Discrete breathers in crystals
NASA Astrophysics Data System (ADS)
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
Dissipative discrete breathers: periodic, quasiperiodic, chaotic, and mobile.
Martínez, P J; Meister, M; Floría, L M; Falo, F
2003-06-01
The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations. PMID:12777126
Discrete breathers in graphane: Effect of temperature
NASA Astrophysics Data System (ADS)
Baimova, J. A.; Murzaev, R. T.; Lobzenko, I. P.; Dmitriev, S. V.; Zhou, Kun
2016-05-01
The discrete breathers in graphane in thermodynamic equilibrium in the temperature range 50-600 K are studied by molecular dynamics simulation. A discrete breather is a hydrogen atom vibrating along the normal to a sheet of graphane at a high amplitude. As was found earlier, the lifetime of a discrete breather at zero temperature corresponds to several tens of thousands of vibrations. The effect of temperature on the decay time of discrete breathers and the probability of their detachment from a sheet of graphane are studied in this work. It is shown that closely spaced breathers can exchange energy with each other at zero temperature. The data obtained suggest that thermally activated discrete breathers can be involved in the dehydrogenation of graphane, which is important for hydrogen energetics.
Discrete breathers in hexagonal dusty plasma lattices
Koukouloyannis, V.; Kourakis, I.
2009-08-15
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.
Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site.
Jason, Peter; Johansson, Magnus
2016-01-01
We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers. PMID:26871085
Energy Criterion for the Spectral Stability of Discrete Breathers.
Kevrekidis, Panayotis G; Cuevas-Maraver, Jesús; Pelinovsky, Dmitry E
2016-08-26
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. PMID:27610856
Long-lived discrete breathers in free-standing graphene
NASA Astrophysics Data System (ADS)
Fraile, Alberto; Koukaras, Emmanuel N.; Papagelis, Konstantinos; Lazarides, Nikos; Tsironis, G. P.
2016-06-01
Intrinsic localized modes or discrete breathers are investigated by molecular dynamics simulations in free-standing graphene. Discrete breathers are generated either through thermal quenching of the graphene lattice or by proper initialization, with frequencies and lifetimes sensitively depending on the interatomic potential describing the carbon-carbon interaction. In the most realistic scenario, for which temperature-dependent molecular dynamics simulations in three dimension using a graphene-specific interatomic potential are performed, the breather lifetimes increase to hundreds of picoseconds even at relatively high temperatures. These lifetimes are much higher than those anticipated from earlier calculations, and may enable direct breather observation in Raman spectroscopy experiments.
Discrete breathers in the Peyrard-Bishop model of DNA
NASA Astrophysics Data System (ADS)
Fakhretdinov, M. I.; Zakir'yanov, F. K.
2013-07-01
The Peyrard-Bishop model, which describes the dynamics of a DNA molecule, is considered. The solutions that represent discrete breathers are derived in the framework of the model. The dynamic stability of the stationary discrete breathers with respect to small perturbations is studied. The solutions can be interpreted as the experimentally observed opening of the base pairs in the DNA double strand at the initial stages of denaturation. It is also demonstrated that the model allows the existence of mobile breathers that move in the absence of perturbations in the environment. The interaction of the mobile breathers is numerically simulated. The Peierls-Nabarro barrier and the effective mass and velocity of the breather are estimated.
Energy Exchange Between the Discrete Breathers in Graphane
NASA Astrophysics Data System (ADS)
Baimova, J. A.; Dmitriev, S. V.
2015-10-01
Discrete breathers in graphane (fully hydrogenated graphene) are studied by the molecular dynamics method. It has previously been demonstrated that in graphane, there are discrete breathers in the form of single hydrogen atoms oscillating with the big amplitude in the direction perpendicular to the graphane plane with a frequency lying in the bandgap of the phonon spectrum. In this work, the possibility of the existence of longlived clusters of discrete breathers of different configurations is shown, their properties are studied, and the possibility of energy exchange between the discrete breathers in the cluster is demonstrated. These results are important for the discussion of physical processes occurring during dehydrogenation of graphane at high temperatures, which, in turn, is of great importance for the development of the hydrogen storage and transport devices based on sp2-carbon materials.
Discrete breathers in alpha-uranium
NASA Astrophysics Data System (ADS)
Murzaev, Ramil T.; Babicheva, Rita I.; Zhou, Kun; Korznikova, Elena A.; Fomin, Sergey Yu.; Dubinko, Vladimir I.; Dmitriev, Sergey V.
2016-07-01
Uranium is an important radioactive material used in the field of nuclear energy and it is interesting from the scientific point of view because it possesses unique structure and properties. There exist several experimental reports on anomalies of physical properties of uranium that have not been yet explained. Manley et al. [Phys. Rev. Lett. 96, 125501 (2006); Phys. Rev. B 77, 214305 (2008)] speculate that the excitation of discrete breathers (DBs) could be the reason for anisotropy of thermal expansion and for the deviation of heat capacity from the theoretical prediction in the high temperature range. In the present work, with the use of molecular dynamics, the existence of DBs in α-uranium is demonstrated and their properties are studied. It is found that DB frequency lies above the phonon band and increases with DB amplitude. DB is localized on half a dozen of atoms belonging to a straight atomic chain. DB in uranium, unlike DBs in fcc, bcc and hcp metals, is almost immobile. Thus, the DB reported in this study cannot contribute to thermal conductivity and the search for other types of DBs in α-uranium should be continued. Our results demonstrate that even metals with low-symmetry crystal lattices such as the orthorhombic lattice of α-uranium can support DBs.
Ab initio simulation of gap discrete breathers in strained graphene
NASA Astrophysics Data System (ADS)
Lobzenko, I. P.; Chechin, G. M.; Bezuglova, G. S.; Baimova, Yu. A.; Korznikova, E. A.; Dmitriev, S. V.
2016-03-01
The methods of the density functional theory were used for the first time for the simulation of discrete breathers in graphene. It is demonstrated that breathers can exist with frequencies lying in the gap of the phonon spectrum, induced by uniaxial tension of a monolayer graphene sheet in the "zigzag" direction (axis X), polarized in the "armchair" direction (axis Y). The found gap breathers are highly localized dynamic objects, the core of which is formed by two adjacent carbon atoms located on the Y axis. The atoms surrounding the core vibrate at much lower amplitudes along both the axes ( X and Y). The dependence of the frequency of these breathers on amplitude is found, which shows a soft type of nonlinearity. No breathers of this type were detected in the gap induced by stretching along the Y axis. It is shown that the breather vibrations may be approximated by the Morse oscillators, the parameters of which are determined from ab initio calculations. The results are of fundamental importance, as molecular dynamics calculations based on empirical potentials cannot serve as a reliable proof of the existence of breathers in crystals.
Discrete breathers in one-dimensional diatomic granular crystals.
Boechler, N; Theocharis, G; Job, S; Kevrekidis, P G; Porter, Mason A; Daraio, C
2010-06-18
We report the experimental observation of modulational instability and discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both theoretically and experimentally. We then illustrate theoretically and numerically the modulational instability of the lower edge of the optical band. This leads to the dynamical formation of long-lived breather structures, whose families of solutions we compute throughout the linear spectral gap. Finally, we experimentally observe the manifestation of the modulational instability and the resulting generation of localized breathing modes with quantitative characteristics that agree with our numerical results. PMID:20867305
Dynamics of Discrete Breathers in a Pt3Al Crystal
NASA Astrophysics Data System (ADS)
Starostenkov, M. D.; Potekaev, A. I.; Dmitriev, S. V.; Zakharov, P. V.; Eremin, A. M.; Kulagina, V. V.
2016-01-01
The discrete breathers in a Pt3Al crystal, which exhibit soft (DB1) and hard (DB2) nonlinearity, are shown to possess a number of principal differences. Unlike an immobile and stable DB1, a DB2 breather is mainly localized on four Al atoms and is stretched along one of the close-packed rows of crystals. On the other hand, DB2 can displace hundreds of nanometers along one of the directions of close packing. Having localized a considerable amount of energy, both DB1 and DB2 breathers slowly emit it during their lifetime. A collision of DB1 and DB2 results in part of their energy being released into the Al sublattice, the larger part lost by DB2 that is destroyed faster than DB1. The DB2 breather can effectively transport the energy throughout the crystal, and a collision of DBs results in its considerable localization in the crystal. A capability of transferring the energy can thus give rise to structural transformations far from the focus of excitation of such localized objects.
Symmetric Potential Lattice and Smooth Propagation of Tail-Free Discrete Breathers.
Doi, Yusuke; Yoshimura, Kazuyuki
2016-07-01
We present a particular type of one-dimensional nonlinear lattice that supports smoothly propagating discrete breathers. The lattice is constructed by imposing a particular symmetry on its potential function. This symmetry crucially affects the profile and motion of a traveling discrete breather. We show that any traveling discrete breather is truly localized with no tail and can smoothly propagate with a constant velocity. Theoretical analysis using an average Lagrangian explains this numerical observation. PMID:27419571
Symmetric Potential Lattice and Smooth Propagation of Tail-Free Discrete Breathers
NASA Astrophysics Data System (ADS)
Doi, Yusuke; Yoshimura, Kazuyuki
2016-07-01
We present a particular type of one-dimensional nonlinear lattice that supports smoothly propagating discrete breathers. The lattice is constructed by imposing a particular symmetry on its potential function. This symmetry crucially affects the profile and motion of a traveling discrete breather. We show that any traveling discrete breather is truly localized with no tail and can smoothly propagate with a constant velocity. Theoretical analysis using an average Lagrangian explains this numerical observation.
Exact discretization by Fourier transforms
NASA Astrophysics Data System (ADS)
Tarasov, Vasily E.
2016-08-01
A discretization of differential and integral operators of integer and non-integer orders is suggested. New type of differences, which are represented by infinite series, is proposed. A characteristic feature of the suggested differences is an implementation of the same algebraic properties that have the operator of differentiation (property of algebraic correspondence). Therefore the suggested differences are considered as an exact discretization of derivatives. These differences have a property of universality, which means that these operators do not depend on the form of differential equations and the parameters of these equations. The suggested differences operators allows us to have difference equations whose solutions are equal to the solutions of corresponding differential equations. The exact discretization of the derivatives of integer orders is given by the suggested differences of the same integer orders. Similarly, the exact discretization of the Riesz derivatives and integrals of integer and non-integer order is given by the proposed fractional differences of the same order.
From Discrete Breathers to Many Body Localization and Flatbands
NASA Astrophysics Data System (ADS)
Flach, Sergej
Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves. Also at New Zealand Institute of Advanced Study, Massey University, Auckland, New Zealand.
Nonlinear nano-scale localized breather modes in a discrete weak ferromagnetic spin lattice
NASA Astrophysics Data System (ADS)
Kavitha, L.; Parasuraman, E.; Gopi, D.; Prabhu, A.; Vicencio, Rodrigo A.
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.
Signatures of discrete breathers in coherent state quantum dynamics
Igumenshchev, Kirill; Ovchinnikov, Misha; Prezhdo, Oleg; Maniadis, Panagiotis
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
Breather Solutions of the Discrete p-Schrödinger Equation
NASA Astrophysics Data System (ADS)
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.
Cuevas, J.; Palmero, F.
2009-11-15
We propose analytical lower and upper estimates on the excitation threshold for breathers (in the form of spatially localized and time periodic solutions) in discrete nonlinear Schroedinger (DNLS) lattices with power nonlinearity. The estimation, depending explicitly on the lattice parameters, is derived by a combination of a comparison argument on appropriate lower bounds depending on the frequency of each solution with a simple and justified heuristic argument. The numerical studies verify that the analytical estimates can be of particular usefulness, as a simple analytical detection of the activation energy for breathers in DNLS lattices.
Discrete breathers in a nonlinear electric line: modeling, computation, and experiment.
Palmero, F; English, L Q; Cuevas, J; Carretero-González, R; Kevrekidis, P G
2011-08-01
We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor, coupled together in a periodic ring configuration through inductors and driven uniformly by a harmonic external voltage source. A simple model for each cell is proposed by using a nonlinear form for the varactor characteristics through the current and capacitance dependence on the voltage. For an electrical line composed of 32 elements, we find the regions, in driver voltage and frequency, where n-peaked breather solutions exist and characterize their stability. The results are compared to experimental measurements with good quantitative agreement. We also examine the spontaneous formation of n-peaked breathers through modulational instability of the homogeneous steady state. The competition between different discrete breathers seeded by the modulational instability eventually leads to stationary n-peaked solutions whose precise locations is seen to sensitively depend on the initial conditions. PMID:21929126
NASA Astrophysics Data System (ADS)
Tang, Bing; Li, De-Jun
2016-05-01
A theoretical work on quantum breathers in a nonlinear Klein-Gordon lattice model with nearest and next-nearest neighbor interactions is presented. The semiclassical and the full quantum cases are respectively considered. For the semiclassical case, we obtain the analytical solution of discrete breather, and find that the wave number corresponding to the appearance of discrete breather changes when the ratio of the next-nearest- to -nearest - neighbor harmonic force constants is greater than 1/4. For the full quantum case, by calculating the energy spectrum of the system containing two quanta, we prove numerically the existence of quantum breathers (two-quanta bound states) and find the shape of energy spectrum changes dramatically as the value of next -nearest neighbor harmonic force constant increasing.
Bai, Xiao-Dong; Xue, Ju-Kui
2012-12-01
By considering a general discrete nonlinear Schrödinger model with arbitrary values of nonlinearity power and disorder, the existence and stability of a discrete breather (DB) in a general nonlinear lattice are discussed. It is found that nonlinearity and disorder play important roles in determining the existence and stability of the DB. Nonlinearity (expressed by the interparticle interaction) and disorder can enhance the stability of the DB. Remarkably, we find that the DB is most stable when the nonlinearity power is equal to a critical value. The effects of nonlinearity, nonlinearity power, and disorder on the stability of the DB are strongly coupled. PMID:23368070
NASA Astrophysics Data System (ADS)
Johansson, Magnus; Prilepsky, Jaroslaw E.; Derevyanko, Stanislav A.
2014-04-01
We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau-type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. 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 the 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 by lattice commensurability and exhibit period-doubling bifurcations to chaotically "walking" modes under parameter variations. If the model is augmented by intersite Kerr nonlinearity, thereby reducing the Peierls-Nabarro barrier of the conservative system, the existence regime for moving solitons increases considerably, and a richer scenario appears including Hopf bifurcations to incommensurately moving solutions and phase-locking intervals. Stable moving breathers also survive in the presence of weak disorder.
Transfer of Bose-Einstein condensates through discrete breathers in an optical lattice
Hennig, H.; Dorignac, J.; Campbell, D. K.
2010-11-15
We study the effect of discrete breathers (DBs) on the transfer of a Bose-Einstein condensate (BEC) in an optical lattice using the discrete nonlinear Schroedinger equation. In previous theoretical (primarily numerical) investigations of the dynamics of BECs in leaking optical lattices, collisions between a DB and a lattice excitation, e.g., a moving breather (MB) or phonon, were studied. These collisions led to the transmission of a fraction of the incident (atomic) norm of the MB through the DB, while the DB can be shifted in the direction of the incident lattice excitation. Here we develop an analytic understanding of this phenomenon, based on the study of a highly localized system--namely, a nonlinear trimer--which predicts that there exists a total energy threshold of the trimer, above which the lattice excitation can trigger the destabilization of the DB and that this is the mechanism leading to the movement of the DB. Furthermore, we give an analytic estimate of upper bound to the norm that is transmitted through the DB. We then show numerically that a qualitatively similar threshold exists in extended lattices. Our analysis explains the results of the earlier numerical studies and may help to clarify functional operations with BECs in optical lattices such as blocking and filtering coherent (atomic) beams.
NASA Astrophysics Data System (ADS)
Palmero, F.; Han, J.; English, L. Q.; Alexander, T. J.; Kevrekidis, P. G.
2016-01-01
We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes, also known as discrete breathers, can exist. Recently, the existence of multifrequency breathers via subharmonic driving has been theoretically proposed and numerically illustrated by Xu et al. (2014) [21]. In this paper, we verify this prediction experimentally. Comparison of the experimental results to numerical simulations with realistic system parameters (including a Floquet stability analysis), and wherever possible to analytical results (e.g. for the subharmonic response of the single driven-damped pendulum), yields good agreement. Finally, we report the period-1 and multifrequency edge breathers which are localized at the open boundaries of the chain, for which we have again found good agreement between experiments and numerical computations.
Bezuglova, G S; Chechin, G M; Goncharov, P P
2011-09-01
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in two- and three-dimensional lattice dynamical models is developed. This approach is demonstrated for the scalar models on the plane square lattice. The symmetry-determined invariant manifolds admitting existence of localized vibrations are found, and some types of discrete breathers are constructed on these manifolds. A general method using the apparatus of matrix representations of symmetry groups to simplify the standard linear stability analysis is discussed. This method allows one to decompose the corresponding system of linear differential equations with time-dependent coefficients into a number of independent subsystems whose dimensions are less than the full dimension of the considered system. PMID:22060521
Breathers in a locally resonant granular chain with precompression
NASA Astrophysics Data System (ADS)
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.
Breathers in a locally resonant granular chain with precompression
Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; Vainchtein, Anna
2016-05-24
Here 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. In turn, this 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. Moreover, the stability and bifurcation structure of numerically computedmore » 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.« less
NASA Astrophysics Data System (ADS)
Stockhofe, J.; Schmelcher, P.
2016-08-01
We study a one-dimensional discrete nonlinear Schrödinger model with hopping to the first and a selected Nth neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability properties of this equation, identifying distinctive multi-stage instability cascades due to the helicoidal hopping term. Bistability is a characteristic feature of the intrinsically localized breather modes, and it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. Based on this argument, we derive analytical estimates of the critical parameters at which the fundamental on-site breather branch of solutions turns unstable. In the limit of large N, these estimates predict the emergence of an effective threshold behavior, which can be viewed as the result of a dimensional crossover to a two-dimensional square lattice.
Exact evolution of discrete relativistic cosmological models
Clifton, Timothy; Tavakol, Reza; Gregoris, Daniele; Rosquist, Kjell E-mail: danielegregoris@libero.it E-mail: r.tavakol@qmul.ac.uk
2013-11-01
We study the effects of inhomogeneities on the evolution of the Universe, by considering a range of cosmological models with discretized matter content. This is done using exact and fully relativistic methods that exploit the symmetries in and about submanifolds of spacetimes that themselves possess no continuous global symmetries. These methods allow us to follow the evolution of our models throughout their entire history, far beyond what has previously been possible. We find that while some space-like curves collapse to anisotropic singularities in finite time, others remain non-singular forever. The resulting picture is of a cosmological spacetime in which some behaviour remains close to Friedmann-like, while other behaviours deviate radically. In particular, we find that large-scale acceleration is possible without any violation of the energy conditions.
Zakharov, P. V.; Starostenkov, M. D.; Dmitriev, S. V.; Medvedev, N. N.; Eremin, A. M.
2015-08-15
It is known that, in a molecular dynamics model of Pt{sub 3}Al crystal, a discrete breather (DB) with soft type nonlinearity (DB1) can be excited, which is characterized by a high degree of localization on a light atom (Al), stationarity, as well as a frequency that lies in the gap of the phonon spectrum and decreases with increasing amplitude of the DB. In this paper, it is demonstrated that a DB with hard type nonlinearity (DB2) can be excited in a Pt{sub 3}Al nanofiber; this DB is localized on several light atoms, can move along the crystal, and has a frequency that lies above the phonon spectrum and increases with the DB amplitude. It is noteworthy that the presence of free surfaces of a nanofiber does not prevent the existence of DB1 and DB2 in it. Collisions of two DBs counterpropagating with equal velocities, as well as a collision of DB2 with a standing DB1, are considered. Two colliding DBs with hard type nonlinearity are repelled almost elastically, losing only insignificant part of their energy during the interaction. DB2 is also reflected from a standing DB1; in this case, the energy of the breathers is partially scattered into the Al sublattice. The results obtained indicate that DBs can transfer energy along a crystal over large distances. During the collision of two or more DBs, the energy localized in space can be as high as a few electron-volts; this allows one to raise the question of the participation of DBs in structural transformations of the crystal.
Breathers on quantized superfluid vortices.
Salman, Hayder
2013-10-18
We consider the propagation of breathers along a quantized superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger 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 localized in both space and time. The emergent structures on the vortex filament are analogous to loop solitons but arise from the dual action of bending and twisting of the vortex. 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 crossover range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings. PMID:24182275
Breathers on Quantized Superfluid Vortices
NASA Astrophysics Data System (ADS)
Salman, Hayder
2013-10-01
We consider the propagation of breathers along a quantized superfluid vortex. Using the correspondence between the local induction approximation (LIA) and the nonlinear Schrödinger 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 localized in both space and time. The emergent structures on the vortex filament are analogous to loop solitons but arise from the dual action of bending and twisting of the vortex. 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 crossover range of scales in superfluid turbulence. Moreover, the observation of breather solutions on vortices in a field model suggests that these solutions are expected to arise in a wide range of other physical contexts from classical vortices to cosmological strings.
Zhang, Hao; Douglas, Jack F.
2012-01-01
Recent studies of the dynamics of diverse condensed amorphous materials have indicated significant heterogeneity in the local mobility and a progressive increase in collective particle motion upon cooling that takes the form of string-like particle rearrangements. In a previous paper (Part I), we examined the possibility that fluctuations in potential energy E and particle mobility μ associated with this ‘dynamic heterogeneity’ might offer information about the scale of collective motion in glassy materials based on molecular dynamics simulations of the glassy interfacial region of Ni nanoparticles (NPs) at elevated temperatures. We found that the noise exponent associated with fluctuations in the Debye-Waller factor, a mobility related quantity, was directly proportional to the scale of collective motion L under a broad range of conditions, but the noise exponent associated with E(t) fluctuations was seemingly unrelated to L. In the present work, we focus on this unanticipated difference between potential energy and mobility fluctuations by examining these quantities at an atomic scale. We find that the string atoms exhibit a jump-like motion between two well-separated bands of energy states and the rate at which these jumps occur seems to be consistent with the phenomenology of the ‘slow-beta’ relaxation process of glass-forming liquids. Concurrently with these local E(t) jumps, we also find ‘quake-like’ particle displacements having a power-law distribution in magnitude so that particle displacement fluctuations within the strings are strikingly different from local E(t) fluctuations. An analysis of these E(t) fluctuations suggests that we are dealing with ‘discrete breather’ excitations in which large energy fluctuations develop in arrays of non-linear oscillators by virtue of large anharmonicity in the interparticle interactions and discreteness effects associated with particle packing. We quantify string collective motions on a fast caging
Unified theory of exactly and quasiexactly solvable ''discrete'' quantum mechanics. I. Formalism
Odake, Satoru; Sasaki, Ryu
2010-08-15
We present a simple recipe to construct exactly and quasiexactly solvable Hamiltonians in one-dimensional ''discrete'' quantum mechanics, in which the Schroedinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ones. An essential role is played by the sinusoidal coordinate, which generates the closure relation and the Askey-Wilson algebra together with the Hamiltonian. The relationship between the closure relation and the Askey-Wilson algebra is clarified.
Breathers in oscillator chains with Hertzian interactions
NASA Astrophysics Data System (ADS)
James, Guillaume; Kevrekidis, Panayotis G.; Cuevas, Jesús
2013-05-01
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. We show the existence of breathers in such systems, using both direct numerical computations and a simplified asymptotic model of the oscillator chain, the so-called discrete p-Schrödinger (DpS) equation. From a spectral analysis, we determine breather stability and explain their translational motion under very weak perturbations. Numerical simulations demonstrate the excitation of traveling breathers from simple initial conditions corresponding to small perturbations at the first site of the chain. This regime is well described by the DpS equation, and is found to occur for physical parameter values in granular chains with stiff local oscillators. In addition, traveling breather propagation can be hindered or even suppressed in other parameter regimes. For soft on-site potentials, a part of the energy remains trapped near the boundary and forms a surface mode. For hard on-site potentials and large to moderate initial excitations, one observes a “boomeron”, i.e. a traveling breather displaying spontaneous direction-reversing motion. In addition, dispersion is significantly enhanced when a precompression is applied to the chain. Depending on parameters, this results either in the absence of traveling breather excitation on long time scales, or in the formation of a “nanopteron” characterized by a sizable wave train lying at both sides of the localized excitation.
Exactly solvable potentials with finitely many discrete eigenvalues of arbitrary choice
NASA Astrophysics Data System (ADS)
Sasaki, Ryu
2014-06-01
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 Korteweg de Vries (KdV) hierarchy. An N-soliton potential has the time t and 2N positive parameters, k1 < ⋯ < kN and {cj}, j = 1, …, N, corresponding to N discrete eigenvalues lbrace -k_j^2rbrace. The eigenfunctions are elementary functions expressed by the ratio of determinants. The Darboux-Crum-Krein-Adler transformations or the Abraham-Moses transformations based on eigenfunction deletions produce lower soliton number potentials with modified parameters lbrace c^' }_jrbrace. We explore various identities satisfied by the eigenfunctions of the soliton potentials, which reflect the uniqueness theorem of Gel'fand-Levitan-Marchenko equations for separable (degenerate) kernels.
NASA Astrophysics Data System (ADS)
Li, Jibin; Chen, Fengjuan
In this paper, we consider a modulated equation in a discrete nonlinear electrical transmission line. This model is an integrable planar dynamical system having three singular straight lines. By using the theory of singular systems to investigate the dynamical behavior for this system, we obtain bifurcations of phase portraits under different parameter conditions. Corresponding to some special level curves, we derive exact explicit parametric representations of solutions (including smooth solitary wave solutions, peakons, compactons, periodic cusp wave solutions) under different parameter conditions.
Quantum Two-breathers Formed by Ultracold Bosonic Atoms in Optical Lattices
NASA Astrophysics Data System (ADS)
Tang, Bing
2016-06-01
Two-discrete breathers are the bound states of two localized modes that can appear in classical nonlinear lattices. I investigate the quantum signature of two-discrete breathers in the system of ultracold bosonic atoms in optical lattices, which is modeled as Bose-Hubbard model containing n bosons. When the number of bosons is small, I find numerically quantum two-breathers by making use of numerical diagonalization and perturbation theory. For the cases of a large number of bosons, I can successfully construct quantum two-breather states in the Hartree approximation.
Discretization error estimation and exact solution generation using the method of nearby problems.
Sinclair, Andrew J.; Raju, Anil; Kurzen, Matthew J.; Roy, Christopher John; Phillips, Tyrone S.
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.
Coherent Backscattering by Polydisperse Discrete Random Media: Exact T-Matrix Results
NASA Technical Reports Server (NTRS)
Mishchenko, Michael I.; Dlugach, Janna M.; Mackowski, Daniel W.
2011-01-01
The numerically exact superposition T-matrix method is used to compute, for the first time to our knowledge, electromagnetic scattering by finite spherical volumes composed of polydisperse mixtures of spherical particles with different size parameters or different refractive indices. The backscattering patterns calculated in the far-field zone of the polydisperse multiparticle volumes reveal unequivocally the classical manifestations of the effect of weak localization of electromagnetic waves in discrete random media, thereby corroborating the universal interference nature of coherent backscattering. The polarization opposition effect is shown to be the least robust manifestation of weak localization fading away with increasing particle size parameter.
Event-driven Monte Carlo: Exact dynamics at all time scales for discrete-variable models
NASA Astrophysics Data System (ADS)
Mendoza-Coto, Alejandro; Díaz-Méndez, Rogelio; Pupillo, Guido
2016-06-01
We present an algorithm for the simulation of the exact real-time dynamics of classical many-body systems with discrete energy levels. In the same spirit of kinetic Monte Carlo methods, a stochastic solution of the master equation is found, with no need to define any other phase-space construction. However, unlike existing methods, the present algorithm does not assume any particular statistical distribution to perform moves or to advance the time, and thus is a unique tool for the numerical exploration of fast and ultra-fast dynamical regimes. By decomposing the problem in a set of two-level subsystems, we find a natural variable step size, that is well defined from the normalization condition of the transition probabilities between the levels. We successfully test the algorithm with known exact solutions for non-equilibrium dynamics and equilibrium thermodynamical properties of Ising-spin models in one and two dimensions, and compare to standard implementations of kinetic Monte Carlo methods. The present algorithm is directly applicable to the study of the real-time dynamics of a large class of classical Markovian chains, and particularly to short-time situations where the exact evolution is relevant.
Self-gravitating scalar breathers with a negative cosmological constant
NASA Astrophysics Data System (ADS)
Fodor, Gyula; Forgács, Péter; Grandclément, Philippe
2015-07-01
Breather-type (time-periodic and spatially localized) solutions with spherical symmetry are investigated in a massless scalar field theory coupled to Einstein's gravity with cosmological constant in d spatial dimensions imposing anti-de Sitter (AdS) asymptotics on space-time. Using a code constructed with the Kadath library that enables the use of spectral methods, the phase space of breather solutions is explored in detail for d =3 and d =4 . It is found that there are discrete families of solutions indexed by an integer and by their frequency. Using a time evolution code these AdS breathers are found to be stable for up to a critical central density, in analogy to boson stars. Using an analytical perturbative expansion small amplitude breathers are worked out for arbitrary dimensions d .
Experimental long term evolution of breathers in water waves
NASA Astrophysics Data System (ADS)
Chabchoub, Amin
2014-05-01
Oceanic rogue waves may occur, due to the modulation instability, also referred to as the Benjamin-Feir instability. This instability can be also discussed within the framework of the nonlinear Schrödinger equation (NLS), which describes the dynamics of unstable packets in deep-water. In particular, through exact breather solutions of the NLS. Breathers are currently under intensive study, since their recent experimental observation in optics, water waves and in plasma proved the validity of the NLS to describe strong localizations in nonlinear dispersive media. We present evolution characteristics of breather, propagating over a long propagation distance in deep-water. In addition, we present several analytical and promising techniques, based on the theory of nonlinear wave theory, how an early stage of breather dynamics may be detected, before the occurrence of strong wave focusing.
NASA Astrophysics Data System (ADS)
İsmail, Aslan
2014-05-01
The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before.
Breather mechanism of the void ordering in crystals under irradiation
NASA Astrophysics Data System (ADS)
Dubinko, Vladimir
2009-09-01
The void ordering has been observed in very different radiation environments ranging from metals to ionic crystals. In the present paper the ordering phenomenon is considered as a consequence of the energy transfer along the close packed directions provided by self-focusing discrete breathers. The self-focusing breathers are energetic, mobile and highly localized lattice excitations that propagate great distances in atomic-chain directions in crystals. This points to the possibility of atoms being ejected from the void surface by the breather-induced mechanism, which is similar to the focuson-induced mechanism of vacancy emission from voids proposed in our previous paper. The main difference between focusons and breathers is that the latter are stable against thermal motion. There is evidence that breathers can occur in various crystals, with path lengths ranging from 104 to 107 unit cells. Since the breather propagating range can be larger than the void spacing, the voids can shield each other from breather fluxes along the close packed directions, which provides a driving force for the void ordering. Namely, the vacancy emission rate for "locally ordered" voids (which have more immediate neighbors along the close packed directions) is smaller than that for the "interstitial" ones, and so they have some advantage in growth. If the void number density is sufficiently high, the competition between them makes the "interstitial" voids shrink away resulting in the void lattice formation. The void ordering is intrinsically connected with a saturation of the void swelling, which is shown to be another important consequence of the breather-induced vacancy emission from voids.
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. PMID:23193246
Numerical computation of travelling breathers in Klein Gordon chains
NASA Astrophysics Data System (ADS)
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.
Existence and non-existence of breather solutions in damped and driven nonlinear lattices
NASA Astrophysics Data System (ADS)
Hennig, D.
2013-10-01
We investigate the existence of spatially localised solutions, in the form of discrete breathers, in general damped and driven nonlinear lattice systems of coupled oscillators. Conditions for the exponential decay of the difference between the maximal and minimal amplitudes of the oscillators are provided which proves that initial non-uniform spatial patterns representing breathers attain exponentially fast a spatially uniform state preventing the formation and/or preservation of any breather solution at all. Strikingly our results are generic in the sense that they hold for arbitrary dimension of the system, any attractive interaction, coupling strength and on-site potential and general driving fields. Furthermore, our rigorous quantitative results establish conditions under which discrete breathers in general damped and driven nonlinear lattices can exist at all and open the way for further research on the emergent dynamical scenarios, in particular features of pattern formation, localisation and synchronisation, in coupled cell networks.
NASA Astrophysics Data System (ADS)
Vishnampet, Ramanathan; Bodony, Daniel; Freund, Jonathan
2014-11-01
Finite-difference operators satisfying a summation-by-parts property enable discretization of PDEs such that the adjoint of the discretization is consistent with the continuous-adjoint equation. The advantages of this include smooth discrete-adjoint fields that converge with mesh refinement and superconvergence of linear functionals. We present a high-order dual-consistent discretization of the compressible flow equations with temperature-dependent viscosity and Fourier heat conduction in generalized curvilinear coordinates. We demonstrate dual-consistency for aeroacoustic control of a mixing layer by verifying superconvergence and show that the accuracy of the gradient is only limited by computing precision. We anticipate dual-consistency to play a key role in compressible turbulence control, for which the continuous-adjoint method, despite being robust, introduces adjoint-field errors that grow exponentially. Our dual-consistent formulation can leverage this robustness, while simultaneously providing an exact sensitivity gradient. We also present a strategy for extending dual-consistency to temporal discretization and show that it leads to implicit multi-stage schemes. Our formulation readily extends to multi-block grids through penalty-like enforcement of interface conditions.
NASA Astrophysics Data System (ADS)
Liu, Jun; Dai, Zheng-De; Lin, Song-Qing
2010-05-01
Exact heteroclinic breather-wave solutions for Davey-Stewartson (DSI, DSII) system with periodic boundary condition are constructed using Hirota's bilinear form method and generalized ansatz method. The heteroclinic structure of wave is investigated.
Exact meta-analysis approach for discrete data and its application to 2 × 2 tables with rare events
Liu, Dungang; Liu, Regina Y.
2014-01-01
This paper proposes a general exact meta-analysis approach for synthesizing inferences from multiple studies of discrete data. The approach combines the p-value functions (also known as significance functions) associated with the exact tests from individual studies. It encompasses a broad class of exact meta-analysis methods, as it permits broad choices for the combining elements, such as tests used in individual studies, and any parameter of interest. The approach yields statements that explicitly account for the impact of individual studies on the overall inference, in terms of efficiency/power and the type I error rate. Those statements also give rises to empirical methods for further enhancing the combined inference. Although the proposed approach is for general discrete settings, for convenience, it is illustrated throughout using the setting of meta-analysis of multiple 2 × 2 tables. In the context of rare events data, such as observing few, zero or zero total (i.e., zero events in both arms) outcomes in binomial trials or 2 × 2 tables, most existing meta-analysis methods rely on the large-sample approximations which may yield invalid inference. The commonly used corrections to zero outcomes in rare events data, aiming to improve numerical performance can also incur undesirable consequences. The proposed approach applies readily to any rare event setting, including even the zero total event studies without any artificial correction. While debates continue on whether or how zero total event studies should be incorporated in meta-analysis, the proposed approach has the advantage of automatically including those studies and thus making use of all available data. Through numerical studies in rare events settings, the proposed exact approach is shown to be efficient and, generally, outperform commonly used meta-analysis methods, including Mental-Haenszel and Peto methods. PMID:25620825
The role of superregular breathers in the development of modulation instability
NASA Astrophysics Data System (ADS)
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
Hormuzdiar, J.N.; Hsu, S.D.
1999-02-01
We describe a class of pionic breather solutions (PBS) which appear in the chiral Lagrangian description of low-energy QCD. These configurations are long lived, with lifetimes greater than 10{sup 3} fm/c, and could arise as remnants of disoriented chiral condensate (DCC) formation at RHIC. We show that the chiral Lagrangian equations of motion for a uniformly isospin-polarized domain reduce to those of the sine-Gordon model. Consequently, our solutions are directly related to the breather solutions of sine-Gordon theory in 3+1 dimensions. We investigate the possibility of PBS formation from multiple domains of DCC, and show that the probability of formation is non-negligible. {copyright} {ital 1999} {ital The American Physical Society}
Superfluid fermi gas in optical lattices: self-trapping, stable, moving solitons and breathers.
Xue, Ju-Kui; Zhang, Ai-Xia
2008-10-31
We predict the existence of self-trapping, stable, moving solitons and breathers of Fermi wave packets along the Bose-Einstein condensation (BEC)-BCS crossover in one dimension (1D), 2D, and 3D optical lattices. The dynamical phase diagrams for self-trapping, solitons, and breathers of the Fermi matter waves along the BEC-BCS crossover are presented analytically and verified numerically by directly solving a discrete nonlinear Schrödinger equation. We find that the phase diagrams vary greatly along the BEC-BCS crossover; the dynamics of Fermi wave packet are different from that of Bose wave packet. PMID:18999797
Perturbation-induced perestroika of a nonlinear-Schrödinger breather
NASA Astrophysics Data System (ADS)
Malomed, Boris A.
1991-04-01
The evolution of an N-soliton state (breather) is considered in the nonlinear Schrödinger equation with a sufficinetly arbitrary conservative perturbing term. Arguments are given in favor of a perestroika (rearrangement) of the breather into the exact one-soliton state via emission of radiation. For the two-soliton breather, it is demonstrated that an approximate kinematic analysis, based on the balance equation for the wave action and energy, makes it possible to find the amplitude of the one-soliton state as a function of the two initial amplitudes of the breather, provided one of them is sufficiently small compared to the other. The expression for the final amplitude proves to be very simple, and it is universal in the sense that it does not depend on a particular form of the conservative perturbation. As an example, nonlinear surface elastic modes in a crystal are considered. It is shown that N-soliton surface modes may undergo the emission-assisted prestroika into the exact one-soliton mode under the action of a nonlinear correction to the boundary condition at the surface.
The noncommutative sine-Gordon breather
Fischer, Andre; Lechtenfeld, Olaf
2009-09-15
As shown by Lechtenfeld et al. [Nucl. Phys. B 705, 447 (2005)], there exists a noncommutative deformation of the sine-Gordon model which remains (classically) integrable but features a second scalar field. We employ the dressing method (adapted to the Moyal-deformed situation) for constructing the deformed kink-antikink and breather configurations. Explicit results and plots are presented for the leading noncommutativity correction to the breather. Its temporal periodicity is unchanged.
NASA Astrophysics Data System (ADS)
Delzanno, G. L.
2015-11-01
A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method. It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.
14 CFR 121.243 - Engine breather lines.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 14 Aeronautics and Space 3 2014-01-01 2014-01-01 false Engine breather lines. 121.243 Section 121... REQUIREMENTS: DOMESTIC, FLAG, AND SUPPLEMENTAL OPERATIONS Special Airworthiness Requirements § 121.243 Engine breather lines. (a) Engine breather lines must be so arranged that condensed water vapor that may...
14 CFR 121.243 - Engine breather lines.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 14 Aeronautics and Space 3 2011-01-01 2011-01-01 false Engine breather lines. 121.243 Section 121... REQUIREMENTS: DOMESTIC, FLAG, AND SUPPLEMENTAL OPERATIONS Special Airworthiness Requirements § 121.243 Engine breather lines. (a) Engine breather lines must be so arranged that condensed water vapor that may...
14 CFR 121.243 - Engine breather lines.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 14 Aeronautics and Space 3 2013-01-01 2013-01-01 false Engine breather lines. 121.243 Section 121... REQUIREMENTS: DOMESTIC, FLAG, AND SUPPLEMENTAL OPERATIONS Special Airworthiness Requirements § 121.243 Engine breather lines. (a) Engine breather lines must be so arranged that condensed water vapor that may...
14 CFR 121.243 - Engine breather lines.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 3 2012-01-01 2012-01-01 false Engine breather lines. 121.243 Section 121... REQUIREMENTS: DOMESTIC, FLAG, AND SUPPLEMENTAL OPERATIONS Special Airworthiness Requirements § 121.243 Engine breather lines. (a) Engine breather lines must be so arranged that condensed water vapor that may...
14 CFR 121.243 - Engine breather lines.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 14 Aeronautics and Space 3 2010-01-01 2010-01-01 false Engine breather lines. 121.243 Section 121... REQUIREMENTS: DOMESTIC, FLAG, AND SUPPLEMENTAL OPERATIONS Special Airworthiness Requirements § 121.243 Engine breather lines. (a) Engine breather lines must be so arranged that condensed water vapor that may...
Avalanches, breathers, and flow reversal in a continuous Lorenz-96 model.
Blender, R; Wouters, J; Lucarini, V
2013-07-01
For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model. PMID:23944570
NASA Astrophysics Data System (ADS)
Dai, Chao-Qing; Zhu, Hai-Ping
2014-02-01
The one-to-one correspondence between a (3+1)-dimensional variable-coefficient nonlinear Schrödinger equation with linear and parabolic potentials and a standard nonlinear Schrödinger equation is given, and an exact superposed Akhmediev breather solution in certain parameter conditions is obtained. These precise expressions for the peak, width, center and phase indicate that diffraction and chirp factors influence the evolutional characteristics such as phase, center and width, while the gain/loss parameter only affects the evolution of the peak. Moreover, by modulating the relation between the terminal accumulated time Te or the maximum accumulated time Tm and the accumulated time T0 based on the maximum amplitude of Akhmediev breather, the controllability for the type of excitation such as postpone, maintenance and restraint of the superposed Akhmediev breather is discussed.
NASA Astrophysics Data System (ADS)
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 management in the derivative nonlinear Schrödinger equation with variable coefficients
Zhong, Wei-Ping; Belić, Milivoj; Malomed, Boris A.; Huang, Tingwen
2015-04-15
We investigate breather solutions of the generalized derivative nonlinear Schrödinger (DNLS) equation with variable coefficients, which is used in the description of femtosecond optical pulses in inhomogeneous media. The solutions are constructed by means of the similarity transformation, which reduces a particular form of the generalized DNLS equation into the standard one, with constant coefficients. Examples of bright and dark breathers of different orders, that ride on finite backgrounds and may be related to rogue waves, are presented. - Highlights: • Exact solutions of a generalized derivative NLS equation are obtained. • The solutions are produced by means of a transformation to the usual integrable equation. • The validity of the solutions is verified by comparing them to numerical counterparts. • Stability of the solutions is checked by means of direct simulations. • The model applies to the propagation of ultrashort pulses in optical media.
Nonlinear dynamics of breathers in the spiral structures of magnets
NASA Astrophysics Data System (ADS)
Kiselev, V. V.; Raskovalov, A. A.
2016-06-01
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.
Transformation of internal breathers in the idealised shelf sea conditions
NASA Astrophysics Data System (ADS)
Rouvinskaya, Ekaterina; Talipova, Тatyana; Kurkina, Oxana; Soomere, Tarmo; Tyugin, Dmitry
2015-11-01
We address the propagation and transformation of long internal breather-like wave in an idealised but realistic stratification and in the conditions matching the average summer stratification in the southern part of the Baltic Sea. The focus is on changes in the properties of the breather when the water depth increases and the coefficient at the cubic nonlinear term changes its sign, equivalently, the breather cannot exist anymore. The simulations are performed in parallel in the framework of weakly nonlinear Gardner equation and using fully nonlinear Euler equations. The amplitudes of breathers in these frameworks have slightly different courses in idealised conditions (when Earth's rotation is neglected) whereas a decrease in the amplitude is faster in the fully nonlinear simulation. The impact of the background (Earth's) rotation substantially depends on the spectral width of the initial breather. The evolution of narrow-banded breathers is almost the same for rotating and non-rotating situations but amplitudes of breathers with a wide spectrum experience substantial changes in realistic situation with the background rotation. The propagation of a narrow-banded breather along a path in the Baltic Sea over a location where the cubic nonlinear term changes its sign reveals fast disintegration of the breather into a precursor soliton and a transient dispersive wave group.
Multiple breathers on a vortex filament
NASA Astrophysics Data System (ADS)
Salman, H.
2014-10-01
In this paper we investigate the correspondence between the Da Rios-Betchov equation, which appears in the three-dimensional motion of a vortex filament, and the nonlinear Schrödinger equation. Using this correspondence we map a set of solutions corresponding to breathers in the nonlinear Schrödinger equation to waves propagating along a vortex filament. The work presented generalizes the recently derived family of vortex configurations associated with these breather solutions to a wider class of configurations that are associated with combination homoclinic/heteroclinic orbits of the 1D self-focussing nonlinear Schrödinger equation. We show that by considering these solutions of the governing nonlinear Schrödinger equation, highly nontrivial vortex filament configurations can be obtained that are associated with a pair of breather excitations. These configurations can lead to loop-like excitations emerging from an otherwise weakly perturbed helical vortex. The results presented further demonstrate the rich class of solutions that are supported by the Da Rios-Betchov equation that is recovered within the local induction approximation for the motion of a vortex filament.
Solitons in the discrete nonpolynomial Schrödinger equation
NASA Astrophysics Data System (ADS)
Maluckov, Aleksandra; Hadžievski, Ljupčo; Malomed, Boris A.; Salasnich, Luca
2008-07-01
We introduce a species of the discrete nonlinear Schrödinger (DNLS) equation, which is a model for a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction. The equation is derived as a discretization of the respective nonlinear nonpolynomial Schrödinger equation. Unlike previously considered varieties of one-dimensional DNLS equations, the present discrete model admits on-site collapse. We find two families of unstaggered on-site-centered discrete solitons, stable and unstable ones, which include, respectively, broad and narrow solitons, their stability exactly complying with the Vakhitov-Kolokolov criterion. Unstable on-site solitons either decay or transform themselves into robust breathers. Intersite-centered unstaggered solitons are unstable to collapse; however, they may be stabilized by the application of a sufficiently strong kick, which turns them into moving localized modes. Persistently moving solitons can be readily created too by the application of the kick to stable on-site unstaggered solitons. In the same model, staggered solitons, which are counterparts of gap solitons in the continuum medium, are possible if the intrinsic nonlinearity is self-repulsive. All on-site staggered solitons are stable, while intersite ones have a small instability region. The staggered solitons are immobile.
Transfer of dipolar gas through the discrete localized mode.
Bai, Xiao-Dong; Zhang, Ai-Xia; Xue, Ju-Kui
2013-12-01
By considering the discrete nonlinear Schrödinger model with dipole-dipole interactions for dipolar condensate, the existence, the types, the stability, and the dynamics of the localized modes in a nonlinear lattice are discussed. It is found that the contact interaction and the dipole-dipole interactions play important roles in determining the existence, the type, and the stability of the localized modes. Because of the coupled effects of the contact interaction and the dipole-dipole interactions, rich localized modes and their stability nature can exist: when the contact interaction is larger and the dipole-dipole interactions is smaller, a discrete bright breather occurs. In this case, while the on-site interaction can stabilize the discrete breather, the dipole-dipole interactions will destabilize the discrete breather; when both the contact interaction and the dipole-dipole interactions are larger, a discrete kink appears. In this case, both the on-site interaction and the dipole-dipole interactions can stabilize the discrete kink, but the discrete kink is more unstable than the ordinary discrete breather. The predicted results provide a deep insight into the dynamics of blocking, filtering, and transfer of the norm in nonlinear lattices for dipolar condensates. PMID:24483540
Nano breathers and molecular dynamics simulations in hydrogen-bonded chains.
Kavitha, L; Muniyappan, A; Prabhu, A; Zdravković, S; Jayanthi, S; Gopi, D
2013-01-01
Non-linear localization phenomena in biological lattices have attracted a steadily growing interest and their existence has been predicted in a wide range of physical settings. We investigate the non-linear proton dynamics of a hydrogen-bonded chain in a semi-classical limit using the coherent state method combined with a Holstein-Primakoff bosonic representation. We demonstrate that even a weak inherent discreteness in the hydrogen-bonded (HB) chain may drastically modify the dynamics of the non-linear system, leading to instabilities that have no analog in the continuum limit. We suggest a possible localization mechanism of polarization oscillations of protons in a hydrogen-bonded chain through modulational instability analysis. This mechanism arises due to the neighboring proton-proton interaction and coherent tunneling of protons along hydrogen bonds and/or around heavy atoms. We present a detailed analysis of modulational instability, and highlight the role of the interaction strength of neighboring protons in the process of bioenergy localization. We perform molecular dynamics simulations and demonstrate the existence of nanoscale discrete breather (DB) modes in the hydrogen-bonded chain. These highly localized and long-lived non-linear breather modes may play a functional role in targeted energy transfer in biological systems. PMID:23860832
14 CFR 125.141 - Engine breather lines.
Code of Federal Regulations, 2012 CFR
2012-01-01
... OPERATIONS: AIRPLANES HAVING A SEATING CAPACITY OF 20 OR MORE PASSENGERS OR A MAXIMUM PAYLOAD CAPACITY OF 6... oil emitted from the line does not impinge upon the pilots' windshield. (c) Engine breathers may...
14 CFR 125.141 - Engine breather lines.
Code of Federal Regulations, 2011 CFR
2011-01-01
... OPERATIONS: AIRPLANES HAVING A SEATING CAPACITY OF 20 OR MORE PASSENGERS OR A MAXIMUM PAYLOAD CAPACITY OF 6... oil emitted from the line does not impinge upon the pilots' windshield. (c) Engine breathers may...
14 CFR 125.141 - Engine breather lines.
Code of Federal Regulations, 2010 CFR
2010-01-01
... OPERATIONS: AIRPLANES HAVING A SEATING CAPACITY OF 20 OR MORE PASSENGERS OR A MAXIMUM PAYLOAD CAPACITY OF 6... oil emitted from the line does not impinge upon the pilots' windshield. (c) Engine breathers may...
14 CFR 125.141 - Engine breather lines.
Code of Federal Regulations, 2013 CFR
2013-01-01
... OPERATIONS: AIRPLANES HAVING A SEATING CAPACITY OF 20 OR MORE PASSENGERS OR A MAXIMUM PAYLOAD CAPACITY OF 6... oil emitted from the line does not impinge upon the pilots' windshield. (c) Engine breathers may...
14 CFR 125.141 - Engine breather lines.
Code of Federal Regulations, 2014 CFR
2014-01-01
... OPERATIONS: AIRPLANES HAVING A SEATING CAPACITY OF 20 OR MORE PASSENGERS OR A MAXIMUM PAYLOAD CAPACITY OF 6... oil emitted from the line does not impinge upon the pilots' windshield. (c) Engine breathers may...
Higher order Peregrine breathers solutions to the NLS equation
NASA Astrophysics Data System (ADS)
Gaillard, Pierre
2015-09-01
The solutions to the one dimensional focusing nonlinear Schrodinger equation (NLS) can be written as a product of an exponential depending on t by a quotient of two polynomials of degree N(N + 1) in x and t. These solutions depend on 2N - 2 parameters : when all these parameters are equal to 0, we obtain the famous Peregrine breathers which we call PN breathers. Between all quasi-rational solutions of rank N fixed by the condition that its absolute value tends to 1 at infinity and its highest maximum is located at point (x = 0,t = 0), the PN breather is distinguished by the fact that PN (0, 0) = 2N + 1. We construct Peregrine breathers of the rank N explicitly for N ≤ 11. We give figures of these PN breathers in the (x; t) plane; plots of the solutions PN (0; t), PN (x;0), never given for 6 < N < 11 are constructed in this work. It is the first time that the Peregrine breather of order 11 is explicitly constructed.
Alterations in Maxillary Sinus Volume among Oral and Nasal Breathers
Agacayak, Kamil Serkan; Gulsun, Belgin; Koparal, Mahmut; Atalay, Yusuf; Aksoy, Orhan; Adiguzel, Ozkan
2015-01-01
Background Oral breathing causes many changes in the facial anatomical structures in adult patients. In this study we aimed to determine the effects of long-term oral breathing (>5 years) on the maxillary sinus volumes among adult male patients. Material/Methods We accessed medical records of 586 patients who had undergone cone beam computed tomography (CBCT) for any reason between September 2013 and April 2014. Patients who had undergone cone-beam dental volumetric tomography scans for any reason and who had answered a questionnaire about breathing were screened retrospectively. Cone beam dental volumetric tomography (I-Cat, Imaging Sciences International, Hatfield, PA, USA) was used to take the images of the maxillo-facial area at a setting of 120 kVp and 3.7 mA. This study involved male patients older than 21 years of age. Results The study included a total of 239 male patients, of which 68 were oral breathers and 171 were nasal breathers. The mean age of the oral breathers was 48.4 years and that of the nasal breathers was 46.7 years and the difference was not statistically significant (p>0.05). The mean maxillary sinus volumes of the oral and nasal breathers were 9043.49±1987.90 and 10851.77±2769.37, respectively, and the difference in maxillary sinus volume between the 2 groups was statistically significant (p<0.001). Conclusions The volume of maxillary sinus in oral breathers (>5 years) was significantly lower than in nasal breathers, but it remains unclear whether this is due to malfunctioning of the nasal cavity or due to the underlying pathological condition. PMID:25553770
Breather-like structures in modified sine-Gordon models
NASA Astrophysics Data System (ADS)
Ferreira, L. A.; Zakrzewski, Wojtek J.
2016-05-01
We report analytical and numerical results on breather-like field configurations in a theory which is a deformation of the integrable sine-Gordon model in (1 + 1) dimensions. The main motivation of our study is to test the ideas behind the recently proposed concept of quasi-integrability, which emerged from the observation that some field theories possess an infinite number of quantities which are asymptotically conserved in the scattering of solitons, and periodic in time in the case of breather-like configurations. Even though the mechanism responsible for such phenomena is not well understood yet, it is clear that special properties of the solutions under a space-time parity transformation play a crucial role. The numerical results of the present paper give support for the ideas on quasi-integrability, as it is found that extremely long-lived breather configurations satisfy these parity properties. We also report on a mechanism, particular to the theory studied here, that favours the existence of long lived breathers even in cases of significant deformations of the sine-Gordon potential. We also find numerically that our breather-like configurations decay through the gradual increase of their frequency of oscillations.
Collision of Akhmediev Breathers in Nonlinear Fiber Optics
NASA Astrophysics Data System (ADS)
Frisquet, B.; Kibler, B.; Millot, G.
2013-10-01
We report here a novel fiber-based test bed using tailored spectral shaping of an optical-frequency comb to excite the formation of two Akhmediev breathers that collide during propagation. We have found specific initial conditions by controlling the phase and velocity differences between breathers that lead, with certainty, to their efficient collision and the appearance of a giant-amplitude wave. Temporal and spectral characteristics of the collision dynamics are in agreement with the corresponding analytical solution. We anticipate that experimental evidence of breather-collision dynamics is of fundamental importance in the understanding of extreme ocean waves and in other disciplines driven by the continuous nonlinear Schrödinger equation.
On exactly conservative integrators
Bowman, J.C.; Shadwick, B.A.; Morrison, P.J.
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.
Lifetime and decay of seeded breathers in the FPU system
NASA Astrophysics Data System (ADS)
Westley, Matthew; Demeglio, Nicholas; Sen, Surajit; Mohan, T. R. Krishna
2014-03-01
The Fermi-Pasta-Ulam problem consists of a chain of N oscillators with linear and nonlinear nearest neighbor interactions. Using velocity-Verlet integration, we study the evolution of the system after a perturbation that consists of a single stretched bond at the center of the chain. This perturbation results in the localization of most of the system's energy in the center particles in the form of a ``breather'' up to reasonably long times, which leaks energy at a rate depending on the potential parameters and the perturbation amplitude. The breather eventually undergoes a catastrophic breakdown, releasing all of its energy into acoustic noise and solitary waves. We explore the conditions on the amplitude and the parameters α, β for which a seeded breather will be most or least stable. Also we show how the overlap or lack thereof between the breather's primary frequencies and the acoustic frequencies influences its long-time stability. Research supported by a US Army Research Office STIR grant.
Changes in pharyngeal aerobic microflora in oral breathers after palatal rapid expansion
Cazzolla, Angela Pia; Campisi, Giuseppina; Lacaita, Grazia Maria; Cuccia, Marco Antonino; Ripa, Antonio; Testa, Nunzio Francesco; Ciavarella, Domenico; Lo Muzio, Lorenzo
2006-01-01
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 < 0.0001; Z = -4,512 by Wilcoxon Rank test) vs T0. No significant changes were found for the other examined microrganisms. 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. PMID:16426457
Internal wave breather propagation under the influence of the Earth rotation
NASA Astrophysics Data System (ADS)
Talipova, Tatiana; Rouvinskaya, Ekaterina; Kurkina, Oxana
2015-04-01
The internal wave breather propagation under the influence of the Earth rotation is studied in the frames of the asymptotic model based on the Gardner equation as well as the fully nonlinear Euler equations. It is obtained that the amplitude and shape of short breathers depend on the Earth rotation very weakly but the wide breathers change the amplitude and shape sufficiently. This effect is studied in the model situation adapted to the Baltic Sea hydrological conditions. The rate of the breather amplitude damping upon the even bottom is shown.
Treating hypoxia in a feeble breather with Rett syndrome.
Julu, Peter O O; Witt Engerström, Ingegerd; Hansen, Stig; Apartopoulos, Flora; Engerström, Bengt
2013-03-01
Rett syndrome (RS) is a unique X-linked dominant neurodevelopmental disorder affecting 1 in 10,000 females. Mutations in the MECP2 gene located on Xq28 have been identified. Many of the characteristic features evolve due to immaturity of the brain in RS. Cardiorespiratory function should be investigated early to characterise the clinical phenotype of the person with RS because each of the three cardiorespiratory phenotypes; apneustic, feeble and forceful breathers have unique and different management strategies. We report a case of a feeble breather showing a correlation between cortical function and tissue pO(2) and pCO(2). We conclude that subtle changes in the levels of blood gases significantly affect cortical function in RS. PMID:22617859
Vishnu Priya, N; Senthilvelan, M; Lakshmanan, M
2013-08-01
We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of the two-component nonlinear Schrödinger (NLS) equation, namely Manakov equation. We derive these solutions through two different routes. In the forward route, we first construct a suitable periodic envelope soliton solution to this model from which we derive GB, AB, MS, and RW solutions. We then consider the RW solution as the starting point and derive AB, MS, and GB in the reverse direction. The second approach has not been illustrated so far for the two component NLS equation. Our results show that the above rational solutions of the Manakov system can be derived from the standard scalar nonlinear Schrödinger equation with a modified nonlinearity parameter. Through this two-way approach we establish a broader understanding of these rational solutions, which will be of interest in a variety of situations. PMID:24032912
NASA Astrophysics Data System (ADS)
Volkov, A. V.; Parshkov, O. M.
2008-09-01
The formation and collisions of breathers excited by laser radiation at the inhomogeneously broadened J = 0 → J = 1 quantum transition are studied by numerical simulations in the slowly varying envelope approximation. Conditions are obtained under which laser pulses with the initial shape quite simply realised in experiments can be transformed into elliptically polarised breathers in the medium, each of the components of their field being a breather described by the theory of self-induced transparency at a nondegenerate quantum transition. It is shown that the collision of such breathers is not elastic in the general case and leads to the appearance of more general types of resonance breather-like pulses. Taking into account relaxation processes, the possibility of the formation of a breather at the 6p2 3P0 → 6p7s 3P1 transition in the 208Pb isotope is investigated. It is found that relaxation in some case not only causes the pulse decay but also changes the eccentricity of its polarisation ellipse.
Bello-Rivas, Juan M.; Elber, Ron
2015-01-01
A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied. PMID:25747056
Bello-Rivas, Juan M.; Elber, Ron
2015-03-07
A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied.
Bello-Rivas, Juan M; Elber, Ron
2015-03-01
A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied. PMID:25747056
Computed tomographic evaluation of mouth breathers among paediatric patients
Farid, MM; Metwalli, N
2010-01-01
Objectives Mouth breathing causes many serious problems in the paediatric population. It has been maintained that enlarged adenoids are principally responsible for mouth breathing. This study was designed to evaluate whether other mechanical obstacles might predispose the child to mouth breathing. Methods 67 children with ages ranging from 10 to 15 years were studied and grouped into mouth-breathers and nose-breathers. The children first underwent axial CT scans of the brain for which they were originally referred. In addition, they were subjected to a limited coronal CT examination of the paranasal sinuses. Congenital anatomical variations as well as inflammatory changes were assessed. Results 87% of mouth-breathing children had hypertrophied adenoids, 77% had maxillary sinusitis, 74% had pneumatized middle concha, 55% had a deviated nasal septum, 55% had hypertrophied inferior conchae, 45% had ethmoidal sinusitis and 23% showed frontal sinusitis. Such changes were significantly less prevalent in nose-breathers. 12.9% of mouth-breathing children did not have adenoids. Of these children, only 3.3% had one or more congenital or inflammatory change whereas the other 9.6% showed a completely normal CT scan signifying the incidence of habitual non-obstructive mouth breathing. Conclusions It is clear that adenoids have a dominant role in causing mouth breathing. Yet, we recommend that paediatricians should assess other mechanical obstacles if mouth breathing was not corrected after adenoidectomy. Further research should be performed to test the validity of correction of such factors in improving the quality of life of mouth-breathing children. PMID:20089737
Kuznetsov-Ma soliton and Akhmediev breather of higher-order nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Zai-Dong, Li; Xuan, Wu; Qiu-Yan, Li; P, B. He
2016-01-01
In terms of Darboux transformation, we have exactly solved the higher-order nonlinear Schrödinger equation that describes the propagation of ultrashort optical pulses in optical fibers. We discuss the modulation instability (MI) process in detail and find that the higher-order term has no effect on the MI condition. Under different conditions, we obtain Kuznetsov-Ma soliton and Akhmediev breather solutions of higher-order nonlinear Schrödinger equation. The former describes the propagation of a bright pulse on a continuous wave background in the presence of higher-order effects and the soliton’s peak position is shifted owing to the presence of a nonvanishing background, while the latter implies the modulation instability process that can be used in practice to produce a train of ultrashort optical soliton pulses. Project supported by the Key Project of Scientific and Technological Research in Hebei Province, China (Grant No. ZD2015133).
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.
Relativistic breather-type solitary waves with linear polarization in cold plasmas.
Sánchez-Arriaga, G; Siminos, E; Saxena, V; Kourakis, I
2015-03-01
Linearly polarized solitary waves, arising from the interaction of an intense laser pulse with a plasma, are investigated. Localized structures, in the form of exact numerical nonlinear solutions of the one-dimensional Maxwell-fluid model for a cold plasma with fixed ions, are presented. Unlike stationary circularly polarized solitary waves, the linear polarization gives rise to a breather-type behavior and a periodic exchange of electromagnetic energy and electron kinetic energy at twice the frequency of the wave. A numerical method based on a finite-differences scheme allows us to compute a branch of solutions within the frequency range Ωmin<Ω<ωpe, where ωpe and Ωmin are the electron plasma frequency and the frequency value for which the plasma density vanishes locally, respectively. A detailed description of the spatiotemporal structure of the waves and their main properties as a function of Ω is presented. Small-amplitude oscillations appearing in the tail of the solitary waves, a consequence of the linear polarization and harmonic excitation, are explained with the aid of the Akhiezer-Polovin system. Direct numerical simulations of the Maxwell-fluid model show that these solitary waves propagate without change for a long time. PMID:25871219
Breather and double-pole solutions for the Benjamin-Ono equation in a stratified fluid
NASA Astrophysics Data System (ADS)
Sun, Wen-Rong; Tian, Bo; Zhong, Hui; Liu, Rong-Xiang
2016-04-01
The Benjamin-Ono equation is hereby investigated, which arises in the context of long internal gravity waves in a stratified fluid. With the Hirota method and symbolic computation, breather solutions are derived. Propagation of the breather and elastic collisions between the breather and soliton are graphically analyzed. The collision period and the bunch number in a wave packet are relevant to the ratio of the real part to the imaginary of the wavenumber. Through the coalescence of wavenumbers in the two-soliton solutions, we obtain the double-pole solutions.
Akhmediev, N; Soto-Crespo, J M; Devine, N
2016-08-01
Turbulence in integrable systems exhibits a noticeable scientific advantage: it can be expressed in terms of the nonlinear modes of these systems. Whether the majority of the excitations in the system are breathers or solitons defines the properties of the turbulent state. In the two extreme cases we can call such states "breather turbulence" or "soliton turbulence." The number of rogue waves, the probability density functions of the chaotic wave fields, and their physical spectra are all specific for each of these two situations. Understanding these extreme cases also helps in studies of mixed turbulent states when the wave field contains both solitons and breathers, thus revealing intermediate characteristics. PMID:27627303
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. PMID:23405086
Effect of a breather soliton in Kerr frequency combs on optical communication systems.
Bao, Changjing; Liao, Peicheng; Zhang, Lin; Yan, Yan; Cao, Yinwen; Xie, Guodong; Mohajerin-Ariaei, Amirhossein; Li, Long; Ziyadi, Morteza; Almaiman, Ahmed; Kimerling, Lionel C; Michel, Jurgen; Willner, Alan E
2016-04-15
In this study, we numerically investigate the effect of Kerr-comb-generated breather soliton pulses on optical communication systems. The breather soliton pulse amplitude and spectrum envelope oscillate periodically in time. Simulations show that the spectrum of each comb line in the breather soliton state has multiple sub-teeth due to the periodic oscillation of the comb spectrum. In the simulation, the comb output is modulated with different formats. We find that the sub-teeth distort quadrature phase-shift-keyed signals but have less of an effect on on-off-keyed signals. PMID:27082339
Twenty Parameters Families of Solutions to the NLS Equation and the Eleventh Peregrine Breather
NASA Astrophysics Data System (ADS)
Pierre, Gaillard; Mickaël, Gastineau
2016-02-01
The Peregrine breather of order eleven (P11 breather) solution to the focusing one-dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given: when all parameters are equal to 0 we recover the famous P11 breather. We obtain new families of quasi-rational solutions to the NLS equation in terms of explicit quotients of polynomials of degree 132 in x and t by a product of an exponential depending on t. We study these solutions by giving patterns of their modulus in the (x; t) plane, in function of the different parameters.
The breakdown of breathers in the Fermi-Pasta-Ulam-Tsingou system
NASA Astrophysics Data System (ADS)
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; Tang, Yi; Li, De-Jun
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.
NASA Astrophysics Data System (ADS)
Zhou, Guo-Quan; Dai, Chao-Qing; Chen, Yi-Xiang
2015-06-01
A (3+1)-dimensional coupled nonlinear Schrödinger equation in parity-time symmetric inhomogeneous nonlinear couplers with gain and loss is investigated, and PT-symmetric and PT-antisymmetric superposed Akhmediev breather solutions are derived via the Darboux transformation method. Nonlinear tunnelling for controllable behaviors of the superposed Akhmediev breather is discussed when the superposed Akhmediev breather passes through the diffraction/dispersion barrier and well on an exponential background. Results indicate that the diffraction/dispersion barrier and well have different effects on different types of controllable behaviors of superposed Akhmediev breather. When the restrained and sustained superposed Akhmediev breathers pass through the diffraction/dispersion barrier or well, their amplitudes both magnify or both diminish, respectively, while the postponed Akhmediev breather passes through the diffraction/dispersion barrier or well, its amplitude attenuates or adds, respectively.
Evaluation of Respiratory Muscle Strength in Mouth Breathers: Clinical Evidences
Andrade da Cunha, Renata; Andrade da Cunha, Daniele; Assis, Roberta Borba; Bezerra, Luciana Ângelo; Justino da Silva, Hilton
2013-01-01
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. PMID:25992108
From NLS breathers to sea-keeping tests
NASA Astrophysics Data System (ADS)
Onorato, M.; Proment, D.; Clauss, G.; Klein, M.
2012-04-01
Nowadays there is a general consensus on the existence of rogue waves in the ocean. During the last years many efforts in the community of physicists and oceanographers have been devoted to the understanding of their origin. At the same time, engineers and naval architectures have been interested on the consequences of the impact of rogue wave on offshore structures and ships. Recently, in the Technical University of Berlin (TUB) breather solutions of the Nonlinear Schrödinger (NLS) equation have been successfully produced and used for the first time in sea-keeping tests, opening up new perspectives in the methodology of examining offshore structures and ships against rogue waves. Results on a LNG carrier and a chemical tanker will be presented.
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan
2016-02-01
We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.
Instability dynamics and breather formation in a horizontally shaken pendulum chain.
Xu, Y; Alexander, T J; Sidhu, H; Kevrekidis, P G
2014-10-01
Inspired by the experimental results of Cuevas et al. [Phys. Rev. Lett. 102, 224101 (2009)], we consider theoretically the behavior of a chain of planar rigid pendulums suspended in a uniform gravitational field and subjected to a horizontal periodic driving force applied to the pendulum pivots. We characterize the motion of a single pendulum, finding bistability near the fundamental resonance and near the period-3 subharmonic resonance. We examine the development of modulational instability in a driven pendulum chain and find both a critical chain length and a critical frequency for the appearance of the instability. We study the breather solutions and show their connection to the single-pendulum dynamics and extend our analysis to consider multifrequency breathers connected to the period-3 periodic solution, showing also the possibility of stability in these breather states. Finally we examine the problem of breather generation and demonstrate a robust scheme for generation of on-site and off-site breathers. PMID:25375581
NASA Astrophysics Data System (ADS)
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", 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, 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.
NASA Astrophysics Data System (ADS)
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.
Manipulating matter rogue waves and breathers in Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Manikandan, K.; Muruganandam, P.; Senthilvelan, M.; Lakshmanan, M.
2014-12-01
We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.
Modulation of breathers in the three-dimensional nonlinear Gross-Pitaevskii equation
Avelar, A. T.; Cardoso, W. B.; Bazeia, D.
2010-11-15
In this paper we present analytical breather solutions of the three-dimensional nonlinear generalized Gross-Pitaevskii equation. We use an Ansatz to reduce the three-dimensional equation with space- and time-dependent coefficients into a one-dimensional equation with constant coefficients. The key point is to show that both the space- and time-dependent coefficients of the nonlinear equation can contribute to modulate the breather excitations. We briefly discuss the experimental feasibility of the results in Bose-Einstein condensates.
Akhmediev breathers, Kuznetsov-Ma solitons and rogue waves in a dispersion varying optical fiber
NASA Astrophysics Data System (ADS)
Sun, Wen-Rong; Tian, Bo; Sun, Ya; Chai, Jun; Jiang, Yan
2016-03-01
Dispersion varying fibres have applications in optical pulse compression techniques. We investigate Akhmediev breathers, Kuznetsov-Ma (KM) solitons and optical rogue waves in a dispersion varying optical fibre based on a variable-coefficient nonlinear Schrödinger equation. Analytical solutions in the forms of Akhmediev breathers, KM solitons and rogue waves up to the second order of that equation are obtained via the generalised Darboux transformation and integrable constraint. The properties of Akhmediev breathers, KM solitons and rogue waves in a dispersion varying optical fibre, e.g. dispersion decreasing fibre (DDF) or a periodically distributed system (PDS), are discussed: in a DDF we observe the compression behaviours of KM solitons and rogue waves on a monotonically increasing background. The amplitude of each peak of the KM soliton increases, while the width of each peak of the KM soliton gradually decreases along the propagation distance; in a PDS, the amplitude of each peak of the KM soliton varies periodically along the propagation distance on a periodic background. Different from the KM soliton, the Akhmediev breather and rogue waves repeat their behaviours along the propagation distance without the compression.
ERIC Educational Resources Information Center
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…
Quantum Breathers in Anisotropy Ferromagnetic Chains with Second-Order Coupling
NASA Astrophysics Data System (ADS)
Tang, Bing
2016-03-01
Under considering the next-nearest-neighbor interaction, quantum breathers in one-dimensional anisotropy ferromagnetic chains are theortically studied. By introducing the Dyson-Maleev transformation for spin operators, a map to a Heisenberg ferromagnetic spin lattice into an extended Bose-Hubbard model can be established. In the case of a small number of bosons, by means of the numerical diagonalization technique, the energy spectrum of the corresponding extended Bose-Hubbard model containing two bosons is calculated. When the strength of the single-ion anisotropy is enough large, a isolated single band appears. This isolated single band corresponds to two-boson bound state, which is the simplest quantum breather state. It is shown that the introduction of the next-nearest-neighbor interaction will lead to interesting band structures. In the case of a large number of bosons, by applying the time-dependent Hartree approximation, quantum breather states for the system is constructed. In this case, the effect of the next-nearest-neighbor interaction on quantum breathers is also analyzed.
Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices
Cuevas-Maraver, Jesus; Kevrekidis, Panayotis G.; Pelinovsky, Dmitry E.
2015-12-14
Here, we explore the possibility of multi-site breather states in a nonlinear Klein–Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this nonlinear instability is through the resonance with the wave continuum of a multiple of an internal mode eigenfrequency in the linearization of excited breather states. For the nonlinear instability, the internal mode must have its Krein signature opposite to that of the wave continuum. This mechanism is not only theoretically proposed, but also numerically corroborated through two concrete examples of the Klein–Gordon lattice with a soft (Morse) and amore » hard (Φ4) potential. Compared to the case of the nonlinear Schrödinger lattice, the Krein signature of the internal mode relative to that of the wave continuum may change depending on the period of the multi-site breather state. For the periods for which the Krein signatures of the internal mode and the wave continuum coincide, multi-site breather states are observed to be nonlinearly stable.« less
Quantum Breathers in Anisotropy Ferromagnetic Chains with Second-Order Coupling
NASA Astrophysics Data System (ADS)
Tang, Bing
2016-08-01
Under considering the next-nearest-neighbor interaction, quantum breathers in one-dimensional anisotropy ferromagnetic chains are theortically studied. By introducing the Dyson-Maleev transformation for spin operators, a map to a Heisenberg ferromagnetic spin lattice into an extended Bose-Hubbard model can be established. In the case of a small number of bosons, by means of the numerical diagonalization technique, the energy spectrum of the corresponding extended Bose-Hubbard model containing two bosons is calculated. When the strength of the single-ion anisotropy is enough large, a isolated single band appears. This isolated single band corresponds to two-boson bound state, which is the simplest quantum breather state. It is shown that the introduction of the next-nearest-neighbor interaction will lead to interesting band structures. In the case of a large number of bosons, by applying the time-dependent Hartree approximation, quantum breather states for the system is constructed. In this case, the effect of the next-nearest-neighbor interaction on quantum breathers is also analyzed.
Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices
Cuevas-Maraver, Jesus; Kevrekidis, Panayotis G.; Pelinovsky, Dmitry E.
2015-12-14
Here, we explore the possibility of multi-site breather states in a nonlinear Klein–Gordon lattice to become nonlinearly unstable, even if they are found to be spectrally stable. The mechanism for this nonlinear instability is through the resonance with the wave continuum of a multiple of an internal mode eigenfrequency in the linearization of excited breather states. For the nonlinear instability, the internal mode must have its Krein signature opposite to that of the wave continuum. This mechanism is not only theoretically proposed, but also numerically corroborated through two concrete examples of the Klein–Gordon lattice with a soft (Morse) and a hard (Φ^{4}) potential. Compared to the case of the nonlinear Schrödinger lattice, the Krein signature of the internal mode relative to that of the wave continuum may change depending on the period of the multi-site breather state. For the periods for which the Krein signatures of the internal mode and the wave continuum coincide, multi-site breather states are observed to be nonlinearly stable.
Activity spread and breathers induced by finite transmission speeds in two-dimensional neural fields
NASA Astrophysics Data System (ADS)
Hutt, Axel; Rougier, Nicolas
2010-11-01
The work studies the spatiotemporal activity propagation in a two-dimensional spatial system involving a finite transmission speed. We derive a numerical scheme in detail to integrate the corresponding evolution equation and validate the derived algorithm by a study of a spatially periodic system. Finally, the work demonstrates numerically transmission delay-induced breathers subjected to anisotropic external input.
Guo, Rui Hao, Hui-Qin
2014-05-15
In nonlinear erbium doped fibers, the Hirota–Maxwell–Bloch system with higher order effects usually governs the propagation of ultrashort pulses. New soliton solutions for this system are constructed on the constant backgrounds including one and two breathers and first and higher order localized soliton solutions. Considering the influence of higher order effects, propagation properties of those soliton solutions are discussed. -- Highlights: •The AB and Ma-breathers are derived on the constant backgrounds. •Dynamic features of two-breathers are discussed. •Localized solutions are generated from two different ways.
Microscopic derivation of discrete hydrodynamics.
Español, Pep; Anero, Jesús G; Zúñiga, Ignacio
2009-12-28
By using the standard theory of coarse graining based on Zwanzig's projection operator, we derive the dynamic equations for discrete hydrodynamic variables. These hydrodynamic variables are defined in terms of the Delaunay triangulation. The resulting microscopically derived equations can be understood, a posteriori, as a discretization on an arbitrary irregular grid of the Navier-Stokes equations. The microscopic derivation provides a set of discrete equations that exactly conserves mass, momentum, and energy and the dissipative part of the dynamics produces strict entropy increase. In addition, the microscopic derivation provides a practical implementation of thermal fluctuations in a way that the fluctuation-dissipation theorem is satisfied exactly. This paper points toward a close connection between coarse-graining procedures from microscopic dynamics and discretization schemes for partial differential equations. PMID:20059064
NASA Astrophysics Data System (ADS)
Ling, Liming; Feng, Bao-Feng; Zhu, Zuonong
2016-07-01
In the present paper, we are concerned with the general analytic solutions to the complex short pulse (CSP) equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the N-bright soliton solution in a compact determinant form, the N-breather solution including the Akhmediev breather and a general higher order rogue wave solution. The first and second order rogue wave solutions are given explicitly and analyzed. The asymptotic analysis is performed rigorously for both the N-soliton and the N-breather solutions. All three forms of the analytical solutions admit either smoothed-, cusped- or looped-type ones for the CSP equation depending on the parameters. It is noted that, due to the reciprocal (hodograph) transformation, the rogue wave solution to the CSP equation can be a smoothed, cusponed or a looped one, which is different from the rogue wave solution found so far.
Exactly solvable chaos in an electromechanical oscillator.
Owens, Benjamin A M; Stahl, Mark T; Corron, Ned J; Blakely, Jonathan N; Illing, Lucas
2013-09-01
A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rössler's folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations. PMID:24089945
Exactly solvable chaos in an electromechanical oscillator
NASA Astrophysics Data System (ADS)
Owens, Benjamin A. M.; Stahl, Mark T.; Corron, Ned J.; Blakely, Jonathan N.; Illing, Lucas
2013-09-01
A novel electromechanical chaotic oscillator is described that admits an exact analytic solution. The oscillator is a hybrid dynamical system with governing equations that include a linear second order ordinary differential equation with negative damping and a discrete switching condition that controls the oscillatory fixed point. The system produces provably chaotic oscillations with a topological structure similar to either the Lorenz butterfly or Rössler's folded-band oscillator depending on the configuration. Exact solutions are written as a linear convolution of a fixed basis pulse and a sequence of discrete symbols. We find close agreement between the exact analytical solutions and the physical oscillations. Waveform return maps for both configurations show equivalence to either a shift map or tent map, proving the chaotic nature of the oscillations.
Zabolotin, V.V.; Uvarova, L.A.
2015-03-10
A numerical simulation of the interaction of laser radiation with dispersed particles in the course of propagation of breather in the surface layer of the liquid breather was performed. The shape and amplitude of the acoustic signal formed in this interaction were obtained. Two acoustic signals, before and after the impact of a breather on the process of optical sound generation, were compared. Results of the comparison showed that the breather spreading over the surface of the liquid medium affecst the acoustic signal and its effect must be considered in the measurements.
NASA Astrophysics Data System (ADS)
Pathak, Pallabi; Sharma, S. K.; Nakamura, Y.; Bailung, H.
2016-02-01
The experimental observation of second order ion acoustic Peregrine breathers in multicomponent plasma with negative ions is reported. A long wavelength initial perturbation on a continuous carrier frequency ˜0.5 ωpi (where ωpi is the ion plasma frequency) of finite amplitude is found to undergo self-modulation due to the interplay between nonlinear dispersive effect and group velocity dispersion because of modulational instability. Wave energy focusses to a smaller localized and isolated group of waves within the packet with amplitude amplification up to 5 times of the background carrier wave. The experimental results are compared with second order breather solution of nonlinear Schrodinger equation. The wavelet analysis and fast Fourier transform analysis of the experimental time series data indicate strong nonlinear evolution (wave energy focusing and spectral broadening) conforming to the formation of second order Peregrine solitons.
Amplification of matter rogue waves and breathers in quasi-two-dimensional Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Manikandan, K.; Senthilvelan, M.; Kraenkel, R. A.
2016-02-01
We construct rogue wave and breather solutions of a quasi-two-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap. We show that the trapping potential and an arbitrary functional parameter that present in the similarity transformation should satisfy a constraint for the considered equation to be integrable and yield the desired solutions. We consider two different forms of functional parameters and investigate how the density of the rogue wave and breather profiles vary with respect to these functional parameters. We also construct vector localized solutions of a two coupled quasi-two-dimensional Bose-Einstein condensate system. We then investigate how the vector localized density profiles modify in the constant density background with respect to the functional parameters. Our results may help to manipulate matter rogue waves experimentally in the two-dimensional Bose-Einstein condensate systems.
NASA Astrophysics Data System (ADS)
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.
Breather boundary form factors in sine-Gordon theory
NASA Astrophysics Data System (ADS)
Lencsés, M.; Takács, G.
2011-11-01
A previously conjectured set of exact form factors of boundary exponential operators in the sinh-Gordon model is tested against numerical results from boundary truncated conformal space approach in boundary sine-Gordon theory, related by analytic continuation to sinh-Gordon model. We find that the numerical data strongly support the validity of the form factors themselves; however, we also report a discrepancy in the case of diagonal matrix elements, which remains unresolved for the time being.
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. PMID:18958598
Exactly solvable birth and death processes
Sasaki, Ryu
2009-10-15
Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly solvable 'matrix' quantum mechanics, which is recently proposed by Odake and the author [S. Odake and R. Sasaki, J. Math. Phys. 49, 053503 (2008)]. The (q-) Askey scheme of hypergeometric orthogonal polynomials of a discrete variable and their dual polynomials play a central role. The most generic solvable birth/death rates are rational functions of q{sup x} (with x being the population) corresponding to the q-Racah polynomial.
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
2015-12-01
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
NASA Astrophysics Data System (ADS)
Vivaldi, Franco
The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.
Breaking and Restoring of Diffeomorphism Symmetry in Discrete Gravity
Bahr, B.; Dittrich, B.
2009-12-15
We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible to construct discrete actions, so-called perfect actions, with exact symmetries and we will review first steps towards this end.
Vector Breathers in an Averaged Dispersion-Managed Birefringent Fiber System
NASA Astrophysics Data System (ADS)
Li, Ji-Tao; Han, Jin-Zhong; Zhang, Xian-Tu
2015-07-01
A variable-coefficient coupled nonlinear Schrödinger equation in an averaged dispersion-managed birefringent fiber is investigated. Based on the one-to-one correspondence between variable-coefficient and constant-coefficient equations, an analytical breather solution is derived. As an example to exhibit dynamical behaviors of solution, its controllable excitations including rear excitation, peak excitation and initial excitation are discussed. Supported by the Science and Technology Department of Henan Province under Grant No. 142300410043, and by the Education Department of Henan Province under Grant No. 13A140113
Quantum breathers in Klein-Gordon lattice: Non-periodic boundary condition approach
NASA Astrophysics Data System (ADS)
Mandal, Subhra Jyoti; Choudhary, Kamal; Biswas, Arindam; Bandyopadhyay, A. K.; Bhattacharjee, A. K.; Mandal, D.
2011-12-01
The presence of classical breathers and two-phonon bound state (TPBS) or quantum breather (QB) state through detailed quantum calculations have already been shown in technologically important ferroelectric materials, such as lithium niobate with antisite niobium charge defects concerning pinning transition, its control, and application. The latter was done in a periodic boundary condition with Bloch function in terms of significant variations of TPBS parameters against impurity, which is related to nonlinearity. In further extension of this work, in a non-periodic boundary condition and number-conserving approach, apart from various techniques available, only the temporal evolution of the number of quanta (i.e., phonons) in more sites is detailed in this present investigation for a generalized Klein-Gordon system with applications in ferroelectrics, metamaterials, and DNA. The critical time of redistribution of quanta that is proportional to the QB's lifetime in these materials shows different types of behavior in the femtosecond range, which gives rise to the possibilities for making various devices.
Breather solutions of a nonlinear DNA model including a longitudinal degree of freedom
NASA Astrophysics Data System (ADS)
Agarwal, J.; Hennig, D.
2003-05-01
We present a model of the DNA double helix assigning three degrees of freedom to each pair of nucleotides. The model is an extension of the Barbi-Cocco-Peyrard (BCP) model in the sense that the current model allows for longitudinal motions of the nucleotides parallel to the helix axis. The molecular structure of the double helix is modelled by a system of coupled oscillators. The nucleotides are represented by point masses and coupled via point-point interaction potentials. The latter describe the covalent and hydrogen bonds responsible for the secondary structure of DNA. We obtain breather solutions using an established method for the construction of breathers on nonlinear lattices starting from the anti-coupling limit. In order to apply this method we analyse the phonon spectrum of the linearised system corresponding to our model. The obtained breathing motion consists of a local opening and re-closing of base pairs combined with a local untwist of the helix. The motions in longitudinal direction are of much lower amplitudes than the radial and angular elongations.
Local relativistic exact decoupling.
Peng, Daoling; Reiher, Markus
2012-06-28
We present a systematic hierarchy of approximations for local exact decoupling of four-component quantum chemical Hamiltonians based on the Dirac equation. Our ansatz reaches beyond the trivial local approximation that is based on a unitary transformation of only the atomic block-diagonal part of the Hamiltonian. Systematically, off-diagonal Hamiltonian matrix blocks can be subjected to a unitary transformation to yield relativistically corrected matrix elements. The full hierarchy is investigated with respect to the accuracy reached for the electronic energy and for selected molecular properties on a balanced test molecule set that comprises molecules with heavy elements in different bonding situations. Our atomic (local) assembly of the unitary exact-decoupling transformation--called local approximation to the unitary decoupling transformation (DLU)--provides an excellent local approximation for any relativistic exact-decoupling approach. Its order-N(2) scaling can be further reduced to linear scaling by employing a neighboring-atomic-blocks approximation. Therefore, DLU is an efficient relativistic method well suited for relativistic calculations on large molecules. If a large molecule contains many light atoms (typically hydrogen atoms), the computational costs can be further reduced by employing a well-defined nonrelativistic approximation for these light atoms without significant loss of accuracy. We also demonstrate that the standard and straightforward transformation of only the atomic block-diagonal entries in the Hamiltonian--denoted diagonal local approximation to the Hamiltonian (DLH) in this paper--introduces an error that is on the order of the error of second-order Douglas-Kroll-Hess (i.e., DKH2) when compared with exact-decoupling results. Hence, the local DLH approximation would be pointless in an exact-decoupling framework, but can be efficiently employed in combination with the fast to evaluate DKH2 Hamiltonian in order to speed up calculations
Exact Relativistic `Antigravity' Propulsion
NASA Astrophysics Data System (ADS)
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.
Exact folded-band chaotic oscillator.
Corron, Ned J; Blakely, Jonathan N
2012-06-01
An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Rössler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar. PMID:22757520
NASA Astrophysics Data System (ADS)
Wang, Qi-Min; Gao, Yi-Tian; Su, Chuan-Qi; Zuo, Da-Wei
2015-10-01
In this paper, a higher-order nonlinear Schrödinger-Maxwell-Bloch system with quintic terms is investigated, which describes the propagation of ultrashort optical pulses, up to the attosecond duration, in an erbium-doped fiber. Multi-soliton, breather and rogue-wave solutions are derived by virtue of the Darboux transformation and the limiting procedure. Features and interaction patterns of the solitons, breathers and rogue waves are discussed. (i) The solitonic amplitudes, widths and velocities are exhibited, and solitonic amplitudes and widths are proved to have nothing to do with the higher-order terms. (ii) The higher-order terms and frequency detuning affect the growth rate of periodic modulation and skewing angle for the breathers, except for the range of the frequency of modulation. (iii) The quintic terms and frequency detuning have the effects on the temporal duration for the rogue waves. (iv) Breathers are classified into two types, according to the range of the modulation instability. (v) Interaction between the two solitons is elastic. When the two solitons interact with each other, the periodic structure occurs, which is affected by the higher-order terms and frequency detuning. (vi) Interaction between the two Akhmediev-like breathers or two Kuznetsov-Ma-like solitons shows the different patterns with different ratios of the relative modulation frequencies, while the interaction area induced by the two breathers looks like a higher-order rogue wave.
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.
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Kinematics of foldable discrete space cranes
NASA Technical Reports Server (NTRS)
Nayfeh, A. H.
1985-01-01
Exact kinematic description of a NASA proposed prototype foldable-deployable discrete space crane are presented. A computer program is developed which maps the geometry of the crane once controlling parameters are specified. The program uses a building block type approach in which it calculates the local coordinates of each repeating cell and then combines them with respect to a global coordinates system.
Combined Akhmediev breather and Kuznetsov-Ma solitons in a two-dimensional graded-index waveguide
NASA Astrophysics Data System (ADS)
Zhu, Hai-Ping; Pan, Zhen-Huan
2014-04-01
We study the (2 + 1)-dimensional coupled nonlinear Schrödinger equation with variable coefficients in a graded-index waveguide, and present a combined Akhmediev breather and Kuznetsov-Ma soliton solution with nonautonomous characteristics for certain functional relations. From this solution, by modulating the relation between the maximum effective propagation distance Zmax and the periodic locations Zm based on the maximum amplitude of soliton solution, different types of controllable excitation behaviors such as limitation excitation, maintenance and postponement are demonstrated.
Efficient exact motif discovery
Marschall, Tobias; Rahmann, Sven
2009-01-01
Motivation: The motif discovery problem consists of finding over-represented patterns in a collection of biosequences. It is one of the classical sequence analysis problems, but still has not been satisfactorily solved in an exact and efficient manner. This is partly due to the large number of possibilities of defining the motif search space and the notion of over-representation. Even for well-defined formalizations, the problem is frequently solved in an ad hoc manner with heuristics that do not guarantee to find the best motif. Results: We show how to solve the motif discovery problem (almost) exactly on a practically relevant space of IUPAC generalized string patterns, using the p-value with respect to an i.i.d. model or a Markov model as the measure of over-representation. In particular, (i) we use a highly accurate compound Poisson approximation for the null distribution of the number of motif occurrences. We show how to compute the exact clump size distribution using a recently introduced device called probabilistic arithmetic automaton (PAA). (ii) We define two p-value scores for over-representation, the first one based on the total number of motif occurrences, the second one based on the number of sequences in a collection with at least one occurrence. (iii) We describe an algorithm to discover the optimal pattern with respect to either of the scores. The method exploits monotonicity properties of the compound Poisson approximation and is by orders of magnitude faster than exhaustive enumeration of IUPAC strings (11.8 h compared with an extrapolated runtime of 4.8 years). (iv) We justify the use of the proposed scores for motif discovery by showing our method to outperform other motif discovery algorithms (e.g. MEME, Weeder) on benchmark datasets. We also propose new motifs on Mycobacterium tuberculosis. Availability and Implementation: The method has been implemented in Java. It can be obtained from http://ls11-www
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Su, Chuan-Qi; Gao, Yi-Tian; Xue, Long; Wang, Qi-Min
2016-07-01
Under investigation in this paper is the Gross-Pitaevskii equation which describes the dynamics of the Bose-Einstein condensate. Lax pair, conservation laws and Darboux transformation (DT) are constructed. Nonautonomous solitons and breathers are derived based on the DT obtained. A kind of modulation instability process is generated. Nonautonomous rogue waves are obtained via the generalized DT. Influence of the nonlinearity, linear external potential, harmonic external potential, and spectral parameter on the propagation and interaction of the nonautonomous solitons, breathers and rogue waves is also discussed. Amplitude of the first-order nonautonomous soliton is proportional to the imaginary part of the spectral parameter and inversely proportional to the nonlinearity parameter. Linear external potential parameter affects the location of the first-order nonautonomous soliton. Head-on interaction, overtaking interaction and bound-state-like nonautonomous solitons can be formed based on the signs of the real parts of the spectral parameters. Quasi-periodic behaviors are exhibited for the nonautonomous breathers. If the harmonic external potential parameter is negative, quasi-period decreases along the positive time axis, with an increase in the amplitude and a compression in the width. Quasi-period decreases with the increase of the nonlinearity parameter. The second-order nonautonomous rogue wave can split into three first-order ones. Nonlinearity parameter has an effect on the amplitude of the rogue wave. Linear external potential parameter influences the location of the rogue wave, while harmonic external potential parameter affects the curved direction of the background.
Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail
2012-06-01
We present an explicit analytic form for the two-breather solution of the nonlinear Schrödinger equation with imaginary eigenvalues. It describes various nonlinear combinations of Akhmediev breathers and Kuznetsov-Ma solitons. The degenerate case, when the two eigenvalues coincide, is quite involved. The standard inverse scattering technique does not generally provide an answer to this scenario. We show here that the solution can still be found as a special limit of the general second-order expression and appears as a mixture of polynomials with trigonometric and hyperbolic functions. A further restriction of this particular case, where the two eigenvalues are equal to i, produces the second-order rogue wave with two free parameters considered as differential shifts. The illustrations reveal a precarious dependence of wave profile on the degenerate eigenvalues and differential shifts. Thus we establish a hierarchy of second-order solutions, revealing the interrelated nature of the general case, the rogue wave, and the degenerate breathers. PMID:23005231
ERIC Educational Resources Information Center
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2013-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics ("two" means exactly two), many linguistic accounts propose that numbers have lower-bounded semantics (at least two), and…
Exact approaches for scaffolding
2015-01-01
This paper presents new structural and algorithmic results around the scaffolding problem, which occurs prominently in next generation sequencing. The problem can be formalized as an optimization problem on a special graph, the "scaffold graph". We prove that the problem is polynomial if this graph is a tree by providing a dynamic programming algorithm for this case. This algorithm serves as a basis to deduce an exact algorithm for general graphs using a tree decomposition of the input. We explore other structural parameters, proving a linear-size problem kernel with respect to the size of a feedback-edge set on a restricted version of Scaffolding. Finally, we examine some parameters of scaffold graphs, which are based on real-world genomes, revealing that the feedback edge set is significantly smaller than the input size. PMID:26451725
High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA.
Yao, Ying-Bo; Wang, Xiao-Yun; Tang, Bing
2016-03-01
By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system. PMID:26489740
ERIC Educational Resources Information Center
Ghezzi, Patrick M.
2007-01-01
The advantages of emphasizing discrete trials "teaching" over discrete trials "training" are presented first, followed by a discussion of discrete trials as a method of teaching that emerged historically--and as a matter of necessity for difficult learners such as those with autism--from discrete trials as a method for laboratory research. The…
Photoexcited breathers in conjugated polyenes: An excited-state molecular dynamics study
Tretiak, S.; Saxena, A.; Martin, R. L.; Bishop, A. R.
2003-01-01
π-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. PMID:12594339
NASA Astrophysics Data System (ADS)
Wang, Lei; Zhang, Jian-Hui; Wang, Zi-Qi; Liu, Chong; Li, Min; Qi, Feng-Hua; Guo, Rui
2016-01-01
We study the nonlinear waves on constant backgrounds of the higher-order generalized nonlinear Schrödinger (HGNLS) equation describing the propagation of ultrashort optical pulse in optical fibers. We derive the breather, rogue wave, and semirational solutions of the HGNLS equation. Our results show that these three types of solutions can be converted into the nonpulsating soliton solutions. In particular, we present the explicit conditions for the transitions between breathers and solitons with different structures. Further, we investigate the characteristics of the collisions between the soliton and breathers. Especially, based on the semirational solutions of the HGNLS equation, we display the novel interactions between the rogue waves and other nonlinear waves. In addition, we reveal the explicit relation between the transition and the distribution characteristics of the modulation instability growth rate.
Wang, Lei; Zhang, Jian-Hui; Wang, Zi-Qi; Liu, Chong; Li, Min; Qi, Feng-Hua; Guo, Rui
2016-01-01
We study the nonlinear waves on constant backgrounds of the higher-order generalized nonlinear Schrödinger (HGNLS) equation describing the propagation of ultrashort optical pulse in optical fibers. We derive the breather, rogue wave, and semirational solutions of the HGNLS equation. Our results show that these three types of solutions can be converted into the nonpulsating soliton solutions. In particular, we present the explicit conditions for the transitions between breathers and solitons with different structures. Further, we investigate the characteristics of the collisions between the soliton and breathers. Especially, based on the semirational solutions of the HGNLS equation, we display the novel interactions between the rogue waves and other nonlinear waves. In addition, we reveal the explicit relation between the transition and the distribution characteristics of the modulation instability growth rate. PMID:26871080
NASA Astrophysics Data System (ADS)
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.
The exact fundamental solution for the Benes tracking problem
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Gaillard, Pierre; Gastineau, Mickaël
2016-06-01
In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the ( x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a quotient of two determinants by an exponential depending on t. This formulation gives in the case of the order 3 and 4, solutions with, respectively 4 and 6 parameters. With this method, beside Peregrine breathers, we construct all characteristic patterns for the modulus of solutions, like triangular configurations, ring and others.
NASA Astrophysics Data System (ADS)
Gaillard, Pierre; Gastineau, Mickaël
2016-01-01
In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a quotient of two determinants by an exponential depending on t. This formulation gives in the case of the order 3 and 4, solutions with, respectively 4 and 6 parameters. With this method, beside Peregrine breathers, we construct all characteristic patterns for the modulus of solutions, like triangular configurations, ring and others.
New exact solutions to some difference differential equations
NASA Astrophysics Data System (ADS)
Wang, Zhen; Zhang, Hong-Qing
2006-10-01
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.
Discrete differential geometry: The nonplanar quadrilateral mesh
NASA Astrophysics Data System (ADS)
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.
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. PMID:23005244
Quantum walks and discrete gauge theories
NASA Astrophysics Data System (ADS)
Arnault, Pablo; Debbasch, Fabrice
2016-05-01
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E ×B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.
Correlated Lloyd model: Exact solution
NASA Astrophysics Data System (ADS)
Kozlov, G. G.
2014-11-01
We describe an exactly solvable model of a disordered system that is a generalized Lloyd model; it differs from the classical model because the random potential is not a δ-correlated random process. We show that the exact average Green's function in this case is independent of the correlation radius of the random potential and, as in the classical Lloyd model, is a crystal Green's function whose energy argument acquires an imaginary part dependent on the disorder degree.
Izuka, Edna Namiko; Feres, Murilo Fernando Neuppmann; Pignatari, Shirley Shizue Nagata
2015-01-01
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. PMID:26154455
Wang, Lei Li, Min; Qi, Feng-Hua; Xu, Tao
2015-03-15
Under investigation in this paper is a variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equation modeling the nonlinear Alfvén waves in the inhomogeneous plasmas. The modulation instability is examined for this inhomogeneous nonlinear model. The nonautonomous breather and rogue wave solutions of the vc-DNLS equation are obtained via the modified Darboux transformation. It is found that the velocity and amplitude of the breather can be controlled by the inhomogeneous magnetic field and nonuniform density. Such novel phenomena as breather amplification and nonlinear Talbot effect-like property are demonstrated with the proper choices of the inhomogeneous parameters. Furthermore, dynamics of the fundamental rogue wave, periodical rogue wave, and composite rogue wave are graphically discussed. The trajectories and amplitudes of the rogue waves can be manipulated by the inhomogeneous magnetic field and nonuniform density. In addition, the nonlinear tunneling of the rogue waves and breathers is studied. As an application, a sample model is treated with our results, and the graphical illustrations exhibit the compressing, expanding, and fluctuating phenomena of the Alfvén rogue waves.
Natural discretization in noncommutative field theory
NASA Astrophysics Data System (ADS)
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.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
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.
Principles of Discrete Time Mechanics
NASA Astrophysics Data System (ADS)
Jaroszkiewicz, George
2014-04-01
1. Introduction; 2. The physics of discreteness; 3. The road to calculus; 4. Temporal discretization; 5. Discrete time dynamics architecture; 6. Some models; 7. Classical cellular automata; 8. The action sum; 9. Worked examples; 10. Lee's approach to discrete time mechanics; 11. Elliptic billiards; 12. The construction of system functions; 13. The classical discrete time oscillator; 14. Type 2 temporal discretization; 15. Intermission; 16. Discrete time quantum mechanics; 17. The quantized discrete time oscillator; 18. Path integrals; 19. Quantum encoding; 20. Discrete time classical field equations; 21. The discrete time Schrodinger equation; 22. The discrete time Klein-Gordon equation; 23. The discrete time Dirac equation; 24. Discrete time Maxwell's equations; 25. The discrete time Skyrme model; 26. Discrete time quantum field theory; 27. Interacting discrete time scalar fields; 28. Space, time and gravitation; 29. Causality and observation; 30. Concluding remarks; Appendix A. Coherent states; Appendix B. The time-dependent oscillator; Appendix C. Quaternions; Appendix D. Quantum registers; References; Index.
Two-dimensional discrete solitons in dipolar Bose-Einstein condensates
Gligoric, Goran; Stepic, Milutin; Hadzievski, Ljupco; Maluckov, Aleksandra; Malomed, Boris A.
2010-01-15
We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk's plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, which differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying three-dimensional Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on the effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site, and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.
Construction of Superconvergent Discretizations with Differential-Difference Invariants
R.A. Axford
2005-08-12
To incorporate symmetry properties of second-order differential equations into finite difference equations, the concept of differential-difference invariants is introduced. This concept is applied to discretizing homogeneous eigenvalue problems and inhomogeneous two-point boundary value problems with various combinations of Dirichlet, Neumann, and Robin boundary conditions. It is demonstrated that discretizations constructed with differential-difference invariants yield exact results for eigenvalue spectra and superconvergent results for numerical solutions of differential equations.
A discretization of Boltzmann's collision operator with provable convergence
NASA Astrophysics Data System (ADS)
Brechtken, Stefan
2014-12-01
The discretization of the right-hand side of the Boltzmann equation (aka the collision operator) on uniform grids generally suffers from some well known problems prohibiting the construction of deterministic high order discretizations which exactly sustain the basic properties of the collision operator. These problems mainly relate to problems arising from the discretization of spheres on uniform grids and the necessity that the discretization must possess some symmetry properties in order to provide the discrete versions of properties stemming from the continuous collision operator (number of collision invariants, avoidance of artificial collision invariants, type of equilibrium solutions, H-Theorem). We present a scheme to construct discretizations in 2 dimensions with arbitrarily high convergence orders on uniform grids, which are comparable to the approach by Rogier and Schneider [1] and the subsequent works by Michel and Schneider as well as Panferov and Heintz [2, 3] who used Farey sequences for the discretization. Moreover we take a closer look at this discretization in the framework of discrete velocity models to present results governing the correct collision invariants, lack of artificial collision invariants, the H-Theorem and the correct equilibrium solutions. Furthermore we classify lattice group models (LGpM) in the context of DVMs to transfer the high convergence order of these discretizations into the context of LGpMs and finally we take a short look at the numerical complexity.
Nuclear models and exact algorithms
NASA Astrophysics Data System (ADS)
Bes, D. R.; Dobaczewski, J.; Draayer, J. P.; Szymański, Z.
1992-07-01
Discussion Group E on Nuclear Models and Exact Algorithms received contributions from the following individuals: L. Egido, S. Frauendorf, F. Iachello, P. Ring, H. Sagawa, W. Satula, N. C. Schmeing, M. Vincent, A. J. Zucker. The report that follows is an attempt by the leaders of the discussion to summarize the presentations and to give an impression of the subject matter.
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.
Soliton, Breather, and Rogue Wave for a (2+1)-Dimensional Nonlinear Schrödinger Equation
NASA Astrophysics Data System (ADS)
Zhang, Hai-Qiang; Liu, Xiao-Li; Wen, Li-Li
2016-02-01
In this paper, a (2+1)-dimensional nonlinear Schrödinger (NLS) equation, which is a generalisation of the NLS equation, is under investigation. The classical and generalised N-fold Darboux transformations are constructed in terms of determinant representations. With the non-vanishing background and iterated formula, a family of the analytical solutions of the (2+1)-dimensional NLS equation are systematically generated, including the bright-line solitons, breathers, and rogue waves. The interaction mechanisms between two bright-line solitons and among three bright-line solitons are both elastic. Several patterns for first-, second, and higher-order rogue wave solutions fixed at space are displayed, namely, the fundamental pattern, triangular pattern, and circular pattern. The two-dimensional space structures of first-, second-, and third-order rogue waves fixed at time are also demonstrated.
Synchronous Discrete Harmonic Oscillator
Antippa, Adel F.; Dubois, Daniel M.
2008-10-17
We introduce the synchronous discrete harmonic oscillator, and present an analytical, numerical and graphical study of its characteristics. The oscillator is synchronous when the time T for one revolution covering an angle of 2{pi} in phase space, is an integral multiple N of the discrete time step {delta}t. It is fully synchronous when N is even. It is pseudo-synchronous when T/{delta}t is rational. In the energy conserving hyperincursive representation, the phase space trajectories are perfectly stable at all time scales, and in both synchronous and pseudo-synchronous modes they cycle through a finite number of phase space points. Consequently, both the synchronous and the pseudo-synchronous hyperincursive modes of time-discretization provide a physically realistic and mathematically coherent, procedure for dynamic, background independent, discretization of spacetime. The procedure is applicable to any stable periodic dynamical system, and provokes an intrinsic correlation between space and time, whereby space-discretization is a direct consequence of background-independent time-discretization. Hence, synchronous discretization moves the formalism of classical mechanics towards that of special relativity. The frequency of the hyperincursive discrete harmonic oscillator is ''blue shifted'' relative to its continuum counterpart. The frequency shift has the precise value needed to make the speed of the system point in phase space independent of the discretizing time interval {delta}t. That is the speed of the system point is the same on the polygonal (in the discrete case) and the circular (in the continuum case) phase space trajectories.
Carlsten, B.E.; Haynes, W.B.
1996-08-01
The authors theoretically and numerically investigate the operation and behavior of the discrete monotron oscillator, a novel high-power microwave source. The discrete monotron differs from conventional monotrons and transit time oscillators by shielding the electron beam from the monotron cavity`s RF fields except at two distinct locations. This makes the discrete monotron act more like a klystron than a distributed traveling wave device. As a result, the oscillator has higher efficiency and can operate with higher beam powers than other single cavity oscillators and has more stable operation without requiring a seed input signal than mildly relativistic, intense-beam klystron oscillators.
Häyry, Matti
2015-01-01
Philosophers should express their ideas clearly. They should do this in any field of specialization, but especially when they address issues of practical consequence, as they do in bioethics. This article dissects a recent and much-debated contribution to philosophical bioethics by Alberto Giubilini and Francesca Minerva, examines how exactly it fails to meet the requirement of clarity, and maps a way forward by outlining the ways in which philosophical argumentation could validly and soundly proceed in bioethics. PMID:25473863
Exact dynamics of finite Glauber-Fock photonic lattices
Rodriguez-Lara, B. M.
2011-11-15
The dynamics of Glauber-Fock lattice of size N is given through exact diagonalization of the corresponding Hamiltonian; the spectra {l_brace}{lambda}{sub k}{r_brace} is given as the roots of the Nth Hermite polynomial, H{sub N}({lambda}{sub k}/{radical}(2))=0, and the eigenstates are given in terms of Hermite polynomials evaluated at these roots. The exact dynamics is used to study coherent phenomena in discrete lattices. Due to the symmetry and spacing of the eigenvalues {l_brace}{lambda}{sub k}{r_brace}, oscillatory behavior is predicted with highly localized spectra, that is, near complete revivals of the photon number and partial recovery of the initial state at given waveguides.
Exact results for models of multichannel quantum nonadiabatic transitions
Sinitsyn, N. A.
2014-12-11
We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicitmore » expressions for scattering probabilities in such systems.« less
Exact results for models of multichannel quantum nonadiabatic transitions
Sinitsyn, N. A.
2014-12-11
We consider nonadiabatic transitions in explicitly time-dependent systems with Hamiltonians of the form Hˆ(t)=Aˆ+Bˆt+Cˆ/t, where t is time and Aˆ,Bˆ,Cˆ are Hermitian N × N matrices. We show that in any model of this type, scattering matrix elements satisfy nontrivial exact constraints that follow from the absence of the Stokes phenomenon for solutions with specific conditions at t→–∞. This allows one to continue such solutions analytically to t→+∞, and connect their asymptotic behavior at t→–∞ and t→+∞. This property becomes particularly useful when a model shows additional discrete symmetries. Specifically, we derive a number of simple exact constraints and explicit expressions for scattering probabilities in such systems.
Exact results for a noise-induced bistable system.
Houchmandzadeh, Bahram; Vallade, Marcel
2015-02-01
A stochastic system where bistability is caused by noise has been recently investigated by Biancalani et al. [Phys. Rev. Lett. 112, 038101 (2014)]. They have computed the mean switching time for such a system using a continuous Fokker-Planck equation derived from the Taylor expansion of the master equation to estimate the parameter of such a system from experiment. In this article, we provide the exact solution for the full discrete system without resorting to continuous approximation and obtain the expression for the mean switching time. We further extend this investigation by solving exactly the master equation and obtaining the expression of other quantities of interests such as the dynamics of the moments and the equilibrium time. PMID:25768466
ERIC Educational Resources Information Center
Peters, James V.
2004-01-01
Using the methods of finite difference equations the discrete analogue of the parabolic and catenary cable are analysed. The fibonacci numbers and the golden ratio arise in the treatment of the catenary.
Exact element modal analysis of beam/oscillator systems
NASA Technical Reports Server (NTRS)
Broome, Taft H., Jr.
1993-01-01
Exact modal analysis of a beam/many-oscillator system is presented. Each oscillator consists of a discrete mass having rotational inertia, and two locally-dependent springs: one being rotational and the other, translational. A constant longitudinal force is applied to the mass, and its effect is coupled with the dynamic modes. The beam's distributed mass and other material properties, and its geometric properties, do not vary within spans bounded by the oscillators, but may vary from span to span. The classical separation-of-variables technique is used to obtain a dosedform description of the dynamic matrix, and the modal frequencies are determined as the zeros of this determinant.
Discretizations of axisymmetric systems
NASA Astrophysics Data System (ADS)
Frauendiener, Jörg
2002-11-01
In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space.
Dynamics and bifurcations of a planar map modeling dispersion managed breathers
Holmes, P. ); Kutz, J.N. Lucent Technologies, Murray Hill, NJ . Bell Labs.)
1999-05-01
The authors study a nonautonomous ODE with piecewise-constant coefficients and its associated two-dimensional Poincare mapping. The ODE models variations in amplitude and phase of a pulse propagating in a lossless optical fiber with periodically varying dispersion. They derive semiexplicit exact solutions and use them to locate fixed points and to describe their bifurcations and stability types. They also discuss the global structure of the Poincare map and interpret the results for modulated pulse propagation.
Partitioning technique for discrete quantum systems
Jin, L.; Song, Z.
2011-06-15
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show that the effective Hamiltonian on the central graph can be constructed by adding additional potentials on the branch-root nodes, which generates the same result as does the the original Hamiltonian on the entire graph. Exactly solvable models are presented to demonstrate the main points of this paper.
Familial sinistrals avoid exact numbers.
Sauerland, Uli; Gotzner, Nicole
2013-01-01
We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society) index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere. PMID:23544052
Generalized computer-aided discrete time domain modeling and analysis of dc-dc converters
NASA Technical Reports Server (NTRS)
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.
A discrete fractional random transform
NASA Astrophysics Data System (ADS)
Liu, Zhengjun; Zhao, Haifa; Liu, Shutian
2005-11-01
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of the fractional Fourier transform along with some fantastic features of its own. As a primary application, the discrete fractional random transform has been used for image encryption and decryption.
Discrete Newtonian cosmology: perturbations
NASA Astrophysics Data System (ADS)
Ellis, George F. R.; Gibbons, Gary W.
2015-03-01
In a previous paper (Gibbons and Ellis 2014 Discrete Newtonian cosmology Class. Quantum Grav. 31 025003), we showed how a finite system of discrete particles interacting with each other via Newtonian gravitational attraction would lead to precisely the same dynamical equations for homothetic motion as in the case of the pressure-free Friedmann-Lemaître-Robertson-Walker cosmological models of general relativity theory, provided the distribution of particles obeys the central configuration equation. In this paper we show that one can obtain perturbed such Newtonian solutions that give the same linearized structure growth equations as in the general relativity case. We also obtain the Dmitriev-Zel’dovich equations for subsystems in this discrete gravitational model, and show how it leads to the conclusion that voids have an apparent negative mass.
AESS: Accelerated Exact Stochastic Simulation
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
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.
High Resolution Thermometry for EXACT
NASA Technical Reports Server (NTRS)
Panek, J. S.; Nash, A. E.; Larson, M.; Mulders, N.
2000-01-01
High Resolution Thermometers (HRTs) based on SQUID detection of the magnetization of a paramagnetic salt or a metal alloy has been commonly used for sub-nano Kelvin temperature resolution in low temperature physics experiments. The main applications to date have been for temperature ranges near the lambda point of He-4 (2.177 K). These thermometers made use of materials such as Cu(NH4)2Br4 *2H2O, GdCl3, or PdFe. None of these materials are suitable for EXACT, which will explore the region of the He-3/He-4 tricritical point at 0.87 K. The experiment requirements and properties of several candidate paramagnetic materials will be presented, as well as preliminary test results.
Exact Bremsstrahlung and effective couplings
NASA Astrophysics Data System (ADS)
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.
Time Discretization Approach to Dynamic Localization Conditions
NASA Astrophysics Data System (ADS)
Papp, E.
An alternative wavefunction to the description of the dynamic localization of a charged particle moving on a one-dimensional lattice under the influence of a periodic time dependent electric field is written down. For this purpose the method of characteristics such as applied by Dunlap and Kenkre [Phys. Rev. B 34, 3625 (1986)] has been modified by using a different integration variable. Handling this wavefunction one is faced with the selection of admissible time values. This results in a conditionally exactly solvable problem, now by accounting specifically for the implementation of a time discretization working in conjunction with a related dynamic localization condition. In addition, one resorts to the strong field limit, which amounts to replace, to leading order, the large order zeros of the Bessel function J0(z), used before in connection with the cosinusoidal modulation, by integral multiples of π. Here z stands for the ratio between the field amplitude and the frequency. The modulation function of the electric field vanishes on the nodal points of the time grid, which stands for an effective field-free behavior. This opens the way to propose quickly tractable dynamic localization conditions for arbitrary periodic modulations. We have also found that the present time discretization approach produces the minimization of the mean square displacement characterizing the usual exact wavefunction. Other realizations and comparisons have also been presented.
ERIC Educational Resources Information Center
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Discrete Variational Approach for Modeling Laser-Plasma Interactions
NASA Astrophysics Data System (ADS)
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.
Binary classification of real sequences by discrete-time systems
NASA Technical Reports Server (NTRS)
Kaliski, M. E.; Johnson, T. L.
1979-01-01
This paper considers a novel approach to coding or classifying sequences of real numbers through the use of (generally nonlinear) finite-dimensional discrete-time systems. This approach involves a finite-dimensional discrete-time system (which we call a real acceptor) in cascade with a threshold type device (which we call a discriminator). The proposed classification scheme and the exact nature of the classification problem are described, along with two examples illustrating its applicability. Suggested approaches for further research are given.
Gravity cutoff in theories with large discrete symmetries.
Dvali, Gia; Redi, Michele; Sibiryakov, Sergey; Vainshtein, Arkady
2008-10-10
We set an upper bound on the gravitational cutoff in theories with exact quantum numbers of large N periodicity, such as Z(N) discrete symmetries. The bound stems from black hole physics. It is similar to the bound appearing in theories with N particle species, though a priori, a large discrete symmetry does not imply a large number of species. Thus, there emerges a potentially wide class of new theories that address the hierarchy problem by lowering the gravitational cutoff due to the existence of large Z(10(32))-type symmetries. PMID:18999587
Exact exchange for correlated electrons
NASA Astrophysics Data System (ADS)
Novák, P.; Kune?, J.; Chaput, L.; Pickett, W. E.
The cover picture is taken from the article by Pavel Novák that was chosen as Editor's Choice of this issue [1]. The figure shows the density of minority spin states in nickel oxide calculated by three commonly used approximations (LSDA, GGA, LDA+U) as well as using the newly proposed ?Exact Exchange for Correlated Electrons? (EECE) method. The EECE method treats the interactions between correlated electrons in a Hartree-Fock way, while all other interactions are described by the density functional theory. EECE is a promising starting point for the improvement of orbital-dependent functionals within the density functional theory.Pavel Novák is the head of the ?Spectroscopy of Magnetic Oxides? group at the Institute of Physics of ASCR, Prague, Czech Republic. Most of his scientific activity is devoted to the calculation of the electronic structure of solids, but he also closely cooperates with several experimental groups. Particular attention is focused on the nuclear magnetic resonance and electronic structure of magnetic oxides with mixed valency of the cations
Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.
Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K
2007-07-01
Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved
Discreteness induced extinction
NASA Astrophysics Data System (ADS)
dos Santos, Renato Vieira; da Silva, Linaena Méricy
2015-11-01
Two simple models based on ecological problems are discussed from the point of view of non-equilibrium statistical mechanics. It is shown how discrepant may be the results of the models that include spatial distribution with discrete interactions when compared with the continuous analogous models. In the continuous case we have, under certain circumstances, the population explosion. When we take into account the finiteness of the population, we get the opposite result, extinction. We will analyze how these results depend on the dimension d of the space and describe the phenomenon of the "Discreteness Inducing Extinction" (DIE). The results are interpreted in the context of the "paradox of sex", an old problem of evolutionary biology.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
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.
Exact averaging of laminar dispersion
NASA Astrophysics Data System (ADS)
Ratnakar, Ram R.; Balakotaiah, Vemuri
2011-02-01
We use the Liapunov-Schmidt (LS) technique of bifurcation theory to derive a low-dimensional model for laminar dispersion of a nonreactive solute in a tube. The LS formalism leads to an exact averaged model, consisting of the governing equation for the cross-section averaged concentration, along with the initial and inlet conditions, to all orders in the transverse diffusion time. We use the averaged model to analyze the temporal evolution of the spatial moments of the solute and show that they do not have the centroid displacement or variance deficit predicted by the coarse-grained models derived by other methods. We also present a detailed analysis of the first three spatial moments for short and long times as a function of the radial Peclet number and identify three clearly defined time intervals for the evolution of the solute concentration profile. By examining the skewness in some detail, we show that the skewness increases initially, attains a maximum for time scales of the order of transverse diffusion time, and the solute concentration profile never attains the Gaussian shape at any finite time. Finally, we reason that there is a fundamental physical inconsistency in representing laminar (Taylor) dispersion phenomena using truncated averaged models in terms of a single cross-section averaged concentration and its large scale gradient. Our approach evaluates the dispersion flux using a local gradient between the dominant diffusive and convective modes. We present and analyze a truncated regularized hyperbolic model in terms of the cup-mixing concentration for the classical Taylor-Aris dispersion that has a larger domain of validity compared to the traditional parabolic model. By analyzing the temporal moments, we show that the hyperbolic model has no physical inconsistencies that are associated with the parabolic model and can describe the dispersion process to first order accuracy in the transverse diffusion time.
A paradigm for discrete physics
Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.
1987-01-01
An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity.
Algerian Women in the Exact Sciences
NASA Astrophysics Data System (ADS)
Kesri, Naziha
2009-04-01
In the exact sciences, which include physics, chemistry, and mathematics, women comprise 53% of the total graduates in Algeria. Fifty percent of persons working in careers in the exact sciences are women. We focus our analysis on graduate and postgraduate trends for women in the exact sciences and on women's careers in physics in universities and research laboratories, where the "leaky pipeline" is in evidence.
Surface pauses in relation to dive duration in imperial cormorants; how much time for a breather?
Wilson, Rory P; Quintana, Flavio
2004-05-01
Air-breathing animals diving to forage can optimize time underwater by diving with just enough oxygen for the projected performance underwater. By so doing they surface with minimal body oxygen levels, which leads to maximal rates of oxygen uptake. We examined whether imperial cormorants Phalacrocorax atriceps adhere to this by examining dive:pause ratios in birds diving for extended, continuous periods to constant depths, assuming that the oxygen used underwater was exactly replenished by the periods at the surface. Examination of the cumulative time spent in surface pauses relative to the cumulative time spent in diving showed that surface pauses increase according to a power curve function of time spent in the dive or water depth. In a simplistic model we considered the rate at which birds expended energy underwater to be constant and that the rate of oxygen replenishment during the surface pause was directly proportional to the oxygen deficit. We then worked out values for the rate constant for the surface pause before using this constant to examine bird body oxygen levels immediately pre- and post dive. The model predicted that imperial cormorants do not submerge with just enough oxygen to cover their projected dive performance but rather dive with substantial reserves, although these reserves decrease with increasing dive depth/duration. We speculate that these oxygen reserves may be used to enhance bird survival when rare events, such as the appearance of predators or discovery of large prey requiring extended handling time, occur. The form of the oxygen saturation curve over time at the surface means that the time costs for maintaining constant oxygen reserves become particularly onerous for long, deep dives, so the observed decrease in reserves with increasing dive duration is expected in animals benefiting by optimizing for time. PMID:15107434
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Kotulski, Zbigniew; Szczepaski, Janusz
In the paper we propose a new method of constructing cryptosystems utilising a nonpredictability property of discrete chaotic systems. We formulate the requirements for such systems to assure their safety. We also give examples of practical realisation of chaotic cryptosystems, using a generalisation of the method presented in [7]. The proposed algorithm of encryption and decryption is based on multiple iteration of a certain dynamical chaotic system. We assume that some part of the initial condition is a plain message. As the secret key we assume the system parameter(s) and additionally another part of the initial condition.
Two-flavor QCD simulation with exact chiral symmetry
Aoki, S.; Fukaya, H.; Hashimoto, S.; Kaneko, T.; Yamada, N.; Ishikawa, K-I.; Okawa, M.; Kanaya, K.; Matsufuru, H.; Okamoto, M.; Onogi, T.; Ukawa, A; Yoshie, T.
2008-07-01
We perform numerical simulations of lattice QCD with two flavors of dynamical overlap quarks, which have exact chiral symmetry on the lattice. While this fermion discretization is computationally demanding, we demonstrate the feasibility to simulate reasonably large and fine lattices by a careful choice of the lattice action and algorithmic improvements. Our production runs are carried out on a 16{sup 3}x32 lattice at a single lattice spacing around 0.12 fm. We explore the sea quark mass region down to m{sub s}/6, where m{sub s} is the physical strange quark mass, for a good control of the chiral extrapolation in future calculations of physical observables. We describe in detail our setup and algorithmic properties of the production simulations and present results for the static quark potential to fix the lattice scale and the locality of the overlap operator.
Exact Adler Function in Supersymmetric QCD
NASA Astrophysics Data System (ADS)
Shifman, M.; Stepanyantz, K.
2015-02-01
The Adler function D is found exactly in supersymmetric QCD. Our exact formula relates D (Q2) to the anomalous dimension of the matter superfields γ (αs(Q2)) . En route we prove another theorem: the absence of the so-called singlet contribution to D . While such singlet contributions are present in individual supergraphs, they cancel in the sum.
Exact Results in Frustrated Quantum Magnetism
NASA Astrophysics Data System (ADS)
Miyahara, Shin
Most of the exact results in frustrated spin systems have for a long time been regarded as of purely academic interest, being realized only due to the special geometry of the lattices concerned. However, recent developments in material design offer the genuine possibility of producing such exact states in real materials. In fact, the exact dimer singlet state of the two-dimensional Shastry-Sutherland model has already been found as the ground state of the quasi-two-dimensional material SrCu2(BO3)2. The cooperation between experimentalists and theorists in investigating this material has caused rapid development in the understanding of low-dimensional frustrated spin systems in general, due to the extreme utility of cases where the ground state is known exactly. This fact provides information essential to recognizing novel magnetic behavior in external magnetic fields, at finite temperatures, and in other regimes. In this chapter, we introduce spin-1 / 2 models which have an exact ground state, considering first exactly solvable spin-1 / 2 Heisenberg models, exemplified by the sawtooth-chain model, the Majumdar-Ghosh model, the two-dimensional Shastry-Sutherland model, and a frustrated ladder model. Such exact states can be realized due to special symmetries on geometrically frustrated lattices. As a second class of examples, we introduce also some exact ground states in spin-1/2 models with multiple-spin interactions.
A space-time discretization procedure for wave propagation problems
NASA Technical Reports Server (NTRS)
Davis, Sanford
1989-01-01
Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.
A three-level BDDC algorithm for Mortar discretizations
Kim, H.; Tu, X.
2007-12-09
In this paper, a three-level BDDC algorithm is developed for the solutions of large sparse algebraic linear systems arising from the mortar discretization of elliptic boundary value problems. The mortar discretization is considered on geometrically non-conforming subdomain partitions. In two-level BDDC algorithms, the coarse problem needs to be solved exactly. However, its size will increase with the increase of the number of the subdomains. To overcome this limitation, the three-level algorithm solves the coarse problem inexactly while a good rate of convergence is maintained. This is an extension of previous work, the three-level BDDC algorithms for standard finite element discretization. Estimates of the condition numbers are provided for the three-level BDDC method and numerical experiments are also discussed.
Probabilistic flood forecast: Exact and approximate predictive distributions
NASA Astrophysics Data System (ADS)
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.
EXACT2: the semantics of biomedical protocols
2014-01-01
Background 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. Methods We have developed the ontology EXACT2 (EXperimental ACTions) that is designed to capture the full semantics of biomedical protocols required for their 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. Results 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. Conclusions 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
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2011-08-01
The original continuous-time ''goldfish'' dynamical system is characterized by two neat formulas, the first of which provides the N Newtonian equations of motion of this dynamical system, while the second provides the solution of the corresponding initial-value problem. Several other, more general, solvable dynamical systems ''of goldfish type'' have been identified over time, featuring, in the right-hand (''forces'') side of their Newtonian equations of motion, in addition to other contributions, a velocity-dependent term such as that appearing in the right-hand side of the first formula mentioned above. The solvable character of these models allows detailed analyses of their behavior, which in some cases is quite remarkable (for instance isochronous or asymptotically isochronous). In this paper we introduce and discuss various discrete-time dynamical systems, which are as well solvable, which also display interesting behaviors (including isochrony and asymptotic isochrony) and which reduce to dynamical systems of goldfish type in the limit when the discrete-time independent variable l=0,1,2,... becomes the standard continuous-time independent variable t, 0≤t<∞.
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.
NASA Astrophysics Data System (ADS)
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
Exact optics - III. Schwarzschild's spectrograph camera revised
NASA Astrophysics Data System (ADS)
Willstrop, R. V.
2004-03-01
Karl Schwarzschild identified a system of two mirrors, each defined by conic sections, free of third-order spherical aberration, coma and astigmatism, and with a flat focal surface. He considered it impractical, because the field was too restricted. This system was rediscovered as a quadratic approximation to one of Lynden-Bell's `exact optics' designs which have wider fields. Thus the `exact optics' version has a moderate but useful field, with excellent definition, suitable for a spectrograph camera. The mirrors are strongly aspheric in both the Schwarzschild design and the exact optics version.
EXACT Software Repository v 1.1
Energy Science and Technology Software Center (ESTSC)
2007-01-07
The EXACT Software Repository contains a variety of software packages for describing, controlling, and analyzing computer experiments. The EXACT Python framework provides the experimentalist with convenient software tools to ease and organize the entire experimental process, including the description of factors and levels, the design of experiments, the control of experimental runs, the archiving of results, and analysis of results. The FAST package provides a Framework for Agile Software Testing. FAST manage the distributed executionmore » of EXACT, as well as summaries of test results.« less
Noyes, H.P. ); Starson, S. )
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 Sibson interpolation.
Park, Sung W; Linsen, Lars; Kreylos, Oliver; Owens, John D; Hamann, Bernd
2006-01-01
Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds. PMID:16509383
Immigration and Prosecutorial Discretion
Apollonio, Dorie; Lochner, Todd; Heddens, Myriah
2015-01-01
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. PMID:26146530
Discrete Pearson distributions
Bowman, K.O.; Shenton, L.R.; Kastenbaum, M.A.
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.
Discrete stability in stochastic programming
Lepp, R.
1994-12-31
In this lecture we study stability properties of stochastic programs with recourse where the probability measure is approximated by a sequence of weakly convergent discrete measures. Such discrete approximation approach gives us a possibility to analyze explicitly the behavior of the second stage correction function. The approach is based on modern functional analytical methods of an approximation of extremum problems in function spaces, especially on the notion of the discrete convergence of vectors to an essentially bounded measurable function.
NASA Astrophysics Data System (ADS)
Yang, Jianjun; Fang, Dagang; Sha, Kan
In this paper, the self-impedance and mutual coupling of electromagnetically coupled microstrip dipoles are computed using recently developed, discrete, exact images. The mixed potential integral equation used for numerical analysis is solved using a moment method with rooftop subsectional basis functions. The procedure described here can be generalized to the treatment of other microstrip antennas and discontinuities and more involved multilayered structures.
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. PMID:26342705
Guide for the program EXACT-NL
NASA Astrophysics Data System (ADS)
Vanvledder, G. Ph.; Weber, S. L.
1987-02-01
A set of programs called EXACT-NL, which computes fetch or duration limited wave growth with an explicit expression for the resonant four-wave interactions is described. The manual is based on experience with EXACT-NL for the computation of shallow water growth curves and the investigation of the directional response of waves to variations in the wind field. Modifications necessary for these specific purposes are also described.
Exact relativistic {beta} decay endpoint spectrum
Masood, S. S.; Nasri, S.; Schechter, J.; Tortola, M. A.; Valle, J. W. F.
2007-10-15
The exact relativistic form for the {beta} decay endpoint spectrum is derived and presented in a simple factorized form. We show that our exact formula can be well approximated to yield the endpoint form used in the fit method of the KATRIN Collaboration. We also discuss the three-neutrino case and how information from neutrino oscillation experiments may be useful in analyzing future {beta} decay endpoint experiments.
Exactness of the original Grover search algorithm
Diao Zijian
2010-10-15
It is well-known that when searching one out of four, the original Grover's search algorithm is exact; that is, it succeeds with certainty. It is natural to ask the inverse question: If we are not searching one out of four, is Grover's algorithm definitely not exact? In this article we give a complete answer to this question through some rationality results of trigonometric functions.
Dipolar matter-wave solitons in two-dimensional anisotropic discrete lattices
NASA Astrophysics Data System (ADS)
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 Mathematics and Curriculum Reform.
ERIC Educational Resources Information Center
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Discrete Mathematics and Its Applications
ERIC Educational Resources Information Center
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…
A semi-discrete integrable multi-component coherently coupled nonlinear Schrödinger system
NASA Astrophysics Data System (ADS)
Zhao, Hai-qiong; Yuan, Jinyun
2016-07-01
A new integrable semi-discrete version is proposed for the multi-component coherently coupled nonlinear Schrödinger equation. The integrability of the semi-discrete system is confirmed by existence of Lax pair and infinite number of conservation laws. With the aid of gauge transformations, explicit formulas for N-fold Darboux transformations are derived whereby some physically important solutions of the system are presented. Furthermore, the theory of the semi-discrete system including Lax pair, Darboux transformations, exact solutions and infinite number of conservation laws are shown for their continuous counterparts in the continuous limit.
Huang, Z. )
1992-12-01
We examine an interesting scenario to solve the domain-wall problem recently suggested by Preskill, Trivedi, Wilczek, and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as {ital CP} and {ital Z}{sub 2} can be anomalous due to a so-called {ital K} term induced by instantons. We point out that the {ital Z}{sub 2} domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the {ital CP}-conserving one and the {ital CP}-breaking one. In the first case, there exist two {ital Z}{sub 2}-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of {ital CP} violation are discussed and shown to be well within the experimental limits in weak interactions.
Discreteness inducing coexistence
NASA Astrophysics Data System (ADS)
dos Santos, Renato Vieira
2013-12-01
Consider two species that diffuse through space. Consider further that they differ only in initial densities and, possibly, in diffusion constants. Otherwise they are identical. What happens if they compete with each other in the same environment? What is the influence of the discrete nature of the interactions on the final destination? And what are the influence of diffusion and additive fluctuations corresponding to random migration and immigration of individuals? This paper aims to answer these questions for a particular competition model that incorporates intra and interspecific competition between the species. Based on mean field theory, the model has a stationary state dependent on the initial density conditions. We investigate how this initial density dependence is affected by the presence of demographic multiplicative noise and additive noise in space and time. There are three main conclusions: (1) Additive noise favors denser populations at the expense of the less dense, ratifying the competitive exclusion principle. (2) Demographic noise, on the other hand, favors less dense populations at the expense of the denser ones, inducing equal densities at the quasi-stationary state, violating the aforementioned principle. (3) The slower species always suffers the more deleterious effects of statistical fluctuations in a homogeneous medium.
Khan, M M; Varma, M P; Cleland, J; O'Kane, H O; Webb, S W; Mulholland, H C; Adgey, A A
1981-01-01
Data concerning 17 consecutive patients with discrete subaortic stenosis are recorded. Twelve patients underwent operative resection of the obstructing lesion. Of these all except one were symptomatic and all had electrocardiographic evidence of left ventricular hypertrophy or left ventricular hypertrophy with strain. They had a peak resting systolic left ventricular outflow tract gradient of greater than 50 mmHg as predicted from the combined cuff measurement of systolic blood pressure and the echocardiographically estimated left ventricular systolic pressure and/or as determined by cardiac catheterisation. The outflow tract gradient as predicted from M-mode echocardiography and peak systolic pressure showed close correlation with that measured at cardiac catheterisation or operation. During the postoperative follow-up from one month to 11 years, of 11 patients, one patient required a further operation for recurrence of the obstruction four years after the initial operation. All patients are now asymptomatic. Five patients have not had an operation. The left ventricular outflow tract gradient as assessed at the time of cardiac catheterisation was greater than 50 mmHg. One patient has been lost to follow-up. The remaining four have been followed from four to eight years and have remained asymptomatic and the electrocardiograms have remained unchanged. Careful follow-up of all patients is essential with continuing clinical assessment, electrocardiograms, M-mode and two-dimensional echocardiograms, and if necessary cardiac catheterisation. Prophylaxis against bacterial endocarditis is also essential. Images PMID:6457617
NASA Astrophysics Data System (ADS)
Ellis, George F. R.; Gibbons, Gary W.
2014-01-01
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 point particle viewpoint laid down in this paper and show consistency with much standard theory usually obtained by more complicated and conceptually less clear continuum methods. Apart from its potential use in large scale structure studies, we believe that our approach has great pedagogic advantages over existing elementary treatments of the expanding universe, since it requires no use of general relativity or continuum mechanics but concentrates on the basic physics: Newton’s laws for gravitationally interacting particles.
Landscape of an exact energy functional
NASA Astrophysics Data System (ADS)
Cohen, Aron J.; Mori-Sánchez, Paula
2016-04-01
One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this paper the asymmetric two-site Hubbard model is studied, which has a two-dimensional universe of density matrices. The exact functional becomes a simple function of two variables whose three-dimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of pure-state density matrices that are not v representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional.
Linearly exact parallel closures for slab geometry
NASA Astrophysics Data System (ADS)
Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun
2013-08-01
Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients).
Linearly exact parallel closures for slab geometry
Ji, Jeong-Young; Held, Eric D.; Jhang, Hogun
2013-08-15
Parallel closures are obtained by solving a linearized kinetic equation with a model collision operator using the Fourier transform method. The closures expressed in wave number space are exact for time-dependent linear problems to within the limits of the model collision operator. In the adiabatic, collisionless limit, an inverse Fourier transform is performed to obtain integral (nonlocal) parallel closures in real space; parallel heat flow and viscosity closures for density, temperature, and flow velocity equations replace Braginskii's parallel closure relations, and parallel flow velocity and heat flow closures for density and temperature equations replace Spitzer's parallel transport relations. It is verified that the closures reproduce the exact linear response function of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for Landau damping given a temperature gradient. In contrast to their approximate closures where the vanishing viscosity coefficient numerically gives an exact response, our closures relate the heat flow and nonvanishing viscosity to temperature and flow velocity (gradients)
The discrete variational derivative method based on discrete differential forms
NASA Astrophysics Data System (ADS)
Yaguchi, Takaharu; Matsuo, Takayasu; Sugihara, Masaaki
2012-05-01
As is well known, for PDEs that enjoy a conservation or dissipation property, numerical schemes that inherit this property are often advantageous in that the schemes are fairly stable and give qualitatively better numerical solutions in practice. Lately, Furihata and Matsuo have developed the so-called “discrete variational derivative method” that automatically constructs energy preserving or dissipative finite difference schemes. Although this method was originally developed on uniform meshes, the use of non-uniform meshes is of importance for multi-dimensional problems. On the other hand, the theories of discrete differential forms have received much attention recently. These theories provide a discrete analogue of the vector calculus on general meshes. In this paper, we show that the discrete variational derivative method and the discrete differential forms by Bochev and Hyman can be combined. Applications to the Cahn-Hilliard equation and the Klein-Gordon equation on triangular meshes are provided as demonstrations. We also show that the schemes for these equations are H1-stable under some assumptions. In particular, one for the nonlinear Klein-Gordon equation is obtained by combination of the energy conservation property and the discrete Poincaré inequality, which are the temporal and spacial structures that are preserved by the above methods.
A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system
NASA Astrophysics Data System (ADS)
Manzini, G.; Delzanno, G. L.; Vencels, J.; Markidis, S.
2016-07-01
We present the design and implementation of an L2-stable spectral method for the discretization of the Vlasov-Poisson model of a collisionless plasma in one space and velocity dimension. The velocity and space dependence of the Vlasov equation are resolved through a truncated spectral expansion based on Legendre and Fourier basis functions, respectively. The Poisson equation, which is coupled to the Vlasov equation, is also resolved through a Fourier expansion. The resulting system of ordinary differential equation is discretized by the implicit second-order accurate Crank-Nicolson time discretization. The non-linear dependence between the Vlasov and Poisson equations is iteratively solved at any time cycle by a Jacobian-Free Newton-Krylov method. In this work we analyze the structure of the main conservation laws of the resulting Legendre-Fourier model, e.g., mass, momentum, and energy, and prove that they are exactly satisfied in the semi-discrete and discrete setting. The L2-stability of the method is ensured by discretizing the boundary conditions of the distribution function at the boundaries of the velocity domain by a suitable penalty term. The impact of the penalty term on the conservation properties is investigated theoretically and numerically. An implementation of the penalty term that does not affect the conservation of mass, momentum and energy, is also proposed and studied. A collisional term is introduced in the discrete model to control the filamentation effect, but does not affect the conservation properties of the system. Numerical results on a set of standard test problems illustrate the performance of the method.
Novel approach to data discretization
NASA Astrophysics Data System (ADS)
Borowik, Grzegorz; Kowalski, Karol; Jankowski, Cezary
2015-09-01
Discretization is an important preprocessing step in data mining. The data discretization method involves determining the ranges of values for numeric attributes, which ultimately represent discrete intervals for new attributes. The ranges for the proposed set of cuts are analyzed, in order to obtain a minimal set of ranges while retaining the possibility of classification. For this purpose, a special discernibility function can be constructed as a conjunction of alternative cuts set for each pair of different objects of different decisions- cuts discern these objects. However, the data mining methods based on discernibility matrix are insufficient for large databases. The purpose of this paper is the idea of implementation of a new data discretization algorithm that is based on statistics of attribute values and that avoids building the discernibility matrix explicitly. Evaluation of time complexity has shown that the proposed method is much more efficient than currently available solutions for large data sets.