbitrary...
Odake, Satoru; Sasaki, Ryu
2011-01-01
A comprehensive review of the discrete quantum mechanics with the pure imaginary shifts and the real shifts is presented in parallel with the corresponding results in the ordinary quantum mechanics. The main subjects to be covered are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modification), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creati...
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
Convergence of posteriors for discretized log Gaussian Cox processes
Waagepetersen, Rasmus Plenge
2004-01-01
In Markov chain Monte Carlo posterior computation for log Gaussian Cox processes (LGCPs) a discretization of the continuously indexed Gaussian field is required. It is demonstrated that approximate posterior expectations computed from discretized LGCPs converge to the exact posterior expectations...
Chin, Siu A; Belic, Milivoj R
2015-01-01
By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrodinger equation, the modulation instability (MI) of its n = 1 Fourier mode on a finite background automatically triggers a further cascading instability, forcing all the higher modes to grow exponentially in locked-step with the n = 1 mode. This fundamental insight, the enslavement of all higher modes to the n = 1 mode, explains the formation of a triangular-shaped spectrum which generates the Akhmediev breather, predicts its formation time analytically from the initial modulation amplitude, and shows that the Fermi-Pasta-Ulam (FPU) recurrence is just a matter of energy conservation with a period twice the breather's formation time. For higher order MI with more than one initial unstable modes, while most evolutions are expected to be chaotic, we show that it is possible to have isolated cases of "super-recurrence", where the FPU period is much longer than that of a single unstable mode.
Chin, Siu A.; Ashour, Omar A.; Belić, Milivoj R.
2015-12-01
By invoking Bogoliubov's spectrum, we show that for the nonlinear Schrödinger equation, the modulation instability (MI) of its n =1 Fourier mode on a finite background automatically triggers a further cascading instability, forcing all the higher modes to grow exponentially in locked step with the n =1 mode. This fundamental insight, the enslavement of all higher modes to the n =1 mode, explains the formation of a triangular-shaped spectrum that generates the Akhmediev breather, predicts its formation time analytically from the initial modulation amplitude, and shows that the Fermi-Pasta-Ulam (FPU) recurrence is just a matter of energy conservation with a period twice the breather's formation time. For higher-order MI with more than one initial unstable mode, while most evolutions are expected to be chaotic, we show that it is possible to have isolated cases of "super-recurrence," where the FPU period is much longer than that of a single unstable mode.
Observation of Fermi-Pasta-Ulam Recurrence Induced by Breather Solitons in an Optical Microresonator
Bao, Chengying; Jaramillo-Villegas, Jose A.; Xuan, Yi; Leaird, Daniel E.; Qi, Minghao; Weiner, Andrew M.
2016-10-01
We present, experimentally and numerically, the observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in a high-Q SiN microresonator. Breather solitons can be excited by increasing the pump power at a relatively small pump phase detuning in microresonators. Out of phase power evolution is observed for groups of comb lines around the center of the spectrum compared to groups of lines in the spectral wings. The evolution of the power spectrum is not symmetric with respect to the spectrum center. Numerical simulations based on the generalized Lugiato-Lefever equation are in good agreement with the experimental results and unveil the role of stimulated Raman scattering in the symmetry breaking of the power spectrum evolution. Our results show that optical microresonators can be exploited as a powerful platform for the exploration of soliton dynamics.
Darboux Transformation for Coupled Non-Linear Schrödinger Equation and Its Breather Solutions
Feng, Lili; Yu, Fajun; Li, Li
2017-01-01
Starting from a 3×3 spectral problem, a Darboux transformation (DT) method for coupled Schrödinger (CNLS) equation is constructed, which is more complex than 2×2 spectral problems. A scheme of soliton solutions of an integrable CNLS system is realised by using DT. Then, we obtain the breather solutions for the integrable CNLS system. The method is also appropriate for more non-linear soliton equations in physics and mathematics.
Perfil da fala do respirador oral Speech profile of the mouth breather
Cintia Megumi Nishimura
2010-06-01
Full Text Available TEMA: alteração de fala em respiradores orais. OBJETIVO: o presente estudo investigou através de levantamento bibliográfico dos últimos dez anos o perfil de fala em respiradores orais. CONCLUSÃO: constata-se a necessidade em realizar estudos mais profundos sobre este assunto para identificar as características da fala dos respiradores orais. Tais informações são muito úteis para o fonoaudiólogo, tanto para a realização de uma boa avaliação como no melhor atendimento destes indivíduos.BACKGROUND: alteration of speech in mouth breathers. PURPOSE: this study carried out a bibliographic review over the last ten years about mouth breathers' speech profile. CONCLUSION: there is a need to carry out more thorough studies on this subject to identify the speech characteristics of mouth breathers. Such information is very useful for the speech therapist, both for making a good assessment as well as for providing the best care for these individuals.
Discrete Stein characterizations and discrete information distances
Ley, Christophe
2012-01-01
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distributions and discrete information functionals.
Baldisserotto, Bernardo; Copatti, Carlos E; Gomes, Levy C; Chagas, Edsandra C; Brinn, Richard P; Roubach, Rodrigo
2008-12-01
Fishes that live in the Amazon environment may be exposed to several kinds of water: black water (BW), acidic black water (pH 3.5) (ABW) and white water (WW), among others. The aim of the present study was to analyze net ion fluxes in the facultative air-breather Hoplosternum littorale (tamoata) and the obligate air-breather Arapaima gigas (pirarucu) exposed to different types of water. Fishes were acclimated in well water and later placed in individual chambers containing one type of water for ion flux measurements. After 4 h, the water in the chambers was replaced by a different type of water. The transfer of both species to ABW (independent of previous water exposure) increased net ion loss. Tamoatas transferred from ABW to BW or WW presented a net ion influx, but pirarucus showed only small changes on net ion efflux. These results allow us to conclude that tamoatas and pirarucus present differences in terms of ion regulation but that the general aspects of the ion flux are similar: (1) exposure to ABW led to net ion loss; (2) transfer from BW to WW or vice-versa induced only minor changes on net ion fluxes. These observations demonstrate that any osmoregulatory difficulties encountered by either species during changes between these latter two waters can be easily overcome.
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Intrinsically localized chaos in discrete nonlinear extended systems
Martínez, P J; Falo, F; Mazo, J J
1999-01-01
The phenomenon of intrinsic localization in discrete nonlinear extended systems, i.e. the (generic) existence of discrete breathers, is shown to be not restricted to periodic solutions but it also extends to more complex (chaotic) dynamical behaviour. We illustrate this with two different forced and damped systems exhibiting this type of solutions: In an anisotropic Josephson junction ladder, we obtain intrinsically localized chaotic solutions by following periodic rotobreather solutions through a cascade of period-doubling bifurcations. In an array of forced and damped van der Pol oscillators, they are obtained by numerical continuation (path-following) methods from the uncoupled limit, where its existence is trivially ascertained, following the ideas of the anticontinuum limit.
Singleton, Jr., Robert [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Israel, Daniel M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Doebling, Scott William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Woods, Charles Nathan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kaul, Ann [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Walter, Jr., John William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Rogers, Michael Lloyd [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-05-09
For code verification, one compares the code output against known exact solutions. There are many standard test problems used in this capacity, such as the Noh and Sedov problems. ExactPack is a utility that integrates many of these exact solution codes into a common API (application program interface), and can be used as a stand-alone code or as a python package. ExactPack consists of python driver scripts that access a library of exact solutions written in Fortran or Python. The spatial profiles of the relevant physical quantities, such as the density, fluid velocity, sound speed, or internal energy, are returned at a time specified by the user. The solution profiles can be viewed and examined by a command line interface or a graphical user interface, and a number of analysis tools and unit tests are also provided. We have documented the physics of each problem in the solution library, and provided complete documentation on how to extend the library to include additional exact solutions. ExactPack’s code architecture makes it easy to extend the solution-code library to include additional exact solutions in a robust, reliable, and maintainable manner.
Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2010-01-01
We initiate a systematic study of constant depth Boolean circuits built using exact threshold gates. We consider both unweighted and weighted exact threshold gates and introduce corresponding circuit classes. We next show that this gives a hierarchy of classes that seamlessly interleave with the ......We initiate a systematic study of constant depth Boolean circuits built using exact threshold gates. We consider both unweighted and weighted exact threshold gates and introduce corresponding circuit classes. We next show that this gives a hierarchy of classes that seamlessly interleave...... with the well-studied corresponding hierarchies defined using ordinary threshold gates. A major open problem in Boolean circuit complexity is to provide an explicit super-polynomial lower bound for depth two threshold circuits. We identify the class of depth two exact threshold circuits as a natural subclass...
Waelbroeck, H
1999-01-01
We propose a theory of deterministic chaos for discrete systems, based on their representations in symbolic history spaces Ømega. These are spaces of semi-infinite sequences, as the one-sided shift spaces, but endowed with a more general topology which we call a semicausal topology. We show that define metrical properties, including the correlation dimension of the attractor. Examples are considered: Asymmetric neural networks and random cellular automata are not chaotic. A neural network model with memory, on the other hand, does appear to be an example of discrete chaos.
Caltagirone, Jean-Paul
2014-01-01
This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H
Augusto Hernández Vidal
2011-12-01
Full Text Available In order to strengthen the concept of municipal autonomy, this essay proposes an extensive interpretation of administrative discretion. Discretion is the exercise of free judgment given by law to authorities for performing official acts. This legislative technique seems to be suitable whenever the legislative is intended to legislate over the essential core of municipal autonomy. This way, an eventual abuse of that autonomy could be avoided, for the disproportional restriction of the local faculty to oversee the local issues. This alternative is presented as a tool to provide with dynamism the performing of administrative activities as well, aiming to assimilate public administration new practices.
Exactly Solvable Quantum Mechanics
Sasaki, Ryu
2014-01-01
A comprehensive review of exactly solvable quantum mechanics is presented with the emphasis of the recently discovered multi-indexed orthogonal polynomials. The main subjects to be discussed are the factorised Hamiltonians, the general structure of the solution spaces of the Schroedinger equation (Crum's theorem and its modifications), the shape invariance, the exact solvability in the Schroedinger picture as well as in the Heisenberg picture, the creation/annihilation operators and the dynamical symmetry algebras, coherent states, various deformation schemes (multiple Darboux transformations) and the infinite families of multi-indexed orthogonal polynomials, the exceptional orthogonal polynomials, and deformed exactly solvable scattering problems.
Mittag-Leffler function for discrete fractional modelling
Guo-Cheng Wu
2016-01-01
Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.
Combining Exact and Heuristic Approaches for Discrete Optimization
2009-02-18
XPRESS . This success has stimulated the need for methodology to solve even much larger problems and the desire to solve problems in real-time. We...problems that cannot be solved to optimalitv using the leading commercial solvers such as CPLEX and XPRESS . These problems are either too large or too...an improved solution is found then Update the global solution end if end while The key to making this approach work is problem dependent. We
Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides.
Dai, Chaoqing; Wang, Yueyue; Zhang, Xiaofei
2014-12-01
The PT-symmetric and PT-antisymmetric Akhmediev breather (AB) and Kuznetsov-Ma (KM) soliton train solutions of a (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in PT-symmetric coupled waveguides with gain and loss are derived via the Darboux transformation method. From these analytical solutions, we investigate the controllable behaviors of AB and KM soliton trains in a diffraction decreasing system with exponential profile. By adjusting the relation between the maximum Zm of effective propagation distance and the peak locations Zi of AB and KM soliton trains, we can control the restraint, maintenance and postpone excitations of AB and KM soliton trains.
Zhukov, Alexander V.; Bouffanais, Roland; Fedorov, Eduard G.; Belonenko, Mikhail B.
2013-10-01
We study the propagation of extremely short electromagnetic three-dimensional bipolar pulses in an array of semiconductor carbon nanotubes. The heterogeneity of the pulse field along the axis of the nanotubes is accounted for the first time. The evolution of the electromagnetic field and the charge density of the sample are described by Maxwell's equations supplemented by the continuity equation. Our analysis reveals for the first time the possibility of propagation of three-dimensional electromagnetic breathers in CNTs arrays. Specifically, we found that the propagation of short electromagnetic pulse induces a redistribution of the electron density in the sample.
Sørensen, John Aasted
2011-01-01
examples on regular languages. Apply these concepts to new problems. Finite state machines: Define a finite state machine as a 6-tuble; describe simple finite state machines by tables and graphs; pattern recognition by finite state machines; minimizing the number of states in a finite state machine......The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... of natural numbers. Apply these concepts to new problems. Division and factorizing: Define a prime number and apply Euclid´s algorithm for factorizing an integer. Regular languages: Define a language from the elements of a set; define a regular language; form strings from a regular language; construct...
Discretized configurations and partial partitions
Abrams, Aaron; Hower, Valerie
2010-01-01
We show that the discretized configuration space of $k$ points in the $n$-simplex is homotopy equivalent to a wedge of spheres of dimension $n-k+1$. This space is homeomorphic to the order complex of the poset of ordered partial partitions of $\\{1,\\...,n+1\\}$ with exactly $k$ parts. We also compute the Euler characteristic in two different ways, thereby obtaining a topological proof of a combinatorial recurrence satisfied by the Stirling numbers of the second kind.
Photoexcited breathers in conjugated polyenes: an excited-state molecular dynamics study.
Tretiak, S; Saxena, A; Martin, R L; Bishop, A R
2003-03-04
pi-conjugated polymers have become an important class of materials for electronic devices. Design of these devices requires understanding such processes as photochemical reactions, spatial dynamics of photoexcitations, and energy and charge transport, which in turn involve complex coupled electron-vibrational dynamics. Here we study nonlinear photoexcitation dynamics in the polyene oligomers by using a quantum-chemical method suitable for the simulation of excited-state molecular dynamics in extended molecular systems with sizes up to hundreds of atoms. The method is based on the adiabatic propagation of the ground-state and transition single-electron density matrices along the trajectory. The simulations reveal formation of a self-localized vibronic excitation ("breather" or multiquanta bound state) with a typical period of 34 fs and allows us to identify specific slow and fast nuclear motions strongly coupled to the electronic degrees of freedom. The effect of chain imperfections and chemical defects on the dynamics is also investigated. A complementary two-dimensional analysis of corresponding transition density matrices provides an efficient way to monitor time-dependent real-space localization of the photoexcitation by identifying the underlying changes in charge densities and bond orders. Possible correlated electronic and vibrational spectroscopic signatures of photoexcited breathers are predicted, and generalizations to energy localization in complex macromolecules are discussed.
Traveling waves and breathers in an excitatory-inhibitory neural field
Folias, Stefanos E.
2017-03-01
We study existence and stability of traveling activity bump solutions in an excitatory-inhibitory (E-I) neural field with Heaviside firing rate functions by deriving existence conditions for traveling bumps and an Evans function to analyze their spectral stability. Subsequently, we show that these existence and stability results reduce, in the limit of wave speed c →0 , to the equivalent conditions developed for the stationary bump case. Using the results for the stationary bump case, we show that drift bifurcations of stationary bumps serve as a mechanism for generating traveling bump solutions in the E-I neural field as parameters are varied. Furthermore, we explore the interrelations between stationary and traveling types of bumps and breathers (time-periodic oscillatory bumps) by bridging together analytical and simulation results for stationary and traveling bumps and their bifurcations in a region of parameter space. Interestingly, we find evidence for a codimension-2 drift-Hopf bifurcation occurring as two parameters, inhibitory time constant τ and I-to-I synaptic connection strength w¯i i, are varied and show that the codimension-2 point serves as an organizing center for the dynamics of these four types of spatially localized solutions. Additionally, we describe a case involving subcritical bifurcations that lead to traveling waves and breathers as τ is varied.
Fast Mojette Transform for Discrete Tomography
Chandra, Shekhar S; Kingston, Andrew; Guédon, Jeanpierre; Svalbe, Imants
2010-01-01
A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slice...
Parker, R Gary
1988-01-01
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas o
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
Exact Penalization in Stochastic Programming—Calmness and Constraint Qualification
Martin Branda
2014-01-01
We deal with the conditions which ensure exact penalization in stochastic programming problems under finite discrete distributions. We give several sufficient conditions for problem calmness including graph calmness, existence of an error bound, and generalized Mangasarian-Fromowitz constraint qualification. We propose a new version of the theorem on asymptotic equivalence of local minimizers of chance constrained problems and problems with exact penalty objective. We apply the theory to a pr...
Exact and Approximate Quadratures for Curvature Tensor Estimation
Langer, Torsten; Belyaev, Alexander; Seidel, Hans-Peter; Greiner, Günther; Hornegger, Joachim; Niemann, Heinrich; Stamminger, Marc
2005-01-01
Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. In this paper, we derive exact quadrature formulae for mean curvature, Gaussian curvature, and the Taubin integral representation of the curvature tensor. The exact quadratures are then used to obtain reliable estimates of the curvature tensor of a smooth surface approximated by a dense triangle me...
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
Exact Relativistic 'Antigravity' Propulsion
Felber, F S
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3^-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Exact Relativistic `Antigravity' Propulsion
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
Symmetric Morse potential is exactly solvable
Sasaki, Ryu
2016-01-01
Morse potential $V_M(x)= g^2\\exp (2x)-g(2h+1)\\exp(x)$ is defined on the full line, $-\\infty
Exact probability distribution functions for Parrondo's games
Zadourian, Rubina; Saakian, David B.; Klümper, Andreas
2016-12-01
We study the discrete time dynamics of Brownian ratchet models and Parrondo's games. Using the Fourier transform, we calculate the exact probability distribution functions for both the capital dependent and history dependent Parrondo's games. In certain cases we find strong oscillations near the maximum of the probability distribution with two limiting distributions for odd and even number of rounds of the game. Indications of such oscillations first appeared in the analysis of real financial data, but now we have found this phenomenon in model systems and a theoretical understanding of the phenomenon. The method of our work can be applied to Brownian ratchets, molecular motors, and portfolio optimization.
Approximation-Exact Penalty Function Method for Solving a Class of Stochastic Programming
Wang Guang-min; Wan Zhong-ping
2003-01-01
We present an approximation-exact penalty function method for solving the single stage stochastic programming problem with continuous random variable. The original problem is transformed into a determinate nonlinear programming problem with a discrete random variable sequence, which is obtained by some discrete method. We construct an exact penalty function and obtain an unconstrained optimization. It avoids the difficulty in solution by the rapid growing of the number of constraints for discrete precision. Under lenient conditions, we prove the equivalence of the minimum solution of penalty function and the solution of the determinate programming, and prove that the solution sequences of the discrete problem converge to a solution to the original problem.
SU(N) affine Toda solitons and breathers from transparent Dirac potentials
Thies, Michael
2016-01-01
Transparent scalar and pseudoscalar potentials in the one-dimensional Dirac equation play an important role as self-consistent mean fields in 1+1 dimensional four-fermion theories (Gross-Neveu, Nambu-Jona Lasinio models) and quasi-one dimensional superconductors (Bogoliubov-De Gennes equation). Here, we show that they also serve as seed to generate a large class of classical multi-soliton and multi-breather solutions of su(N) affine Toda field theories, including the Lax representation and the corresponding vector. This generalizes previous findings about the relationship between real kinks in the Gross-Neveu model and classical solitons of the sinh-Gordon equation to complex twisted kinks.
Bright and Dark Solitons and Breathers in Strongly Repulsive Bose-Einstein Condensates
Reinhardt, William P; Robbins, Bryce; Clark, Charles W
2011-01-01
Collisional dynamics of solitary matter waves of superfluid hard core bosons, consisting of dark and bright non-linear waves as well as supersonic periodic trains, reveals remarkable richness and coherence, with the phase of the condensate playing a key role. Depending upon the condensate density and their relative velocity, two distinctive collisional types emerge: the intuitively expected repulsive collisions due to the hard core boson constraint; and, also collisions in which they "pass through" one another. In addition to confirming the soliton status of both bright and dark solitary waves, our studies reveal a variety of multi-solitons including multiple families of breathers, that can be produced and precisely controlled via quantum phase engineering.
Närhi, Mikko; Wetzel, Benjamin; Billet, Cyril; Toenger, Shanti; Sylvestre, Thibaut; Merolla, Jean-Marc; Morandotti, Roberto; Dias, Frederic; Genty, Goëry; Dudley, John M.
2016-12-01
Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose-Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics.
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....
AbouEisha, Hassan M.
2014-01-01
The problem of attribute reduction is an important problem related to feature selection and knowledge discovery. The problem of finding reducts with minimum cardinality is NP-hard. This paper suggests a new algorithm for finding exact reducts with minimum cardinality. This algorithm transforms the initial table to a decision table of a special kind, apply a set of simplification steps to this table, and use a dynamic programming algorithm to finish the construction of an optimal reduct. I present results of computer experiments for a collection of decision tables from UCIML Repository. For many of the experimented tables, the simplification steps solved the problem.
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
Localization & Exact Holography
Dabholkar, Atish; Murthy, Sameer
2011-01-01
We consider the AdS_2/CFT_1 holographic correspondence near the horizon of big four-dimensional black holes preserving four supersymmetries in toroidally compactified Type-II string theory. The boundary partition function of CFT_1 is given by the known quantum degeneracies of these black holes. The bulk partition function is given by a functional integral over string fields in AdS_2. Using recent results on localization we reduce the infinite-dimensional functional integral to a finite number of ordinary integrals over a space of localizing instantons. Under reasonable assumptions about the relevant terms in the effective action, these integrals can be evaluated exactly to obtain a bulk partition function. It precisely reproduces all terms in the exact Rademacher expansion of the boundary partition function as nontrivial functions of charges except for the Kloosterman sum which can in principle follow from an analysis of phases in the background of orbifolded instantons. Our results can be regarded as a step ...
Exact reconstruction with directional wavelets on the sphere
Wiaux, Y; Vandergheynst, P; Blanc, O
2007-01-01
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation is firstly identified. A scale discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of intere...
Continuum limit of discrete Sommerfeld problems on square lattice
BASANT LAL SHARMA
2017-05-01
A low-frequency approximation of the discrete Sommerfeld diffraction problems, involving the scattering of a time harmonic lattice wave incident on square lattice by a discrete Dirichlet or a discrete Neumann half-plane, is investigated. It is established that the exact solution of the discrete model converges to the solution of the continuum model, i.e., the continuous Sommerfeld problem, in the discrete Sobolev space defined by Hackbusch. A proof of convergence has been provided for both types of boundary conditions when the imaginary part of incident wavenumber is positive.
Discretization of topological spaces
Amini, Massoud; Golestani, Nasser
2014-01-01
There are several compactification procedures in topology, but there is only one standard discretization, namely, replacing the original topology with the discrete topology. We give a notion of discretization which is dual (in categorical sense) to compactification and give examples of discretizations. Especially, a discretization functor from the category of $\\alpha$-scattered Stonean spaces to the category of discrete spaces is constructed which is the converse of the Stone-\\v{C}ech compact...
Exact Solutions to Maccari's System
PAN Jun-Ting; GONG Lun-Xun
2007-01-01
Based on the generalized Riccati relation, an algebraic method to construct a series of exact solutions to nonlinear evolution equations is proposed. Being concise and straightforward, the method is applied to Maccari's system, and some exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.
Wang, Chuanjian; Dai, Zhengde; Liu, Changfu
2014-07-01
In this paper, two types of multi-parameter breather homoclinic wave solutions—including breather homoclinic wave and rational homoclinic wave solutions—are obtained by using the Hirota technique and ansätz with complexity of parameter for the coupled Schrödinger-Boussinesq equation. Rogue waves in the form of the rational homoclinic solution are derived when the periods of breather homoclinic wave go to infinite. Some novel features of homoclinic wave solutions are discussed and presented. In contrast to the normal bright rogue wave structure, a structure like a four-petaled flower in temporal-spatial distribution is exhibited. Further with the change of the wave number of the plane wave, the bright and dark rogue wave structures may change into each other. The bright rogue wave structure results from the full merger of two nearby peaks, and the dark rogue wave structure results from the full merger of two nearby holes. The dark rogue wave for the uncoupled Boussinesq equation is finally obtained. Its structural properties show that it never takes on bright rogue wave features with the change of parameter. It is hoped that these results might provide us with useful information on the dynamics of the relevant fields in physics.
Discrete Scalar Quantum Field Theory
Gudder, Stan
2016-01-01
We begin with a description of spacetime by a 4-dimensional cubic lattice $\\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\\sscripthat$ corresponds to a cubic lattice of energy-momentum. This description implies that there is a discrete set of possible particle masses. We then define discrete scalar quantum fields on $\\sscript$. These fields are employed to define interaction Hamiltonians and scattering operators. Although the scattering operator $S$ cannot be computed exactly, approximations are possible. Whether $S$ is unitary is an unsolved problem. Besides the definitions of these operators, our main assumption is conservation of energy-momentum for a scattering process. This article concludes with various examples of perturbation approximations. These include simplified versions of electron-electron and electron-proton scattering as well as simple decay processes. We also define scattering cross-sections, decay ...
Luane de Moraes Boton
2011-02-01
Full Text Available OBJETIVO: verificar a atividade elétrica dos músculos orbiculares orais, masseteres e temporais no repouso, nas isometrias, labial e mastigatória, em crianças respiradoras nasais e respiradoras orais viciosas e obstrutivas, comparando-as. MÉTODOS: foram estudadas 59 crianças, 15 respiradoras nasais (RN; 23 respiradoras orais viciosas (ROV e 21 respiradoras orais obstrutivas (ROO. Todas foram submetidas à avaliação otorrinolaringológica, à fonoaudiológica e ao exame eletromiográfico durante repouso, isometrias mastigatória e labial. Foi realizada análise de variância de Kruskal-Wallis para comparação entre os grupos e dos grupos dois a dois e o teste de Wilcoxon para comparação entre os músculos (pPURPOSE: to check, through an electromyographic evaluation, the electrical activity pattern of the orbicular oral, masseter and temporal muscles on nasal breathers, obstructive and vicious oral breathers in order to compare them. METHODS: 59 children, 15 nasal breathers (NB; 23 vicious oral breathers (VOB and 21 obstructive oral breathers (OOB were studied. All were submitted to an otorhinolaringological and speech-language patology evaluation and to an electromyographic exam in rest, masticatoric and labial isometries. We developed a Kruskal-Wallis variance analysis in order to make a comparison between the groups and the two-by-two groups and the Wilcoxon's test in order to compare between the muscles (p<0,05. RESULTS: after comparing the three groups, there were no relevant difference in the studied muscles, except for the right masseter muscle while resting, when the VOB and NB were compared; and to the lower orbicular muscle while resting and left temporal muscle in the masticatoric isometry, when NB and OOB were compared. In the comparison between VOB and OOB, any muscle has showed a relevant difference. The lower orbicular muscle was more active than the upper orbicular muscle while resting and on labial isometry, mainly in
Luciana Vitaliano Voi Trawitzki
2005-12-01
and the history of breast-feeding and of deleterious oral habits was determined. STUDY DESIGN: clinical with transversal cohort. MATERIAL AND METHOD: The study population consisted of 62 children ranging in age from 3 years and 3 months to 6 years and 11 months who were submitted to otorhinolaryngologic evaluation to determine nasal and mouth breathers and to a speech language pathologic interview. The otorhinolaryngologic evaluation involved the following exams: anterior rhinoscopy, oroscopy and radiologic examination. The parents of the children were questioned about the form of feeding (natural and/or artificial, the duration of breast-feeding and the presence of deleterious oral habits (suction and biting. The Fisher exact test was used to compare groups regarding the presence and absence of habits and the different periods of breast-feeding. RESULTS: The breast-feeding period was longer among nasal breathers and was concentrated in the period between 3 and 6 months of age. Regarding the use of bottle, the results showed that most of the children in both groups used this type of feeding during the first years of life, with no significant difference between groups (p=0.58. There was a marked presence of deleterious oral habits among mouth breathers, with a statistically significant difference between groups regarding suction (p=0.004 and biting habits (p=0.0002. CONCLUSION: Mouth breathing children were breast-fed for a shorter period of time and had a history of deleterious oral habits compared to nose breathers.
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Discrete gravity from statistical mechanics
Romano, Antonio Enea
2011-01-01
We show how to construct space time lattices with a Regge action proportional to the energy of a given Ising or Potts model macrostate. This allows to take advantage of the existence of exact solutions for these models to calculate the quantum wave function of the universe using the sum over the histories approach to quantum gravity. Motivated by this isomorphism we show how the Regge equations, i.e. the discrete equivalent of the vacuum Einstein equations, can be derived using statistical mechanics under the assumption that the energy of a given space time geometry is proportional to the Regge action.
Discrete Calculus as a Bridge between Scales
Degiuli, Eric; McElwaine, Jim
2012-02-01
Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310
2015-01-01
The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, ${\\cal K}^{\\infty}$-exact detectability (resp. ${\\cal K}^{WFT}$-exact detectability, ${\\cal K}^{FT}$-exact detectability, ${\\cal K}^{N}$-exact detectability) and ${\\cal K}^{\\infty}$-exact observability (resp. ${\\cal K}^{WFT}$-exact observability, ${\\cal K}^{FT}...
ANALYSIS OF BREATHER STATE IN THIN BAR BY USING COLLECTIVE COORDINATE
ZHAO Guang-hui; ZHANG Nian-mei; YANG Gui-tong
2006-01-01
Considering Peierls-Nabarro (P-N) force and viscous effect of material, the dynamic behavior of one-dimensional infinite metallic thin bar subjected to axially periodic load is investigated. Governing equation, which is sine-Gordon type equation, is derived. By means of collective-coordinates, the partial equation can be reduced to ordinary differential dynamical system to describe motion of breather. Nonlinear dynamic analysis shows that the amplitude and frequency of P-N force would influence positions of hyperbolic saddle points and change subharmonic bifurcation point, while the path to chaos through odd subharmonic bifurcations remains. Several examples are taken to indicate the effects of amplitude and period of P-N force on the dynamical response of the bar. The simulation states that the area of chaos is half-infinite. This area increases along with enhancement of the amplitude of P-N force. And the frequency of P-N force has similar influence on the system.
The exact fundamental solution for the Benes tracking problem
Balaji, Bhashyam
2009-05-01
The universal continuous-discrete tracking problem requires the solution of a Fokker-Planck-Kolmogorov forward equation (FPKfe) for an arbitrary initial condition. Using results from quantum mechanics, the exact fundamental solution for the FPKfe is derived for the state model of arbitrary dimension with Benes drift that requires only the computation of elementary transcendental functions and standard linear algebra techniques- no ordinary or partial differential equations need to be solved. The measurement process may be an arbitrary, discrete-time nonlinear stochastic process, and the time step size can be arbitrary. Numerical examples are included, demonstrating its utility in practical implementation.
Exact Markov chains versus diffusion theory for haploid random mating.
Tyvand, Peder A; Thorvaldsen, Steinar
2010-05-01
Exact discrete Markov chains are applied to the Wright-Fisher model and the Moran model of haploid random mating. Selection and mutations are neglected. At each discrete value of time t there is a given number n of diploid monoecious organisms. The evolution of the population distribution is given in diffusion variables, to compare the two models of random mating with their common diffusion limit. Only the Moran model converges uniformly to the diffusion limit near the boundary. The Wright-Fisher model allows the population size to change with the generations. Diffusion theory tends to under-predict the loss of genetic information when a population enters a bottleneck.
Endom, Joerg
2014-05-01
negligible any more. Locating for example the exact position of joints, rebars on site, getting correct calibration information or overlaying measurements of independent methods requires high accuracy positioning for all data. Different technologies of synchronizing and stabilizing are discussed in this presentation. Furthermore a scale problem for interdisciplinary work between the geotechnical engineer, the civil engineer, the surveyor and the geophysicist is presented. Manufacturers as well as users are addressed to work on a unified methodology that could be implemented in future. This presentation is a contribution to COST Action TU1208.
Exactly solvable cellular automaton traffic jam model.
Kearney, Michael J
2006-12-01
A detailed study is undertaken of the v{max}=1 limit of the cellular automaton traffic model proposed by Nagel and Paczuski [Phys. Rev. E 51, 2909 (1995)]. The model allows one to analyze the behavior of a traffic jam initiated in an otherwise freely flowing stream of traffic. By mapping onto a discrete-time queueing system, itself related to various problems encountered in lattice combinatorics, exact results are presented in relation to the jam lifetime, the maximum jam length, and the jam mass (the space-time cluster size or integrated vehicle waiting time), both in terms of the critical and the off-critical behavior. This sets existing scaling results in their natural context and also provides several other interesting results in addition.
Homological Pisot Substitutions and Exact Regularity
Barge, Marcy; Jones, Leslie; Sadun, Lorenzo
2010-01-01
We consider one-dimensional substitution tiling spaces where the dilatation (stretching factor) is a degree d Pisot number, and where the first rational Cech cohomology is d-dimensional. We construct examples of such "homological Pisot" substitutions that do not have pure discrete spectra. These examples are not unimodular, and we conjecture that the coincidence rank must always divide a power of the norm of the dilatation. To support this conjecture, we show that homological Pisot substitutions exhibit an Exact Regularity Property (ERP), in which the number of occurrences of a patch for a return length is governed strictly by the length. The ERP puts strong constraints on the measure of any cylinder set in the corresponding tiling space.
Groupoids, Discrete Mechanics, and Discrete Variation
GUO Jia-Feng; JIA Xiao-Yu; WU Ke; ZHAO Wei-Zhong
2008-01-01
After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid,we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection between groupoids variation and the methods of the first and second discrete variational principles.
Zhou, Jianqin
2011-01-01
The discrete cosine transform (DCT), introduced by Ahmed, Natarajan and Rao, has been used in many applications of digital signal processing, data compression and information hiding. There are four types of the discrete cosine transform. In simulating the discrete cosine transform, we propose a generalized discrete cosine transform with three parameters, and prove its orthogonality for some new cases. A new type of discrete cosine transform is proposed and its orthogonality is proved. Finally, we propose a generalized discrete W transform with three parameters, and prove its orthogonality for some new cases.
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro
2007-12-01
Full Text Available Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences of Fichera about discrete and continuous world, we shall present some considerations about discrete phenomena which arise when designing numerical methods or discrete models for some classical physical problems.
An exact quantification of backreaction in relativistic cosmology
Clifton, Timothy; Tavakol, Reza
2012-01-01
An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modelled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (100), however, then our measures of backreaction become small (<1%). This result does n...
New exact solutions to some difference differential equations
Wang Zhen; Zhang Hong-Qing
2006-01-01
In this paper, we use our method to solve the extended Lotka-Volterra equation and discrete KdV equation. With the help of Maple, we obtain a number of exact solutions to the two equations including soliton solutions presented by hyperbolic functions of sinh and cosh, periodic solutions presented by trigonometric functions of sin and cos, and rational solutions. This method can be used to solve some other nonlinear difference-differential equations.
Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian
2016-07-01
Under investigation in this work is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the propagation of small-amplitude, long wave in shallow water. By virtue of Bell's polynomials, an effective way is presented to succinctly construct its bilinear form. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the breather wave solution, rogue-wave solution and solitary-wave solution of the equation are well constructed. Our results can be used to enrich the dynamical behavior of the generalized (2+1)-dimensional nonlinear wave fields.
Seidl, Gerhart
2014-01-01
We present a simple generalization of Noether's theorem for discrete symmetries in relativistic continuum field theories. We calculate explicitly the conserved current for several discrete spacetime and internal symmetries. In addition, we formulate an analogue of the Ward-Takahashi identity for the Noether current associated with a discrete symmetry.
Discrete differential geometry: the nonplanar quadrilateral mesh.
Twining, Carole J; Marsland, Stephen
2012-06-01
We consider the problem of constructing a discrete differential geometry defined on nonplanar quadrilateral meshes. Physical models on discrete nonflat spaces are of inherent interest, as well as being used in applications such as computation for electromagnetism, fluid mechanics, and image analysis. However, the majority of analysis has focused on triangulated meshes. We consider two approaches: discretizing the tensor calculus, and a discrete mesh version of differential forms. While these two approaches are equivalent in the continuum, we show that this is not true in the discrete case. Nevertheless, we show that it is possible to construct mesh versions of the Levi-Civita connection (and hence the tensorial covariant derivative and the associated covariant exterior derivative), the torsion, and the curvature. We show how discrete analogs of the usual vector integral theorems are constructed in such a way that the appropriate conservation laws hold exactly on the mesh, rather than only as approximations to the continuum limit. We demonstrate the success of our method by constructing a mesh version of classical electromagnetism and discuss how our formalism could be used to deal with other physical models, such as fluids.
Exact solution for generalized pairing
Pan, Feng; J.P. Draayer
1997-01-01
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with some numerical examples.
Exact cosmological solutions for MOG
Roshan, Mahmood [Ferdowsi University of Mashhad, Department of Physics, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)
2015-09-15
We find some new exact cosmological solutions for the covariant scalar-tensor-vector gravity theory, the so-called modified gravity (MOG). The exact solution of the vacuum field equations has been derived. Also, for non-vacuum cases we have found some exact solutions with the aid of the Noether symmetry approach. More specifically, the symmetry vector and also the Noether conserved quantity associated to the point-like Lagrangian of the theory have been found. Also we find the exact form of the generic vector field potential of this theory by considering the behavior of the relevant point-like Lagrangian under the infinitesimal generator of the Noether symmetry. Finally, we discuss the cosmological implications of the solutions. (orig.)
Edna Namiko Izuka
2015-06-01
Full Text Available OBJECTIVE: To assess short-term tomographic changes in the upper airway dimensions and quality of life of mouth breathers after rapid maxillary expansion (RME. METHODS: A total of 25 mouth breathers with maxillary atresia and a mean age of 10.5 years old were assessed by means of cone-beam computed tomography (CBCT and a standardized quality of life questionnaire answered by patients' parents/legal guardians before and immediately after rapid maxillary expansion. RESULTS: Rapid maxillary expansion resulted in similar and significant expansion in the width of anterior (2.8 mm, p < 0.001 and posterior nasal floor (2.8 mm, p < 0.001. Although nasopharynx and nasal cavities airway volumes significantly increased (+1646.1 mm3, p < 0.001, oropharynx volume increase was not statistically significant (+1450.6 mm3, p = 0.066. The results of the quality of life questionnaire indicated that soon after rapid maxillary expansion, patients' respiratory symptoms significantly decreased in relation to their initial respiratory conditions. CONCLUSIONS: It is suggested that RME produces significant dimensional increase in the nasal cavity and nasopharynx. Additionally, it also positively impacts the quality of life of mouth-breathing patients with maxillary atresia.
Formalising the Continuous/Discrete Modeling Step
Wen Su
2011-06-01
Full Text Available Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.
Formalising the Continuous/Discrete Modeling Step
Banach, Richard; Su, Wen; Huang, Runlei; 10.4204/EPTCS.55.8
2011-01-01
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.
Natural discretization in noncommutative field theory
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.
Spitsin I. A.
2014-11-01
Full Text Available The paper presents an assessment of the impact of the developed breather gear the resource tractor transmission and analyzes methods for the determination of wear and tear by spectral analysis of the oil, and the essence of the method of measuring the intensity of X-ray fluorescence emission of iron accumulated in the oil
Discrete Modeling of the Worm Spread with Random Scanning
Uchida, Masato
In this paper, we derive a set of discrete time difference equations that models the spreading process of computer worms such as Code-Red and Slammer, which uses a common strategy called “random scanning” to spread through the Internet. We show that the derived set of discrete time difference equations has an exact relationship with the Kermack and McKendrick susceptible-infectious-removed (SIR) model, which is known as a standard continuous time model for worm spreading.
Leistedt, B
2012-01-01
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact harmonic transform on the radial line using damped Laguerre polynomials and develop a corresponding quadrature rule. Combined with the spherical harmonic transform, this approach leads to a sampling theorem on the ball and a novel three-dimensional decomposition which we call the Fourier-Laguerre transform. We relate this new transform to the well-known Fourier-Bessel decomposition and show that band-limitness in the Fourier-Laguerre basis is a sufficient condition to compute the Fourier-Bessel decomposition exactly. We then construct the flaglet transform on the ball through a harmonic tiling, which is exact thanks to the exactness of the Fourier-Laguerre transform (from which the name flaglets is coined). The corresponding wavelet kernels have compact localisation properties in real and harmonic space and their angular aperture is i...
Exact completions and small sheaves
Shulman, Michael
2012-01-01
We prove a general theorem which includes most notions of "exact completion". The theorem is that "k-ary exact categories" are a reflective sub-2-category of "k-ary sites", for any regular cardinal k. A k-ary exact category is an exact category with disjoint and universal k-small coproducts, and a k-ary site is a site whose covering sieves are generated by k-small families and which satisfies a weak size condition. For different values of k, this includes the exact completions of a regular category or a category with (weak) finite limits; the pretopos completion of a coherent category; and the category of sheaves on a small site. For a large site with k the size of the universe, it gives a well-behaved "category of small sheaves". Along the way, we define a slightly generalized notion of "morphism of sites", and show that k-ary sites are equivalent to a type of "enhanced allegory".
Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy Permana
2016-01-01
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, restrictions are given to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.
A characterisation of algebraic exactness
Garner, Richard
2011-01-01
An algebraically exact category in one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these limits and colimits as hold in any variety. Such categories were studied by Ad\\'amek, Lawvere and Rosick\\'y: they characterised them as the categories with small limits and sifted colimits for which the functor taking sifted colimits is continuous. They conjectured that a complete and sifted-cocomplete category should be algebraically exact just when it is Barr-exact, finite limits commute with filtered colimits, regular epimorphisms are stable by small products, and filtered colimits distribute over small products. We prove this conjecture.
Hayashi, Yusuke; Higuchi, Yusuke; Nomura, Yuji; Ogurisu, Osamu
2016-11-01
On the d-dimensional lattice Z^d and the r-regular tree {T^r}, an exact expression for the number of discrete eigenvalues of a discrete Laplacian with a finitely supported potential is described in terms of the support and the intensities of the potential on each case. In particular, the number of eigenvalues less than the infimum of the essential spectrum is bounded by the number of negative intensities.
Discrete mathematics, discrete physics and numerical methods
Felice Iavernaro; Donato Trigiante
2007-01-01
Discrete mathematics has been neglected for a long time. It has been put in the shade by the striking success of continuous mathematics in the last two centuries, mainly because continuous models in physics proved very reliable, but also because of the greater difﬁculty in dealing with it. This perspective has been rapidly changing in the last years owing to the needs of the numerical analysis and, more recently, of the so called discrete physics. In this paper, starting from some sentences o...
Approximation-Exact Penalty Function Method for Solving a Class of Stochastic Programming
WangGuang-min; WanZhong-ping
2003-01-01
We present an approximation-exact penalty function method for solving the single stage stochastic programming problem with continuous random variable. The original problem is transformed into a determinate nonlinear programming problem with a discrete random variable sequence, which is obtained by some discrete method. We construct an exact penalty function and obtain an unconstrained optimization. It avoids the difficulty in solution by the rapid growing of the number of constraints for discrete precision.Under lenient conditions, we prove the equivalence of the minimum solution of penalty function and the solution of the determinate programming, and prove that the solution sequences of the discrete problem converge to a solution to the original problem.
Modeling Acoustically Driven Microbubbles by Macroscopic Discrete-Mechanical Analogues
Víctor Sánchez-Morcillo
2013-06-01
Full Text Available The dynamics of continuous systems that exhibit circular or spherical symmetry like drops, bubbles or some macromolecules, under the influence of some external excitation, develop surface patters that are hard to predict in most practical situations. In the particular case of acoustically driven microbubbles (ultrasound contrast agent, the study of the behavior of the bubble shell requires complex modeling even for describe the most simple oscillation patterns. Furthermore, due to the smallness of the spatio-temporal scale of the problem, an experimental approach requires expensive hardware setup. Despite the complexity of the particular physical problem, the basic dynamical features of some continuous physical systems can be captured by simple models of coupled oscillators. In this work we consider an analogy between a shelled-gas bubble cavitating under the action of an acoustic field and a discrete mechanical system. Thus, we present a theoretical and experimental study of the spatial instabilities of a circular ring of coupled pendulums parametrically driven by a vertical harmonic force. The system is capable of wave propagation and exhibit nonlinearities and dispersion, so manifest rich dynamics: normal oscillation modes (breathing, dipole, quadrupole... and localized patterns of different types (breathers and kinks witch are predicted by finite-differences numerical solutions and observed experimentally. On the basis of this analogy, the oscillation patterns and localized modes observed experimentally in acoustically driven bubbles are interpreted and discussed.
Discretizing the transcritical and pitchfork bifurcations – conjugacy results
Lóczi, Lajos
2015-01-07
© 2015 Taylor & Francis. We present two case studies in one-dimensional dynamics concerning the discretization of transcritical (TC) and pitchfork (PF) bifurcations. In the vicinity of a TC or PF bifurcation point and under some natural assumptions on the one-step discretization method of order (Formula presented.) , we show that the time- (Formula presented.) exact and the step-size- (Formula presented.) discretized dynamics are topologically equivalent by constructing a two-parameter family of conjugacies in each case. As a main result, we prove that the constructed conjugacy maps are (Formula presented.) -close to the identity and these estimates are optimal.
Discretization of partial differential equations preserving their physical symmetries
Valiquette, F; Winternitz, P [Centre de Recherches Mathematiques, Universite de Montreal, C.P. 6128, succ. Centre-ville, Montreal, QC, H3C 3J7 (Canada)
2005-11-11
A procedure for obtaining a 'minimal' discretization of a partial differential equation, preserving all of its Lie point symmetries, is presented. 'Minimal' in this case means that the differential equation is replaced by a partial difference scheme involving N difference equations, where N is the number of independent and dependent variables. We restrict ourselves to one scalar function of two independent variables. As examples, invariant discretizations of the heat, Burgers and Korteweg-de Vries equations are presented. Some exact solutions of the discrete schemes are obtained.
Discrete Symmetry Transformation of Baryon- and Lepton-Nonconserving Processes
Jafari, Ehsan
2016-01-01
In this paper we consider discrete symmetry (C, P, T and CP) transformations of baryon- and lepton-nonconserving processes. According to our calculation it is not possible to definite exact discrete symmetry transformation for any operator which breaks $B-L$ and changes the number of fundamental fermions between initial and final states. In order to count the net change of fundamental fermions between initial and final states, $F$ number has been introduced. On the other hand from theoretical point of view we are not able to label operators which break $B-L$ and violate F number as $-even$ or $-odd$ under the effect of discrete symmetries.
Weights of Exact Threshold Functions
Babai, László; Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2010-01-01
We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute value) of the coefficients required to represent such functions. These bounds are very close and in the linear case...
Exactly solvable models of nuclei
Van Isacker, P
2014-01-01
In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well as collective modes of motion in the atomic nucleus.
Quasi-exact evaluation of time domain MFIE MOT matrix elements
Shi, Yifei
2013-07-01
A previously proposed quasi-exact scheme for evaluating matrix elements resulting from the marching-on-in-time (MOT) discretization of the time domain electric field integral equation (EFIE) is extended to matrix entries resulting from the discretization of its magnetic field integral equation (MFIE) counterpart. Numerical results demonstrate the accuracy of the scheme as well as the late-time stability of the resulting MOT-MFIE solver. © 2013 IEEE.
Finite Discrete Gabor Analysis
Søndergaard, Peter Lempel
2007-01-01
on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu
2012-01-01
We construct a discrete quantum mechanics using a vector space over the Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discrete quantum mechanics cannot be reproduced with any hidden variable theory.
Exact reconstruction with directional wavelets on the sphere
Wiaux, Y.; McEwen, J. D.; Vandergheynst, P.; Blanc, O.
2008-08-01
A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et al. The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation are first identified. A scale-discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background data, such as the imprint of topological defects, in particular, cosmic strings, and for their reconstruction after separation from the other signal components.
Lee, Taeyoung; McClamroch, N Harris
2007-01-01
Discrete control systems, as considered here, refer to the control theory of discrete-time Lagrangian or Hamiltonian systems. These discrete-time models are based on a discrete variational principle, and are part of the broader field of geometric integration. Geometric integrators are numerical integration methods that preserve geometric properties of continuous systems, such as conservation of the symplectic form, momentum, and energy. They also guarantee that the discrete flow remains on the manifold on which the continuous system evolves, an important property in the case of rigid-body dynamics. In nonlinear control, one typically relies on differential geometric and dynamical systems techniques to prove properties such as stability, controllability, and optimality. More generally, the geometric structure of such systems plays a critical role in the nonlinear analysis of the corresponding control problems. Despite the critical role of geometry and mechanics in the analysis of nonlinear control systems, non...
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...
Burgin, Mark
2010-01-01
Continuous models used in physics and other areas of mathematics applications become discrete when they are computerized, e.g., utilized for computations. Besides, computers are controlling processes in discrete spaces, such as films and television programs. At the same time, continuous models that are in the background of discrete representations use mathematical technology developed for continuous media. The most important example of such a technology is calculus, which is so useful in physics and other sciences. The main goal of this paper is to synthesize continuous features and powerful technology of the classical calculus with the discrete approach of numerical mathematics and computational physics. To do this, we further develop the theory of fuzzy continuous functions and apply this theory to functions defined on discrete sets. The main interest is the classical Intermediate Value theorem. Although the result of this theorem is completely based on continuity, utilization of a relaxed version of contin...
New Results in Discrete-Time Loop Transfer Recovery
Niemann, Hans Henrik; Søgaard-Andersen, Per
1988-01-01
in terms of the system zeros and the corresponding zero-directions. Full-order as well as minimal-order observers are treated. Further it is shown how exact recovery is also applicable to non-minimum phase plants. In this case the achievable performance is parameterized explicitly.......For discrete-time compensators incorporating prediction observers asymptotic loop transfer recovery is not feasible. Instead loop transfer recovery objectives must be satisfied via exact recovery techniques. In this note the model-based compensators which achieves exact recovery are parametrized...
When 'exact recovery' is exact recovery in compressed sensing simulation
Sturm, Bob L.
2012-01-01
In a simulation of compressed sensing (CS), one must test whether the recovered solution \\(\\vax\\) is the true solution \\(\\vx\\), i.e., ``exact recovery.'' Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than...... for a given distribution of \\(\\vx\\)? We show that, in a best case scenario, \\(\\epsilon^2\\) sets a maximum allowed missed detection rate in a majority sense....
Denise Bolzan Berlese
2012-06-01
studied. In the oral breathing group, 40% of the subjects presented lips tension during occlusion and 80% showed a narrow palate, while almost all nasal breathers had normal palate and lips posture (p<0.05. Interposition of the tongue in the dental arches occurred in 47% of oral breathers and none of the nasal breathers. Oral breathers showed the tendency not to repeat the swallowing of the same bolus. No difference was found between groups regarding face appearance, jaw posture, cheeks, and chewing function. CONCLUSION: Oral breathing in obese children and adolescents was accompanied by myofunctional alterations of the stomatognathic system, represented by narrow palate, interposition of the tongue in the dental arches, occlusion of the lips with tension, and swallowing disorders.
Bernays, Sarah; Paparini, Sara; Seeley, Janet; Namukwaya Kihika, Stella; Gibb, Diana; Rhodes, Tim
2017-01-01
Objectives A qualitative study of the BREATHER (PENTA 16) randomised clinical trial, which compared virological control of Short Cycle Therapy (SCT) (5 days on: 2 days off) with continuous efavirenz (EFV)-based antiretroviral therapy (CT) in children and young people (aged 8–24) living with HIV with viral load young people from both arms of the BREATHER trial (31 females and 18 males; 40% of the total trial population in the respective sites; age range 11–24) gave additional consent to participate in the qualitative study. Results Young people from both trial arms had initial concerns about the impact of SCT on their health and adherence, but these decreased over the early months in the trial. Young people randomised to SCT reported preference for SCT compared with CT pre-trial. Attitudes to SCT did not vary greatly by gender or country. Once short-term adaptation challenges were overcome, SCT was positively described as reducing impact of side effects, easing the pressure to carry and remember medication and enabling more weekend social activities. Young people on both arms reported frequent medication side effects and occasional missed doses that they had rarely voiced to clinical staff. Participants liked SCT by trial end but were concerned that peers who had most problems adhering could find SCT disruptive and difficult to manage. Conclusions To realise the potential of SCT (and mitigate possible risks of longer interruptions), careful dissemination and communication post-trial is needed. SCT should be provided alongside a package of monitoring, support and education over 3 months to allow adaptation. Trial registration number NCT 01641016 PMID:28213595
Exact models for isotropic matter
Thirukkanesh, S.; Maharaj, S. D.
2006-04-01
We study the Einstein-Maxwell system of equations in spherically symmetric gravitational fields for static interior spacetimes. The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients. We demonstrate that this difference equation can be solved in general using mathematical induction. Consequently, we can find an explicit exact solution to the Einstein-Maxwell field equations. The metric functions, energy density, pressure and the electric field intensity can be found explicitly. Our result contains models found previously, including the neutron star model of Durgapal and Bannerji. By placing restrictions on parameters arising in the general series, we show that the series terminate and there exist two linearly independent solutions. Consequently, it is possible to find exact solutions in terms of elementary functions, namely polynomials and algebraic functions.
From discrete particles to continuum fields near a boundary
Weinhart, Thomas; Thornton, Anthony Richard; Luding, Stefan; Bokhove, Onno
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents’ degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation presented by Goldhirsch in [I.Goldhirsch,
From discrete particles to continuum fields near a boundary
Weinhart, Thomas; Thornton, Anthony R.; Luding, Stefan; Bokhove, Onno
2011-01-01
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents’ degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation presented by Goldhirsch in [I.Goldhirsch, G
Torus Bifurcation Under Discretization
邹永魁; 黄明游
2002-01-01
Parameterized dynamical systems with a simple zero eigenvalue and a couple of purely imaginary eigenvalues are considered. It is proved that this type of eigen-structure leads to torns bifurcation under certain nondegenerate conditions. We show that the discrete systems, obtained by discretizing the ODEs using symmetric, eigen-structure preserving schemes, inherit the similar torus bifurcation properties. Fredholm theory in Banach spaces is applied to obtain the global torns bifurcation. Our results complement those on the study of discretization effects of global bifurcation.
Hewson, S F
1996-01-01
We investigate non-abelian gaugings of WZNW models. When the gauged group is semisimple we are able to present exact formulae for the dual conformal field theory, for all values of the level k. The results are then applied to non-abelian target space duality in string theory, showing that the standard formulae are quantum mechanically well defined in the low energy limit if the gauged group is semisimple.
Pearls of Discrete Mathematics
Erickson, Martin
2009-01-01
Presents methods for solving counting problems and other types of problems that involve discrete structures. This work illustrates the relationship of these structures to algebra, geometry, number theory and combinatorics. It addresses topics such as information and game theories
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
An Efficient Approach for Identifying Stable Lobes with Discretization Method
Baohai Wu
2013-01-01
Full Text Available This paper presents a new approach for quick identification of chatter stability lobes with discretization method. Firstly, three different kinds of stability regions are defined: absolute stable region, valid region, and invalid region. Secondly, while identifying the chatter stability lobes, three different regions within the chatter stability lobes are identified with relatively large time intervals. Thirdly, stability boundary within the valid regions is finely calculated to get exact chatter stability lobes. The proposed method only needs to test a small portion of spindle speed and cutting depth set; about 89% computation time is savedcompared with full discretization method. It spends only about10 minutes to get exact chatter stability lobes. Since, based on discretization method, the proposed method can be used for different immersion cutting including low immersion cutting process, the proposed method can be directly implemented in the workshop to promote machining parameters selection efficiency.
Discrete computational structures
Korfhage, Robert R
1974-01-01
Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize
An hp-adaptive strategy for the solution of the exact kernel curved wire Pocklington equation
Lahaye, D.; Hemker, P.W.
2007-01-01
In this paper we introduce an adaptive method for the numerical solution of the Pocklington integro-differential equation with exact kernel for the current induced in a smoothly curved thin wire antenna. The hp-adaptive technique is based on the representation of the discrete solution, which is expa
Exact solutions of the spinor Bethe-Salpeter equation for tightly bound states
Suttorp, L.G.
1975-01-01
Exact solutions are obtained for the spinor Bethe-Salpeter equation that describes tightly bound states of spin-/sup 1///sub 2/ fermions with massless-boson exchange. The corresponding coupling constants form a discrete spectrum that depends continuously on the parameters characterizing the type of
Exact solutions of the spinor Bethe-Salpeter equation for tightly bound states
Suttorp, L.G.
1975-01-01
Exact solutions are obtained for the spinor Bethe-Salpeter equation that describes tightly bound states of spin-/sup 1///sub 2/ fermions with massless-boson exchange. The corresponding coupling constants form a discrete spectrum that depends continuously on the parameters characterizing the type of
Exact analytic solutions for a Dirac electron moving in graphene under magnetic fields.
Kuru, S; Negro, J; Nieto, L M
2009-11-11
Exact analytical solutions for the bound states of a graphene Dirac electron in various magnetic fields with translational symmetry are obtained. In order to solve the time-independent Dirac-Weyl equation the factorization method used in supersymmetric quantum mechanics is adapted to this problem. The behavior of the discrete spectrum, probability and current densities are discussed.
Nieto, L M; Suzko, A A
2003-01-01
The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger equation. New families of exactly solvable multichannel Hamiltonians are found.
Exact analytical solutions for ADAFs
Habibi, Asiyeh; Shadmehri, Mohsen
2016-01-01
We obtain two-dimensional exact analytic solutions for the structure of the hot accretion flows without wind. We assume that the only non-zero component of the stress tensor is $T_{r\\varphi}$. Furthermore we assume that the value of viscosity coefficient $\\alpha$ varies with $\\theta$. We find radially self-similar solutions and compare them with the numerical and the analytical solutions already studied in the literature. The no-wind solution obtained in this paper may be applied to the nuclei of some cool-core clusters.
EXACT ALGORITHM FOR BIN COVERING
无
2001-01-01
This paper presents a new arc flow model for the one-dimensional bin covering problem and an algorithm to solve the problem exactly through a branch-and-bound procedure and the technique of column generation. The subproblems occuring in the procedure of branch-and-bound have the same structure and therefore can be solved by the same algorithm. In order to solve effectively the subproblems which are generally large scale, a column generation algorithm is employed. Many rules found in this paper can improve the performance of the methods.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
Generalized computer-aided discrete time domain modeling and analysis of dc-dc converters
Lee, F. C.; Iwens, R. P.; Yu, Y.; Triner, J. E.
1977-01-01
A generalized discrete time domain modeling and analysis technique is presented for all types of switching regulators using any type of duty-cycle controller, and operating in both continuous and discontinuous inductor current. State space techniques are employed to derive an equivalent nonlinear discrete time model that describes the converter exactly. The system is linearized about its equilibrium state to obtain a linear discrete time model for small signal performance evaluations, such as stability, audiosusceptibility and transient response. The analysis makes extensive use of the digital computer as an analytical tool. It is universal, exact and easy to use.
Exact Renormalization of Massless QED2
Casana, R; Casana, Rodolfo; Dias, Sebastiao Alves
2001-01-01
We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.
Exact Renormalization of Massless QED2
Casana, Rodolfo; Dias, Sebastião Alves
We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.
Prateek Sharma
2015-04-01
Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.
Kondakci, H Esat; Saleh, Bahaa E A
2016-01-01
When a disordered array of coupled waveguides is illuminated with an extended coherent optical field, discrete speckle develops: partially coherent light with a granular intensity distribution on the lattice sites. The same paradigm applies to a variety of other settings in photonics, such as imperfectly coupled resonators or fibers with randomly coupled cores. Through numerical simulations and analytical modeling, we uncover a set of surprising features that characterize discrete speckle in one- and two-dimensional lattices known to exhibit transverse Anderson localization. Firstly, the fingerprint of localization is embedded in the fluctuations of the discrete speckle and is revealed in the narrowing of the spatial coherence function. Secondly, the transverse coherence length (or speckle grain size) is frozen during propagation. Thirdly, the axial coherence depth is independent of the axial position, thereby resulting in a coherence voxel of fixed volume independently of position. We take these unique featu...
Discrete systems and integrability
Hietarinta, J; Nijhoff, F W
2016-01-01
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...
Discrete Classical Electromagnetic Fields
De Souza, M M
1997-01-01
The classical electromagnetic field of a spinless point electron is described in a formalism with extended causality by discrete finite transverse point-vector fields with discrete and localized point interactions. These fields are taken as a classical representation of photons, ``classical photons". They are all transversal photons; there are no scalar nor longitudinal photons as these are definitely eliminated by the gauge condition. The angular distribution of emitted photons coincides with the directions of maximum emission in the standard formalism. The Maxwell formalism and its standard field are retrieved by the replacement of these discrete fields by their space-time averages, and in this process scalar and longitudinal photons are necessarily created and added. Divergences and singularities are by-products of this averaging process. This formalism enlighten the meaning and the origin of the non-physical photons, the ones that violate the Lorentz condition in manifestly covariant quantization methods.
AESS: Accelerated Exact Stochastic Simulation
Jenkins, David D.; Peterson, Gregory D.
2011-12-01
The Stochastic Simulation Algorithm (SSA) developed by Gillespie provides a powerful mechanism for exploring the behavior of chemical systems with small species populations or with important noise contributions. Gene circuit simulations for systems biology commonly employ the SSA method, as do ecological applications. This algorithm tends to be computationally expensive, so researchers seek an efficient implementation of SSA. In this program package, the Accelerated Exact Stochastic Simulation Algorithm (AESS) contains optimized implementations of Gillespie's SSA that improve the performance of individual simulation runs or ensembles of simulations used for sweeping parameters or to provide statistically significant results. Program summaryProgram title: AESS Catalogue identifier: AEJW_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJW_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: University of Tennessee copyright agreement No. of lines in distributed program, including test data, etc.: 10 861 No. of bytes in distributed program, including test data, etc.: 394 631 Distribution format: tar.gz Programming language: C for processors, CUDA for NVIDIA GPUs Computer: Developed and tested on various x86 computers and NVIDIA C1060 Tesla and GTX 480 Fermi GPUs. The system targets x86 workstations, optionally with multicore processors or NVIDIA GPUs as accelerators. Operating system: Tested under Ubuntu Linux OS and CentOS 5.5 Linux OS Classification: 3, 16.12 Nature of problem: Simulation of chemical systems, particularly with low species populations, can be accurately performed using Gillespie's method of stochastic simulation. Numerous variations on the original stochastic simulation algorithm have been developed, including approaches that produce results with statistics that exactly match the chemical master equation (CME) as well as other approaches that approximate the CME. Solution
Exact finite elements for conduction and convection
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Introductory discrete mathematics
Balakrishnan, V K
2010-01-01
This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well a
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Obtaining exact value by approximate computations
Jing-zhong ZHANG; Yong FENG
2007-01-01
Numerical approximate computations can solve large and complex problems fast. They have the advantage of high efficiency. However they only give approximate results, whereas we need exact results in some fields. There is a gap between approximate computations and exact results.In this paper, we build a bridge by which exact results can be obtained by numerical approximate computations.
Weakly exact categories and the snake lemma
Jafari, Amir
2009-01-01
We generalize the notion of an exact category and introduce weakly exact categories. A proof of the snake lemma in this general setting is given. Some applications are given to illustrate how one can do homological algebra in a weakly exact category.
Obtaining exact value by approximate computations
2007-01-01
Numerical approximate computations can solve large and complex problems fast.They have the advantage of high efficiency.However they only give approximate results,whereas we need exact results in some fields.There is a gap between approximate computations and exact results. In this paper,we build a bridge by which exact results can be obtained by numerical approximate computations.
Exact propagators in harmonic superspace
Kuzenko, Sergei M.
2004-10-01
Within the background field formulation in harmonic superspace for quantum N = 2 super-Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in arxiv:hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super-Yang-Mills theory.
Exact propagators in harmonic superspace
Kuzenko, S M
2004-01-01
Within the background field formulation in harmonic superspace for quantum N = 2 super Yang-Mills theories, the propagators of the matter, gauge and ghost superfields possess a complicated dependence on the SU(2) harmonic variables via the background vector multiplet. This dependence is shown to simplify drastically in the case of an on-shell vector multiplet. For a covariantly constant background vector multiplet, we exactly compute all the propagators. In conjunction with the covariant multi-loop scheme developed in hep-th/0302205, these results provide an efficient (manifestly N = 2 supersymmetric) technical setup for computing multi-loop quantum corrections to effective actions in N = 2 supersymmetric gauge theories, including the N = 4 super Yang-Mills theory.
Exact Bremsstrahlung and Effective Couplings
Mitev, Vladimir
2015-01-01
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of $\\mathcal{N}=2$ SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the $\\mathcal{N}=4$ SYM ones, we obtain interpolating functions $f(g^2)$ such that a given $\\mathcal{N}=2$ SCFT observable is obtained by replacing in the corresponding $\\mathcal{N}=4$ SYM result the coupling constant by $f(g^2)$. These ``exact effective couplings'' encode the finite, relative renormalization between the $\\mathcal{N}=2$ and the $\\mathcal{N}=4$ gluon propagator, they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
Exact Bremsstrahlung and effective couplings
Mitev, Vladimir; Pomoni, Elli
2016-06-01
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of mathcal{N} = 2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the mathcal{N} = 4 SYM ones, we obtain interpolating functions f ( g 2) such that a given mathcal{N} = 2 SCFT observable is obtained by replacing in the corresponding mathcal{N} = 4 SYM result the coupling constant by f ( g 2). These "exact effective couplings" encode the finite, relative renormalization between the mathcal{N} = 2 and the mathcal{N} = 4 gluon propagator and they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
Exact Bremsstrahlung and effective couplings
Mitev, Vladimir [Mainz Univ. (Germany). Inst. fuer Physik, WA THEP; Humboldt-Univ. Berlin (Germany). Inst. fuer Mathematik und Inst. fuer Physik; Pomoni, Elli [DESY Hamburg (Germany). Theory Group; National Technical Univ., Athens (Greece). Physics Div.
2015-11-15
We calculate supersymmetric Wilson loops on the ellipsoid for a large class of N=2 SCFT using the localization formula of Hama and Hosomichi. From them we extract the radiation emitted by an accelerating heavy probe quark as well as the entanglement entropy following the recent works of Lewkowycz-Maldacena and Fiol-Gerchkovitz-Komargodski. Comparing our results with the N=4 SYM ones, we obtain interpolating functions f(g{sup 2}) such that a given N=2 SCFT observable is obtained by replacing in the corresponding N=4 SYM result the coupling constant by f(g{sup 2}). These ''exact effective couplings'' encode the finite, relative renormalization between the N = 2 and the N = 4 gluon propagator, they interpolate between the weak and the strong coupling. We discuss the range of their applicability.
Dorlas, T. C.; Thomas, E. G. F.
2008-01-01
We construct a genuine Radon measure with values in B(l(2)(Z(d))) on the set of paths in Z(d) representing Feynman's integral for the discrete Laplacian on l(2)(Z(d)), and we prove the Feynman integral formula for the solutions of the Schrodinger equation with Hamiltonian H=-1/2 Delta+ V, where Delt
Bergstra, J.A.; Baeten, J.C.M.
1996-01-01
The axiom system ACP of [BeK84a] was extended with real time features in [BaB91]. Here we proceed to define a discrete time extension of ACP, along the lines of ATP [NiS94]. We present versions based on relative timing and on absolute timing. Both approaches are integrated using parametric timing. T
de Wild Propitius, M.D.F.; Bais, F.A.
1999-01-01
In these lectures, we present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group $H$ via the Higgs mechanism. The main focus is on the discrete $H$ gauge theory describing the long distance physics of such a model. The spectrum features global $H$ cha
Exact solutions to model surface and volume charge distributions
Mukhopadhyay, S.; Majumdar, N.; Bhattacharya, P.; Jash, A.; Bhattacharya, D. S.
2016-10-01
Many important problems in several branches of science and technology deal with charges distributed along a line, over a surface and within a volume. Recently, we have made use of new exact analytic solutions of surface charge distributions to develop the nearly exact Boundary Element Method (neBEM) toolkit. This 3D solver has been successful in removing some of the major drawbacks of the otherwise elegant Green's function approach and has been found to be very accurate throughout the computational domain, including near- and far-field regions. Use of truly distributed singularities (in contrast to nodally concentrated ones) on rectangular and right-triangular elements used for discretizing any three-dimensional geometry has essentially removed many of the numerical and physical singularities associated with the conventional BEM. In this work, we will present this toolkit and the development of several numerical models of space charge based on exact closed-form expressions. In one of the models, Particles on Surface (ParSur), the space charge inside a small elemental volume of any arbitrary shape is represented as being smeared on several surfaces representing the volume. From the studies, it can be concluded that the ParSur model is successful in getting the estimates close to those obtained using the first-principles, especially close to and within the cell. In the paper, we will show initial applications of ParSur and other models in problems related to high energy physics.
Discrete Variational Approach for Modeling Laser-Plasma Interactions
Reyes, J. Paxon; Shadwick, B. A.
2014-10-01
The traditional approach for fluid models of laser-plasma interactions begins by approximating fields and derivatives on a grid in space and time, leading to difference equations that are manipulated to create a time-advance algorithm. In contrast, by introducing the spatial discretization at the level of the action, the resulting Euler-Lagrange equations have particular differencing approximations that will exactly satisfy discrete versions of the relevant conservation laws. For example, applying a spatial discretization in the Lagrangian density leads to continuous-time, discrete-space equations and exact energy conservation regardless of the spatial grid resolution. We compare the results of two discrete variational methods using the variational principles from Chen and Sudan and Brizard. Since the fluid system conserves energy and momentum, the relative errors in these conserved quantities are well-motivated physically as figures of merit for a particular method. This work was supported by the U. S. Department of Energy under Contract No. DE-SC0008382 and by the National Science Foundation under Contract No. PHY-1104683.
p-form electromagnetism on discrete spacetimes
Wise, Derek K [Department of Mathematics, University of California, Riverside, CA 92521 (United States)
2006-09-07
We investigate p-form electromagnetism-with the Maxwell and Kalb-Ramond fields as lowest-order cases-on discrete spacetimes, including not only the regular lattices commonly used in lattice gauge theory, but also more general examples. After constructing a maximally general model of discrete spacetime suitable for our purpose-a chain complex equipped with an inner product on (p + 1)-cochains-we study both the classical and quantum versions of the theory, with either R or U(1) as gauge group. We find results-such as a 'p-form Bohm-Aharonov effect'-that depend in interesting ways on the cohomology of spacetime. We quantize the theory via the Euclidean path integral formalism, where the natural kernels in the U(1) theory are not Gaussians but theta functions. As a special case of the general theory, we show that p-form electromagnetism in p + 1 dimensions has an exact solution which reduces when p = 1 to the Abelian case of 2D Yang-Mills theory as studied by Migdal and Witten. Our main result describes p-form electromagnetism as a 'chain field theory'-a theory analogous to a topological quantum field theory, but with chain complexes replacing manifolds. This makes precise a notion of time evolution in the context of discrete spacetimes of arbitrary topology.
ZHANG Ming-Jiang; FANG Jian-Hui; LU Kai; ZHANG Ke-Jun; LI Yan
2009-01-01
The perturbation to Noether symmetry and Noether adiabatic invariants of general discrete holonomic systems are studied.First,the discrete Noether exact invariant induced directly from the Noether symmetry of the system without perturbation is given.Secondly,the concept of discrete high-order adiabatic invariant is presented,the criterion of the perturbation to Noether symmetry is established,and the discrete Noether adiabatic invariant induced directly from the perturbation to Noether symmetry is obtained.Lastly,an example is discussed to illustrate the application of the results.
Boundary Control of Linear Evolution PDEs - Continuous and Discrete
Rasmussen, Jan Marthedal
2004-01-01
of literature exists in the area of theoretical results concerning control of partial differential equations. The results have included existence and uniqueness of controls, minimum time requirements, regularity of domains, and many others. Another huge research field is that of control theory for ordinary di......- and exact controllability. We will consider discrete systems with a viewpoint similar to that used for the continuous systems. Most importantly, we study what is required of a discretization scheme in order for computed control functions to converge to the true, continuous, control function. Examples exist...
Ferreira, L. A.; Shnir, Ya.
2017-09-01
We introduce a Skyrme type model with the target space being the sphere S3 and with an action possessing, as usual, quadratic and quartic terms in field derivatives. The novel character of the model is that the strength of the couplings of those two terms are allowed to depend upon the space-time coordinates. The model should therefore be interpreted as an effective theory, such that those couplings correspond in fact to low energy expectation values of fields belonging to a more fundamental theory at high energies. The theory possesses a self-dual sector that saturates the Bogomolny bound leading to an energy depending linearly on the topological charge. The self-duality equations are conformally invariant in three space dimensions leading to a toroidal ansatz and exact self-dual Skyrmion solutions. Those solutions are labelled by two integers and, despite their toroidal character, the energy density is spherically symmetric when those integers are equal and oblate or prolate otherwise.
On the exact calculation of the mean stock level in the base stock periodic review policy
Eugenia Babiloni
2011-07-01
Full Text Available Purpose: One of the most usual indicators to measure the performance of any inventory policy is the mean stock level. In the generalized base stock, periodic review policy, the expected mean stock during the replenishment cycle is usually estimated by practitioners and researchers with the traditional Hadley-Whitin approximation. However it is not accurate enough and exact methods suggested on the related literature focus on specific demand distributions. This paper proposes a generalized method to compute the exact value of the expected mean stock to be used when demand is modelled by any uncorrelated, discrete and stationary demand pattern.Design/methodology/approach: The suggested method is based on computing the probability of every stock level at every point of the replenishment cycle for which it is required to know the probability of any stock level at the beginning of the cycle and the probability transition matrix between two consecutive periods of time. Furthermore, the traditional Hadley-Whitin approximation is compared with the proposed exact method over different discrete demand distributionsFindings: This paper points out the lack of accuracy that the Hadley-Whitin approximation shows over a wide range of service levels and discrete demand distributions. Research limitations/implications: The suggested method requires the availability of appropriate tools as well as a sound mathematical background. For this reason, approximations to it are the logical further research of this work. Practical implications: The use of the Hadley-Whitin approximation instead of an exact method can lead to underestimate systematically the expected mean stock level. This fact may increase total costs of the inventory system.Originality/value: The original derivation of an exact method to compute the expected mean stock level for the base stock, periodic review policy when demand is modelled by any discrete function and backlog is not allowed.
Sirenko, Kostyantyn
2013-07-01
Exact absorbing and periodic boundary conditions allow to truncate grating problems\\' infinite physical domains without introducing any errors. This work presents exact absorbing boundary conditions for 3D diffraction gratings and describes their discretization within a high-order time-domain discontinuous Galerkin finite element method (TD-DG-FEM). The error introduced by the boundary condition discretization matches that of the TD-DG-FEM; this results in an optimal solver in terms of accuracy and computation time. Numerical results demonstrate the superiority of this solver over TD-DG-FEM with perfectly matched layers (PML)-based domain truncation. © 2013 IEEE.
Discrete mathematics with applications
Koshy, Thomas
2003-01-01
This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects*...
Brunner, Ilka; Plencner, Daniel
2014-01-01
Orbifolding two-dimensional quantum field theories by a symmetry group can involve a choice of discrete torsion. We apply the general formalism of `orbifolding defects' to study and elucidate discrete torsion for topological field theories. In the case of Landau-Ginzburg models only the bulk sector had been studied previously, and we re-derive all known results. We also introduce the notion of `projective matrix factorisations', show how they naturally describe boundary and defect sectors, and we further illustrate the efficiency of the defect-based approach by explicitly computing RR charges. Roughly half of our results are not restricted to Landau-Ginzburg models but hold more generally, for any topological field theory. In particular we prove that for a pivotal bicategory, any two objects of its orbifold completion that have the same base are orbifold equivalent. Equivalently, from any orbifold theory (including those based on nonabelian groups) the original unorbifolded theory can be be obtained by orbifo...
Discrete Variational Optimal Control
Jimenez, Fernando; de Diego, David Martin
2012-01-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher-dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical and a practical examples, e.g. the control of an underwater vehicle, will illustrate the application of the proposed approach.
Discrete Variational Optimal Control
Jiménez, Fernando; Kobilarov, Marin; Martín de Diego, David
2013-06-01
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of variational principles. The key point is to solve the optimal control problem as a variational integrator of a specially constructed higher dimensional system. The developed framework applies to systems on tangent bundles, Lie groups, and underactuated and nonholonomic systems with symmetries, and can approximate either smooth or discontinuous control inputs. The resulting methods inherit the preservation properties of variational integrators and result in numerically robust and easily implementable algorithms. Several theoretical examples and a practical one, the control of an underwater vehicle, illustrate the application of the proposed approach.
Salinelli, Ernesto
2014-01-01
This book provides an introduction to the analysis of discrete dynamical systems. The content is presented by an unitary approach that blends the perspective of mathematical modeling together with the ones of several discipline as Mathematical Analysis, Linear Algebra, Numerical Analysis, Systems Theory and Probability. After a preliminary discussion of several models, the main tools for the study of linear and non-linear scalar dynamical systems are presented, paying particular attention to the stability analysis. Linear difference equations are studied in detail and an elementary introduction of Z and Discrete Fourier Transform is presented. A whole chapter is devoted to the study of bifurcations and chaotic dynamics. One-step vector-valued dynamical systems are the subject of three chapters, where the reader can find the applications to positive systems, Markov chains, networks and search engines. The book is addressed mainly to students in Mathematics, Engineering, Physics, Chemistry, Biology and Economic...
Time Discretization Techniques
Gottlieb, S.
2016-10-12
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Steerable Discrete Cosine Transform
Fracastoro, Giulia; Fosson, Sophie; Magli, Enrico
2017-01-01
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely, a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, an...
Pinheiro Ladalardo, Thereza C. C. G.; Cappellette, Mario, Jr.; Zanin, Fatima A. A.; Brugnera, Aldo, Jr.; Anthero de Azevedo, Ramiro; Pignatari, Shirley; Weckx, Luc L. M.
2003-06-01
Mouth breathing unbalances the physiological mechanisms of the dental surface hydration by compromising lip closure, and, very often, causing the vestibular positioning of upper incisors. That variance leads to the interruption of the dental demineralization and remineralization feedback, prevailing a demineralized condition of the dental surface which increases caries risk. The laser fluorescence examination allows an early demineralization diagnosis, thus it makes possible through preventive measures to minimize the risk factor - dental mineral structure loss - in the bacterial infection of the demineralized area, and hence, preventing invasive therapeutical procedures. A DIAGNOdent apparatus was used to evaluate the mineralization degree of the upper central incisors in 40 patients - twenty of them with a mouth breathing diagnosis; the remaining twenty were nasal breathers (control group). Age ranging from 6 to 12 years, both male and female. To measure the vestibular surface of the incisors, it was divided into 3 segments: cervical, medial and incisal. The average of the results pertaining to the mouth breathing patients was as follows: tooth 11 cervical third - 5.45, medial third - 7.15, incisal third - 7.95, and tooth 21 - cervical third - 5.95, medial third - 7.25, incisal third - 8.15. The control patients, nasal breathers, presented the following results: tooth 11 cervical third - 1.75, medial third - 2.30, incisal third - 1.85, and tooth 21 - cervical third - 1.80, medial third - 2.20, incisal third - 2.15. The mouth breathing patients showed demineralization in the teeth examined at the initial stage, subclinical, comparing with the control patients, nasal breathers, who did not present any mineral deficit in these teeth.
Wang, Lei; Zhang, Jian-Hui; Liu, Chong; Li, Min; Qi, Feng-Hua
2016-06-01
We study a variable-coefficient nonlinear Schrödinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multipeak solitons, antidark soliton, periodic wave, and W -shaped soliton. In particular, the transition condition requiring the group velocity dispersion (GVD) and third-order dispersion (TOD) to scale linearly is obtained analytically. We display several kinds of elastic interactions between the transformed nonlinear waves. We discuss the dispersion management of the multipeak soliton, which indicates that the GVD coefficient controls the number of peaks of the wave while the TOD coefficient has compression effect. The gain or loss has influence on the amplitudes of the multipeak soliton. We further derive the breather multiple births and Peregrine combs by using multiple compression points of Akhmediev breathers and Peregrine rogue waves in optical fiber systems with periodic GVD modulation. In particular, we demonstrate that the Peregrine comb can be converted into a Peregrine wall by the proper choice of the amplitude of the periodic GVD modulation. The Peregrine wall can be seen as an intermediate state between rogue waves and W -shaped solitons. We finally find that the modulational stability regions with zero growth rate coincide with the transition condition using rogue wave eigenvalues. Our results could be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in diverse physical systems modeled by vc-NLS equation with higher-order effects.
Exact Solutions in Modified Gravity Models
Valery V. Obukhov
2012-06-01
Full Text Available We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.
Exact Solutions in Modified Gravity Models
Makarenko, Andrey N
2012-01-01
We review the exact solutions in modified gravity. It is one of the main problems of mathematical physics for the gravity theory. One can obtain an exact solution if the field equations reduce to a system of ordinary differential equations. In this paper we consider a number of exact solutions obtained by the method of separation of variables. Some applications to Cosmology and BH entropy are briefly mentioned.
Exact Surface States in Photonic Superlattices
Xie, Qiongtao
2012-01-01
We develop an analytical method to derive exact surface states in photonic superlattices. In a kind of infinite bichromatic superlattices satisfying some certain conditions, we analytically obtain their in-gap states, which are superpositions of finite numbers of unstable Bloch waves. By using the unstable in-gap states, we construct exactly several stable surface states in various photonic superlattices. We analytically explore the parametric dependence of these exact surface states. Our analysis provides an exact demonstration for the existence of surface states and would be also helpful to understand surface states in other lattice systems.
3D particle tracking velocimetry using dynamic discrete tomography
Alpers, Andreas; Moseev, Dmitry; Salewski, Mirko
2013-01-01
Particle tracking velocimetry in 3D is becoming an increasingly important imaging tool in the study of fluid dynamics, combustion as well as plasmas. We introduce a dynamic discrete tomography algorithm for reconstructing particle trajectories from projections. The algorithm is efficient for data from two projection directions and exact in the sense that it finds a solution consistent with the experimental data. Non-uniqueness of solutions can be detected and solutions can be tracked individually.
3D particle tracking velocimetry using dynamic discrete tomography
Alpers, Andreas; Gritzmann, Peter; Moseev, Dmitry
2015-01-01
Particle tracking velocimetry in 3D is becoming an increasingly important imaging tool in the study of fluid dynamics and combustion as well as plasmas. We introduce a dynamic discrete tomography algorithm for reconstructing particle trajectories from projections. The algorithm is efficient...... for data from two projection directions and exact in the sense that it finds a solution consistent with the experimental data. Non-uniqueness of solutions can be detected and solutions can be tracked individually....
From discrete particles to continuum fields near a boundary
Weinhart, T.; Thornton, A R; Luding, S.; Bokhove, O
2011-01-01
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents’ degrees of freedom and interaction forces. Starting point is the exact and general coarse graining formulation presented by Goldhirsch in [I.Goldhirsch, Gran.Mat., 12(3):239-252, 2010], which is consistent with the continuum equations everywhere but does not account for boundaries. Our extension accounts for the boundary interaction forces in a self...
New treatment of breakup continuum in the method of continuum discretized coupled channels
Matsumoto, T; Ogata, K; Iseri, Y; Hiyama, E; Kamimura, M; Yahiro, M
2003-01-01
In the method of continuum discretized coupled channels (CDCC) for treating three-body processes in projectile breakup reactions, the discretization of continuous breakup channels is essential. We propose a practical method of the discretization. The validity of the method is numerically tested and confirmed for two realistic examples, $d+^{58}$Ni scattering at 80 MeV and $^{6}Li+^{40}$Ca scattering at 156 MeV. Calculated elastic and breakup S-matrix elements based on the new method converge as the number of discretized breakup channels is increased. The converged S-matrix element agrees with the exact one which is derived with average (Av) discretization established as an accurate method. The new discretization requires a smaller number of breakup channels than the Av method. The feasibility of the new method for more complicated reactions is also discussed.
Brauer, Fred; Feng, Zhilan; Castillo-Chavez, Carlos
2010-01-01
The mathematical theory of single outbreak epidemic models really began with the work of Kermack and Mackendrick about decades ago. This gave a simple answer to the long-standing question of why epidemics woould appear suddenly and then disappear just as suddenly without having infected an entire population. Therefore it seemed natural to expect that theoreticians would immediately proceed to expand this mathematical framework both because the need to handle recurrent single infectious disease outbreaks has always been a priority for public health officials and because theoreticians often try to push the limits of exiting theories. However, the expansion of the theory via the inclusion of refined epidemiological classifications or through the incorporation of categories that are essential for the evaluation of intervention strategies, in the context of ongoing epidemic outbreaks, did not materialize. It was the global threat posed by SARS in that caused theoreticians to expand the Kermack-McKendrick single-outbreak framework. Most recently, efforts to connect theoretical work to data have exploded as attempts to deal with the threat of emergent and re-emergent diseases including the most recent H1N1 influenza pandemic, have marched to the forefront of our global priorities. Since data are collected and/or reported over discrete units of time, developing single outbreak models that fit collected data naturally is relevant. In this note, we introduce a discrete-epidemic framework and highlight, through our analyses, the similarities between single-outbreak comparable classical continuous-time epidemic models and the discrete-time models introduced in this note. The emphasis is on comparisons driven by expressions for the final epidemic size.
Exact Discrete Analogs of Derivatives of Integer Orders: Differences as Infinite Series
Vasily E. Tarasov
2015-01-01
Full Text Available New differences of integer orders, which are connected with derivatives of integer orders not approximately, are proposed. These differences are represented by infinite series. A characteristic property of the suggested differences is that its Fourier series transforms have a power-law form. We demonstrate that the proposed differences of integer orders n are directly connected with the derivatives ∂n/∂xn. In contrast to the usual finite differences of integer orders, the suggested differences give the usual derivatives without approximation.
Exact Coleman-de Luccia Instantons
Kanno, Sugumi
2011-01-01
We present exact Coleman-de Luccia (CdL) instantons, which describe vacuum decay from Anti de Sitter (AdS) space, de Sitter (dS) space and Minkowski space to AdS space. We systematically obtain these exact solutions by considering deformation of Hawking-Moss (HM) instantons. We analytically calculate decay rates and discuss a subtlety in the interpretation.
Exact Solutions for Einstein's Hyperbolic Geometric Flow
HE Chun-Lei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.
Conjugation-uniqueness of exact Borel subalgebras
张跃辉
1999-01-01
It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other. Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.
Exact, almost and delayed fault detection
Niemann, Hans Henrik; Saberi, Ali; Stoorvogel, Anton A.;
1999-01-01
Considers the problem of fault detection and isolation while using zero or almost zero threshold. A number of different fault detection and isolation problems using exact or almost exact disturbance decoupling are formulated. Solvability conditions are given for the formulated design problems. Th...
An alternative to exact renormalization equations
Alexandre, Jean
2005-01-01
An alternative point of view to exact renormalization equations is discussed, where quantum fluctuations of a theory are controlled by the bare mass of a particle. The procedure is based on an exact evolution equation for the effective action, and recovers usual renormalization results.
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
Probabilistic flood forecast: Exact and approximate predictive distributions
Krzysztofowicz, Roman
2014-09-01
For quantification of predictive uncertainty at the forecast time t0, the future hydrograph is viewed as a discrete-time continuous-state stochastic process {Hn: n=1,…,N}, where Hn is the river stage at time instance tn>t0. The probabilistic flood forecast (PFF) should specify a sequence of exceedance functions {F‾n: n=1,…,N} such that F‾n(h)=P(Zn>h), where P stands for probability, and Zn is the maximum river stage within time interval (t0,tn], practically Zn=max{H1,…,Hn}. This article presents a method for deriving the exact PFF from a probabilistic stage transition forecast (PSTF) produced by the Bayesian forecasting system (BFS). It then recalls (i) the bounds on F‾n, which can be derived cheaply from a probabilistic river stage forecast (PRSF) produced by a simpler version of the BFS, and (ii) an approximation to F‾n, which can be constructed from the bounds via a recursive linear interpolator (RLI) without information about the stochastic dependence in the process {H1,…,Hn}, as this information is not provided by the PRSF. The RLI is substantiated by comparing the approximate PFF against the exact PFF. Being reasonably accurate and very simple, the RLI may be attractive for real-time flood forecasting in systems of lesser complexity. All methods are illustrated with a case study for a 1430 km headwater basin wherein the PFF is produced for a 72-h interval discretized into 6-h steps.
Discrete flavor symmetries in D-brane models
Marchesano, Fernando; Vázquez-Mercado, Liliana
2013-01-01
We study the presence of discrete flavor symmetries in D-brane models of particle physics. By analyzing the compact extra dimensions of these models one can determine when such symmetries exist both in the context of intersecting and magnetized D-brane constructions. Our approach allows to distinguish between approximate and exact discrete symmetries, and it can be applied to compactification manifolds with continuous isometries or to manifolds that only contain discrete isometries, like Calabi-Yau three-folds. We analyze in detail the class of rigid D-branes models based on a Z_2 x Z'_2 toroidal orientifold, for which the flavor symmetry group is either the dihedral group D_4 or tensor products of it. We construct explicit Pati-Salam examples in which families transform in non-Abelian representations of the flavor symmetry group, constraining Yukawa couplings beyond the effect of massive U(1) D-brane symmetries.
Efficient and exact maximum likelihood quantisation of genomic features using dynamic programming.
Song, Mingzhou; Haralick, Robert M; Boissinot, Stéphane
2010-01-01
An efficient and exact dynamic programming algorithm is introduced to quantise a continuous random variable into a discrete random variable that maximises the likelihood of the quantised probability distribution for the original continuous random variable. Quantisation is often useful before statistical analysis and modelling of large discrete network models from observations of multiple continuous random variables. The quantisation algorithm is applied to genomic features including the recombination rate distribution across the chromosomes and the non-coding transposable element LINE-1 in the human genome. The association pattern is studied between the recombination rate, obtained by quantisation at genomic locations around LINE-1 elements, and the length groups of LINE-1 elements, also obtained by quantisation on LINE-1 length. The exact and density-preserving quantisation approach provides an alternative superior to the inexact and distance-based univariate iterative k-means clustering algorithm for discretisation.
EXACT2: the semantics of biomedical protocols.
Soldatova, Larisa N; Nadis, Daniel; King, Ross D; Basu, Piyali S; Haddi, Emma; Baumlé, Véronique; Saunders, Nigel J; Marwan, Wolfgang; Rudkin, Brian B
2014-01-01
The reliability and reproducibility of experimental procedures is a cornerstone of scientific practice. There is a pressing technological need for the better representation of biomedical protocols to enable other agents (human or machine) to better reproduce results. A framework that ensures that all information required for the replication of experimental protocols is essential to achieve reproducibility. To construct EXACT2 we manually inspected hundreds of published and commercial biomedical protocols from several areas of biomedicine. After establishing a clear pattern for extracting the required information we utilized text-mining tools to translate the protocols into a machine amenable format. We have verified the utility of EXACT2 through the successful processing of previously 'unseen' (not used for the construction of EXACT2)protocols. We have developed the ontology EXACT2 (EXperimental ACTions) that is designed to capture the full semantics of biomedical protocols required for their reproducibility. The paper reports on a fundamentally new version EXACT2 that supports the semantically-defined representation of biomedical protocols. The ability of EXACT2 to capture the semantics of biomedical procedures was verified through a text mining use case. In this EXACT2 is used as a reference model for text mining tools to identify terms pertinent to experimental actions, and their properties, in biomedical protocols expressed in natural language. An EXACT2-based framework for the translation of biomedical protocols to a machine amenable format is proposed. The EXACT2 ontology is sufficient to record, in a machine processable form, the essential information about biomedical protocols. EXACT2 defines explicit semantics of experimental actions, and can be used by various computer applications. It can serve as a reference model for for the translation of biomedical protocols in natural language into a semantically-defined format.
Schunert, Sebastian; Azmy, Yousry Y., E-mail: snschune@ncsu.edu, E-mail: yyazmy@ncsu.edu [Department of Nuclear Engineering, North Carolina State University, Raleigh, NC (United States); Fournier, Damien; Le Tellier, Romain, E-mail: damien.fournier@cea.fr, E-mail: romain.le-tellier@cea.fr [CEA, DEN, DER/SPRC/LEPh, Cadarache, Saint Paul-lez-Durance (France)
2011-07-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen's benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semi analytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation. (author)
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
Sebastian Schunert; Yousry Y. Azmy; Damien Fournier
2011-05-01
We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the discontinuous Galerkin Finite Element method (DGFEM) and the recently proposed higher order diamond difference method (HODD) of spatial expansion orders 0 through 3. While AHOTN and AHOTC rely on approximate analytical solutions of the transport equation within a mesh cell, DGFEM and HODD utilize a polynomial expansion to mimick the angular flux profile across each mesh cell. Intuitively, due to the higher degree of analyticity, we expect AHOTN and AHOTC to feature superior accuracy compared with DGFEM and HODD, but at the price of potentially longer grind times and numerical instabilities. The latter disadvantages can result from the presence of exponential terms evaluated at the cell optical thickness that arise from the semianalytical solution process. This work quantifies the order of accuracy and the magnitude of the error of all four discretization methods for different optical thicknesses, scattering ratios and degrees of smoothness of the underlying exact solutions in order to verify or contradict the aforementioned intuitive expectation.
An Algebraic Method for Constructing Exact Solutions to Difference-Differential Equations
无
2006-01-01
In this paper, we present a method to solve difference differential equation(s). As an example, we apply this method to discrete KdV equation and Ablowitz-Ladik lattice equation. As a result, many exact solutions are obtained with the help of Maple including soliton solutions presented by hyperbolic functions sinh and cosh, periodic solutions presented by sin and cos and rational solutions. This method can also be used to other nonlinear difference-differential equation(s).
An exact solution on the ferromagnetic Face-Cubic spin model on a Bethe lattice
Ohanyan, V. R.; Ananikyan, L. N.; Ananikian, N. S.
2006-01-01
The lattice spin model with $Q$--component discrete spin variables restricted to have orientations orthogonal to the faces of $Q$-dimensional hypercube is considered on the Bethe lattice, the recursive graph which contains no cycles. The partition function of the model with dipole--dipole and quadrupole--quadrupole interaction for arbitrary planar graph is presented in terms of double graph expansions. The latter is calculated exactly in case of trees. The system of two recurrent relations wh...
State exact reconstruction for switched linear systems via a super-twisting algorithm
Bejarano, Francisco J.; Fridman, Leonid
2011-05-01
This article discusses the problem of state reconstruction synthesis for switched linear systems. Based only on the continuous output information, an observer is proposed ensuring the reconstruction of the entire state (continuous and discrete) in finite time. For the observer design an exact sliding mode differentiator is used, which allows the finite time convergence of the observer trajectories to the actual trajectories. The design scheme includes both cases: zero control input and nonzero control input. Simulations illustrate the effectiveness of the proposed observer.
Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm
LUO Xu-Dong; GUO Han-Ying; LI Yu-Qi; WU Ke
2004-01-01
We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory.
Modélisation des effets capillaires en mécanique des milieux discrets
Caltagirone, Jean-Paul
2016-01-01
The modeling of the capillary effects is approached starting from the concepts developed in discrete mechanics. The capillary force is supported by the edge on which is derived the discrete momentum equation. The formulation presented and the numerical methodology put in work make it possible to find exactly simple analytical solutions like the law of Laplace. A very detailed attention is devoted to obtaining the at rest state of drops, bubbles, or meniscuses; it is shown that these static st...
Mishchenko, Michael I.; Dlugach, Janna M.; Yurkin, Maxim A.; Bi, Lei; Cairns, Brian; Liu, Li; Panetta, R. Lee; Travis, Larry D.; Yang, Ping; Zakharova, Nadezhda T.
2016-05-01
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell's equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of
Mishchenko, Michael I., E-mail: michael.i.mishchenko@nasa.gov [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Dlugach, Janna M. [Main Astronomical Observatory of the National Academy of Sciences of Ukraine, 27 Zabolotny Str., 03680, Kyiv (Ukraine); Yurkin, Maxim A. [Voevodsky Institute of Chemical Kinetics and Combustion, SB RAS, Institutskaya str. 3, 630090 Novosibirsk (Russian Federation); Novosibirsk State University, Pirogova 2, 630090 Novosibirsk (Russian Federation); Bi, Lei [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Cairns, Brian [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Liu, Li [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Columbia University, 2880 Broadway, New York, NY 10025 (United States); Panetta, R. Lee [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Travis, Larry D. [NASA Goddard Institute for Space Studies, 2880 Broadway, New York, NY 10025 (United States); Yang, Ping [Department of Atmospheric Sciences, Texas A& M University, College Station, TX 77843 (United States); Zakharova, Nadezhda T. [Trinnovim LLC, 2880 Broadway, New York, NY 10025 (United States)
2016-05-16
A discrete random medium is an object in the form of a finite volume of a vacuum or a homogeneous material medium filled with quasi-randomly and quasi-uniformly distributed discrete macroscopic impurities called small particles. Such objects are ubiquitous in natural and artificial environments. They are often characterized by analyzing theoretically the results of laboratory, in situ, or remote-sensing measurements of the scattering of light and other electromagnetic radiation. Electromagnetic scattering and absorption by particles can also affect the energy budget of a discrete random medium and hence various ambient physical and chemical processes. In either case electromagnetic scattering must be modeled in terms of appropriate optical observables, i.e., quadratic or bilinear forms in the field that quantify the reading of a relevant optical instrument or the electromagnetic energy budget. It is generally believed that time-harmonic Maxwell’s equations can accurately describe elastic electromagnetic scattering by macroscopic particulate media that change in time much more slowly than the incident electromagnetic field. However, direct solutions of these equations for discrete random media had been impracticable until quite recently. This has led to a widespread use of various phenomenological approaches in situations when their very applicability can be questioned. Recently, however, a new branch of physical optics has emerged wherein electromagnetic scattering by discrete and discretely heterogeneous random media is modeled directly by using analytical or numerically exact computer solutions of the Maxwell equations. Therefore, the main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell–Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell–Lorentz equations, we trace the development
Poisson hierarchy of discrete strings
Ioannidou, Theodora, E-mail: ti3@auth.gr [Faculty of Civil Engineering, School of Engineering, Aristotle University of Thessaloniki, 54249, Thessaloniki (Greece); Niemi, Antti J., E-mail: Antti.Niemi@physics.uu.se [Department of Physics and Astronomy, Uppsala University, P.O. Box 803, S-75108, Uppsala (Sweden); Laboratoire de Mathematiques et Physique Theorique CNRS UMR 6083, Fédération Denis Poisson, Université de Tours, Parc de Grandmont, F37200, Tours (France); Department of Physics, Beijing Institute of Technology, Haidian District, Beijing 100081 (China)
2016-01-28
The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Exact Renormalization Group for Point Interactions
Eröncel, Cem
2014-01-01
Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble non-abelian gauge theories, yet it can be treated exactly in this nontrivial geometry.
Quaternionic formulation of the exact parity model
Brumby, S.P.; Foot, R.; Volkas, R.R.
1996-02-28
The exact parity model (EPM) is a simple extension of the standard model which reinstates parity invariance as an unbroken symmetry of nature. The mirror matter sector of the model can interact with ordinary matter through gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through neutrino mixing. The last effect has experimental support through the observed solar and atmospheric neutrino anomalies. In the paper it is shown that the exact parity model can be formulated in a quaternionic framework. This suggests that the idea of mirror matter and exact parity may have profound implications for the mathematical formulation of quantum theory. 13 refs.
EXACT RENORMALIZATION GROUP FOR POINT INTERACTIONS
Osman Teoman Turgut Teoman Turgut
2014-04-01
Full Text Available Renormalization is one of the deepest ideas in physics, yet its exact implementation in any interesting problem is usually very hard. In the present work, following the approach by Glazek and Maslowski in the flat space, we will study the exact renormalization of the same problem in a nontrivial geometric setting, namely in the two dimensional hyperbolic space. Delta function potential is an asymptotically free quantum mechanical problem which makes it resemble nonabelian gauge theories, yet it can be treated exactly in this nontrivial geometry.
Discrete R Symmetries and Anomalies
Michael Dine(Santa Cruz Institute for Particle Physics and Department of Physics, Santa Cruz CA 95064, U.S.A.); Angelo Monteux(Santa Cruz Institute for Particle Physics, University of California Santa Cruz, 1156 High Street, Santa Cruz, U.S.A.)
2012-01-01
We comment on aspects of discrete anomaly conditions focussing particularly on $R$ symmetries. We review the Green-Schwarz cancellation of discrete anomalies, providing a heuristic explanation why, in the heterotic string, only the "model-independent dilaton" transforms non-linearly under discrete symmetries; this argument suggests that, in other theories, multiple fields might play a role in anomaly cancellations, further weakening any anomaly constraints at low energies. We provide examples...
LIHua-Mei; LINJi; XUYou-Sheng
2005-01-01
In this paper, we extend the hyperbolic function approach for constructing the exact solutions of nonlinear differential-difference equation (NDDE) in a unified way. Applying the extended approach and with the aid of Maple,we have studied the discrete complex Ginzburg-Landau equation (dCGLE). As a result, we find a set of exact solutions which include bright and dark soliton solutions.
Steerable Discrete Cosine Transform
Fracastoro, Giulia; Fosson, Sophie M.; Magli, Enrico
2017-01-01
In image compression, classical block-based separable transforms tend to be inefficient when image blocks contain arbitrarily shaped discontinuities. For this reason, transforms incorporating directional information are an appealing alternative. In this paper, we propose a new approach to this problem, namely a discrete cosine transform (DCT) that can be steered in any chosen direction. Such transform, called steerable DCT (SDCT), allows to rotate in a flexible way pairs of basis vectors, and enables precise matching of directionality in each image block, achieving improved coding efficiency. The optimal rotation angles for SDCT can be represented as solution of a suitable rate-distortion (RD) problem. We propose iterative methods to search such solution, and we develop a fully fledged image encoder to practically compare our techniques with other competing transforms. Analytical and numerical results prove that SDCT outperforms both DCT and state-of-the-art directional transforms.
Discrete Thermodynamics of Lasers
Zilbergleyt, B
2007-01-01
The paper offers a discrete thermodynamic model of lasers. Laser is an open system; its equilibrium is based on a balance of two thermodynamic forces, one related to the incoming pumping power and another to the emitted light. The basic expression for such equilibrium is a logistic map, graphical solutions to which are pitchfork bifurcation diagrams. As pumping force increases, the relative populations on the ground and lasing branches tend to zero and unity correspondingly. An interesting feature of this model is the line spectrum of the up and down transitions between the branches beyond bifurcation point. Even in a simple case of 2-level laser with only 2 possible transition types (up and down), the spectra look like sets of the line packets, starting well before the population inversion. This effect is an independent confirmation of the Einstein's prohibition on practical realization of 2-level laser. Multilevel lasers may be approached by employing the idea of thermodynamic activity for the emitting atom...
Noyes, H. Pierre; Starson, Scott
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields with the relativistic Wheeler-Feynman action at a distance, allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound.
Noyes, H.P. (Stanford Linear Accelerator Center, Menlo Park, CA (USA)); Starson, S. (STARSON Corp. (USA))
1991-03-01
Discrete physics, because it replaces time evolution generated by the energy operator with a global bit-string generator (program universe) and replaces fields'' with the relativistic Wheeler-Feynman action at a distance,'' allows the consistent formulation of the concept of signed gravitational charge for massive particles. The resulting prediction made by this version of the theory is that free anti-particles near the surface of the earth will fall'' up with the same acceleration that the corresponding particles fall down. So far as we can see, no current experimental information is in conflict with this prediction of our theory. The experiment crusis will be one of the anti-proton or anti-hydrogen experiments at CERN. Our prediction should be much easier to test than the small effects which those experiments are currently designed to detect or bound. 23 refs.
Discrete Pearson distributions
Bowman, K.O. [Oak Ridge National Lab., TN (United States); Shenton, L.R. [Georgia Univ., Athens, GA (United States); Kastenbaum, M.A. [Kastenbaum (M.A.), Basye, VA (United States)
1991-11-01
These distributions are generated by a first order recursive scheme which equates the ratio of successive probabilities to the ratio of two corresponding quadratics. The use of a linearized form of this model will produce equations in the unknowns matched by an appropriate set of moments (assumed to exist). Given the moments we may find valid solutions. These are two cases; (1) distributions defined on the non-negative integers (finite or infinite) and (2) distributions defined on negative integers as well. For (1), given the first four moments, it is possible to set this up as equations of finite or infinite degree in the probability of a zero occurrence, the sth component being a product of s ratios of linear forms in this probability in general. For (2) the equation for the zero probability is purely linear but may involve slowly converging series; here a particular case is the discrete normal. Regions of validity are being studied. 11 refs.
Immigration and Prosecutorial Discretion.
Apollonio, Dorie; Lochner, Todd; Heddens, Myriah
Immigration has become an increasingly salient national issue in the US, and the Department of Justice recently increased federal efforts to prosecute immigration offenses. This shift, however, relies on the cooperation of US attorneys and their assistants. Traditionally federal prosecutors have enjoyed enormous discretion and have been responsive to local concerns. To consider how the centralized goal of immigration enforcement may have influenced federal prosecutors in regional offices, we review their prosecution of immigration offenses in California using over a decade's worth of data. Our findings suggest that although centralizing forces influence immigration prosecutions, individual US attorneys' offices retain distinct characteristics. Local factors influence federal prosecutors' behavior in different ways depending on the office. Contrary to expectations, unemployment rates did not affect prosecutors' willingness to pursue immigration offenses, nor did local popular opinion about illegal immigration.
McKenzie, Alan
2016-01-01
The Many Worlds Interpretation (MWI) famously avoids the issue of wave function collapse. Different MWI trees representing the same quantum events can have different topologies, depending upon the observer. However, they are all isomorphic to the group of block universes containing all of the outcomes of all of the events, and so, in that sense, the group of block universes is a more fundamental representation. Different branches of the MWI tree, representing different universes in MWI, ultimately share the same quantum state in a common ancestor branch. This branching topology is incompatible with that of the Minkowski block universe; the resolution is to replace the branches with discrete, parallel block universes, each of which extends from the trunk to the outermost twigs. The number of universes in a branch is proportional to its thickness which, in turn, depends upon the absolute square of the probability amplitude for the state in that branch. Every quantum event may be represented by a kernel of unive...
Thermodynamics of discrete quantum processes
Anders, Janet; Giovannetti, Vittorio
2013-03-01
We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete trajectory that consists of a sequence of these primitives, linking both equilibrium and non-equilibrium configurations. Moreover, in the limit of a discrete trajectory that passes through an infinite number of configurations, i.e. in the reversible limit, we recover the saturation of the second law. Finally, we show that for a discrete Carnot cycle operating between four configurations one recovers Carnot's thermal efficiency.
Principles of discrete time mechanics
Jaroszkiewicz, George
2014-01-01
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
Gibbons, Gary W
2013-01-01
In this paper we lay down the foundations for a purely Newtonian theory of cosmology, valid at scales small compared with the Hubble radius, using only Newtonian point particles acted on by gravity and a possible cosmological term. We describe the cosmological background which is given by an exact solution of the equations of motion in which the particles expand homothetically with their comoving positions constituting a central configuration. We point out, using previous work, that an important class of central configurations are homogeneous and isotropic, thus justifying the usual assumptions of elementary treatments. The scale factor is shown to satisfy the standard Raychaudhuri and Friedmann equations without making any fluid dynamic or continuum approximations. Since we make no commitment as to the identity of the point particles, our results are valid for cold dark matter, galaxies, or clusters of galaxies. In future publications we plan to discuss perturbations of our cosmological background from the p...
Badreddine, Fauze Ramez; Fujita, Reginaldo Raimundo; Cappellette, Mario
2017-06-26
Rapid maxillary expansion is an orthodontic and orthopedic procedure that can change the form and function of the nose. The soft tissue of the nose and its changes can influence the esthetics and the stability of the results obtained by this procedure. The objective of this study was to assess the changes in nose dimensions after rapid maxillary expansion (RME) in oral breathers with maxillary atresia, using a reliable and reproducible methodology through computed tomography. A total of 30 mouth-breathing patients with maxillary atresia were analyzed and divided into a treatment group who underwent RME (20 patients, 10 of which were male and 10 female, with a MA of 8.9 years and a SD of 2.16, ranging from 6.5 to 12.5 years) and a Control Group (10 patients, 5 of which were male and 5 female, with a MA of 9.2 years, SD of 2.17, ranging from 6.11 to 13.7 years). In the treatment group, multislice computed tomography scans were obtained at the start of the treatment (T1) and 3 months after expansion (T2). The patients of the control group were submitted to the same exams at the same intervals of time. Four variables related to soft tissue structures of the nose were analyzed (alar base width, alar width, height of soft tissue of the nose and length of soft tissue of the nose), and the outcomes between T1 and T2 were compared using Osirix MD software. In the TG, the soft tissues of the nose exhibited significant increases in all variables studied (p0.05). In the treatment group, mean alar base width increased by 4.87% (p=0.004), mean alar width increased by 4.04% (p=0.004), mean height of the soft tissues of the nose increased by 4.84% (p=0.003) and mean length of the soft tissues of the nose increased by 4.29% (p=0.012). In short-term, RME provided a statistically significant increase in the dimensions of the soft tissues of the nose. Copyright © 2017 Associação Brasileira de Otorrinolaringologia e Cirurgia Cérvico-Facial. Published by Elsevier Editora Ltda. All
Mathematical Models of Quasi-Species Theory and Exact Results for the Dynamics.
Saakian, David B; Hu, Chin-Kun
2016-01-01
We formulate the Crow-Kimura, discrete-time Eigen model, and continuous-time Eigen model. These models are interrelated and we established an exact mapping between them. We consider the evolutionary dynamics for the single-peak fitness and symmetric smooth fitness. We applied the quantum mechanical methods to find the exact dynamics of the evolution model with a single-peak fitness. For the smooth symmetric fitness landscape, we map exactly the evolution equations into Hamilton-Jacobi equation (HJE). We apply the method to the Crow-Kimura (parallel) and Eigen models. We get simple formulas to calculate the dynamics of the maximum of distribution and the variance. We review the existing mathematical tools of quasi-species theory.
Deriving the exact nonadiabatic quantum propagator in the mapping variable representation
Hele, Timothy J H
2016-01-01
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting expression is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact propagator lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated error term for each method. Furthermore, by combining the imaginary-time path-integral representation of the Boltzmann operator with the exact propagator, we obtain an analytic expression for thermal quantum real-time correlation functions. These results provide a rigorous theoretical foundation for the development of accurate and efficient classical-like dynamics to compute observables such as electron transfer reaction r...
Fast Exact Euclidean Distance (FEED) Transformation
Schouten, Theo; Broek, van den Egon; Kittler, J.; Petrou, M.; Nixon, M.
2004-01-01
Fast Exact Euclidean Distance (FEED) transformation is introduced, starting from the inverse of the distance transformation. The prohibitive computational cost of a naive implementation of traditional Euclidean Distance Transformation, is tackled by three operations: restriction of both the number o
An Exact Black Hole Entropy Bound
Birmingham, Daniel; Birmingham, Danny; Sen, Siddhartha
2001-01-01
We show that a Rademacher expansion can be used to establish an exact bound for the entropy of black holes within a conformal field theory framework. This convergent expansion includes all subleading corrections to the Bekenstein-Hawking term.
Exact Mappings in Condensed Matter Physics
Lee, Ching Hua
2016-01-01
Condensed matter systems are complex yet simple. Amidst their complexity, one often find order specified by not more than a few parameters. Key to such a reductionistic description is an appropriate choice of basis, two of which I shall describe in this thesis. The first, an exact mapping known as the Wannier State Representation (WSR), provides an exact Hilbert space correspondence between two intensely-studied topological systems, the Fractional Quantum Hall (FQH) and Fractional Chern Insul...
New exact wave solutions for Hirota equation
M Eslami; M A Mirzazadeh; A Neirameh
2015-01-01
In this paper, we construct the topological or dark solitons of Hirota equation by using the first integral method. This approach provides first integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solution is constructed through the established first integrals. This method is a powerful tool for searching exact travelling solutions of nonlinear partial differential equations (NPDEs) in mathematical physics.
Exactly solvable one-dimensional inhomogeneous models
Derrida, B.; France, M.M.; Peyriere, J.
1986-11-01
The authors present a simple way of constructing one-dimensional inhomogeneous models (random or quasiperiodic) which can be solved exactly. They treat the example of an Ising chain in a varying magnetic field, but their procedure can easily be extended to other one-dimensional inhomogeneous models. For all the models they can construct, the free energy and its derivatives with respect to temperature can be computed exactly at one particular temperature.
Exact Algorithms for Solving Stochastic Games
Hansen, Kristoffer Arnsfelt; Koucky, Michal; Lauritzen, Niels;
2012-01-01
Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games.......Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms for exactly solving these games....
New exact solutions in standard inflationary models
Chervon, S V; Shchigolev, V K
1997-01-01
The exact solutions in the standard inflationary model based on the self-interacting scalar field minimally coupled to gravity are considered. The shape's freedom of the self-interacting potential $V(\\phi)$ is postulated to obtain a new set of the exact solutions in the framework of Friedmann-Robertson-Walker Universes. The general solution was found in the case of power law inflation. We obtained new solutions and compared them with obtained ones earlir for the exponential type inflation.
Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices
Chen, Huaiyu; Liu, Yan; Zhang, Qiang; Shi, Yuhan; Pang, Wei; Li, Yongyao
2016-05-01
We numerically demonstrate two-dimensional (2D) matter-wave solitons in the disk-shaped dipolar Bose-Einstein condensates (BECs) trapped in strongly anisotropic optical lattices (OLs) in a disk's plane. The considered OLs are square lattices which can be formed by interfering two pairs of plane waves with different intensities. The hopping rates of the condensates between two adjacent lattices in the orthogonal directions are different, which gives rise to a linearly anisotropic system. We find that when the polarized orientation of the dipoles is parallel to disk's plane with the same direction, the combined effects of the linearly anisotropy and the nonlocal nonlinear anisotropy strongly influence the formations, as well as the dynamics of the lattice solitons. Particularly, the isotropy-pattern solitons (IPSs) are found when these combined effects reach a balance. Motion, collision, and rotation of the IPSs are also studied in detail by means of systematic simulations. We further find that these IPSs can move freely in the 2D anisotropic discrete system, hence giving rise to an anisotropic effective mass. Four types of collisions between the IPSs are identified. By rotating an external magnetic field up to a critical angular velocity, the IPSs can still remain localized and play as a breather. Finally, the influences from the combined effects between the linear and the nonlocal nonlinear anisotropy with consideration of the contact and/or local nonlinearity are discussed too.
Discrete phase space - II: The second quantization of free relativistic wave fields
Das, A
2008-01-01
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential equations in the arena of discrete phase space and continuous time. The scalar field and electromagnetic fields are quantized with commutation relations. The spin-1/2 field is quantized with anti-commutation relations. Moreover, the total momentum, energy and charge of these free relativisitic quantized fields in the discrete phase space and continuous time are computed exactly. The results agree completely with those computed from the relativisitic fields defned on the space-time continuum.
Discrete dynamics versus analytic dynamics
Toxværd, Søren
2014-01-01
For discrete classical Molecular dynamics obtained by the “Verlet” algorithm (VA) with the time increment h there exists a shadow Hamiltonian H˜ with energy E˜(h) , for which the discrete particle positions lie on the analytic trajectories for H˜ . Here, we proof that there, independent...
Discretization error of Stochastic Integrals
Fukasawa, Masaaki
2010-01-01
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.
Discrete Mathematics and Its Applications
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
Discretization and implicit mapping dynamics
Luo, Albert C J
2015-01-01
This unique book presents the discretization of continuous systems and implicit mapping dynamics of periodic motions to chaos in continuous nonlinear systems. The stability and bifurcation theory of fixed points in discrete nonlinear dynamical systems is reviewed, and the explicit and implicit maps of continuous dynamical systems are developed through the single-step and multi-step discretizations. The implicit dynamics of period-m solutions in discrete nonlinear systems are discussed. The book also offers a generalized approach to finding analytical and numerical solutions of stable and unstable periodic flows to chaos in nonlinear systems with/without time-delay. The bifurcation trees of periodic motions to chaos in the Duffing oscillator are shown as a sample problem, while the discrete Fourier series of periodic motions and chaos are also presented. The book offers a valuable resource for university students, professors, researchers and engineers in the fields of applied mathematics, physics, mechanics,...
Exact solutions for a class of quasi-exactly solvable models: A unified treatment
Hatami, N.; Setare, M. R.
2017-07-01
The exact solution of the Schrödinger equation for the four quasi-exactly solvable potentials is presented using the functional Bethe ansatz method. It is shown that all models give rise to the same basic differential equation which is quasi-exactly solvable. The eigenvalues, eigenfunctions and the allowed potential parameters are given for each of the four models in terms of the roots of a set of algebraic Bethe ansatz equations.
Exact Sequences in Non-Exact Categories (An Application to Semimodules)
Abuhlail, Jawad
2011-01-01
We consider a notion of exact sequences in any -not necessarily exact- pointed category relative to a given (E;M)-factorization structure. We apply this notion to introduce and investigate a new notion of exact sequences of semimodules over semirings relative to the canonical image factorization. Several homological results are proved using the new notion of exactness including some restricted versions of the Short Five Lemma and the Snake Lemma opening the door for introducing and investigating homology objects in such categories. Our results apply in particular to the variety of commutative monoids extending results in homological varieties to relative homological varieties.
Discrete Darboux transformation for discrete polynomials of hypergeometric type
Bangerezako, Gaspard
1998-03-01
The Darboux transformation, well known in second-order differential operator theory, is applied to the difference equations satisfied by the discrete hypergeometric polynomials (Charlier, Meixner-Kravchuk, Hahn).
Classes of exact Einstein Maxwell solutions
Komathiraj, K.; Maharaj, S. D.
2007-12-01
We find new classes of exact solutions to the Einstein Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.
Exact coherent structures for the turbulent cascade
Eckhardt, Bruno; Zammert, Stefan
2016-11-01
The exact coherent structures that are connected with the transition to turbulence in interior flows usually extend across the full height of the domain. Using exact coherent states that are localized in the shear direction together with scaling ideas for the Navier-Stokes equation that combine length and Reynolds number, we show how such large scale structures can be morphed into smaller scale coherent structures. As the Reynolds number increases, more of these states with ever smaller scales appear, all the way down to the Kolmogorov scale. We present the structure and dynamical properties of several families of exact coherent solution in plane Couette flow, with different degrees of spatial localization: Some of them remain localized in the center and help to built the turbulence cascade, others are localized near the walls and contribute to shaping the boundary layer profile.
Supersymmetric QCD: Exact Results and Strong Coupling
Dine, Michael; Pack, Lawrence; Park, Chang-Soon; Ubaldi, Lorenzo; Wu, Weitao
2011-01-01
We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is...
Exact solutions in three-dimensional gravity
Garcia-Diaz, Alberto A
2017-01-01
A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...
Strict System Equivalence of 2D Linear Discrete State Space Models
Mohamed S. Boudellioua
2012-01-01
Full Text Available The connection between the polynomial matrix descriptions (PMDs of the well-known regular and singular 2D linear discrete state space models is considered. It is shown that the transformation of strict system equivalence in the sense of Fuhrmann provides the basis for this connection. The exact form of the transformation is established for both the regular and singular cases.
Risto, M.; Martens, M.H.
2014-01-01
With specific headway instructions drivers are not able to attain the exact headways as instructed. In this study, the effects of discrete headway feedback (and the direction of headway adjustment) on headway accuracy for drivers carrying out time headway instructions were assessed experimentally.
Risto, Malte; Martens, Marieke Hendrikje
2014-01-01
With specific headway instructions drivers are not able to attain the exact headways as instructed. In this study, the effects of discrete headway feedback (and the direction of headway adjustment) on headway accuracy for drivers carrying out time headway instructions were assessed experimentally.
Solitary Solution of Discrete mKdV Equation by Homotopy Analysis Method
XU Xi-Xiang; WANG Zhen; YANG Hong-Xiang; ZOU Li; LU Rong-Wu; ZHANG Hong-Qing
2008-01-01
In this paper, we apply homotopy analysis method to solve discrete mKdV equation and successfully obtain the bell-shaped solitary solution to mKdV equation. Comparison between our solution and the exact solution shows that homotopy analysis method is effective and validity in solving hybrid nonlinear problems, including solitary solution of difference-differential equation.
Discrete Parametric Oscillation and Nondiffracting Beams in a Glauber-Fock Oscillator
Oztas, Z
2016-01-01
We consider a Glauber-Fock oscillator and show that diffraction can be managed. We show how to design arrays of waveguides where light beams experience zero diffraction. We find an exact analytical family of nondiffracting localized solution. We predict discrete parametric oscillation in the Glauber-Fock oscillator.
The origin of discrete particles
Bastin, T
2009-01-01
This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (10 7 ). Sample Chapter(s). Foreword (56 KB). Chapter 1: Introduction
Exact solution of the robust knapsack problem☆
Monaci, Michele; Pferschy, Ulrich; Serafini, Paolo
2013-01-01
We consider an uncertain variant of the knapsack problem in which the weight of the items is not exactly known in advance, but belongs to a given interval, and an upper bound is imposed on the number of items whose weight differs from the expected one. For this problem, we provide a dynamic programming algorithm and present techniques aimed at reducing its space and time complexities. Finally, we computationally compare the performances of the proposed algorithm with those of different exact algorithms presented so far in the literature for robust optimization problems. PMID:24187428
Exact two-qubit universal quantum circuit
Zhang, J; Sastry, S; Whaley, K B; Zhang, Jun; Vala, Jiri; Sastry, Shankar
2003-01-01
We provide an analytic way to implement any arbitrary two-qubit unitary operation, given an entangling two-qubit gate together with local gates. This is shown to provide explicit construction of a universal quantum circuit that exactly simulates arbitrary two-qubit gates. Each block in this circuit is given in a closed form solution. We also analyze the efficiency of different entangling gates, and find that exactly half of all the controlled-unitary gates can be used to implement two-qubit operations as efficiently as the commonly used CNOT gate.
DFT calculations with the exact functional
Burke, Kieron
2014-03-01
I will discuss several works in which we calculate the exact exchange-correlation functional of density functional theory, mostly using the density-matrix renormalization group method invented by Steve White, our collaborator. We demonstrate that a Mott-Hubard insulator is a band metal. We also perform Kohn-Sham DFT calculations with the exact functional and prove that a simple algoritm always converges. But we find convergence becomes harder as correlations get stronger. An example from transport through molecular wires may also be discussed. Work supported by DOE grant DE-SC008696.
Exact Classical Correspondence in Quantum Cosmology
John, Moncy V
2014-01-01
We find a Friedmann model with appropriate matter/energy density such that the solution of the Wheeler-DeWitt equation exactly corresponds to the classical evolution. The well-known problems in quantum cosmology disappear in the resulting coasting evolution. The exact quantum-classical correspondence is demonstrated with the help of the de Broglie-Bohm and modified de Broglie-Bohm approaches to quantum mechanics. It is reassuring that such a solution leads to a robust model for the universe, which agrees well with cosmological expansion indicated by SNe Ia data.
Exact Results for the BTZ Black Hole
Birmingham, Daniel; Sen, S; Birmingham, Danny; Sachs, Ivo; Sen, Siddhartha
2001-01-01
In this review, we summarize exact results for the three-dimensional BTZ black hole. We use rigorous mathematical results to clarify the general structure and properties of this black hole spacetime and its microscopic description. In particular, we study the formation of the black hole by point particle collisions, leading to an exact analytic determination of the Choptuik scaling parameter. We also show that a `No Hair Theorem' follows immediately from a mathematical theorem of hyperbolic geometry, due to Sullivan. A microscopic understanding of the Bekenstein-Hawking entropy, and decay rate for massless scalars, is shown to follow from standard results of conformal field theory.
Exact analysis of bi-periodic structures
Cai, C W; Chan, H C
2002-01-01
By using the U-transformation method, it is possible to uncouple linear simultaneous equations, either algebraic or differential, with cyclic periodicity. This book presents a procedure for applying the U-transformation technique twice to uncouple the two sets of unknown variables in a doubly periodic structure to achieve an analytical exact solution. Explicit exact solutions for the static and dynamic analyses for certain engineering structures with doubly periodic properties - such as a continuous truss with any number of spans, cable network and grillwork on supports with periodicity, and g
Exact Chern-Simons / Topological String duality
Krefl, Daniel
2015-01-01
We invoke universal Chern-Simons theory to analytically calculate the exact free energy of the refined topological string on the resolved conifold. In the unrefined limit we reproduce non-perturbative corrections for the resolved conifold found elsewhere in the literature, thereby providing strong evidence that the Chern-Simons / topological string duality is exact, and in particular holds at arbitrary N as well. In the refined case, the non-perturbative corrections we find are novel and appear to be non-trivial. We show that non-perturbatively special treatment is needed for rational valued deformation parameter. Above results are also extend to refined Chern-Simons with orthogonal groups.
Necessity of Exact Calculation for Transition Probability
LIU Fu-Sui; CHEN Wan-Fang
2003-01-01
This paper shows that exact calculation for transition probability can make some systems deviate fromFermi golden rule seriously. This paper also shows that the corresponding exact calculation of hopping rate inducedby phonons for deuteron in Pd-D system with the many-body electron screening, proposed by Ichimaru, can explainthe experimental fact observed in Pd-D system, and predicts that perfection and low-dimension of Pd lattice are veryimportant for the phonon-induced hopping rate enhancement in Pd-D system.
Discrete geodesics and cellular automata
Arrighi, Pablo
2015-01-01
This paper proposes a dynamical notion of discrete geodesics, understood as straightest trajectories in discretized curved spacetime. The notion is generic, as it is formulated in terms of a general deviation function, but readily specializes to metric spaces such as discretized pseudo-riemannian manifolds. It is effective: an algorithm for computing these geodesics naturally follows, which allows numerical validation---as shown by computing the perihelion shift of a Mercury-like planet. It is consistent, in the continuum limit, with the standard notion of timelike geodesics in a pseudo-riemannian manifold. Whether the algorithm fits within the framework of cellular automata is discussed at length. KEYWORDS: Discrete connection, parallel transport, general relativity, Regge calculus.
Causal Dynamics of Discrete Surfaces
Pablo Arrighi
2014-03-01
Full Text Available We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
Discrete Event Programming with Simkit
Buss, Arnold
2001-01-01
This paper is a brief introduction to the use of Simkit, a software package for implementing Discrete Event Simulation (DES) models. Simkit is written in Java (for any operating system with Java 2TM ).
Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets
Rubinstein, Robert; Luo, Li-Shi
2007-01-01
In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.
Multiscale expansions in discrete world
Ömer Ünsal; Filiz Taşcan; Mehmet Naci Özer
2014-07-01
In this paper, we show the attainability of KdV equation from some types of nonlinear Schrödinger equation by using multiscale expansions discretely. The power of this manageable method is confirmed by applying it to two selected nonlinear Schrödinger evolution equations. This approach can also be applied to other nonlinear discrete evolution equations. All the computations have been made with Maple computer packet program.
Discrete solitons in graphene metamaterials
Bludov, Yuliy V.; Smirnova, Daria A.; Kivshar, Yuri S.; Peres, N. M. R.; Vasilevskiy, Mikhail
2014-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schr\\"{o}dinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states. Fundação para a Ciência e a Tecnolog...
Discrete solitons in graphene metamaterials
Bludov, Yu. V.; Smirnova, D. A.; Kivshar, Yu. S.; Peres, N. M. R.; Vasilevskiy, M. I.
2015-01-01
We study nonlinear properties of multilayer metamaterials created by graphene sheets separated by dielectric layers. We demonstrate that such structures can support localized nonlinear modes described by the discrete nonlinear Schrödinger equation and that its solutions are associated with stable discrete plasmon solitons. We also analyze the nonlinear surface modes in truncated graphene metamaterials being a nonlinear analog of surface Tamm states.
EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION
无
2011-01-01
In this paper,we use an invariant set to construct exact solutions to a nonlinear wave equation with a variable wave speed. Moreover,we obtain conditions under which the equation admits a nonclassical symmetry. Several different nonclassical symmetries for equations with different diffusion terms are presented.
Exact Optimum Design of Segmented Thermoelectric Generators
M. Zare
2016-01-01
Full Text Available A considerable difference between experimental and theoretical results has been observed in the studies of segmented thermoelectric generators (STEGs. Because of simplicity, the approximate methods are widely used for design and optimization of the STEGs. This study is focused on employment of exact method for design and optimization of STEGs and comparison of exact and approximate results. Thus, using new highly efficient thermoelectric materials, four STEGs are proposed to operate in the temperature range of 300 to 1300 kelvins. The proposed STEGs are optimally designed to achieve maximum efficiency. Design and performance characteristics of the optimized generators including maximum conversion efficiency and length of elements are calculated through both exact and approximate methods. The comparison indicates that the approximate method can cause a difference up to 20% in calculation of some design characteristics despite its appropriate results in efficiency calculation. The results also show that the maximum theoretical efficiency of 23.08% is achievable using the new proposed STEGs. Compatibility factor of the selected materials for the proposed STEGs is also calculated using both exact and approximate methods. The comparison indicates a negligible difference in calculation of compatibility factor, despite the considerable difference in calculation of reduced efficiency (temperature independence efficiency.
Exactly solvable models of baryon structure
Bijker, R
1998-01-01
We present a qualitative analysis of the gross features of baryon spectroscopy (masses and form factors) in terms of various exactly solvable models. It is shown that a collective model, in which baryon resonances are interpreted as rotations and vibrations of an oblate symmetric top, provides a good starting point for a more detailed quantitative study.
Exactly solvable models of baryon structure
Bijker, R. [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico. Apartado Postal 70-543, 04510 Mexico D.F. (Mexico); Leviatan, A. [Racah Institute of Physics, The Hebrew University. Jerusalem 91904, Israel (Israel)
1998-12-31
We present a qualitative analysis of the gross features of baryon spectroscopy (masses and form factors) in terms of various exactly solvable models. It is shown that a collective model, in which baryon resonances are interpreted as rotations and vibrations of an oblate symmetric top, provides a good starting point for a more detailed quantitative study. (Author)
BSA - exact algorithm computing LTS estimate
Klouda, Karel
2010-01-01
The main result of this paper is a new exact algorithm computing the estimate given by the Least Trimmed Squares (LTS). The algorithm works under very weak assumptions. To prove that, we study the respective objective function using basic techniques of analysis and linear algebra.
Exact Vacuum Solutions to the Einstein Equation
无
2007-01-01
In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations,which are much convenient for the resolution.
Solitons in nonlocal nonlinear media: Exact solutions
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...
Gorensteinness and Tate Cohomology in Exact Categories
WANG Zhi-cheng
2015-01-01
Motivated by the classical Gorenstein homological theory and structure of Tate cohomology, we develop a theory of Gorenstein projective objects and Tate cohomology in an exact category A with enough projectives. We study some properties of Gorenstein projective objects and establish Tate cohomology of objects with finite Gorenstein projective dimension.
Exact internal controllability for shallow shells
FENG Shaoji; FENG Dexing
2006-01-01
The internal control problem is considered, based on the linear displacement equations of shallow shell. It is shown, with some checkable geometric conditions on control region, that the undergoing shallow shell is exactly controllable by using Hilbert uniqueness method (HUM), piecewise multiplier method and Riemannian geometry method. Then some examples are given to show the assumed geometric conditions.
Spectral geometry: two exactly solvable models
Kuperin, Yu.A. (International Solvay Institutes for Physics and Chemistry, C.P. 231, Boulevard du Triomphe, 1050, Brussels (Belgium) Department of Mathematical and Computational Physics, Saint Petersburg State University, 198904, Saint Petersburg (Russian Federation) Institute for Physical Research and Technology, Saint Petersburg (Russian Federation)); Pavlov, B.S. (International Solvay Institutes for Physics and Chemistry, C.P. 231, Boulevard du Triomphe, 1050, Brussels (Belgium) Department of Mathematical and Computational Physics, Saint Petersburg State University, 198904, Saint Petersburg (Russian Federation)); Rudin, G.E. (Department of Mathematical and Computational Physics, Saint Petersburg State University, 198904, Saint Petersburg (Russian Federation)); Vinitsky, S.I. (International Solvay Institutes for Physics and Chemistry, C.P. 231, Boulevard du Triomphe, 1050, Brussels (Belgium) Institute for Physical Research and Technology, Saint Petersburg (Russian Federation) Joi
1994-10-24
Two exactly solvable models illustrating the links between spectral properties of Hamiltonians, connections on the induced Hilbert bundles and topological characteristics of the basis spaces are considered. The first of them is based on the extension theory for symmetric operators and the second on the one-dimensional Laplace operator with parametrical boundary conditions. ((orig.))
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.
On Exact and Inexact Differentials and Applications
Cortez, L. A. B.; de Oliveira, E. Capelas
2017-01-01
Considering the important role played by mathematical derivatives in the study of physical-chemical processes, this paper discusses the different possibilities and formulations of this concept and its application. In particular, in Chemical Thermodynamics, we study exact differentials associated with the so-called state functions and inexact…
Alfa, Attahiru S
2016-01-01
This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...
Bayesian estimation of the discrete coefficient of determination.
Chen, Ting; Braga-Neto, Ulisses M
2016-12-01
The discrete coefficient of determination (CoD) measures the nonlinear interaction between discrete predictor and target variables and has had far-reaching applications in Genomic Signal Processing. Previous work has addressed the inference of the discrete CoD using classical parametric and nonparametric approaches. In this paper, we introduce a Bayesian framework for the inference of the discrete CoD. We derive analytically the optimal minimum mean-square error (MMSE) CoD estimator, as well as a CoD estimator based on the Optimal Bayesian Predictor (OBP). For the latter estimator, exact expressions for its bias, variance, and root-mean-square (RMS) are given. The accuracy of both Bayesian CoD estimators with non-informative and informative priors, under fixed or random parameters, is studied via analytical and numerical approaches. We also demonstrate the application of the proposed Bayesian approach in the inference of gene regulatory networks, using gene-expression data from a previously published study on metastatic melanoma.
Belmonte-Beitia, Juan [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: juan.belmonte@uclm.es; Calvo, Gabriel F. [Departamento de Matematicas, E.T.S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)], E-mail: gabriel.fernandez@uclm.es
2009-01-19
In this Letter, by means of similarity transformations, we construct explicit solutions to the quintic nonlinear Schroedinger equation with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general approach and use it to study some examples and find nontrivial explicit solutions such as periodic (breathers), quasiperiodic and bright and dark soliton solutions.
Haydock's recursive solution of self-adjoint problems. Discrete spectrum
Moroz, Alexander
2014-12-01
Haydock's recursive solution is shown to underline a number of different concepts such as (i) quasi-exactly solvable models, (ii) exactly solvable models, (iii) three-term recurrence solutions based on Schweber's quantization criterion in Hilbert spaces of entire analytic functions, and (iv) a discrete quantum mechanics of Odake and Sasaki. A recurrent theme of Haydock's recursive solution is that the spectral properties of any self-adjoint problem can be mapped onto a corresponding sequence of polynomials {pn(E) } in energy variable E. The polynomials {pn(E) } are orthonormal with respect to the density of states n0(E) and energy eigenstate | E > is the generating function of {pn(E) } . The generality of Haydock's recursive solution enables one to see the different concepts from a unified perspective and mutually benefiting from each other. Some results obtained within the particular framework of any of (i) to (iv) may have much broader significance.
On Discrete Killing Vector Fields and Patterns on Surfaces
Ben-Chen, Mirela
2010-09-21
Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape\\'s aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented using infinitesimal rigid transformations, which are given as tangent vector fields on the surface - known as Killing Vector Fields. As exact symmetries are quite rare, especially when considering noisy sampled surfaces, we propose a method for relaxing the exact symmetry constraint to allow for approximate symmetries and approximate Killing Vector Fields, and show how to discretize these concepts for generating such vector fields on a triangulated mesh. We discuss the properties of approximate Killing Vector Fields, and propose an application to utilize them for texture and geometry synthesis. Journal compilation © 2010 The Eurographics Association and Blackwell Publishing Ltd.
Tais Regina Hennig
2009-12-01
Full Text Available OBJETIVO: avaliar e comparar a deglutição de sujeitos respiradores orais e nasais, por meio da avaliação clínica e eletromiográfica dos músculos orbiculares orais, superior e inferior. MÉTODOS: participaram deste estudo 16 sujeitos na faixa etária de 6:8 a 10:10 distribuídos em dois grupos, um de respiradores orais e outro de respiradores nasais. Foram submetidos à avaliação clínica fonoaudiológica e eletromiográfica de superfície. O exame fonoaudiológico contemplou as estruturas e funções do sistema estomatognático, e a avaliação eletromiográfica consistiu na captação da atividade elétrica dos músculos orbiculares orais, superior e inferior, durante as situações de isometria e de deglutição. Da avaliação clínica consideraram-se somente os resultados referentes à deglutição, observando-se a presença de ação labial e mentual, e de projeção lingual, as quais foram analisados de forma descritiva. Para análise estatística dos dados eletromiográficos, utilizou-se o Teste t para comparação entre os grupos. A significância adotada foi de 5% (p PURPOSE: to evaluate and compare the swallowing of mouth and nose breathers through of speech-language and electromyography evaluation concerning the orbicularis oris muscles, and lower and upper lips. METHODS: 16 subjects aged 6:8 - 10:10 and divided on two groups participated in this study, one with mouth and another one with nose breathers. Both groups were submitted to clinical and surface electromyography evaluation. The speech-language evaluation contemplated the exam of the structures and functions of the stomatognathic system. The electromyography evaluation consisted of the captivation of the electrical activity at the orbicularis oris muscles, and lower and upper lips, during isometry and swallowing situations. In the clinical results were considered only the swallowing variables. Therefore, our study could observe the presence of labial and mentalis
A parametric LTR solution for discrete-time systems
Niemann, Hans Henrik; Jannerup, Ole Erik
1989-01-01
and the full loop transfer function, is manipulated into a general form involving the target loop transfer matrix and the fundamental recovery matrix. A parametric LTR solution based on the recovery matrix is developed. It is shown that the LQR/LTR (linear quadratic Gaussian/loop transfer recovery) solution......A parametric LTR (loop transfer recovery) solution for discrete-time compensators incorporating filtering observers which achieve exact recovery is presented for both minimum- and non-minimum-phase systems. First the recovery error, which defines the difference between the target loop transfer...
Empirical likelihood estimation of discretely sampled processes of OU type
SUN ShuGuang; ZHANG XinSheng
2009-01-01
This paper presents an empirical likelihood estimation procedure for parameters of the discretely sampled process of Ornstein-Uhlenbeck type. The proposed procedure is based on the condi-tional characteristic function, and the maximum empirical likelihood estimator is proved to be consistent and asymptotically normal. Moreover, this estimator is shown to be asymptotically efficient under some tensity parameter can be exactly recovered, and we study the maximum empirical likelihood estimator with the plug-in estimated intensity parameter. Testing procedures based on the empirical likelihood ratio statistic are developed for parameters and for estimating equations, respectively. Finally, Monte Carlo simulations are conducted to demonstrate the performance of proposed estimators.
An exactly conservative integrator for the n-body problem
Kotovych, Oksana; Bowman, John C. [Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB (Canada)]. E-mail: bowman@math.ualberta.ca
2002-09-20
The two-dimensional n-body problem of classical mechanics is a non-integrable Hamiltonian system for n>2. Traditional numerical integration algorithms, which are polynomials in the time step, typically lead to systematic drifts in the computed value of the total energy and angular momentum. Even symplectic integration schemes exactly conserve only an approximate Hamiltonian. We present an algorithm that conserves the true Hamiltonian and the total angular momentum to machine precision. It is derived by applying conventional discretizations in a new space obtained by transformation of the dependent variables. We develop the method first for the restricted circular three-body problem, then for the general two-dimensional three-body problem and finally for the planar n-body problem. Jacobi coordinates are used to reduce the two-dimensional n-body problem to an (n-1)-body problem that incorporates the constant linear momentum and centre-of-mass constraints. For a four-body choreography, we find that a larger time step can be used with our conservative algorithm than with symplectic and conventional integrators. (author)
Discrete Curvature Theories and Applications
Sun, Xiang
2016-08-25
Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the
Computing an Exact Gaussian Scale-Space
Ives Rey Otero; Mauricio Delbracio
2016-01-01
Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a discrete counterpart to the continuous Gaussian operator. This study is focused on low blur levels, th...
Palha, Artur
2016-01-01
In this work we present a mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured grids. The essential ingredients to achieve this are: (i) a velocity-vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular grids.
Palha, A.; Gerritsma, M.
2017-01-01
In this work we present a mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured triangular grids. The essential ingredients to achieve this are: (i) a velocity-vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular triangular grids.
Analysis of Discrete Mittag - Leffler Functions
N. Shobanadevi
2015-03-01
Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2016-09-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G) -expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Exact solutions for nonlinear foam drainage equation
Zayed, E. M. E.; Al-Nowehy, Abdul-Ghani
2017-02-01
In this paper, the modified simple equation method, the exp-function method, the soliton ansatz method, the Riccati equation expansion method and the ( G^' }/G)-expansion method are used to construct exact solutions with parameters of the nonlinear foam drainage equation. When these parameters are taken to be special values, the solitary wave solutions and the trigonometric function solutions are derived from the exact solutions. The obtained results confirm that the proposed methods are efficient techniques for analytic treatments of a wide variety of nonlinear partial differential equations in mathematical physics. We compare our results together with each other yielding from these integration tools. Also, our results have been compared with the well-known results of others.
Sampling exactly from the normal distribution
Karney, Charles F F
2013-01-01
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in the same base. Thereafter, uniform random digits are copied directly into the representation of the normal deviate. Thus, in constrast to existing methods, it is possible to generate normal deviates exactly rounded to any precision with a mean cost that scales linearly in the precision. The method performs no arbitrary precision arithmetic, calls no transcendental functions, and, indeed, uses no floating point arithmetic whatsoever; it uses only simple integer operations. The algorithm is inspired by von Neumann's algorithm for sampling from the exponential distribution; an improvement to von Neumann's algorithm is also given.
Exact cosmological solutions from Hojman conservation quantities
Capozziello, Salvatore, E-mail: capozzie@na.infn.it [Dipartimento di Fisica, Università di Napoli “Federico II”, Napoli (Italy); INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli (Italy); Roshan, Mahmood, E-mail: rowshan@alumni.ut.ac.ir [Department of Physics, Ferdowsi University of Mashhad, P.O. Box 1436, Mashhad (Iran, Islamic Republic of)
2013-10-07
We present a new approach to find exact solutions for cosmological models. By requiring the existence of a symmetry transformation vector for the equations of motion of the given cosmological model (without using either Lagrangian or Hamiltonian), one can find corresponding Hojman conserved quantities. With the help of these conserved quantities, the analysis of the cosmological model can be simplified. In the case of quintessence scalar–tensor models, we show that the Hojman conserved quantities exist for a wide range of V(ϕ)-potentials and allow to find exact solutions for the cosmic scale factor and the scalar field. Finally, we investigate the general cosmological behavior of solutions by adopting a phase-space view.
Exact cosmological solutions from Hojman conservation quantities
Capozziello, Salvatore
2013-01-01
We present a new approach to find exact solutions for cosmological models. By requiring the existence of a symmetry transformation vector for the equations of motion of the given cosmological model (without using either Lagrangian or Hamiltonian), one can find corresponding Hojman conserved quantities. With the help of these conserved quantities, the analysis of the cosmological model can be simplified. In the case of quintessence scalar-tensor models, we show that the Hojman conserved quantities exist for a wide range of V(\\phi)-potentials and allow to find exact solutions for the cosmic scale factor and the scalar field. Finally, we investigate the general cosmological behavior of solutions by adopting a phase-space view.
Representing exact number visually using mental abacus.
Frank, Michael C; Barner, David
2012-02-01
Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation.
Remarks on Exactly Solvable Noncommutative Quantum Field
WANG Ning
2007-01-01
We study exactly the solvable noncommutative scalar quantum Geld models of (2n) or (2n + 1) dimensions. By writing out an equivalent action of the noncommutative field, it is shown that the special condition B·θ =±I in field theoretic context means the full restoration of the maximal U(∞) gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n- dimensional exactly solvable noncommutative φ4 quantum field model closely related to the 1+1- dimensional Moyal/ matrix-valued nonlinear Schr(o)dinger (MNLS) equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.
Exact four-spinon dynamical correlation function
Abada, A; Si-Lakhal, B; Seba, S; Abada, As
1998-01-01
We discuss some properties of the exact four-spinon dynamical correlation function in the antiferromagnetic spin 1/2 XXX-model the expression of which we derived recently. We show that the region in which it is not identically zero is different from and larger than the spin-wave continuum. We discuss its behavior as a function of the neutron momentum transfer $k$ for fixed values of the neutron energy $\\omega$ and compare it to the one corresponding to the exact two-spinon dynamical correlation function. We show that the overall shapes are quite similar but there are differences that we discuss. Particular is the fact that the symmetry about the axis $k=\\pi$ present in the two-spinon case seems to be lost in the four-spinon one. We finish with concluding remarks.
Exact solution to fractional logistic equation
West, Bruce J.
2015-07-01
The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.
Exact Relativistic Magnetized Haloes around Rotating Disks
Antonio C. Gutiérrez-Piñeres
2015-01-01
Full Text Available The study of the dynamics of magnetic fields in galaxies is one of important problems in formation and evolution of galaxies. In this paper, we present the exact relativistic treatment of a rotating disk surrounded by a magnetized material halo. The features of the halo and disk are described by the distributional energy-momentum tensor of a general fluid in canonical form. All the relevant quantities and the metric and electromagnetic potentials are exactly determined by an arbitrary harmonic function only. For instance, the generalized Kuzmin-disk potential is used. The particular class of solutions obtained is asymptotically flat and satisfies all the energy conditions. Moreover, the motion of a charged particle on the halo is described. As far as we know, this is the first relativistic model describing analytically the magnetized halo of a rotating disk.
Exact Jacobians in an implicit Newton method for two-phase flow in porous media
Büsing, H.; Clauser, C.
2012-04-01
Geological storage of CO2 is one option for mitigating the effects of CO2 emissions on global warming. Since extensive on-site monitoring of the CO2 plume propagation is expensive, numerical simulations are an attractive alternative for gaining deeper insight in the dynamics of this system. We consider a model for two-phase flow in porous media for representing the injection stage of a CO2 sequestration scenario, when the plume propagation is dominated by advection. The porous medium filled by the two phases CO2 and brine is modelled as an initial-boundary-value problem consisting of two nonlinear, coupled partial differential equations, which are complemented by appropriate boundary and initial conditions. We present a new numerical approach to solve this fully coupled system using exact Jacobians. The method is based on the finite element, finite volume, box method [Huber & Helmig(2000)] for the space discretization and, since stability of the method is one of the main concerns, the fully implicit Euler method for the time discretization. A simple first order upwind method takes into account advective contributions. The resulting system of nonlinear algebraic equations is linearized by Newton's method. The required Jacobians can be obtained elegantly by automatic differentiation (AD) [Griewank & Walther(2008), Rall(1981)], a source code transformation giving exact derivatives of the discretized equations with respect to primary variables. The resulting system of linear equations is then solved by an iterative method (BiCGStab) with ILU0 preconditioning in every Newton step. We compare the forward AD differentiation mode to the standard finite difference method in terms of precision and performance. It turns out that AD performs favourable in both aspects. We also illustrate the advantages of exact Jacobians for two-phase flow in a sequestration scenario investigating the evolution of pressure and saturation.
Compiling Relational Bayesian Networks for Exact Inference
Jaeger, Manfred; Chavira, Mark; Darwiche, Adnan
2004-01-01
We describe a system for exact inference with relational Bayesian networks as defined in the publicly available \\primula\\ tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference by evaluating...... and differentiating these circuits in time linear in their size. We report on experimental results showing the successful compilation, and efficient inference, on relational Bayesian networks whose {\\primula}--generated propositional instances have thousands of variables, and whose jointrees have clusters...
Exact BPS bound for noncommutative baby Skyrmions
Domrin, Andrei, E-mail: domrin@mi.ras.ru [Department of Mathematics and Mechanics, Moscow State University, Leninskie gory, 119992, GSP-2, Moscow (Russian Federation); Lechtenfeld, Olaf, E-mail: lechtenf@itp.uni-hannover.de [Institut für Theoretische Physik and Riemann Center for Geometry and Physics, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover (Germany); Linares, Román, E-mail: lirr@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F. (Mexico); Maceda, Marco, E-mail: mmac@xanum.uam.mx [Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F. (Mexico)
2013-11-25
The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory.
NEW EXACTLY SOLVABLE SUPERSYMMETRIC PERIODIC POTENTIALS
LIU KE-JIA; HE LI; ZHOU GUO-LI; WU YU-JIAO
2001-01-01
Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of onedimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schrodinger equation for this potential is named the Mathieu equation mathematically.We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities.
EXACT SOLUTIONS OF A DIPOLAR FLUID FLOW
T. HAYAT
2003-01-01
Exact solutions for three canonical flow problems of a dipolar fluid are obtained: (i)The flow of a dipolar fluid due to a suddenly accelerated plate, (ii) The flow generated by periodic oscillation of a plate, (iii) The flow due to plate oscillation in the presence of a transverse magnetic field. The solutions of some interesting flows caused by an arbitrary velocity of the plate and of certain special oscillations are also obtained.
Introduction to Hubbard model and exact diagonalization
S. Akbar Jafari
2008-06-01
Full Text Available Hubbard model is an important model in the theory of strongly correlated electron systems. In this contribution we introduce this model and the concepts of electron correlation by building on a tight binding model. After enumerating various methods of tackling the Hubbard model, we introduce the numerical method of exact diagonalization in detail. The book keeping and practical implementation aspects are illustrated with analytically solvable example of two-site Hubbard model.
Exact plane gravitational waves and electromagnetic fields
Enrico MontanariUniversity of Ferrara and INFN sezione di Ferrara, Italy; Mirco Calura(University of Ferrara and INFN sezione di Ferrara, Italy)
2000-01-01
The behaviour of a "test" electromagnetic field in the background of an exact gravitational plane wave is investigated in the framework of Einstein's general relativity. We have expressed the general solution to the de Rham equations as a Fourier-like integral. In the general case we have reduced the problem to a set of ordinary differential equations and have explicitly written the solution in the case of linear polarization of the gravitational wave. We have expressed our ...
Exact axisymmetric Taylor states for shaped plasmas
Cerfon, Antoine J., E-mail: cerfon@cims.nyu.edu; O' Neil, Michael, E-mail: oneil@cims.nyu.edu [Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 (United States)
2014-06-15
We present a general construction for exact analytic Taylor states in axisymmetric toroidal geometries. In this construction, the Taylor equilibria are fully determined by specifying the aspect ratio, elongation, and triangularity of the desired plasma geometry. For equilibria with a magnetic X-point, the location of the X-point must also be specified. The flexibility and simplicity of these solutions make them useful for verifying the accuracy of numerical solvers and for theoretical studies of Taylor states in laboratory experiments.
Exact solution of phantom dark energy model
Wang Wen-Fu; Shui Zheng-Wei; Tang Bin
2010-01-01
We investigate the phantom dark energy model derived from the scalar field with a negative kinetic term. By assuming a particular relation between the time derivative of the phantom field and the Hubble function, an exact solution of the model is constructed. Absence of the 'big rip' singularity is shown explicitly. We then derive special features of phantom dark energy model and show that its predictions are consistent with all astrophysical observations.
Coherent states for exactly solvable potentials
Shreecharan, T.; Panigrahi, Prasanta. K.; Banerji, J.
2003-01-01
A general algebraic procedure for constructing coherent states of a wide class of exactly solvable potentials e.g., Morse and P{\\"o}schl-Teller, is given. The method, {\\it a priori}, is potential independent and connects with earlier developed ones, including the oscillator based approaches for coherent states and their generalizations. This approach can be straightforwardly extended to construct more general coherent states for the quantum mechanical potential problems, like the nonlinear co...
Stripe Ansatzs from Exactly Solved Models
2001-01-01
Using the Boltzmann weights of classical Statistical Mechanics vertex models we define a new class of Tensor Product Ansatzs for 2D quantum lattice systems, characterized by a strong anisotropy, which gives rise to stripe like structures. In the case of the six vertex model we compute exactly, in the thermodynamic limit, the norm of the ansatz and other observables. Employing this ansatz we study the phase diagram of a Hamiltonian given by the sum of XXZ Hamiltonians along the legs coupled by...
Exact quantization conditions for cluster integrable systems
Franco, Sebastián; Hatsuda, Yasuyuki; Mariño, Marcos
2016-06-01
We propose exact quantization conditions for the quantum integrable systems of Goncharov and Kenyon, based on the enumerative geometry of the corresponding toric Calabi-Yau manifolds. Our conjecture builds upon recent results on the quantization of mirror curves, and generalizes a previous proposal for the quantization of the relativistic Toda lattice. We present explicit tests of our conjecture for the integrable systems associated to the resolved {{{C}}3}/{{{Z}}5} and {{{C}}3}/{{{Z}}6} orbifolds.
Exact quantization conditions for cluster integrable systems
Franco, Sebastian; Marino, Marcos
2015-01-01
We propose exact quantization conditions for the quantum integrable systems of Goncharov and Kenyon, based on the enumerative geometry of the corresponding toric Calabi-Yau manifolds. Our conjecture builds upon recent results on the quantization of mirror curves, and generalizes a previous proposal for the quantization of the relativistic Toda lattice. We present explicit tests of our conjecture for the integrable systems associated to the resolved C^3/Z_5 and C^3/Z_6 orbifolds.
On exact solutions of the Bogoyavlenskii equation
Yan-Ze Peng; Ming Shen
2006-09-01
Exact solutions for the Bogoyavlenskii equation are studied by the travelling wave method and the singular manifold method. It is found that the linear superposition of the shock wave solution and the complex solitary wave solution for the physical field is still a solution of the equation of interest, except for a phase-shift. The dromion-like structures with elastic and nonelastic interactions are found.
Exact tests for Hardy-Weinberg proportions.
Engels, William R
2009-12-01
Exact conditional tests are often required to evaluate statistically whether a sample of diploids comes from a population with Hardy-Weinberg proportions or to confirm the accuracy of genotype assignments. This requirement is especially common when the sample includes multiple alleles and sparse data, thus rendering asymptotic methods, such as the common chi(2)-test, unreliable. Such an exact test can be performed using the likelihood ratio as its test statistic rather than the more commonly used probability test. Conceptual advantages in using the likelihood ratio are discussed. A substantially improved algorithm is described to permit the performance of a full-enumeration exact test on sample sizes that are too large for previous methods. An improved Monte Carlo algorithm is also proposed for samples that preclude full enumeration. These algorithms are about two orders of magnitude faster than those currently in use. Finally, methods are derived to compute the number of possible samples with a given set of allele counts, a useful quantity for evaluating the feasibility of the full enumeration procedure. Software implementing these methods, ExactoHW, is provided.
Stochastic TDHF in an exactly solvable model
Lacombe, Lionel; Suraud, Eric; Dinh, Phuong Mai
2016-01-01
We apply in a schematic model a theory beyond mean-field, namely Stochastic Time-Dependent Hartree-Fock (STDHF), which includes dynamical electron-electron collisions on top of an incoherent ensemble of mean-field states by occasional 2-particle-2-hole ($2p2h$) jumps. The model considered here is inspired by a Lipkin-Meshkov-Glick model of $\\Omega$ particles distributed into two bands of energy and coupled by a two-body interaction. Such a model can be exactly solved (numerically though) for small $\\Omega$. It therefore allows a direct comparison of STDHF and the exact propagation. The systematic impact of the model parameters as the density of states, the excitation energy and the bandwidth is presented and discussed. The time evolution of the STDHF compares fairly well with the exact entropy, as soon as the excitation energy is sufficiently large to allow $2p2h$ transitions. Limitations concerning low energy excitations and memory effects are also discussed.
Exact and Approximate Sizes of Convex Datacubes
Nedjar, Sébastien
In various approaches, data cubes are pre-computed in order to efficiently answer Olap queries. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. Previously, we have introduced the concept of convex cube which generalizes all the quoted variants of cubes. More precisely, the convex cube captures all the tuples satisfying a monotone and/or antimonotone constraint combination. This paper is dedicated to a study of the convex cube size. Actually, knowing the size of such a cube even before computing it has various advantages. First of all, free space can be saved for its storage and the data warehouse administration can be improved. However the main interest of this size knowledge is to choose at best the constraints to apply in order to get a workable result. For an aided calibrating of constraints, we propose a sound characterization, based on inclusion-exclusion principle, of the exact size of convex cube as long as an upper bound which can be very quickly yielded. Moreover we adapt the nearly optimal algorithm HyperLogLog in order to provide a very good approximation of the exact size of convex cubes. Our analytical results are confirmed by experiments: the approximated size of convex cubes is really close to their exact size and can be computed quasi immediately.
Exact Eigenfunctions of a Chaotic System
Ausländer, O M
1997-01-01
The interest in the properties of quantum systems, whose classical dynamics are chaotic, derives from their abundance in nature. The spectrum of such systems can be related, in the semiclassical approximation (SCA), to the unstable classical periodic orbits, through Gutzwiller's trace formula. The class of systems studied in this work, tiling billiards on the pseudo-sphere, is special in this correspondence being exact, via Selberg's trace formula. In this work, an exact expression for Green's function (GF) and the eigenfunctions (EF) of tiling billiards on the pseudo-sphere, whose classical dynamics are chaotic, is derived. GF is shown to be equal to the quotient of two infinite sums over periodic orbits, where the denominator is the spectral determinant. Such a result is known to be true for typical chaotic systems, in the leading SCA. From the exact expression for GF, individual EF can be identified. In order to obtain a SCA by finite series for the infinite sums encountered, resummation by analytic contin...
Isogeometric shell discretizations for flexible multibody dynamics
Goyal, Anmol, E-mail: goyal@mathematik.uni-kl.de; Doerfel, Michael R., E-mail: michael.doerfel@web.de; Simeon, Bernd, E-mail: simeon@mathematik.uni-kl.de; Vuong, Anh-Vu, E-mail: vuong@mathematik.uni-kl.de [Technische Universitaet Kaiserslautern, Felix Klein Zentrum fuer Mathematik, FB Mathematik (Germany)
2013-08-01
This work aims at including nonlinear elastic shell models in a multibody framework. We focus our attention to Kirchhoff-Love shells and explore the benefits of an isogeometric approach, the latest development in finite element methods, within a multibody system. Isogeometric analysis extends isoparameteric finite elements to more general functions such as B-splines and NURBS (Non-Uniform Rational B-Splines) and works on exact geometry representations even at the coarsest level of discretizations. Using NURBS as basis functions, high regularity requirements of the shell model, which are difficult to achieve with standard finite elements, are easily fulfilled. A particular advantage is the promise of simplifying the mesh generation step, and mesh refinement is easily performed by eliminating the need for communication with the geometry representation in a CAD (Computer-Aided Design) tool. Target applications are wind turbine blades and twist beam rear suspensions. First numerical examples demonstrate an impressive convergence behavior of the isogeometric approach even for a coarse mesh, while offering substantial savings with respect to the number of degrees of freedom.
Lectures on financial mathematics discrete asset pricing
Anderson, Greg
2010-01-01
This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times--this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of "arbitrage", the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures. The authors' motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged t...
Minisuperspace models of discrete systems
Baytaş, Bekir
2016-01-01
A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous configurations and the dynamical building-up and stability of long-range correlations. Different types of homogeneous minisuperspace models are introduced for the system, including one based on condensate states, and shown to capture different aspects of the discrete system. They are evaluated with effective methods and by means of continuum limits, showing good agreement with operator calculations whenever the latter are available. As a possibly quite general result, it is concluded that an analysis of the building-up of long-range correlations in discrete systems requires non-perturbative solutions of the dynamical equations. Some questions related to stability can be analyzed perturbatively, but suggest that matter couplings may be relevant for this question in the context o...
Interference in discrete Wigner functions
Cormick, C; Cormick, Cecilia; Paz, Juan Pablo
2006-01-01
We analyse some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. to represent quantum states of systems with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101 (2004)]. We consider "cat" states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase-space (including the regions where the two interfering states are localized). This is a generic property which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this...
Boundary field induced first-order transition in the 2D Ising model: exact study
Clusel, Maxime [Institut Laue-Langevin, 6 rue Horowitz BP156 X, 38042 Grenoble Cedex (France); Fortin, Jean-Yves [Laboratoire Poncelet, 119002, Bolshoy Vlasyevskiy Pereulok 11, Moscow (Russian Federation)
2006-02-03
We present in this paper an exact study of a first-order transition induced by an inhomogeneous boundary magnetic field in the 2D Ising model. From a previous analysis of the interfacial free energy in the discrete case (Clusel and Fortin 2005 J. Phys. A: Math. Gen. 38 2849) we identify, using an asymptotic expansion in the thermodynamic limit, the line of transition that separates the regime where the interface is localized near the boundary from the one where it is propagating inside the bulk. In particular, the transition line has a strong dependence on the aspect ratio of the lattice.
An exact solution of unsteady Couette flow of generalized second grade fluid
无
2002-01-01
The fractional calculus approach is introduced into the rheological constitutive model of a generalized second grade fluid. A constitutive model with fractional derivative is developed for the generalized second grade fluid. Unsteady Couette flow of the generalized second grade fluid is studied by using the method of the discrete inverse Laplace transform and generalized Mittag-Leffler function. And then an exact solution is obtained for this problem with arbitrary fractional derivative. This provides a new analytical tool for the study of viscoelastic fluid mechanics.
Notes on the ExactPack Implementation of the DSD Explosive Arc Solver
Kaul, Ann [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Doebling, Scott William [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-12
It has been shown above that the discretization scheme implemented in the ExactPack solver for the DSD Explosive Arc equation is consistent with the Explosive Arc PDE. In addition, a stability analysis has provided a CFL condition for a stable time step. Together, consistency and stability imply convergence of the scheme, which is expected to be close to first-order in time and second-order in space. It is understood that the nonlinearity of the underlying PDE will affect this rate somewhat.
High order discontinuous Galerkin discretizations with discontinuity resolution within the cell
Ekaterinaris, John; Panourgias, Konstantinos
2016-11-01
The nonlinear filter of Yee et al. and used for low dissipative well-balanced high order accurate finite-difference schemes is adapted to the finite element context of discontinuous Galerkin (DG) discretizations. The performance of the proposed nonlinear filter for DG discretizations is demonstrated for different orders of expansions for one- and multi-dimensional problems with exact solutions. It is shown that for higher order discretizations discontinuity resolution within the cell is achieved and the design order of accuracy is preserved. The filter is applied for inviscid and viscous flow test problems including strong shocks interactions to demonstrate that the proposed dissipative mechanism for DG discretizations yields superior results compared to the results obtained with the TVB limiter and high-order hierarchical limiting. The proposed approach is suitable for p-adaptivity in order to locally enhance resolution of three-dimensional flow simulations.
Geometry of discrete quantum computing
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
Andréia Marson
2012-12-01
Full Text Available OBJETIVOS: verificar o efeito da intervenção fonoaudiológica em um grupo de respiradores orais e propor terapia fonoaudiológica mínima no tratamento da respiração oral. MÉTODO: estudo prospectivo longitudinal, casuística de 40 sujeitos respiradores orais tratados no Hospital das Clínicas - setor de Reabilitação Orofacial do Ambulatório de Respirador Oral da Disciplina de Otorrinolaringologia da Faculdade de Ciências Médicas da Universidade Estadual de Campinas - UNICAMP. Realizada documentação fotográfica, avaliação clínica, aplicação de protocolo para categorizar modo respiratório, postura (lábios e bochechas; força e praxias (lábios, bochechas e língua nas semanas 0, 12 e 24. A proposta terapêutica constou de treino e conscientização da respiração nasal; manobras para aquecimento e vascularização da musculatura orofacial; aplicação de pontos e zonas motoras na face; manobras passivas; uso do impulso distal; exercícios miofuncionais e registro da percepção dos pacientes sobre suas condições olfativas e obstruções nasais.Teste estatístico: não paramétrico de Igualdade de Duas Proporções, p PURPOSE: to check the effect of speech and language therapy on a group of mouth breathers, as well proposing a minimum therapy for mouth breathing treatment. METHOD: longitudinal prospective study, casuistic on 40 mouth breather subjects who were patients from the Otorhinolaryngology Ambulatory of UNICAMP Hospital. On weeks 0, 12 and 24, we proceeded photographical documentation, clinical assessment, and protocol application in order to categorize the breathing mode, posture (lips and cheeks, strength and movement (lips, cheeks and tongue. The applied therapeutic proposal consisted of practicing and awareness on nasal breathing; maneuvers to warm and vascularize the orofacial muscles; application of points and motor zones on the face; passive maneuvers; use of distal impulse; myofunctional exercises and register
DISCRETE ROTATIONS AND CELLULAR AUTOMATA
Nouvel, Bertrand
2006-01-01
In a discrete space, such as the set of integer-coordinate points, the modelization of isotropy may lead to noticeable theoretical difficulties. At this time, we do not know any gerometric theory on $\\ZZ^n$ that would be suitable to describe the isotropy the same way it is perceived by Euclidean geometry. With respect to this problematic, our aim is to describe some algorithms that would give to the discrete rotations some properties that would be similar to the properties of the Euclidean ro...
Stable discrete surface light bullets.
Mihalache, Dumitru; Mazilu, Dumitru; Lederer, Falk; Kivshar, Yuri S
2007-01-22
We analyze spatiotemporal light localization near the edge of a semi-infinite array of weakly coupled nonlinear optical waveguides and demonstrate the existence of a novel class of continuous-discrete spatiotemporal solitons, the so-called discrete surface light bullets. We show that their properties are strongly affected by the presence of the surface. To this end the crossover between surface and quasi-bulk bullets is studied by analyzing the families of solitons propagating at different distances from the edge of the waveguide array.
Discrete Hamiltonian for General Relativity
Ziprick, Jonathan
2015-01-01
Beginning from canonical general relativity written in terms of Ashtekar variables, we derive a discrete phase space with a physical Hamiltonian for gravity. The key idea is to define the gravitational fields within a complex of three-dimensional cells such that the dynamics is completely described by discrete boundary variables, and the full theory is recovered in the continuum limit. Canonical quantization is attainable within the loop quantum gravity framework, and we believe this will lead to a promising candidate for quantum gravity.
Kang, Jianhong; Xu, Mingyu
2009-04-01
The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.
Jianhong Kang; Mingyu Xu
2009-01-01
The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit. The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced. We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform. The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.
Computing an Exact Gaussian Scale-Space
Ives Rey Otero
2016-02-01
Full Text Available Gaussian convolution is one of the most important algorithms in image processing. The present work focuses on the computation of the Gaussian scale-space, a family of increasingly blurred images, responsible, among other things, for the scale-invariance of SIFT, a popular image matching algorithm. We discuss and numerically analyze the precision of three different alternatives for defining a discrete counterpart to the continuous Gaussian operator. This study is focused on low blur levels, that are crucial for the scale-space accuracy.
Some discrete multiple orthogonal polynomials
Arvesú, J.; Coussement, J.; van Assche, W.
2003-04-01
In this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317-347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r+1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r=2.
Solving discrete zero point problems
van der Laan, G.; Talman, A.J.J.; Yang, Z.F.
2004-01-01
In this paper an algorithm is proposed to .nd a discrete zero point of a function on the collection of integral points in the n-dimensional Euclidean space IRn.Starting with a given integral point, the algorithm generates a .nite sequence of adjacent integral simplices of varying dimension and termi
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.
Compiling Relational Bayesian Networks for Exact Inference
Jaeger, Manfred; Darwiche, Adnan; Chavira, Mark
2006-01-01
We describe in this paper a system for exact inference with relational Bayesian networks as defined in the publicly available PRIMULA tool. The system is based on compiling propositional instances of relational Bayesian networks into arithmetic circuits and then performing online inference...... by evaluating and differentiating these circuits in time linear in their size. We report on experimental results showing successful compilation and efficient inference on relational Bayesian networks, whose PRIMULA--generated propositional instances have thousands of variables, and whose jointrees have clusters...
Exact diagonalization of quantum-spin models
Lin, H. Q.
1990-10-01
We have developed a technique to replace hashing in implementing the Lanczös method for exact diagonalization of quantum-spin models that enables us to carry out numerical studies on substantially larger lattices than previously studied. We describe the algorithm in detail and present results for the ground-state energy, the first-excited-state energy, and the spin-spin correlations on various finite lattices for spins S=1/2, 1, 3/2, and 2. Results for an infinite system are obtained by extrapolation. We also discuss the generalization of our method to other models.
Maxwell Optics II. An Exact Formalism
Khan, S A
2002-01-01
We present a formalism for light optics starting with the Maxwell equations and casting them into an exact matrix form taking into account the spatial and temporal variations of the permittivity and permeability. This $8 \\times 8$ matrix representation is used to construct the optical Hamiltonian. This has a close analogy with the algebraic structure of the Dirac equation, enabling the use of the rich machinery of the Dirac electron theory. We get interesting wavelength-dependent contributions which can not be obtained in any of the traditional approaches.
Exact solutions for Weyl fermions with gravity
Cianci, Roberto; Fabbri, Luca; Vignolo, Stefano [Universita di Genova, DIME Sez. Metodi e Modelli Matematici, Genoa (Italy)
2015-10-15
We consider the single-handed spinor field in interaction with its own gravitational field described by the set of field equations given by the Weyl field equations written in terms of derivatives that are covariant with respect to the gravitational connection plus Einstein field equations soured with the energy tensor of the spinor: for the Weyl spinor and the ensuing spacetime of Weyl-Lewis-Papapetrou structure, we find all exact solutions. The obtained solution for the metric tensor is that of a PP-wave spacetime, while the spinor field is a flag-dipole. (orig.)
Exact Topological Twistons in Crystalline Polyethylene
Ventura, E; Bazeia, D
2000-01-01
We investigate the presence of topological twistons in crystalline polyethylene. We describe crystalline polyethylene with a model that couples the torsional and longitudinal degrees of freedom of the polymeric chain by means of a system of two real scalar fields. This model supports topological twistons, which are described by exact and stable topological solutions that appear when the interaction between torsional and longitudinal fields is polynomial, containing up to the sixth power in the fields. We calculate the energy of the topological twiston, and the result is in very good agreement with the value obtained via molecular simulation.
The Exact Limit of Some Cubic Towers
Anbar Meidl, Nurdagül; Beelen, Peter; Nguyen, Nhut
2016-01-01
Recently, a new explicit tower of function fields was introduced by Bassa, Beelen, Garcia and Stichtenoth (BBGS). This resulted in currently the best known lower bound for Ihara’s constant in the case of non-prime finite fields. In particular over cubic fields, the tower’s limit is at least as good...... as Zink’s bound; i.e. λ(BBGS/Fq3 ) ≥ 2(q2 - 1)/(q + 2). In this paper, the exact value of λ(BBGS/Fq3 ) is computed. We also settle a question stated by Ihara....
Nonuniform Braneworld Stars: AN Exact Solution
Ovalle, J.
In this paper the first exact interior solution to Einstein's field equations for a static and nonuniform braneworld star with local and nonlocal bulk terms is presented. It is shown that the bulk Weyl scalar U(r) is always negative inside the stellar distribution, and in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behavior inside the distribution. Using a Reissner-Nördstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.
Exact formulas in noncommutative gauge theories
Wallet, Jean-Christophe
2016-01-01
The noncommutative space $\\mathbb{R}^3_\\lambda$, a deformation of $\\mathbb{R}^3$, supports a $3$-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of $\\mathbb{R}^3_\\lambda$. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
An exact approach for aggregated formulations
Gamst, Mette; Spoorendonk, Simon; Røpke, Stefan
optimality cannot be guaranteed by branching on aggregated variables. We present a generic exact solution method to remedy the drawbacks of aggregation. It combines the original and aggregated formulations and applies Benders' decomposition. We apply the method to the Split Delivery Vehicle Routing Problem.......Aggregating formulations is a powerful approach for problems to take on tractable forms. Aggregation may lead to loss of information, i.e. the aggregated formulation may be an approximation of the original problem. In branch-and-bound context, aggregation can also complicate branching, e.g. when...
Discrete implementations of scale transform
Djurdjanovic, Dragan; Williams, William J.; Koh, Christopher K.
1999-11-01
Scale as a physical quantity is a recently developed concept. The scale transform can be viewed as a special case of the more general Mellin transform and its mathematical properties are very applicable in the analysis and interpretation of the signals subject to scale changes. A number of single-dimensional applications of scale concept have been made in speech analysis, processing of biological signals, machine vibration analysis and other areas. Recently, the scale transform was also applied in multi-dimensional signal processing and used for image filtering and denoising. Discrete implementation of the scale transform can be carried out using logarithmic sampling and the well-known fast Fourier transform. Nevertheless, in the case of the uniformly sampled signals, this implementation involves resampling. An algorithm not involving resampling of the uniformly sampled signals has been derived too. In this paper, a modification of the later algorithm for discrete implementation of the direct scale transform is presented. In addition, similar concept was used to improve a recently introduced discrete implementation of the inverse scale transform. Estimation of the absolute discretization errors showed that the modified algorithms have a desirable property of yielding a smaller region of possible error magnitudes. Experimental results are obtained using artificial signals as well as signals evoked from the temporomandibular joint. In addition, discrete implementations for the separable two-dimensional direct and inverse scale transforms are derived. Experiments with image restoration and scaling through two-dimensional scale domain using the novel implementation of the separable two-dimensional scale transform pair are presented.
Yang, L. M.; Shu, C.; Wang, Y.; Sun, Y.
2016-08-01
The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.
Discrete Multiscale Analysis: A Biatomic Lattice System
Contra, G A Cassatella; 10.1142/S1402925110000957
2010-01-01
We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations. We require that also the reduced equation be discrete. To do so coherently we need to discretize the time variable to be able to get asymptotic discrete waves and carry out a discrete multiscale expansion around them. Our resulting nonlinear equation will be a kind of discrete Nonlinear Schr\\"odinger equation. If we make its continuum limit, we obtain the standard Nonlinear Schr\\"odinger differential equation.
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea
2013-01-01
Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.
Discrete Averaging Relations for Micro to Macro Transition
Liu, Chenchen; Reina, Celia
2016-05-01
The well-known Hill's averaging theorems for stresses and strains as well as the so-called Hill-Mandel principle of macrohomogeneity are essential ingredients for the coupling and the consistency between the micro and macro scales in multiscale finite element procedures (FE$^2$). We show in this paper that these averaging relations hold exactly under standard finite element discretizations, even if the stress field is discontinuous across elements and the standard proofs based on the divergence theorem are no longer suitable. The discrete averaging results are derived for the three classical types of boundary conditions (affine displacement, periodic and uniform traction boundary conditions) using the properties of the shape functions and the weak form of the microscopic equilibrium equations. The analytical proofs are further verified numerically through a simple finite element simulation of an irregular representative volume element undergoing large deformations. Furthermore, the proofs are extended to include the effects of body forces and inertia, and the results are consistent with those in the smooth continuum setting. This work provides a solid foundation to apply Hill's averaging relations in multiscale finite element methods without introducing an additional error in the scale transition due to the discretization.
On the uncertainty inequality as applied to discrete signals
Y. V. Venkatesh
2006-01-01
Full Text Available Given a continuous-time bandlimited signal, the Shannon sampling theorem provides an interpolation scheme for exactly reconstructing it from its discrete samples. We analyze the relationship between concentration (or compactness in the temporal/spectral domains of the (i continuous-time and (ii discrete-time signals. The former is governed by the Heisenberg uncertainty inequality which prescribes a lower bound on the product of effective temporal and spectral spreads of the signal. On the other hand, the discrete-time counterpart seems to exhibit some strange properties, and this provides motivation for the present paper. We consider the following problem: for a bandlimited signal, can the uncertainty inequality be expressed in terms of the samples, using thestandard definitions of the temporal and spectral spreads of the signal? In contrast with the results of the literature, we present a new approach to solve this problem. We also present a comparison of the results obtained using the proposed definitions with those available in the literature.
An Exactly Solvable Many-Fermion Model
Zettili, Nouredine
2001-04-01
We deal with the construction of a simple many-body model that can be solved exactly. This model serves as a tool for testing the validity and accuracy of many-body approximation methods. The model consists of a system of two distinguishable, one-dimensional sets of fermions interacting via a schematic two-body force. We construct the Hamiltonian of the model by means of vector operators that satisfy a Lie algebra and which are the generators of an SO(2,1) group. The Hamiltonian depends on an adjustable parameter which regulates the strength of the two-body interaction. The size of the Hamiltonian's matrix is rendered finite by means of a built-in symmetry: the Hamiltonian is represented by a five-diagonal square matrix of finite size. The energy spectrum of the model is obtained by diagonalizing this matrix. The energy eigenvalues obtained from this diagonalization are exact, for we don't resort to any approximation in the diagonalization. This model offers a rich and flexible platform for testing quantitatively the various many-body approximation methods especially those that deal with nuclear collective motion.
An Exactly Solvable Many-Body Model
Zettili, Nouredine; Boukahil, Abdelkrim
2012-03-01
We deal here with the construction of a simple many-body model that can be solved exactly. This model serves as a tool for testing the validity and accuracy of many-body approximation methods, most notably those encountered in nuclear theory. The model consists of a system of two distinguishable, one-dimensional sets fermions interacting via a schematic two-body force. We construct the Hamiltonian of the model by means of vector operators that satisfy a Lie algebra and which are the generators of an SO(2,1) group. The Hamiltonian depends on an adjustable parameter which regulates the strength of the two-body interaction. The size of the Hamiltonian's matrix is rendered finite by means of a built-in symmetry: the Hamiltonian is represented by a five-diagonal square matrix of finite size. The energy spectrum of the model is obtained by diagonalizing this matrix. The energy eigenvalues obtained from this diagonalization are exact, for we don't need to resort to any approximation in the diagonalization. This model offers a rich and flexible platform for testing quantitatively the various many-body approximation methods especially those that deal with nuclear collective motion.
Explicitly broken supersymmetry with exactly massless moduli
Dong, Xi; Freedman, Daniel Z.; Zhao, Yue
2016-06-01
The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a super-gravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.
Exact collisional moments for plasma fluid theories
Pfefferlé, D.; Hirvijoki, E.; Lingam, M.
2017-04-01
The velocity-space moments of the often troublesome nonlinear Landau collision operator are expressed exactly in terms of multi-index Hermite-polynomial moments of distribution functions. The collisional moments are shown to be generated by derivatives of two well-known functions, namely, the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian distribution. The resulting formula has a nonlinear dependency on the relative mean flow of the colliding species normalised to the root-mean-square of the corresponding thermal velocities and a bilinear dependency on densities and higher-order velocity moments of the distribution functions, with no restriction on temperature, flow, or mass ratio of the species. The result can be applied to both the classic transport theory of plasmas that relies on the Chapman-Enskog method, as well as to derive collisional fluid equations that follow Grad's moment approach. As an illustrative example, we provide the collisional ten-moment equations with exact conservation laws for momentum- and energy-transfer rates.
Exact renormalization group and Sine Gordon theory
Oak, Prafulla; Sathiapalan, B.
2017-07-01
The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the differential equation. This is illustrated by reproducing known results in four dimensional ϕ 4 field theory and the two dimensional Sine-Gordon theory. It is shown that the calculation of beta function is somewhat simplified. The technique is also used to calculate the c-function in two dimensional Sine-Gordon theory. This agrees with other prescriptions for calculating c-functions in the literature. If one extrapolates the connection between central charge of a CFT and entanglement entropy in two dimensions, to the c-function of the perturbed CFT, then one gets a value for the entanglement entropy in Sine-Gordon theory that is in exact agreement with earlier calculations (including one using holography) in arXiv:1610.04233.
Focus measurement in 3D focal stack using direct and inverse discrete radon transform
Gómez-Cárdenes, Óscar; Marichal-Hernández, José G.; Trujillo-Sevilla, Juan M.; Carmona-Ballester, David; Rodríguez-Ramos, José M.
2017-05-01
The discrete Radon transform, DRT, calculates, with linearithmic complexity, the sum of pixels through a set of discrete lines covering all possible slopes and intercepts in an image. In 2006, a method was proposed to compute the inverse DRT that remains exact and fast, in spite of being iterative. In this work the DRT pair is used to propose a Ridgelet and a Curvelet transform that perform focus measurement of an image. Then the shape from focus approach based on DRT pair is applied to a focal stack to create a depth map of a scene.
Bertola, Marco
2010-01-01
The semiclassical (zero-dispersion) limit of the one-dimensional focusing Nonlinear Schroedinger equation (NLS) with decaying potentials is studied in a full scaling neighborhood D of the point of gradient catastrophe (x_0,t_0). This neighborhood contains the region of modulated plane wave (with rapid phase oscillations), as well as the region of fast amplitude oscillations (spikes). In this paper we establish the following universal behaviors of the NLS solutions near the point of gradient catastrophe: i) each spike has the height 3|q_0(x_0,t_0,epsilon)| and uniform shape of the rational breather solution to the NLS, scaled to the size O(epsilon); ii) the location of the spikes are determined by the poles of the tritronquee solution of the Painleve I (P1) equation through an explicit diffeomorphism between D and a region into the Painleve plane; iii) if (x,t) belongs to D but lies away from the spikes, the asymptotics of the NLS solution q(x,t,epsilon) is given by the plane wave approximation q_0(x,t,epsilon...
Discrete Gauge Symmetries in Discrete MSSM-like Orientifolds
Ibanez, L E; Uranga, A M
2012-01-01
Motivated by the necessity of discrete Z_N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)xU(2)xU(1)xU(1) and U(3)xSp(2)xU(1)xU(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z_2 (R-parity) and Z_3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.
Discrete gauge symmetries in discrete MSSM-like orientifolds
Ibáñez, L. E.; Schellekens, A. N.; Uranga, A. M.
2012-12-01
Motivated by the necessity of discrete ZN symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z2 (R-parity) and Z3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.
Parameter Estimation of a Class One-Dimensional Discrete Chaotic System
Lidong Liu
2011-01-01
Full Text Available It is of vital importance to exactly estimate the unknown parameters of chaotic systems in chaos control and synchronization. In this paper, we present a method for estimating one-dimensional discrete chaotic system based on mean value method (MVM. It is proposed by exploiting the ergodic and synchronization features of chaos. It can effectively estimate the parameter value, and it is more exact than MVM. Finally, numerical simulations on Chebyshev map and Tent map show that the proposed method has better performance of parameter estimation than MVM.
An exact energy conservation property of the quantum lattice Boltzmann algorithm
Dellar, Paul J., E-mail: dellar@maths.ox.ac.uk [OCIAM, Mathematical Institute, 24-29 St Giles' , Oxford OX1 3LB (United Kingdom)
2011-11-28
The quantum lattice Boltzmann algorithm offers a unitary and readily parallelisable discretisation of the Dirac equation that is free of the fermion-doubling problem. The expectation of the discrete time-advance operator is an exact invariant of the algorithm. Its imaginary part determines the expectation of the Hamiltonian operator, the energy of the solution, with an accuracy that is consistent with the overall accuracy of the algorithm. In the one-dimensional case, this accuracy may be increased from first to second order using a variable transformation. The three-dimensional quantum lattice Boltzmann algorithm uses operator splitting to approximate evolution under the three-dimensional Dirac equation by a sequence of solutions of one-dimensional Dirac equations. The three-dimensional algorithm thus inherits the energy conservation property of the one-dimensional algorithm, although the implementation shown remains only first-order accurate due to the splitting error. -- Highlights: ► The quantum lattice Boltzmann algorithm approximates the Dirac equation. ► It has an exact invariant: the expectation of the discrete time-advance operator. ► The invariant consistently approximates the energy of the continuous system. ► We achieve second-order accuracy through a variable transformation.
Discretizing a backward stochastic differential equation
Yinnan Zhang; Weian Zheng
2002-01-01
We show a simple method to discretize Pardoux-Peng's nonlinear backward stochastic differential equation. This discretization scheme also gives a numerical method to solve a class of semi-linear PDEs.
An exact exponential time algorithm for counting bipartite cliques
Kutzkov, Konstantin
2012-01-01
We present a simple exact algorithm for counting bicliques of given size in a bipartite graph on n vertices. We achieve running time of O(1.249^n), improving upon known exact algorithms for finding and counting bipartite cliques.......We present a simple exact algorithm for counting bicliques of given size in a bipartite graph on n vertices. We achieve running time of O(1.249^n), improving upon known exact algorithms for finding and counting bipartite cliques....
Submerged Landau jet: exact solutions, their meaning and application
Broman, Goran I [Blekinge Institute of Technology, Karlskrona (Sweden); Rudenko, Oleg V [M. V. Lomonosov Moscow State University, Faculty of Physics, Moscow (Russian Federation)
2010-01-31
Exact hydrodynamic solutions generalizing the Landau submerged jet solution are reviewed. It is shown how exact inviscid solutions can be obtained and how boundary layer viscosity can be included by introducing parabolic coordinates. The use of exact solutions in applied hydrodynamics and acoustics is discussed. A historical perspective on the discovery of a class of exact solutions and on the analysis of their physical meaning is presented. (methodological notes)
Exact Controllability and Asymptotic Analysis for Shallow Shells
S. KAIZU; N. SABU
2007-01-01
The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2ε with controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the existence of exact controls, it is shown that the solutions of the three dimensional exact controllability problems converge, as the thickness of the shell goes to zero, to the solution of an exact controllability problem in two dimensions.
Discrete and Continuous Linearizable Equations
Lafortune, S; Ramani, A
1998-01-01
We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one and reduce the system to a single differential equation. This equation is of the form of those singled-out by Painlevé in his quest for integrable forms. In the discrete case, we extend previous results of ours showing that, again by elimination of variables, the general projective system can be written as a mapping for a single variable. We show that this mapping is a member of the family of multilinear systems (which is not integrable in general). The continuous limit of multilinear mappings is also discussed.
Discrete mathematics using a computer
Hall, Cordelia
2000-01-01
Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...
Discrete fields on the lightcone
De Souza, M M
1997-01-01
We introduce a classical field theory based on a concept of extended causality that mimics the causality of a point- particle Classical Mechanics by imposing constraints that are equivalent to a particle initial position and velocity. It results on a description of discrete (pointwise) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant $(1+1)$-dimensional dynamics in a $(3+1)$ spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete fields. Singularities are the by-products of the averaging proccess. This new formalism enlighten the meaning and the problems of field theory, and may allow a softer transition to a quantum th...