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
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)
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.
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, 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, 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, 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
2015-03-07
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
2015-01-01
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
2015-03-01
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).
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
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.
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
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.
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.
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.
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.
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.
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.
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)
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.
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.
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)
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.
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.
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.
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.
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
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
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.
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
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.
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.
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.
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.
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.
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)
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.
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.
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)
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.
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.
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.
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.
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.
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.
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
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
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.
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 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.
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.
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.
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
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)
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).
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.
Chaos in Periodic Discrete Systems
NASA Astrophysics Data System (ADS)
Shi, Yuming; Zhang, Lijuan; Yu, Panpan; Huang, Qiuling
This paper focuses on chaos in periodic discrete systems, whose state space may vary with time. Some close relationships between some chaotic dynamical behaviors of a periodic discrete system and its autonomous induced system are given. Based on these relationships, several criteria of chaos are established and some sufficient conditions for no chaos are given for periodic discrete systems. Further, it is shown that a finite-dimensional linear periodic discrete system is not chaotic in the sense of Li-Yorke or Wiggins. In particular, an interesting problem of whether nonchaotic rules may generate a chaotic system is studied, with some examples provided, one of which surprisingly shows that a composition of globally asymptotically stable maps can be chaotic. In addition, some properties of sign pattern matrices of non-negative square matrices are given for convenience of the study.
Izard, Véronique; Pica, Pierre; Spelke, Elizabeth; Dehaene, Stanislas
2009-01-01
Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of exact numbers: the fact that all numbers can be generated by a successor function, and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Mundurucu (an Amazonian language), and young western children (3–4 years old) understand these fundamental properties of numbers. PMID:20165569
Theory of the Lattice Boltzmann Equation: Symmetry properties of Discrete Velocity Sets
NASA Technical Reports Server (NTRS)
Rubinstein, Robert; Luo, Li-Shi
2007-01-01
In the lattice Boltzmann equation, continuous particle velocity space is replaced by a finite dimensional discrete set. The number of linearly independent velocity moments in a lattice Boltzmann model cannot exceed the number of discrete velocities. Thus, finite dimensionality introduces linear dependencies among the moments that do not exist in the exact continuous theory. Given a discrete velocity set, it is important to know to exactly what order moments are free of these dependencies. Elementary group theory is applied to the solution of this problem. It is found that by decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group, it becomes relatively straightforward to assess the behavior of moments in the theory. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing some new higher dimensional models are suggested.
Description of non-Markovian effect in open quantum system with the discretized environment method
NASA Astrophysics Data System (ADS)
Lacroix, Denis; Sargsyan, Vazgen; Adamian, Gurgen; Antonenko, Nikolai
2015-04-01
An approach, called discretized environment method, is used to treat exactly non-Markovian effects in open quantum systems. In this approach, a complex environment described by a spectral function is mapped into a finite set of discretized states with an appropriate coupling to the system of interest. The finite set of system plus environment degrees of freedom are then explicitly followed in time leading to a quasi-exact description. The present approach is anticipated to be particularly accurate in the low temperature and strongly non-Markovian regime. The discretized environment method is validated on a two-level system (qubit) coupled to a bosonic or fermionic heat-bath. A perfect agreement with the quantum Langevin approach is found. Further illustrations are made on a three-level system (qutrit) coupled to a bosonic heat-bath. Emerging processes due to strong memory effects are discussed.
Exact Solutions to Time-dependent Mdps
NASA Technical Reports Server (NTRS)
Boyan, Justin A.; Littman, Michael L.
2000-01-01
We describe an extension of the Markov decision process model in which a continuous time dimension is included in the state space. This allows for the representation and exact solution of a wide range of problems in which transitions or rewards vary over time. We examine problems based on route planning with public transportation and telescope observation scheduling.
Exact Inference for the Dispersion Matrix
Hutson, Alan D.; Wilding, Gregory E.; Yu, Jihnhee; Vexler, Albert
2016-01-01
We develop a new and novel exact permutation test for prespecified correlation structures such as compound symmetry or spherical structures under standard assumptions. The key feature of the work contained in this note is the distribution free aspect of our procedures that frees us from the standard and sometimes unrealistic multivariate normality constraint commonly needed for other methods. PMID:27034974
Information entropy of conditionally exactly solvable potentials
Dutta, D.; Roy, P.
2011-03-15
We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki-Birula-Mycielski inequality has also been tested for a number of states.
Exact Vlasov Solutions of Kinetic Flux Ropes
NASA Astrophysics Data System (ADS)
Ng, C. S.
2014-12-01
Small-scale magnetic flux ropes have been observed to form within the diffusion region in three-dimensional (3D) kinetic simulations of magnetic reconnection. Such 3D structures and the 2D version of them (plasmoids, secondary islands) could have important dynamical effects on the reconnection physics itself. Small-scale flux ropes have also been observed within the interplanetary space. We have found exact time-steady solutions of kinetic flux ropes by generalizing exact solutions of 2D Bernstein-Greene-Kruskal (BGK) modes in a magnetized plasma with finite magnetic field strength [Ng, Bhattacharjee, and Skiff, Phys. Plasmas 13, 055903 (2006)] to cases with azimuthal magnetic fields so that these structures carry electric current as well as steady electric and magnetic fields. Such fully nonlinear solutions now satisfy exactly the Vlasov-Poisson-Ampere system of equations. Solutions like these could describe small-scale flux ropes observed in reconnection diffusion regions or in the interplanetary space. They are also exact nonlinear solutions that can be used to validate numerical schemes for kinetic simulations. This work is supported by a National Science Foundation grant PHY-1004357.
EXACT VECTORIAL LAW FOR AXISYMMETRIC MAGNETOHYDRODYNAMICS TURBULENCE
Galtier, S.
2009-10-20
Three-dimensional incompressible magnetohydrodynamics turbulence is investigated under the assumptions of homogeneity and axisymmetry. We demonstrate that previous works of Chandrasekhar may be improved significantly by using a different formalism for the representation of two-point correlation tensors. From this axisymmetric kinematics, the equations a la von Karman-Howarth are derived from which an exact relation is found in terms of measurable correlations. The relation is then analyzed in the particular case of a medium permeated by an imposed magnetic field B{sub 0} . We make the ansatz that the development of anisotropy implies an algebraic relation between the axial and the radial components of the separation vector r and we derive an exact vectorial law which is parameterized by the intensity of anisotropy. The critical balance proposed by Goldreich and Sridhar is used to fix this parameter and to obtain a unique exact expression; the particular limits of correlations transverse and parallel to B{sub 0} are given for which simple expressions are found. Predictions for the energy spectra are also proposed by a straightforward dimensional analysis of the exact law; it gives a stronger theoretical background to the heuristic spectra previously proposed in the context of the critical balance. We also discuss the wave turbulence limit of an asymptotically large external magnetic field which appears as a natural limit of the vectorial relation. A new interpretation of the anisotropic solar wind observations is eventually discussed.
Discrete field theories and spatial properties of strings
Klebanov, I.; Susskind, L.
1988-10-01
We use the ground-state wave function in the light-cone gauge to study the spatial properties of fundamental strings. We find that, as the cut-off in the parameter space is removed, the strings are smooth and have a divergent size. Guided by these properties, we consider a large-N lattice gauge theory which has an unstable phase where the size of strings diverges. We show that this phase exactly describes free fundamental strings. The lattice spacing does not have to be taken to zero for this equivalence to hold. Thus, exact rotation and translation invariance is restored in a discrete space. This suggests that the number of fundamental short-distance degrees of freedom in string theory is much smaller than in a conventional field theory. 11 refs., 4 figs.
Large quantum Fourier transforms are never exactly realized by braiding conformal blocks
Freedman, Michael H.; Wang, Zhenghan
2007-03-15
Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set {l_brace}U(2), controlled-NOT{r_brace}, the discrete Fourier transforms F{sub N}=({omega}{sup ij}){sub NxN}, i,j=0,1,...,N-1, {omega}=e{sup 2{pi}}{sup i} at {sup {approx}}{sup sol{approx}} at {sup N}, can be realized exactly by quantum circuits of size O(n{sup 2}), n=ln N, and so can the discrete sine or cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms F{sub N} and the discrete sine or cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that an approximation is unavoidable in the implementation of Fourier transforms by braiding conformal blocks.
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
Turbiner, Alexander
1996-02-20
A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.
Distributed Relaxation for Conservative Discretizations
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.
2001-01-01
A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.
Inhomogeneous mixmaster universes: Some exact solutions
Carmeli, M.; Charach, C.; Feinstein, A.
1983-10-15
Algorithms for generating new exact solutions of the Einstein-Klein-Gordon field equations, which describe inhomogeneous universes with S/sup 3/ topology of spatial sections, are developed. The known exact vacuum and still-fluid solutions with S/sup 3/ topology are used as an input. The methods developed are further applied to derive inhomogeneous generalizations of Bianchi type IX solutions and inhomogeneous S/sup 3/ Gowdy models with gravitational and scalar waves. It is shown that the new solutions, which are generalizations of the Bianchi type IX models, permit identification of the scalar field with the velocity potential of the stiff irrotational fluid. The latter result is further used to study the growth rate of density perturbations of the isotropic and anisotropic Bianchi type IX universes in a fully nonlinear relativistic regime. The role of anisotropy on the rate of growth of density perturbations is studied in detail.
Exact cumulant Kramers-Moyal-like expansion
NASA Astrophysics Data System (ADS)
Morgado, W. A. M.
2015-11-01
We derive an exact equation, a Cumulant Kramers-Moyal Equation (CKME), quite similar to the Kramers-Moyal Equation (KME), for the probability distribution of a Markovian dynamical system. It can be applied to any well behaved (converging cumulants) continuous time systems, such as Langevin equations or other models. An interesting but significant difference with respect to the KME is that their jump-moments are proportional to cumulants of the dynamical variables, but not proportional to central moments, as is the case for the KME. In fact, they still obey a weaker version of Pawula's theorem, namely Marcinkiewicz's theorem. We compare the results derived from the equations herein with the ones obtained by computing via Gaussian and biased, and unbiased, Poisson Langevin dynamics and a Poisson non-Langevin model. We obtain the exact CKME time-evolution equation for the systems, and in several cases, those are distinct from the Fokker-Planck equation or the KME.
Exact holographic mapping in free fermion systems
NASA Astrophysics Data System (ADS)
Lee, Ching Hua; Qi, Xiao-Liang
2016-01-01
In this paper, we perform a detailed analysis of the exact holographic mapping first introduced in arXiv:1309.6282, which was proposed as an explicit example of holographic duality between quantum many-body systems and gravitational theories. We obtain analytic results for free fermion systems that not only confirm previous numerical results, but also elucidate the exact relationships between the various physical properties of the bulk and boundary systems. These analytic results allow us to study the asymptotic properties that are difficult to probe numerically, such as the near-horizon regime of the black-hole geometry. We shall also explore a few interesting but hitherto unexplored bulk geometries, such as that corresponding to a boundary critical fermion with a nontrivial dynamical critical exponent. Our analytic framework also allows us to study the holographic mapping of some of these boundary theories in dimensions 2+1 or higher.
Exact solution to fractional logistic equation
NASA Astrophysics Data System (ADS)
West, Bruce J.
2015-07-01
The logistic equation is one of the most familiar nonlinear differential equations in the biological and social sciences. Herein we provide an exact solution to an extension of this equation to incorporate memory through the use of fractional derivatives in time. The solution to the fractional logistic equation (FLE) is obtained using the Carleman embedding technique that allows the nonlinear equation to be replaced by an infinite-order set of linear equations, which we then solve exactly. The formal series expansion for the initial value solution of the FLE is shown to be expressed in terms of a series of weighted Mittag-Leffler functions that reduces to the well known analytic solution in the limit where the fractional index for the derivative approaches unity. The numerical integration to the FLE provides an excellent fit to the analytic solution. We propose this approach as a general technique for solving a class of nonlinear fractional differential equations.
Manifestly diffeomorphism invariant classical Exact Renormalization Group
NASA Astrophysics Data System (ADS)
Morris, Tim R.; Preston, Anthony W. H.
2016-06-01
We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renor-malization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeo-morphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.
Exact temperature profile for the hillingar mirage
NASA Astrophysics Data System (ADS)
Lehn, Waldemar H.
2001-05-01
In a hillingar mirage, the Earth's surface appears flat, because nearly horizontal light rays have the same curvature as the Earth. A linear temperature profile is traditionally inferred; its gradient is calculated to give this curvature to the exact horizontal ray. To see an image, however, a bundle of rays is required. To ensure that each ray in the bundle have the same curvature, the temperature profile must contain a small positive quadratic term, the coefficient of which is derived.
On higher dimensional exact Courant algebroids
NASA Astrophysics Data System (ADS)
Rengifo, Camilo
2016-09-01
For a smooth manifold X we show an equivalence of categories between the category of OX♯ [ n ] -extensions of TX♯ and the category of higher-dimensional exact Courant algebroids on X. In addition, for any object in the category of R [ n ] dg-principal bundles over X♯ we construct its Atiyah algebroid which gives rise to an example of OX♯ [ n ] -extensions of TX♯.
Exact quantization conditions for cluster integrable systems
NASA Astrophysics Data System (ADS)
Franco, Sebastián; Hatsuda, Yasuyuki; Mariño, Marcos
2016-06-01
We propose exact quantization conditions for the quantum integrable systems of Goncharov and Kenyon, based on the enumerative geometry of the corresponding toric Calabi–Yau manifolds. Our conjecture builds upon recent results on the quantization of mirror curves, and generalizes a previous proposal for the quantization of the relativistic Toda lattice. We present explicit tests of our conjecture for the integrable systems associated to the resolved {{{C}}3}/{{{Z}}5} and {{{C}}3}/{{{Z}}6} orbifolds.
Exact solutions and singularities in string theory
Horowitz, G.T. ); Tseytlin, A.A. )
1994-10-15
We construct two new classes of exact solutions to string theory which are not of the standard plane wave of gauged WZW type. Many of these solutions have curvature singularities. The first class includes the fundamental string solution, for which the string coupling vanishes near the singularity. This suggests that the singularity may not be removed by quantum corrections. The second class consists of hybrids of plane wave and gauged WZW solutions. We discuss a four-dimensional example in detail.
Exact BPS bound for noncommutative baby Skyrmions
NASA Astrophysics Data System (ADS)
Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco
2013-11-01
The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory.
Exact quantization of a paraxial electromagnetic field
Aiello, A.; Woerdman, J. P.
2005-12-15
A nonperturbative quantization of a paraxial electromagnetic field is achieved via a generalized dispersion relation imposed on the longitudinal and the transverse components of the photon wave vector. This theoretical formalism yields a seamless transition between the paraxial- and the Maxwell-equation solutions. This obviates the need to introduce either ad hoc or perturbatively defined field operators. Moreover, our (exact) formalism remains valid beyond the quasimonochromatic paraxial limit.
Cheraghi-Sohi, Sudeh; Calnan, Michael
2013-11-01
There has much debate about the extent to which professional discretion has been challenged by recent organisational changes such as through the new forms of governance associated with the introduction of the principles of the New Public Management (NPM) into health systems and other public sector services. What appears to be missing from these debates is a detailed analysis of the concept of professional discretion itself. This paper attempts to fill this gap by delineating the key concepts of professional discretion evident in the literature and exploring their significance in an empirical study of the influence of the 2004 new general medical services contract (nGMS) and the introduction of the Quality and Outcomes Framework (QOF), a prescriptive pay-for-performance system designed to standardise the quality of care provision in general medical practice in the United Kingdom. The study adopted a longitudinal design using semi-structured interviews with general practitioners (GPs, N = 62) working in the English National Health Service (NHS) between 2007 and 2009. A multi-dimensional conception of discretion was used to explore how GP discretion might have been influenced by contractual changes and in particular, QOF. The findings suggest that through a complex interplay of factors, a post-QOF reduction in GP discretion was identifiable, highlighting different potential sources of constraint such as in the social, organisational and economic dimensions of discretion. The evidence also suggested the emergence of a new form of organisational medical professionalism within general practice characterised by standardisation, bureaucracy and performance management. PMID:24034951
A hierarchical exact accelerated stochastic simulation algorithm
Orendorff, David; Mjolsness, Eric
2012-01-01
A new algorithm, “HiER-leap” (hierarchical exact reaction-leaping), is derived which improves on the computational properties of the ER-leap algorithm for exact accelerated simulation of stochastic chemical kinetics. Unlike ER-leap, HiER-leap utilizes a hierarchical or divide-and-conquer organization of reaction channels into tightly coupled “blocks” and is thereby able to speed up systems with many reaction channels. Like ER-leap, HiER-leap is based on the use of upper and lower bounds on the reaction propensities to define a rejection sampling algorithm with inexpensive early rejection and acceptance steps. But in HiER-leap, large portions of intra-block sampling may be done in parallel. An accept/reject step is used to synchronize across blocks. This method scales well when many reaction channels are present and has desirable asymptotic properties. The algorithm is exact, parallelizable and achieves a significant speedup over the stochastic simulation algorithm and ER-leap on certain problems. This algorithm offers a potentially important step towards efficient in silico modeling of entire organisms. PMID:23231214
An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.
2003-01-01
An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.
Geometry of discrete quantum computing
NASA Astrophysics Data System (ADS)
Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung
2013-05-01
Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.
On exact statistics and classification of ergodic systems of integer dimension
Guralnik, Zachary Guralnik, Gerald; Pehlevan, Cengiz
2014-06-01
We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This definition generalizes the construction of Hamiltonian systems by a Hamiltonian and a symplectic form. Some low dimensional examples are given, as well as a discretized field theory with a large number of degrees of freedom and a local nearest neighbor interaction. We also evaluate unequal-time correlations of these systems without direct numerical simulation, by Padé approximants of a short-time expansion. We briefly speculate on the possibility of constructing chaotic dynamical systems with non-integer dimension and exactly known statistics. In this case there is no probability density, suggesting an alternative construction in terms of a Hopf characteristic function and a two-form.
Exact computation of the unwrapped phase of a finite-length time series
NASA Technical Reports Server (NTRS)
Long, David G.
1988-01-01
McGowan and Kuc (1982) showed that a direct relationship between a time series and its unwrapped phase exists. They proposed an algorithm for computing the unwrapped phase by counting the number of sign changes in a Sturm sequence generated from the real and imaginary parts of the discrete Fourier transform. Their algorithm is limited to relatively short sequences by numerical accuracy. An extension of their algorithm is proposed which, by using all-integer arithmetic, permits exact computation of the number of multiples of pi required to determine the unwrapped phase for rational-valued time sequences of arbitrary length. Since the computation is exact, the extended numerical algorithm should be of interest when accurate phase unwrapping is required.
Exact solution to plane-wave scattering by an ideal "left-handed" wedge
NASA Astrophysics Data System (ADS)
Monzon, Cesar; Forester, Donald W.; Smith, Douglas; Loschialpo, Peter
2006-02-01
An exact analytical solution to the problem of plane-wave diffraction by a penetrable left-handed medium (LHM) epsilon=µ=-1 wedge of arbitrary angle (subject to valid physical constraints) is presented. Standard analysis involving discontinuous angular eigenfunctions and even/odd symmetry decomposition resulted in a discrete spectrum leading to a series solution resembling the traditional perfect electric conductor wedge solution but exhibiting the expected negative refraction phenomenology. Numerical results are presented, some of which seemed paradoxical but are explainable by classical means. A new type of illusory edge radiation is observed and explained. Also, a novel edge-launched interface standing wave is observed on the directly illuminated side. The exact analytical solution is verified by comparison with finite-difference time-domain simulation on causal LHM materials.
Exact finite reduced density matrix and von Neumann entropy for the Calogero model
NASA Astrophysics Data System (ADS)
Osenda, Omar; Pont, Federico M.; Okopińska, Anna; Serra, Pablo
2015-12-01
The information content of continuous quantum variables systems is usually studied using a number of well known approximation methods. The approximations are made to obtain the spectrum, eigenfunctions or the reduced density matrices that are essential to calculate the entropy-like quantities that quantify the information. Even in the sparse cases where the spectrum and eigenfunctions are exactly known, the entanglement spectrum- the spectrum of the reduced density matrices that characterize the problem- must be obtained in an approximate fashion. In this work, we obtain analytically a finite representation of the reduced density matrices of the fundamental state of the N-particle Calogero model for a discrete set of values of the interaction parameter. As a consequence, the exact entanglement spectrum and von Neumann entropy is worked out.
NASA Astrophysics Data System (ADS)
Chen, Guangye; Chacon, Luis
2015-11-01
We discuss a new, conservative, fully implicit 2D3V Vlasov-Darwin particle-in-cell algorithm in curvilinear geometry for non-radiative, electromagnetic kinetic plasma simulations. Unlike standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. Here, we extend these algorithms to curvilinear geometry. The algorithm retains its exact conservation properties in curvilinear grids. The nonlinear iteration is effectively accelerated with a fluid preconditioner for weakly to modestly magnetized plasmas, which allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D (slow shock) and 2D (island coalescense).
Experiments on exactly computing non-linear energy transfer rate in MASNUM-WAM
NASA Astrophysics Data System (ADS)
Jiang, Xingjie; Wang, Daolong; Gao, Dalu; Zhang, Tingting
2016-07-01
The Webb-Resio-Tracy (WRT) method for exact computation of the non-linear energy transfer rate was implemented in MASNUM-WAM, which is a third-generation wave model solving the discrete spectral balance equation. In this paper, we describe the transformation of the spectral space in the original WRT method. Four numerical procedures were developed in which the acceleration techniques in the original WRT method, such as geometric scaling, pre-calculating, and grid-searching, are all reorganized. A series of numerical experiments including two simulations based on real data were performed. The availability of such implementation in both serial and parallel versions of the wave model was proved, and a comparison of computation times showed that some of the developed procedures provided good efficacy. With exact computation of non-linear energy transfer, MASNUM-WAM now can be used to perform numerical experiments for research purposes, which augurs well for further developments of the model.
The exact fundamental solution for the Benes filter: a Feynman path integral derivation
NASA Astrophysics Data System (ADS)
Balaji, Bhashyam
2011-06-01
The Benes filtering problem has been shown to be related to the quantum mechanical simple harmonic oscillator. In a previous paper, the exact fundamental solution for the filtering problem was derived. The methods employed included the method of separation of variables for solving PDEs, results from Strum-Liouville theory, and properties of the Hermite special function. In this paper, the results are rederived more simply and directly using Feynman path integral methods. Numerical examples are included that demonstrate the correctness of formulas and their utility in solving continuous-discrete filtering problems with Benes drift and nonlinear measurement model.
Quasiclassical asymptotics and coherent states for bounded discrete spectra
Gorska, K.; Penson, K. A.; Horzela, A.; Blasiak, P.; Duchamp, G. H. E.; Solomon, A. I.
2010-12-15
We consider discrete spectra of bound states for nonrelativistic motion in attractive potentials V{sub {sigma}}(x)=-|V{sub 0}| |x|{sup -}{sigma}, 0<{sigma}{<=}2. For these potentials the quasiclassical approximation for n{yields}{infinity} predicts quantized energy levels e{sub {sigma}}(n) of a bounded spectrum varying as e{sub {sigma}}(n){approx}-n{sup -}2{sigma}/(2-{sigma}). We construct collective quantum states using the set of wavefunctions of the discrete spectrum assuming this asymptotic behavior. We give examples of states that are normalizable and satisfy the resolution of unity, using explicit positive functions. These are coherent states in the sense of Klauder and their completeness is achieved via exact solutions of Hausdorff moment problems, obtained by combining Laplace and Mellin transform methods. For {sigma} in the range 0 < {sigma}{<=} 2/3 we present exact implementations of such states for the parametrization {sigma}= 2(k-l)/(3k-l) with k and l positive integers satisfying k>l.
Exact, zero-energy, square-integrable solutions of a model related to the Maxwell's fish-eye problem
Makowski, Adam J.
2009-12-15
A model, which admits normalizable wave functions of the Schroedinger equation at the energy of E = 0, is exactly solved and the solutions are compared to the corresponding classical trajectories. The wave functions are proved to be square-integrable for discrete (quantized) values of the coupling constant of the used potential. We also show that our model is a specific version of the well-known Maxwell's fish-eye. This is performed with the help of a suitably chosen conformal mapping.
Reduced discretization error in HZETRN
Slaba, Tony C.; Blattnig, Steve R.; Tweed, John
2013-02-01
The deterministic particle transport code HZETRN is an efficient analysis tool for studying the effects of space radiation on humans, electronics, and shielding materials. In a previous work, numerical methods in the code were reviewed, and new methods were developed that further improved efficiency and reduced overall discretization error. It was also shown that the remaining discretization error could be attributed to low energy light ions (A < 4) with residual ranges smaller than the physical step-size taken by the code. Accurately resolving the spectrum of low energy light particles is important in assessing risk associated with astronaut radiation exposure. In this work, modifications to the light particle transport formalism are presented that accurately resolve the spectrum of low energy light ion target fragments. The modified formalism is shown to significantly reduce overall discretization error and allows a physical approximation to be removed. For typical step-sizes and energy grids used in HZETRN, discretization errors for the revised light particle transport algorithms are shown to be less than 4% for aluminum and water shielding thicknesses as large as 100 g/cm{sup 2} exposed to both solar particle event and galactic cosmic ray environments.
Some discrete multiple orthogonal polynomials
NASA Astrophysics Data System (ADS)
Arvesú, J.; Coussement, J.; van Assche, W.
2003-04-01
In this paper, we extend the theory of discrete orthogonal polynomials (on a linear lattice) to polynomials satisfying orthogonality conditions with respect to r positive discrete measures. First we recall the known results of the classical orthogonal polynomials of Charlier, Meixner, Kravchuk and Hahn (T.S. Chihara, An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978; R. Koekoek and R.F. Swarttouw, Reports of the Faculty of Technical Mathematics and Informatics No. 98-17, Delft, 1998; A.F. Nikiforov et al., Classical Orthogonal Polynomials of a Discrete Variable, Springer, Berlin, 1991). These polynomials have a lowering and raising operator, which give rise to a Rodrigues formula, a second order difference equation, and an explicit expression from which the coefficients of the three-term recurrence relation can be obtained. Then we consider r positive discrete measures and define two types of multiple orthogonal polynomials. The continuous case (Jacobi, Laguerre, Hermite, etc.) was studied by Van Assche and Coussement (J. Comput. Appl. Math. 127 (2001) 317-347) and Aptekarev et al. (Multiple orthogonal polynomials for classical weights, manuscript). The families of multiple orthogonal polynomials (of type II) that we will study have a raising operator and hence a Rodrigues formula. This will give us an explicit formula for the polynomials. Finally, there also exists a recurrence relation of order r+1 for these multiple orthogonal polynomials of type II. We compute the coefficients of the recurrence relation explicitly when r=2.
Supersymmetric QCD: exact results and strong coupling
NASA Astrophysics Data System (ADS)
Dine, Michael; Festuccia, Guido; Pack, Lawrence; Park, Chang-Soon; Ubaldi, Lorenzo; Wu, Weitao
2011-05-01
We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is not reliable, even at short distances. The semiclassical expansion about the instanton is purely formal; if infrared divergences appear, they spoil arguments based on holomorphy. We demonstrate that infrared divergences do not occur in the perturbation expansion about the instanton, but explain that there is no reason to think this captures all contributions from the sector with unit topological charge. That one expects additional contributions is illustrated by dilute gas corrections. These are infrared divergent, and so difficult to define, but if non-zero give order one, holomorphic, corrections to the leading result. Exploiting an earlier analysis of Davies et al, we demonstrate that in the theory compactified on a circle of radius β, due to infrared effects, finite contributions indeed arise which are not visible in the formal β → ∞ limit.
Discrete implementations of scale transform
NASA Astrophysics Data System (ADS)
Djurdjanovic, Dragan; Williams, William J.; Koh, Christopher K.
1999-11-01
Scale as a physical quantity is a recently developed concept. The scale transform can be viewed as a special case of the more general Mellin transform and its mathematical properties are very applicable in the analysis and interpretation of the signals subject to scale changes. A number of single-dimensional applications of scale concept have been made in speech analysis, processing of biological signals, machine vibration analysis and other areas. Recently, the scale transform was also applied in multi-dimensional signal processing and used for image filtering and denoising. Discrete implementation of the scale transform can be carried out using logarithmic sampling and the well-known fast Fourier transform. Nevertheless, in the case of the uniformly sampled signals, this implementation involves resampling. An algorithm not involving resampling of the uniformly sampled signals has been derived too. In this paper, a modification of the later algorithm for discrete implementation of the direct scale transform is presented. In addition, similar concept was used to improve a recently introduced discrete implementation of the inverse scale transform. Estimation of the absolute discretization errors showed that the modified algorithms have a desirable property of yielding a smaller region of possible error magnitudes. Experimental results are obtained using artificial signals as well as signals evoked from the temporomandibular joint. In addition, discrete implementations for the separable two-dimensional direct and inverse scale transforms are derived. Experiments with image restoration and scaling through two-dimensional scale domain using the novel implementation of the separable two-dimensional scale transform pair are presented.
Exactly soluble quantum wormhole in two dimensions
Kim, Won Tae; Son, Edwin J.; Yoon, Myung Seok
2004-11-15
We are presenting a quantum traversable wormhole in an exactly soluble two-dimensional model. This is different from previous works since the exotic negative energy that supports the wormhole is generated from the quantization of classical energy-momentum tensors. This explicit illustration shows the quantum-mechanical energy can be used as a candidate for the exotic source. As for the traversability, after a particle travels through the wormhole, the static initial wormhole geometry gets a back reaction which spoils the wormhole structure. However, it may still maintain the initial structure along with the appropriate boundary condition.
Exact string potential and heavy quarkonia
Bambah, B.A. ); Dharamvir, K.; Kaur, R. ); Sharma, A.C. )
1992-03-01
Using the exact form of the static string potential we reinvestigate previous potential-model calculations of the energy levels of {ital q{bar q}} resonances. We show the effect of higher-order corrections to strings on the quarkonium spectroscopy and the leptonic decays of the {Upsilon} and {ital J}/{psi}, where we find that the roughened form of the string potential has a significant effect. We also propose a new form of the potential which incorporates both the quantum effects and asymptotic freedom.
Exact teleparallel gravity of binary black holes
NASA Astrophysics Data System (ADS)
El Hanafy, W.; Nashed, G. G. L.
2016-02-01
An exact solution of two singularities in the teleparallel equivalent to general relativity theory has been obtained. A holographic visualization of the binary black holes (BBHs) space-time, due to the non vanishing torsion scalar field, has been given. The acceleration tensor of BBHs space-time has been calculated. The results identify the repulsive gravity zones of the BBHs field. The total conserved quantities of the BBHs has been evaluated. Possible gravitational radiation emission by the system has been calculated without assuming a weak field initial data.
Exact solutions for network rewiring models
NASA Astrophysics Data System (ADS)
Evans, T. S.
2007-03-01
Evolving networks with a constant number of edges may be modelled using a rewiring process. These models are used to describe many real-world processes including the evolution of cultural artifacts such as family names, the evolution of gene variations, and the popularity of strategies in simple econophysics models such as the minority game. The model is closely related to Urn models used for glasses, quantum gravity and wealth distributions. The full mean field equation for the degree distribution is found and its exact solution and generating solution are given.
NASA Astrophysics Data System (ADS)
Cisterna, Adolfo; Hassaïne, Mokhtar; Oliva, Julio
2015-11-01
This paper is devoted to showing that the bosonic sector of R2 supergravity in four dimensions, constructed with the F term, admits a variety of exact and analytic solutions which include pp and anti-de Sitter (AdS) waves, asymptotically flat and AdS black holes and wormholes, as well as product spacetimes. The existence of static black holes and wormholes implies that a combination involving the Ricci scalar plus the norm of the field strength of the auxiliary two-form Bμ ν must be a constant. We focus on this sector of the theory, which has two subsectors depending on whether such a combination vanishes.
Exactly solvable self-dual strings
Myers, R.C. ); Periwal, V. )
1990-06-25
Models of random surfaces defined by means of integrals over quaternion-real self-dual random matrices are solved exactly in a double-scaling limit. Coupled nonlinear ordinary differential equations are obtained for the specific heat, which takes the form {ital r}+{ital w}{prime}, where {ital r} is the specific heat of the corresponding Hermitian-matrix model, and {ital w} satisfies a nonlinear differential equation depending on {ital r}. It is shown that the {ital k}=2 theory, which may describe a new phase of two-dimensional quantum gravity, is unitary. An alternative method of solution, based on a set of symplectically orthogonal polynomials, is indicated.
Exact and asymptotic distributions of LULU smoothers
NASA Astrophysics Data System (ADS)
Conradie, W. J.; de Wet, T.; Jankowitz, M.
2006-02-01
This paper considers a class of non-linear smoothers, called LULU smoothers, introduced by Rohwer in the late eighties in the mathematics literature, and since then investigated fairly extensively by a number of authors for its mathematical properties. They have been successfully applied in various engineering and scientific problems. However, to date their distribution theory has not received any attention in the literature. In this paper we derive their exact as well as asymptotic distributions and show their relationship to the upper order statistics.
NASA Astrophysics Data System (ADS)
Yang, L. M.; Shu, C.; Wang, Y.; Sun, Y.
2016-08-01
The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.
Dust grain coagulation modelling : From discrete to continuous
NASA Astrophysics Data System (ADS)
Paruta, P.; Hendrix, T.; Keppens, R.
2016-07-01
In molecular clouds, stars are formed from a mixture of gas, plasma and dust particles. The dynamics of this formation is still actively investigated and a study of dust coagulation can help to shed light on this process. Starting from a pre-existing discrete coagulation model, this work aims to mathematically explore its properties and its suitability for numerical validation. The crucial step is in our reinterpretation from its original discrete to a well-defined continuous form, which results in the well-known Smoluchowski coagulation equation. This opens up the possibility of exploiting previous results in order to prove the existence and uniqueness of a mass conserving solution for the evolution of dust grain size distribution. Ultimately, to allow for a more flexible numerical implementation, the problem is rewritten as a non-linear hyperbolic integro-differential equation and solved using a finite volume discretisation. It is demonstrated that there is an exact numerical agreement with the initial discrete model, with improved accuracy. This is of interest for further work on dynamically coupled gas with dust simulations.
Convergence analysis of the thermal discrete dipole approximation
NASA Astrophysics Data System (ADS)
Edalatpour, Sheila; Čuma, Martin; Trueax, Tyler; Backman, Roger; Francoeur, Mathieu
2015-06-01
The thermal discrete dipole approximation (T-DDA) is a numerical approach for modeling near-field radiative heat transfer in complex three-dimensional geometries. In this work, the convergence of the T-DDA is investigated by comparison against the exact results for two spheres separated by a vacuum gap. The error associated with the T-DDA is reported for various sphere sizes, refractive indices, and vacuum gap thicknesses. The results reveal that for a fixed number of subvolumes, the accuracy of the T-DDA degrades as the refractive index and the sphere diameter to gap ratio increase. A converging trend is observed as the number of subvolumes increases. The large computational requirements associated with increasing the number of subvolumes, and the shape error induced by large sphere diameter to gap ratios, are mitigated by using a nonuniform discretization scheme. Nonuniform discretization is shown to significantly accelerate the convergence of the T-DDA, and is thus recommended for near-field thermal radiation simulations. Errors less than 5% are obtained in 74% of the cases studied by using up to 82 712 subvolumes. Additionally, the convergence analysis demonstrates that the T-DDA is very accurate when dealing with surface polariton resonant modes dominating radiative heat transfer in the near field.
Rainbow-shift mechanism behind discrete optical-potential ambiguities
Brandan, M.E. ); McVoy, K.W. )
1991-03-01
Some years ago, Drisko {ital et} {ital al}. suggested that the discrete ambiguity often encountered for elastic scattering optical potentials could be understood as being due to the interior or small-{ital l} {ital S}-matrix elements for two equivalent'' potentials differing in phase by 2{pi}, {ital l}-by-{ital l}. We point out that the {ital absence} of this phase change for peripheral partial waves is equally essential, and suggest that a deeper understanding of the ambiguity may be achieved by viewing it as a consequence of a farside interference between interior and peripheral partial waves. It is this interference which produces the broad Airy maxima'' of a nuclear rainbow, and we show that a Drisko-type phase-shift increment {delta}{sub {ital l}}{r arrow}({delta}{sub {ital l}}+{pi}) for low-{ital l} phases relative to the high-{ital l} ones is exactly what is needed to shift a farside rainbow pattern by one Airy maximum, thus providing an equivalent rainbow-shift'' interpretation of the discrete ambiguity. The physical importance of both interpretations lies in the fact that the existence of discrete ambiguities (as well as of nuclear rainbows) is explicit evidence for low-{ital l} transparency in nucleus-nucleus collisions. The essential role played by low partial waves explains why peripheral reactions have generally not proven helpful in resolving this ambiguity.
Exact simulation of max-stable processes
Dombry, Clément; Engelke, Sebastian; Oesting, Marco
2016-01-01
Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes their simulation difficult. Algorithms based on finite approximations are often inexact and computationally inefficient. We present a new algorithm for exact simulation of a max-stable process at a finite number of locations. It relies on the idea of simulating only the extremal functions, that is, those functions in the construction of a max-stable process that effectively contribute to the pointwise maximum. We further generalize the algorithm by Dieker & Mikosch (2015) for Brown–Resnick processes and use it for exact simulation via the spectral measure. We study the complexity of both algorithms, prove that our new approach via extremal functions is always more efficient, and provide closed-form expressions for their implementation that cover most popular models for max-stable processes and multivariate extreme value distributions. For simulation on dense grids, an adaptive design of the extremal function algorithm is proposed. PMID:27279659
Protein alignment: Exact versus approximate. An illustration.
Randić, Milan; Pisanski, Tomaž
2015-05-30
We illustrate solving the protein alignment problem exactly using the algorithm VESPA (very efficient search for protein alignment). We have compared our result with the approximate solution obtained with BLAST (basic local alignment search tool) software, which is currently the most widely used for searching for protein alignment. We have selected human and mouse proteins having around 170 amino acids for comparison. The exact solution has found 78 pairs of amino acids, to which one should add 17 individual amino acid alignments giving a total of 95 aligned amino acids. BLAST has identified 64 aligned amino acids which involve pairs of more than two adjacent amino acids. However, the difference between the two outputs is not as large as it may appear, because a number of amino acids that are adjacent have been reported by BLAST as single amino acids. So if one counts all amino acids, whether isolated (single) or in a group of two and more amino acids, then the count for BLAST is 89 and for VESPA is 95, a difference of only six. PMID:25800773
An exactly solvable model for quantum communications.
Smith, Graeme; Smolin, John A
2013-12-12
Information theory establishes the ultimate limits on performance for noisy communication systems. Accurate models of physical communication devices must include quantum effects, but these typically make the theory intractable. As a result, communication capacities--the maximum possible rates of data transmission--are not known, even for transmission between two users connected by an electromagnetic waveguide with Gaussian noise. Here we present an exactly solvable model of communication with a fully quantum electromagnetic field. This gives explicit expressions for all point-to-point capacities of noisy quantum channels, with implications for quantum key distribution and fibre-optic communications. We also develop a theory of quantum communication networks by solving some rudimentary models including broadcast and multiple-access channels. We compare the predictions of our model with the orthodox Gaussian model and in all cases find agreement to within a few bits. At high signal-to-noise ratios, our simple model captures the relevant physics while remaining amenable to exact solution. PMID:24240277
Explicitly broken supersymmetry with exactly massless moduli
NASA Astrophysics Data System (ADS)
Dong, Xi; Freedman, Daniel Z.; Zhao, Yue
2016-06-01
The AdS/CFT correspondence is applied to an analogue of the little hierarchy problem in three-dimensional supersymmetric theories. The bulk is governed by a super-gravity theory in which a U(1) × U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. The bulk-to-boundary propagator of the Chern-Simons fields is a total derivative with respect to the bulk coordinates. Integration by parts and the Ward identity permit evaluation of SUSY breaking effects to all orders in the strength of the deformation. The R-charges of scalars and spinors differ so large SUSY breaking mass shifts are generated. Masses of R-neutral particles such as scalar moduli are not shifted to any order in the deformation strength, despite the fact that they may couple to R-charged fields running in loops. We also obtain a universal deformation formula for correlation functions under an exactly marginal deformation by a product of holomorphic and anti-holomorphic U(1) currents.
Two exactly soluble models of rigidity percolation
Thorpe, M. F.; Stinchcombe, R. B.
2014-01-01
We summarize results for two exactly soluble classes of bond-diluted models for rigidity percolation, which can serve as a benchmark for numerical and approximate methods. For bond dilution problems involving rigidity, the number of floppy modes F plays the role of a free energy. Both models involve pathological lattices with two-dimensional vector displacements. The first model involves hierarchical lattices where renormalization group calculations can be used to give exact solutions. Algebraic scaling transformations produce a transition of the second order, with an unstable critical point and associated scaling laws at a mean coordination 〈r〉=4.41, which is above the ‘mean field’ value 〈r〉=4 predicted by Maxwell constraint counting. The order parameter exponent associated with the spanning rigid cluster geometry is β=0.0775 and that associated with the divergence of the correlation length and the anomalous lattice dimension d is dν=3.533. The second model involves Bethe lattices where the rigidity transition is massively first order by a mean coordination 〈r〉=3.94 slightly below that predicted by Maxwell constraint counting. We show how a Maxwell equal area construction can be used to locate the first-order transition and how this result agrees with simulation results on larger random-bond lattices using the pebble game algorithm. PMID:24379428
Durandal: fast exact clustering of protein decoys.
Berenger, Francois; Shrestha, Rojan; Zhou, Yong; Simoncini, David; Zhang, Kam Y J
2012-02-01
In protein folding, clustering is commonly used as one way to identify the best decoy produced. Initializing the pairwise distance matrix for a large decoy set is computationally expensive. We have proposed a fast method that works even on large decoy sets. This method is implemented in a software called Durandal. Durandal has been shown to be consistently faster than other software performing fast exact clustering. In some cases, Durandal can even outperform the speed of an approximate method. Durandal uses the triangular inequality to accelerate exact clustering, without compromising the distance function. Recently, we have further enhanced the performance of Durandal by incorporating a Quaternion-based characteristic polynomial method that has increased the speed of Durandal between 13% and 27% compared with the previous version. Durandal source code is available under the GNU General Public License at http://www.riken.jp/zhangiru/software/durandal_released_qcp.tgz. Alternatively, a compiled version of Durandal is also distributed with the nightly builds of the Phenix (http://www.phenix-online.org/) crystallographic software suite (Adams et al., Acta Crystallogr Sect D 2010, 66, 213). PMID:22120171
Gap Filling as Exact Path Length Problem.
Salmela, Leena; Sahlin, Kristoffer; Mäkinen, Veli; Tomescu, Alexandru I
2016-05-01
One of the last steps in a genome assembly project is filling the gaps between consecutive contigs in the scaffolds. This problem can be naturally stated as finding an s-t path in a directed graph whose sum of arc costs belongs to a given range (the estimate on the gap length). Here s and t are any two contigs flanking a gap. This problem is known to be NP-hard in general. Here we derive a simpler dynamic programming solution than already known, pseudo-polynomial in the maximum value of the input range. We implemented various practical optimizations to it, and compared our exact gap-filling solution experimentally to popular gap-filling tools. Summing over all the bacterial assemblies considered in our experiments, we can in total fill 76% more gaps than the best previous tool, and the gaps filled by our method span 136% more sequence. Furthermore, the error level of the newly introduced sequence is comparable to that of the previous tools. The experiments also show that our exact approach does not easily scale to larger genomes, where the problem is in general difficult for all tools. PMID:26959081
Inflationary potentials from the exact renormalisation group
NASA Astrophysics Data System (ADS)
Grozdanov, Sašo; Kraljić, David; Svanes, Eirik Eik
2016-08-01
We show that an inflationary slow-roll potential can be derived as an IR limit of the non-perturbative exact renormalisation group equation for a scalar field within the mean-field approximation. The result follows without having to specify a Lagrangian in the UV, which we take to be somewhere below the Planck scale to avoid discussing quantum gravity effects. We assume that the theory contains a scalar mode with suppressed coupling to other fields, and that higher derivative couplings are suppressed. In this framework the exact RG equation becomes a one-dimensional Schrödinger equation, which we solve. The effective IR potential is then dominated by the eigen-states of the RG Hamiltonian with the highest eigenvalues. We find that these potentials can generically give rise to slow-roll inflation, which is fully consistent with recent observations. As an example of how the proposed renormalisation group procedure works, we perform an explicit calculation in the ϕ4 theory in an appendix.
NASA Astrophysics Data System (ADS)
Szczygieł, Bartłomiej; Dudyński, Marek; Kwiatkowski, Kamil; Lewenstein, Maciej; Lapeyre, Gerald John; Wehr, Jan
2016-02-01
We introduce a class of discrete-continuous percolation models and an efficient Monte Carlo algorithm for computing their properties. The class is general enough to include well-known discrete and continuous models as special cases. We focus on a particular example of such a model, a nanotube model of disintegration of activated carbon. We calculate its exact critical threshold in two dimensions and obtain a Monte Carlo estimate in three dimensions. Furthermore, we use this example to analyze and characterize the efficiency of our algorithm, by computing critical exponents and properties, finding that it compares favorably to well-known algorithms for simpler systems.
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
Class of discrete Gabor expansion
NASA Astrophysics Data System (ADS)
Li, Shidong; Healy, Dennis M., Jr.
1994-03-01
We present a new approach to studying a discrete Gabor expansion (DGE). We show that, in general, DGE is not the usual biorthogonal decomposition, but belongs to a larger and looser decomposition scheme which we call pseudo frame decomposition. It includes the DGE scheme proposed as a special case. The standard dual frame decomposition is also a special case. We derive algorithms using techniques for Gabor sequences to compute 'biorthogonal' sequences through proper matrix representation. Our algorithms involve solutions to a linear system to obtain the 'biorthogonal' windows. This approach provides a much broader mathematical view of the DGE, and therefore, establishes a wider mathematical foundation towards the theory of DGE. The general algorithm derived also provides a whole class of discrete Gabor expansions, among which 'good' ones can be generated. Simulation results are also provided.
Systoles in discrete dynamical systems
NASA Astrophysics Data System (ADS)
Fernandes, Sara; Grácio, Clara; Ramos, Carlos Correia
2013-01-01
The fruitful relationship between Geometry and Graph Theory has been explored by several authors benefiting also the Theory of discrete dynamical systems seen as Markov chains in graphs. In this work we will further explore the relation between these areas, giving a geometrical interpretation of notions from dynamical systems. In particular, we relate the topological entropy with the systole, here defined in the context of discrete dynamical systems. We show that for continuous interval maps the systole is trivial; however, for the class of interval maps with one discontinuity point the systole acquires relevance from the point of view of the dynamical behavior. Moreover, we define the geodesic length spectrum associated to a Markov interval map and we compute the referred spectrum in several examples.
Dark Energy from Discrete Spacetime
Trout, Aaron D.
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
Hidden algebra method (quasi-exact-solvability in quantum mechanics)
Turbiner, A. |
1996-02-01
A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland {ital N}-body problems ass ociated with an existence of the hidden algebra {ital sl}{sub {ital N}} is discussed extensively. {copyright} {ital 1996 American Institute of Physics.}
A FORTRAN Program for Discrete Discriminant Analysis
ERIC Educational Resources Information Center
Boone, James O.; Brewer, James K.
1976-01-01
A Fortran program is presented for discriminant analysis of discrete variables. The program assumes discrete, nominal data with no distributional, variance-covariance assumptions. The program handles a maximum of fifty predictor variables and twelve outcome groups. (Author/JKS)
Efficient genetic algorithms using discretization scheduling.
McLay, Laura A; Goldberg, David E
2005-01-01
In many applications of genetic algorithms, there is a tradeoff between speed and accuracy in fitness evaluations when evaluations use numerical methods with varying discretization. In these types of applications, the cost and accuracy vary from discretization errors when implicit or explicit quadrature is used to estimate the function evaluations. This paper examines discretization scheduling, or how to vary the discretization within the genetic algorithm in order to use the least amount of computation time for a solution of a desired quality. The effectiveness of discretization scheduling can be determined by comparing its computation time to the computation time of a GA using a constant discretization. There are three ingredients for the discretization scheduling: population sizing, estimated time for each function evaluation and predicted convergence time analysis. Idealized one- and two-dimensional experiments and an inverse groundwater application illustrate the computational savings to be achieved from using discretization scheduling. PMID:16156928
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
Discrete vortex representation of magnetohydrodynamics
Kinney, R.; Tajima, T.; Petviashvili, N.; McWilliams, J.C.
1993-02-01
We present an alternative approach to statistical analysis of an intermittent ideal MHD fluid in two dimensions, based on the hydrodynamical discrete vortex model applied to the Elsasser variables. The model contains negative temperature states which predict the formation of magnetic islands, but also includes a natural limit under which the equilibrium states revert to the familiar twin-vortex states predicted by hydrodynamical turbulence theories. Numerical dynamical calculations yield equilibrium spectra in agreement with the theoretical predictions.
Discrete-contact nanowire photovoltaics
NASA Astrophysics Data System (ADS)
Chitambar, Michelle J.; Wen, Wen; Maldonado, Stephen
2013-11-01
A series of finite-element simulations have been performed to assess the operational characteristics of a new semiconductor nanowire solar cell design operating under high-level injection conditions. Specifically, the steady-state current-voltage behavior of a cylindrical silicon (Si) nanowire with a series of discrete, ohmic-selective contacts under intense sunlight illumination was investigated. The scope of the analysis was limited to only the factors that impact the net internal quantum yield for solar to electricity conversion. No evaluations were performed with regards to optical light trapping in the modeled structures. Several aspects in a discrete-contact nanowire device that could impact operation were explored, including the size and density of ohmic-selective contacts, the size of the nanowire, the electronic quality and conductivity of the nanowire, the surface defect density of the nanowire, and the type of ohmic selectivity employed at each contact. The analysis showed that there were ranges of values for each parameter that supported good to excellent photoresponses, with certain combinations of experimentally attainable material properties yielding internal energy conversion efficiencies at the thermodynamic limit for a single junction cell. The merits of the discrete-contact nanowire cell were contrasted with "conventional" nanowire photovoltaic cells featuring a uniform conformal contact and also with planar point-contact solar cells. The unique capacity of the discrete-contact nanowire solar cell design to operate at useful energy conversion efficiencies with low quality semiconductor nanowires (i.e., possessing short charge-carrier lifetimes) with only light doping is discussed. This work thus defines the impetus for future experimental work aimed at developing this photovoltaic architecture.
Symmetric Discrete Orthonormal Stockwell Transform
NASA Astrophysics Data System (ADS)
Wang, Yanwei; Orchard, Jeff
2008-09-01
The Stockwell Transform (ST) is a time-frequency signal decomposition that is gaining in popularity, likely because of its direct relation with the Fourier Transform (FT). A discrete and non-redundant version of the ST, denoted the Discrete Orthonormal Stockwell Transform (DOST), has made the use of the ST more feasible. However, the matrix multiplication required by the DOST can still be a formidable computation, especially for high-dimensional data. Moreover, the symmetric property of the ST and FT is not present in the DOST. In this paper, we investigate a new Symmetric Discrete Orthonormal Stockwell Transform (SDOST) that still keeps the non-redundant multiresolution features of the DOST, while maintaining a symmetry property similar to that of the FT. First, we give a brief introduction for the ST and the DOST. Then we analyze the DOST coefficients and modify the transform to get a symmetric version. A small experiment shows that the SDOST has kept the abilities of the DOST and demonstrates the advantage of symmetry when applying the SDOST.
Interference in discrete Wigner functions
Cormick, Cecilia; Paz, Juan Pablo
2006-12-15
We analyze some features of the class of discrete Wigner functions that was recently introduced by Gibbons et al. [Phys. Rev. A 70, 062101 (2004)] to represent quantum states of systems with power-of-prime dimensional Hilbert spaces. We consider ''cat'' states obtained as coherent superpositions of states with positive Wigner function; for such states we show that the oscillations of the discrete Wigner function typically spread over the entire discrete phase space (including the regions where the two interfering states are localized). This is a generic property, which is in sharp contrast with the usual attributes of Wigner functions that make them useful candidates to display the existence of quantum coherence through oscillations. However, it is possible to find subsets of cat states with a natural phase-space representation, in which the oscillatory regions remain localized. We show that this can be done for interesting families of stabilizer states used in quantum error-correcting codes, and illustrate this by analyzing the phase-space representation of the five-qubit error-correcting code.
Observability of discretized partial differential equations
NASA Technical Reports Server (NTRS)
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
An exact accelerated stochastic simulation algorithm
Mjolsness, Eric; Orendorff, David; Chatelain, Philippe; Koumoutsakos, Petros
2009-01-01
An exact method for stochastic simulation of chemical reaction networks, which accelerates the stochastic simulation algorithm (SSA), is proposed. The present “ER-leap” algorithm is derived from analytic upper and lower bounds on the multireaction probabilities sampled by SSA, together with rejection sampling and an adaptive multiplicity for reactions. The algorithm is tested on a number of well-quantified reaction networks and is found experimentally to be very accurate on test problems including a chaotic reaction network. At the same time ER-leap offers a substantial speedup over SSA with a simulation time proportional to the 2∕3 power of the number of reaction events in a Galton–Watson process. PMID:19368432
Exact methods for self interacting neutrinos
Pehlivan, Y.; Balantekin, A. B.; Kajino, Toshitaka
2014-06-24
The effective many-body Hamiltonian which describes vacuum oscillations and self interactions of neutrinos in a two flavor mixing scheme under the single angle approximation has the same dynamical symmetries as the well known BCS pairing Hamiltonian. These dynamical symmetries manifest themselves in terms of a set of constants of motion and can be useful in formulating the collective oscillation modes in an intuitive way. In particular, we show that a neutrino spectral split can be simply viewed as an avoided level crossing between the eigenstates of a mean field Hamiltonian which includes a Lagrange multiplier in order to fix the value of an exact many-body constant of motion. We show that the same dynamical symmetries also exist in the three neutrino mixing scheme by explicitly writing down the corresponding constants of motion.
Complexified Path Integrals, Exact Saddles, and Supersymmetry.
Behtash, Alireza; Dunne, Gerald V; Schäfer, Thomas; Sulejmanpasic, Tin; Ünsal, Mithat
2016-01-01
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semiclassical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex saddle points, even when the parameters in the action are real. We find new exact complex saddles, and show that without their contribution the semiclassical expansion is in conflict with basic properties such as the positive semidefiniteness of the spectrum, as well as constraints of supersymmetry. Generic saddles are not only complex, but also possibly multivalued and even singular. This is in contrast to instanton solutions, which are real, smooth, and single valued. The multivaluedness of the action can be interpreted as a hidden topological angle, quantized in units of π in supersymmetric theories. The general ideas also apply to nonsupersymmetric theories. PMID:26799010
Exact formation of hairy planar black holes
NASA Astrophysics Data System (ADS)
Fan, Zhong-Ying; Chen, Bin
2016-04-01
We consider Einstein gravity minimally coupled to a scalar field with a given potential in general dimensions. We obtain large classes of static hairy planar black holes which are asymptotic to anti-de Sitter (AdS) space-times. In particular, for a special case μ =(n -2 )/2 , we obtain new classes of exact dynamical solutions describing black hole formation. We find there are two classes of collapse solutions. The first class of solutions describes the evolution start from AdS space-time with a naked singularity at the origin. The space-time is linearly unstable and evolves into stationary black hole states even under small perturbation. The second class of solutions describes the space-time spontaneously evolving from AdS vacua into stationary black hole states undergoing nonlinear instability. We also discuss the global properties of all these dynamical solutions.
Annotating Large Genomes With Exact Word Matches
Healy, John; Thomas, Elizabeth E.; Schwartz, Jacob T.; Wigler, Michael
2003-01-01
We have developed a tool for rapidly determining the number of exact matches of any word within large, internally repetitive genomes or sets of genomes. Thus we can readily annotate any sequence, including the entire human genome, with the counts of its constituent words. We create a Burrows-Wheeler transform of the genome, which together with auxiliary data structures facilitating counting, can reside in about one gigabyte of RAM. Our original interest was motivated by oligonucleotide probe design, and we describe a general protocol for defining unique hybridization probes. But our method also has applications for the analysis of genome structure and assembly. We demonstrate the identification of chromosome-specific repeats, and outline a general procedure for finding undiscovered repeats. We also illustrate the changing contents of the human genome assemblies by comparing the annotations built from different genome freezes. PMID:12975312
Diffraction in time: An exactly solvable model
NASA Astrophysics Data System (ADS)
Goussev, Arseni
2014-03-01
In optics, diffraction is typically portrayed as deflection of light incident upon an obstacle with sharp boundaries, that can not be accounted for by reflection or refraction. Interestingly, quantum mechanics allows for an additional, intrinsically time-dependent manifestation of the phenomenon: Owing to the dispersive nature of quantum matter waves, sudden changes in boundary conditions may cause the particle wave function to develop interference fringes akin to those in stationary (optical) diffraction problems. This phenomenon, pioneered in 1952 by Moshinsky [Phys. Rev. 88, 625 (1952)] and presently referred to as ``diffraction in time,'' is at the heart of a vibrant area of experimental and theoretical research concerned with quantum transients. In my talk, I will introduce a new versatile exactly-solvable model of diffraction in time. The model describes dynamics of a quantum particle in the presence of an absorbing time-dependent barrier, and enables a quantitative description of diffraction and interference patterns in a large variety of setups.
Exact Solitary Water Waves with Vorticity
NASA Astrophysics Data System (ADS)
Hur, Vera Mikyoung
2008-05-01
The solitary water wave problem is to find steady free surface waves which approach a constant level of depth in the far field. The main result is the existence of a family of exact solitary waves of small amplitude for an arbitrary vorticity. Each solution has a supercritical parameter value and decays exponentially at infinity. The proof is based on a generalized implicit function theorem of the Nash-Moser type. The first approximation to the surface profile is given by the “KdV” equation. With a supercritical value of the surface tension coefficient, a family of small amplitude solitary waves of depression with subcritical parameter values is constructed for an arbitrary vorticity.
Exact Chi-Square and Fisher's Exact Probability Test for 3 by 2 Cross-Classification Tables.
ERIC Educational Resources Information Center
Berry, Kenneth J.; Mielke, Paul W., Jr.
1987-01-01
Subroutines to calculate exact chi square and Fisher's exact probability tests are presented for 3 by 2 cross-classification tables. A nondirectional probability value for each test is computed recursively. (Author/GDC)
The SMM Model as a Boundary Value Problem Using the Discrete Diffusion Equation
NASA Technical Reports Server (NTRS)
Campbell, Joel
2007-01-01
A generalized single step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.
Multidimensional discretization of conservation laws for unstructured polyhedral grids
Burton, D.E.
1994-08-22
To the extent possible, a discretized system should satisfy the same conservation laws as the physical system. The author considers the conservation properties of a staggered-grid Lagrange formulation of the hydrodynamics equations (SGH) which is an extension of a ID scheme due to von Neumann and Richtmyer (VNR). The term staggered refers to spatial centering in which position, velocity, and kinetic energy are centered at nodes, while density, pressure, and internal energy are at cell centers. Traditional SGH formulations consider mass, volume, and momentum conservation, but tend to ignore conservation of total energy, conservation of angular momentum, and requirements for thermodynamic reversibility. The author shows that, once the mass and momentum discretizations have been specified, discretization for other quantities are dictated by the conservation laws and cannot be independently defined. The spatial discretization method employs a finite volume procedure that replaces differential operators with surface integrals. The method is appropriate for multidimensional formulations (1D, 2D, 3D) on unstructured grids formed from polygonal (2D) or polyhedral (3D) cells. Conservation equations can then be expressed in conservation form in which conserved currents are exchanged between control volumes. In addition to the surface integrals, the conservation equations include source terms derived from physical sources or geometrical considerations. In Cartesian geometry, mass and momentum are conserved identically. Discussion of volume conservation will be temporarily deferred. The author shows that the momentum equation leads to a form-preserving definition for kinetic energy and to an exactly conservative evolution equation for internal energy. Similarly, the author derives a form-preserving definition and corresponding conservation equation for a zone-centered angular momentum.
Coupling of Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences
Slater, C.O.; Lillie, R.A.; Johnson, J.O.; Simpson, D.B.
1998-04-01
A computer code, DRC3, has been developed for coupling Monte Carlo adjoint leakages with three-dimensional discrete ordinates forward fluences in order to solve a special category of geometrically-complex deep penetration shielding problems. The code extends the capabilities of earlier methods that coupled Monte Carlo adjoint leakages with two-dimensional discrete ordinates forward fluences. The problems involve the calculation of fluences and responses in a perturbation to an otherwise simple two- or three-dimensional radiation field. In general, the perturbation complicates the geometry such that it cannot be modeled exactly using any of the discrete ordinates geometry options and thus a direct discrete ordinates solution is not possible. Also, the calculation of radiation transport from the source to the perturbation involves deep penetration. One approach to solving such problems is to perform the calculations in three steps: (1) a forward discrete ordinates calculation, (2) a localized adjoint Monte Carlo calculation, and (3) a coupling of forward fluences from the first calculation with adjoint leakages from the second calculation to obtain the response of interest (fluence, dose, etc.). A description of this approach is presented along with results from test problems used to verify the method. The test problems that were selected could also be solved directly by the discrete ordinates method. The good agreement between the DRC3 results and the direct-solution results verify the correctness of DRC3.
Rosewarne, P J; Wilson, J M; Svendsen, J C
2016-01-01
Metabolic rate is one of the most widely measured physiological traits in animals and may be influenced by both endogenous (e.g. body mass) and exogenous factors (e.g. oxygen availability and temperature). Standard metabolic rate (SMR) and maximum metabolic rate (MMR) are two fundamental physiological variables providing the floor and ceiling in aerobic energy metabolism. The total amount of energy available between these two variables constitutes the aerobic metabolic scope (AMS). A laboratory exercise aimed at an undergraduate level physiology class, which details the appropriate data acquisition methods and calculations to measure oxygen consumption rates in rainbow trout Oncorhynchus mykiss, is presented here. Specifically, the teaching exercise employs intermittent flow respirometry to measure SMR and MMR, derives AMS from the measurements and demonstrates how AMS is affected by environmental oxygen. Students' results typically reveal a decline in AMS in response to environmental hypoxia. The same techniques can be applied to investigate the influence of other key factors on metabolic rate (e.g. temperature and body mass). Discussion of the results develops students' understanding of the mechanisms underlying these fundamental physiological traits and the influence of exogenous factors. More generally, the teaching exercise outlines essential laboratory concepts in addition to metabolic rate calculations, data acquisition and unit conversions that enhance competency in quantitative analysis and reasoning. Finally, the described procedures are generally applicable to other fish species or aquatic breathers such as crustaceans (e.g. crayfish) and provide an alternative to using higher (or more derived) animals to investigate questions related to metabolic physiology. PMID:26768978
NASA Astrophysics Data System (ADS)
Fontich, Ernest; de la Llave, Rafael; Sire, Yannick
2015-09-01
We construct quasi-periodic and almost periodic solutions for coupled Hamiltonian systems on an infinite lattice which is translation invariant. The couplings can be long range, provided that they decay moderately fast with respect to the distance. For the solutions we construct, most of the sites are moving in a neighborhood of a hyperbolic fixed point, but there are oscillating sites clustered around a sequence of nodes. The amplitude of these oscillations does not need to tend to zero. In particular, the almost periodic solutions do not decay at infinity. The main result is an a posteriori theorem. We formulate an invariance equation. Solutions of this equation are embeddings of an invariant torus on which the motion is conjugate to a rotation. We show that, if there is an approximate solution of the invariance equation that satisfies some non-degeneracy conditions, there is a true solution close by. This does not require that the system is close to integrable, hence it can be used to validate numerical calculations or formal expansions. The proof of this a posteriori theorem is based on a Nash-Moser iteration, which does not use transformation theory. Simpler versions of the scheme were developed in [28]. One technical tool, important for our purposes, is the use of weighted spaces that capture the idea that the maps under consideration are local interactions. Using these weighted spaces, the estimates of iterative steps are similar to those in finite dimensional spaces. In particular, the estimates are independent of the number of nodes that get excited. Using these techniques, given two breathers, we can place them apart and obtain an approximate solution, which leads to a true solution nearby. By repeating the process infinitely often, we can get solutions with infinitely many frequencies which do not tend to zero at infinity.
Driven discrete time quantum walks
NASA Astrophysics Data System (ADS)
Hamilton, Craig S.; Barkhofen, Sonja; Sansoni, Linda; Jex, Igor; Silberhorn, Christine
2016-07-01
We introduce the driven discrete time quantum walk (QW), where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original QW. These dynamics have two regimes, which we illustrate using the one-dimensional line. Then, we explore a search application which has certain advantages over current search protocols, namely that it does not require a complicated initial state nor a specific measurement time to observe the marked state. Finally, we describe a potential experimental implementation using existing technology.
Planar hydrogen-like atom in inhomogeneous magnetic fields: Exactly or quasi-exactly solvable models
NASA Astrophysics Data System (ADS)
Liu, Liyan; Hao, Qinghai
2015-05-01
We use a simple mathematical method to solve the problem of a two-dimensional hydrogen-like atom in the inhomogeneous magnetic fields B = ( k/ r)z and B = ( k/ r 3)z. We construct a Hamiltonian that takes the same form as the Hamiltonian of a hydrogen-like atom in the homogeneous magnetic fields and obtain the energy spectrum by comparing the Hamiltonians. The results show that the whole spectrum of the atom in the magnetic field B = ( k/ r)z can be obtained, and the problem is exactly solvable in this case. We find analytic solutions of the Schrödinger equation for the atom in the magnetic field B = ( k/ r 3)z for particular values of the magnetic strength k and thus present a quasi-exactly solvable model.
Exact dynamic properties of molecular motors
NASA Astrophysics Data System (ADS)
Boon, N. J.; Hoyle, R. B.
2012-08-01
Molecular motors play important roles within a biological cell, performing functions such as intracellular transport and gene transcription. Recent experimental work suggests that there are many plausible biochemical mechanisms that molecules such as myosin-V could use to achieve motion. To account for the abundance of possible discrete-stochastic frameworks that can arise when modeling molecular motor walks, a generalized and straightforward graphical method for calculating their dynamic properties is presented. It allows the calculation of the velocity, dispersion, and randomness ratio for any proposed system through analysis of its structure. This article extends work of King and Altman ["A schematic method of deriving the rate laws of enzyme-catalyzed reactions," J. Phys. Chem. 60, 1375-1378 (1956)], 10.1021/j150544a010 on networks of enzymatic reactions by calculating additional dynamic properties for spatially hopping systems. Results for n-state systems are presented: single chain, parallel pathway, divided pathway, and divided pathway with a chain. A novel technique for combining multiple system architectures coupled at a reference state is also demonstrated. Four-state examples illustrate the effectiveness and simplicity of these methods.
Exact dynamic properties of molecular motors.
Boon, N J; Hoyle, R B
2012-08-28
Molecular motors play important roles within a biological cell, performing functions such as intracellular transport and gene transcription. Recent experimental work suggests that there are many plausible biochemical mechanisms that molecules such as myosin-V could use to achieve motion. To account for the abundance of possible discrete-stochastic frameworks that can arise when modeling molecular motor walks, a generalized and straightforward graphical method for calculating their dynamic properties is presented. It allows the calculation of the velocity, dispersion, and randomness ratio for any proposed system through analysis of its structure. This article extends work of King and Altman ["A schematic method of deriving the rate laws of enzyme-catalyzed reactions," J. Phys. Chem. 60, 1375-1378 (1956)] on networks of enzymatic reactions by calculating additional dynamic properties for spatially hopping systems. Results for n-state systems are presented: single chain, parallel pathway, divided pathway, and divided pathway with a chain. A novel technique for combining multiple system architectures coupled at a reference state is also demonstrated. Four-state examples illustrate the effectiveness and simplicity of these methods. PMID:22938213
Exact solutions for extreme black hole magnetospheres
NASA Astrophysics Data System (ADS)
Lupsasca, Alexandru; Rodriguez, Maria J.
2015-07-01
We present new exact solutions of Force-Free Electrodynamics (FFE) in the Near-Horizon region of an Extremal Kerr black hole (NHEK) and offer a complete classifica-tion of the subset that form highest-weight representations of the spacetime's SL(2, ℝ)×U(1) isometry group. For a natural choice of spacetime embedding of this isometry group, the SL(2, ℝ) highest-weight conditions lead to stationary solutions with non-trivial angular de-pendence, as well as axisymmetry when the U(1)-charge vanishes. In addition, we unveil a hidden SL(2, ℂ) symmetry of the equations of FFE that stems from the action of a complex automorphism group, and enables us to generate an SL(2, ℂ) family of (generically time-dependent) solutions. We then obtain still more general solutions with less symmetry by appealing to a principle of linear superposition that holds for solutions with collinear cur-rents. This allows us to resum the highest-weight primaries and their SL(2, ℝ)-descendants.
Exact sum rules for inhomogeneous drums
Amore, Paolo
2013-09-15
We derive general expressions for the sum rules of the eigenvalues of drums of arbitrary shape and arbitrary density, obeying different boundary conditions. The formulas that we present are a generalization of the analogous formulas for one dimensional inhomogeneous systems that we have obtained in a previous paper. We also discuss the extension of these formulas to higher dimensions. We show that in the special case of a density depending only on one variable the sum rules of any integer order can be expressed in terms of a single series. As an application of our result we derive exact sum rules for the homogeneous circular annulus with different boundary conditions, for a homogeneous circular sector and for a radially inhomogeneous circular annulus with Dirichlet boundary conditions. -- Highlights: •We derive an explicit expression for the sum rules of inhomogeneous drums. •We discuss the extension to higher dimensions. •We discuss the special case of an inhomogeneity only along one direction.
Exact strangeness conservation and particle production
NASA Astrophysics Data System (ADS)
Cleymans, J.; Redlich, K.; Suhonen, E.
The production of strange particles is studied in terms of a statistical formalism requiring strangeness to be exactly conserved while baryon number is treated grand canonically using a chemical potential. The gas is considered to be in thermal and chemical equilibrium and to have zero overall strangeness. All particles and resonances having masses up to approximately 2 GeV and strangeness up to plus or minus 3 are included. General formulas for different particle multiplicities in terms of infinite series of modified Bessel functions are derived. In contrast to the integral representation of particle numbers in the canonical ensemble, results can be easily handled numerically since the series converge very rapidly. As an illustration, the above formalism is applied to the description of particle production in proton-proton, proton-nucleus and nucleus-nucleus collisions. In particular the K/pi ratio shows a strong dependence on the interaction volume on the system while, in contrast, the antiLambda/Lambda ratio is almost independent of the volume. These results are in qualitative agreement with experimental data.
Fast ordering algorithm for exact histogram specification.
Nikolova, Mila; Steidl, Gabriele
2014-12-01
This paper provides a fast algorithm to order in a meaningful, strict way the integer gray values in digital (quantized) images. It can be used in any exact histogram specification-based application. Our algorithm relies on the ordering procedure based on the specialized variational approach. This variational method was shown to be superior to all other state-of-the art ordering algorithms in terms of faithful total strict ordering but not in speed. Indeed, the relevant functionals are in general difficult to minimize because their gradient is nearly flat over vast regions. In this paper, we propose a simple and fast fixed point algorithm to minimize these functionals. The fast convergence of our algorithm results from known analytical properties of the model. Our algorithm is equivalent to an iterative nonlinear filtering. Furthermore, we show that a particular form of the variational model gives rise to much faster convergence than other alternative forms. We demonstrate that only a few iterations of this filter yield almost the same pixel ordering as the minimizer. Thus, we apply only few iteration steps to obtain images, whose pixels can be ordered in a strict and faithful way. Numerical experiments confirm that our algorithm outperforms by far its main competitors. PMID:25347881
Exact solutions to magnetized plasma flow
Wang, Zhehui; Barnes, Cris W.
2001-03-01
Exact analytic solutions for steady-state magnetized plasma flow (MPF) using ideal magnetohydrodynamics formalism are presented. Several cases are considered. When plasma flow is included, a finite plasma pressure gradient {nabla}p can be maintained in a force-free state JxB=0 by the velocity gradient. Both incompressible and compressible MPF examples are discussed for a Taylor-state spheromak B field. A new magnetized nozzle solution is given for compressible plasma when U{parallel}B. Transition from a magnetized nozzle to a magnetic nozzle is possible when the B field is strong enough. No physical nozzle would be needed in the magnetic nozzle case. Diverging-, drum- and nozzle-shaped MPF solutions when U{perpendicular}B are also given. The electric field is needed to balance the UxB term in Ohm's law. The electric field can be generated in the laboratory with the proposed conducting electrodes. If such electric fields also exist in stars and galaxies, such as through a dynamo process, then these solutions can be candidates to explain single and double jets.
Exact-exchange-based quasiparticle calculations
Aulbur, Wilfried G.; Staedele, Martin; Goerling, Andreas
2000-09-15
One-particle wave functions and energies from Kohn-Sham calculations with the exact local Kohn-Sham exchange and the local density approximation (LDA) correlation potential [EXX(c)] are used as input for quasiparticle calculations in the GW approximation (GWA) for eight semiconductors. Quasiparticle corrections to EXX(c) band gaps are small when EXX(c) band gaps are close to experiment. In the case of diamond, quasiparticle calculations are essential to remedy a 0.7 eV underestimate of the experimental band gap within EXX(c). The accuracy of EXX(c)-based GWA calculations for the determination of band gaps is as good as the accuracy of LDA-based GWA calculations. For the lowest valence band width a qualitatively different behavior is observed for medium- and wide-gap materials. The valence band width of medium- (wide-) gap materials is reduced (increased) in EXX(c) compared to the LDA. Quasiparticle corrections lead to a further reduction (increase). As a consequence, EXX(c)-based quasiparticle calculations give valence band widths that are generally 1-2 eV smaller (larger) than experiment for medium- (wide-) gap materials. (c) 2000 The American Physical Society.
Correction terms for propagators and d’Alembertians due to spacetime discreteness
NASA Astrophysics Data System (ADS)
Johnston, Steven
2015-10-01
The causal set approach to quantum gravity models spacetime as a discrete structure—a causal set. Recent research has led to causal set models for the retarded propagator for the Klein-Gordon equation and the d’Alembertian operator. These models can be compared to their continuum counterparts via a sprinkling process. It has been shown that the models agree exactly with the continuum quantities in the limit of an infinite sprinkling density—the continuum limit. This paper obtains the correction terms for these models for sprinkled causal sets with a finite sprinkling density. These correction terms are an important step towards testable differences between the continuum and discrete models that could provide evidence of spacetime discreteness.
NASA Technical Reports Server (NTRS)
Barth, Timothy; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.
Discreteness effects in population dynamics
NASA Astrophysics Data System (ADS)
Guevara Hidalgo, Esteban; Lecomte, Vivien
2016-05-01
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions of additive observables for stochastic processes. A method commonly used in order to determine such functions is the so-called cloning algorithm which in its non-constant population version essentially reduces to the determination of the growth rate of a population, averaged over many realizations of the dynamics. However, the averaging of populations is highly dependent not only on the number of realizations of the population dynamics, and on the initial population size but also on the cut-off time (or population) considered to stop their numerical evolution. This may result in an over-influence of discreteness effects at initial times, caused by small population size. We overcome these effects by introducing a (realization-dependent) time delay in the evolution of populations, additional to the discarding of the initial transient regime of the population growth where these discreteness effects are strong. We show that the improvement in the estimation of the large deviation function comes precisely from these two main contributions.
Chirality and Symmetry Breaking in a Discrete Internal Space
NASA Astrophysics Data System (ADS)
Lampe, Bodo
2012-10-01
In previous papers the permutation group S 4 has been suggested as an ordering scheme for quarks and leptons, and the appearance of this finite symmetry group was taken as indication for the existence of a discrete inner symmetry space underlying elementary particle interactions. Here it is pointed out that a more suitable choice than the tetrahedral group S 4 is the pyritohedral group A 4× Z 2 because its vibrational spectrum exhibits exactly the mass multiplet structure of the 3 fermion generations. Furthermore it is noted that the same structure can also be obtained from a primordial symmetry breaking S 4→ A 4. Since A 4 is a chiral group, while S 4 is achiral, an argument can be given why the chirality of the inner pyritohedral symmetry leads to parity violation of the weak interactions.
Sebastian Schunert; Yousry Y. Azmy
2011-05-01
The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally fine mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization error associated with the reference solution is not small compared to the discretization error associated with the mesh under scrutiny. Typically this situation occurs if the mesh of interest is only a couple of refinement levels away from the reference solution or if the order of accuracy of the numerical method (and hence the reference as well) is lower than expected. In this work we present a Method of Manufactured Solutions (MMS) benchmark suite with variable order of smoothness of the underlying exact solution for two-dimensional Cartesian geometries which provides analytical solutions aver- aged over arbitrary orthogonal meshes for scattering and non-scattering media. It should be emphasized that the developed MMS benchmark suite first eliminates the aforementioned limitation of fine mesh reference solutions since it secures knowledge of the underlying true solution and second that it allows for an arbitrary order of smoothness of the underlying ex- act solution. The latter is of importance because even for smooth parameters and boundary conditions the DO equations can feature exact solution with limited smoothness. Moreover, the degree of smoothness is crucial for both the order of accuracy and the magnitude of the discretization error for any spatial discretization scheme.
NASA Astrophysics Data System (ADS)
Lorenz, Ulf; Saalfrank, Peter
2015-02-01
System-bath problems in physics and chemistry are often described by Markovian master equations. However, the Markov approximation, i.e., neglect of bath memory effects is not always justified, and different measures of non-Markovianity have been suggested in the literature to judge the validity of this approximation. Here we calculate several computable measures of non-Markovianity for the non-trivial problem of a harmonic oscillator coupled to a large number of bath oscillators. The Multi Configurational Time Dependent Hartree method is used to provide a numerically converged solution of the system-bath Schrödinger equation, from which the appropriate quantities can be calculated. In particular, we consider measures based on trace-distances and quantum discord for a variety of initial states. These quantities have proven useful in the case of two-level and other small model systems typically encountered in quantum optics, but are less straightforward to interpret for the more complex model systems that are relevant for chemical physics. Supplementary material in the form of one zip file available from the Journal web page at http://dx.doi.org/10.1140/epjd/e2014-50727-8
Exact models for trimerization and tetramerization in spin chains
NASA Astrophysics Data System (ADS)
Rachel, Stephan; Greiter, Martin
2008-10-01
We present exact models for an antiferromagnetic S=1 spin chain describing trimerization as well as for an antiferromagnetic S=3/2 spin chain describing tetramerization. These models can be seen as generalizations of the Majumdar-Ghosh model. For both models, we provide a local Hamiltonian and its exact threefold or fourfold degenerate ground state wave functions, respectively. We numerically confirm the validity of both models using exact diagonalization and discuss the low-lying excitations.
Observers for discrete-time nonlinear systems
NASA Astrophysics Data System (ADS)
Grossman, Walter D.
Observer synthesis for discrete-time nonlinear systems with special applications to parameter estimation is analyzed. Two new types of observers are developed. The first new observer is an adaptation of the Friedland continuous-time parameter estimator to discrete-time systems. The second observer is an adaptation of the continuous-time Gauthier observer to discrete-time systems. By adapting these observers to discrete-time continuous-time parameter estimation problems which were formerly intractable become tractable. In addition to the two newly developed observers, two observers already described in the literature are analyzed and deficiencies with respect to noise rejection are demonstrated. Improved versions of these observers are proposed and their performance demonstrated. The issues of discrete-time observability, discrete-time system inversion, and optimal probing are also addressed.
Multigrid methods for isogeometric discretization.
Gahalaut, K P S; Kraus, J K; Tomar, S K
2013-01-01
We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels [Formula: see text], whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order [Formula: see text], and for [Formula: see text] and [Formula: see text] smoothness. PMID:24511168
Discrete modelling of drapery systems
NASA Astrophysics Data System (ADS)
Thoeni, Klaus; Giacomini, Anna
2016-04-01
Drapery systems are an efficient and cost-effective measure in preventing and controlling rockfall hazards on rock slopes. The simplest form consists of a row of ground anchors along the top of the slope connected to a horizontal support cable from which a wire mesh is suspended down the face of the slope. Such systems are generally referred to as simple or unsecured draperies (Badger and Duffy 2012). Variations such as secured draperies, where a pattern of ground anchors is incorporated within the field of the mesh, and hybrid systems, where the upper part of an unsecured drapery is elevated to intercept rockfalls originating upslope of the installation, are becoming more and more popular. This work presents a discrete element framework for simulation of unsecured drapery systems and its variations. The numerical model is based on the classical discrete element method (DEM) and implemented into the open-source framework YADE (Šmilauer et al., 2010). The model takes all relevant interactions between block, drapery and slope into account (Thoeni et al., 2014) and was calibrated and validated based on full-scale experiments (Giacomini et al., 2012).The block is modelled as a rigid clump made of spherical particles which allows any shape to be approximated. The drapery is represented by a set of spherical particle with remote interactions. The behaviour of the remote interactions is governed by the constitutive behaviour of the wire and generally corresponds to a piecewise linear stress-strain relation (Thoeni et al., 2013). The same concept is used to model wire ropes. The rock slope is represented by rigid triangular elements where material properties (e.g., normal coefficient of restitution, friction angle) are assigned to each triangle. The capabilities of the developed model to simulate drapery systems and estimate the residual hazard involved with such systems is shown. References Badger, T.C., Duffy, J.D. (2012) Drapery systems. In: Turner, A.K., Schuster R
Multigrid methods for isogeometric discretization
Gahalaut, K.P.S.; Kraus, J.K.; Tomar, S.K.
2013-01-01
We present (geometric) multigrid methods for isogeometric discretization of scalar second order elliptic problems. The smoothing property of the relaxation method, and the approximation property of the intergrid transfer operators are analyzed. These properties, when used in the framework of classical multigrid theory, imply uniform convergence of two-grid and multigrid methods. Supporting numerical results are provided for the smoothing property, the approximation property, convergence factor and iterations count for V-, W- and F-cycles, and the linear dependence of V-cycle convergence on the smoothing steps. For two dimensions, numerical results include the problems with variable coefficients, simple multi-patch geometry, a quarter annulus, and the dependence of convergence behavior on refinement levels ℓ, whereas for three dimensions, only the constant coefficient problem in a unit cube is considered. The numerical results are complete up to polynomial order p=4, and for C0 and Cp-1 smoothness. PMID:24511168
Classicality in discrete Wigner functions
Cormick, Cecilia; Galvao, Ernesto F.; Gottesman, Daniel; Paz, Juan Pablo; Pittenger, Arthur O.
2006-01-15
Gibbons et al., [Phys. Rev. A 70, 062101 (2004)] have recently defined discrete Wigner functions W to represent quantum states in a Hilbert space with finite dimension. We show that such a class of Wigner functions W can be defined so that the only pure states having non-negative W for all such functions are stabilizer states, as conjectured by Galvao, [Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving non-negativity of W for all definitions of W in the class form a subgroup of the Clifford group. This means pure states with non-negative W and their associated unitary dynamics are classical in the sense of admitting an efficient classical simulation scheme using the stabilizer formalism.
Determinant Expressions for Discrete Integrable Maps
NASA Astrophysics Data System (ADS)
Sogo, Kiyoshi
2006-08-01
Explicit formulas for several discrete integrable maps with periodic boundary condition are obtained, which give the sequential time developments in a form of the quotient of successive determinants of tri-diagonal matrices. We can expect that such formulas make the corresponding numerical simulations simple and stable. The cases of discrete Lotka-Volterra and discrete KdV equations are demonstrated by using the common algorithm computing determinants of tri-diagonal matrices.
Discrete ordinates with new quadrature sets and modified source conditions
Ganguly, K.; Allen, E.J., Victory, H.D. Jr. )
1989-01-01
A major shortcoming of the discrete ordinates method with the Gauss-Legendre quadrature set is that when the number of secondaries per primary c and the order of approximation N are not too large, all the (N + 1)v (the flux being of the form exp({minus}x/v)) lie in ({minus}1,1). It is known, however, that the largest v{sub j} corresponding to the asymptotic flux is greater than unity. The Legendre polynomial used for obtaining the quadrature set is orthogonal with respect to weight unity in the range ({minus}1,1). However, the Case and Zweifel eigenfunctions derived from the exact solution of one-speed transport theory are orthogonal with respect to a complicated weight function w({mu}) and {mu} in the half-range and full-range cases, respectively. In this paper, the authors have used a set of orthogonal polynomials with respect to w ({mu}) to develop quadrature sets to be used in the discrete ordinates calculation.
Discrete Models of Fluids: Spatial Averaging, Closure, and Model Reduction
Panchenko, Alexander; Tartakovsky, Alexandre; Cooper, Kevin
2014-03-06
The main question addressed in the paper is how to obtain closed form continuum equations governing spatially averaged dynamics of semi-discrete ODE models of fluid flow. In the presence of multiple small scale heterogeneities, the size of these ODE systems can be very large. Spatial averaging is then a useful tool for reducing computational complexity of the problem. The averages satisfy balance equations of mass, momentum and energy. These equations are exact, but they do not form a continuum model in the true sense of the word because calculation of stress and heat flux requires solving the underlying ODE system. To produce continuum equations that can be simulated without resolving micro-scale dynamics, we developed a closure method based on the use of regularized deconvolutions. We mostly deal with non-linear averaging suitable for Lagrangian particle solvers, but consider Eulerian linear averaging where appropriate. The results of numerical experiments show good agreement between our closed form flux approximations and their exact counterparts.
A discrete event method for wave simulation
Nutaro, James J
2006-01-01
This article describes a discrete event interpretation of the finite difference time domain (FDTD) and digital wave guide network (DWN) wave simulation schemes. The discrete event method is formalized using the discrete event system specification (DEVS). The scheme is shown to have errors that are proportional to the resolution of the spatial grid. A numerical example demonstrates the relative efficiency of the scheme with respect to FDTD and DWN schemes. The potential for the discrete event scheme to reduce numerical dispersion and attenuation errors is discussed.
Scalar discrete nonlinear multipoint boundary value problems
NASA Astrophysics Data System (ADS)
Rodriguez, Jesus; Taylor, Padraic
2007-06-01
In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].
Exact cosmological solutions with nonminimal derivative coupling
Sushkov, Sergey V.
2009-11-15
We consider a gravitational theory of a scalar field {phi} with nonminimal derivative coupling to curvature. The coupling terms have the form {kappa}{sub 1}R{phi}{sub ,{mu}}{phi}{sup ,{mu}} and {kappa}{sub 2}R{sub {mu}}{sub {nu}}{phi}{sup ,{mu}}{phi}{sup ,{nu}}, where {kappa}{sub 1} and {kappa}{sub 2} are coupling parameters with dimensions of length squared. In general, field equations of the theory contain third derivatives of g{sub {mu}}{sub {nu}} and {phi}. However, in the case -2{kappa}{sub 1}={kappa}{sub 2}{identical_to}{kappa}, the derivative coupling term reads {kappa}G{sub {mu}}{sub {nu}}{phi}{sup ,{mu}}{phi}{sup ,{nu}} and the order of corresponding field equations is reduced up to second one. Assuming -2{kappa}{sub 1}={kappa}{sub 2}, we study the spatially-flat Friedman-Robertson-Walker model with a scale factor a(t) and find new exact cosmological solutions. It is shown that properties of the model at early stages crucially depend on the sign of {kappa}. For negative {kappa}, the model has an initial cosmological singularity, i.e., a(t){approx}(t-t{sub i}){sup 2/3} in the limit t{yields}t{sub i}; and for positive {kappa}, the Universe at early stages has the quasi-de Sitter behavior, i.e., a(t){approx}e{sup Ht} in the limit t{yields}-{infinity}, where H=(3{radical}({kappa})){sup -1}. The corresponding scalar field {phi} is exponentially growing at t{yields}-{infinity}, i.e., {phi}(t){approx}e{sup -t/{radical}}{sup ({kappa})}. At late stages, the Universe evolution does not depend on {kappa} at all; namely, for any {kappa} one has a(t){approx}t{sup 1/3} at t{yields}{infinity}. Summarizing, we conclude that a cosmological model with nonminimal derivative coupling of the form {kappa}G{sub {mu}}{sub {nu}}{phi}{sup ,{mu}}{phi}{sup ,{nu}} is able to explain in a unique manner both a quasi-de Sitter phase and an exit from it without any fine-tuned potential.
NASA Astrophysics Data System (ADS)
Moteki, Nobuhiro
2016-07-01
An accurate and efficient simulation of light scattering by an atmospheric black carbon (BC)-containing aerosol-a fractal-like cluster of hundreds of carbon monomers that is internally mixed with other aerosol compounds such as sulfates, organics, and water-remains challenging owing to the enormous diversities of such aerosols' size, shape, and mixing state. Although the discrete dipole approximation (DDA) is theoretically an exact numerical method that is applicable to arbitrary non-spherical inhomogeneous targets, in practice, it suffers from severe granularity-induced error and degradation of computational efficiency for such extremely complex targets. To solve this drawback, we propose herein a hybrid DDA method designed for arbitrary BC-containing aerosols: the monomer-dipole assumption is applied to a cluster of carbon monomers, whereas the efficient cubic-lattice discretization is applied to the remaining particle volume consisting of other materials. The hybrid DDA is free from the error induced by the surface granularity of carbon monomers that occurs in conventional cubic-lattice DDA. In the hybrid DDA, we successfully mitigate the artifact of neglecting the higher-order multipoles in the monomer-dipole assumption by incorporating the magnetic dipole in addition to the electric dipole into our DDA formulations. Our numerical experiments show that the hybrid DDA method is an efficient light-scattering solver for BC-containing aerosols in arbitrary mixing states. The hybrid DDA could be also useful for a cluster of metallic nanospheres associated with other dielectric materials.
A numerical method for the exact calculation of airloads associated with impulsively started wings
NASA Technical Reports Server (NTRS)
Summa, J. M.
1977-01-01
A numerical method is developed to calculate three-dimensional potential flows due to the steady and impulsive motion of isolated wing and wing-wing interaction problems. The velocity potential is represented by a discrete set of constant-doublet quadrilaterals on wing and wake surfaces. The exact surface boundary condition is enforced, and the solution is obtained in a step-by-step fashion, configurations being impulsively started from rest. Free-wake geometries are generated for each time step with Rankine or Lamb viscous vortex segments used in wake-velocity calculations. Sample results include calculated performance to steady state for a thick wing and indicial lift of a wing-wing interaction problem.
NASA Astrophysics Data System (ADS)
Campello, E. M. B.; Pimenta, P. M.; Wriggers, P.
2011-08-01
Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.
Exact expression for the number of energy states in lattice models
NASA Astrophysics Data System (ADS)
Fronczak, Agata; Fronczak, Piotr
2014-02-01
We derive a closed-form combinatorial expression for the number of energy states in canonical systems with discrete energy levels. The expression results from the exact low-temperature power series expansion of the partition function. The approach provides interesting insights into basis of statistical mechanics. In particular, it is shown that in some cases the logarithm of the partition function may be considered the generating function for the number of internal states of energy clusters, which characterize system's microscopic configurations. Insights provided by the method allow one to understand the circumstances under which the widespread distributions for the energy, such as the Poisson and exponential distributions, arise. Apart from elementary examples, the framework is validated against the one-dimensional Ising model in zero field.
Terebus, Anna; Cao, Youfang; Liang, Jie
2016-01-01
Gene regulatory networks depict the interactions between genes, proteins, and other components of the cell. These interactions often are stochastic that can influence behavior of the cells. Discrete Chemical Master Equation (dCME) provides a general framework for understanding the stochastic nature of these networks. However solving dCME is challenging due to the enormous state space, one effective approach is to study the behavior of individual modules of the stochastic network. Here we used the finite buffer dCME method and directly calculated the exact steady state probability landscape for the two stochastic networks of Single Input and Coupled Toggle Switch Modules. The first example is a switch network consisting of three genes, and the second example is a double switching network consisting of four coupled genes. Our results show complex switching behavior of these networks can be quantified. PMID:25571172
Exact Statistics of Record Increments of Random Walks and Lévy Flights
NASA Astrophysics Data System (ADS)
Godrèche, Claude; Majumdar, Satya N.; Schehr, Grégory
2016-07-01
We study the statistics of increments in record values in a time series {x0=0 ,x1,x2,…,xn} generated by the positions of a random walk (discrete time, continuous space) of duration n steps. For arbitrary jump length distribution, including Lévy flights, we show that the distribution of the record increment becomes stationary, i.e., independent of n for large n , and compute it explicitly for a wide class of jump distributions. In addition, we compute exactly the probability Q (n ) that the record increments decrease monotonically up to step n . Remarkably, Q (n ) is universal (i.e., independent of the jump distribution) for each n , decaying as Q (n )˜A /√{n } for large n , with a universal amplitude A =e /√{π }=1.533 62 ….
Exact Statistics of Record Increments of Random Walks and Lévy Flights.
Godrèche, Claude; Majumdar, Satya N; Schehr, Grégory
2016-07-01
We study the statistics of increments in record values in a time series {x_{0}=0,x_{1},x_{2},…,x_{n}} generated by the positions of a random walk (discrete time, continuous space) of duration n steps. For arbitrary jump length distribution, including Lévy flights, we show that the distribution of the record increment becomes stationary, i.e., independent of n for large n, and compute it explicitly for a wide class of jump distributions. In addition, we compute exactly the probability Q(n) that the record increments decrease monotonically up to step n. Remarkably, Q(n) is universal (i.e., independent of the jump distribution) for each n, decaying as Q(n)∼A/sqrt[n] for large n, with a universal amplitude A=e/sqrt[π]=1.53362…. PMID:27419552
Inference and Exact Numerical Representation in Early Language Development
ERIC Educational Resources Information Center
Barner, David; Bachrach, Asaf
2010-01-01
How do children as young as 2 years of age know that numerals, like "one," have exact interpretations, while quantifiers and words like "a" do not? Previous studies have argued that only numerals have exact lexical meanings. Children could not use scalar implicature to strengthen numeral meanings, it is argued, since they fail to do so for…
An exact factorization perspective on quantum interferences in nonadiabatic dynamics
NASA Astrophysics Data System (ADS)
Curchod, Basile F. E.; Agostini, Federica; Gross, E. K. U.
2016-07-01
Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface—the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities.
An exact factorization perspective on quantum interferences in nonadiabatic dynamics.
Curchod, Basile F E; Agostini, Federica; Gross, E K U
2016-07-21
Nonadiabatic quantum interferences emerge whenever nuclear wavefunctions in different electronic states meet and interact in a nonadiabatic region. In this work, we analyze how nonadiabatic quantum interferences translate in the context of the exact factorization of the molecular wavefunction. In particular, we focus our attention on the shape of the time-dependent potential energy surface-the exact surface on which the nuclear dynamics takes place. We use a one-dimensional exactly solvable model to reproduce different conditions for quantum interferences, whose characteristic features already appear in one-dimension. The time-dependent potential energy surface develops complex features when strong interferences are present, in clear contrast to the observed behavior in simple nonadiabatic crossing cases. Nevertheless, independent classical trajectories propagated on the exact time-dependent potential energy surface reasonably conserve a distribution in configuration space that mimics one of the exact nuclear probability densities. PMID:27448870
NASA Astrophysics Data System (ADS)
Neto, Alfredo Gay; Martins, Clóvis A.; Pimenta, Paulo M.
2014-01-01
In offshore applications there are elements that can be modeled as long beams, such as umbilical cables, flexible and rigid pipes and hoses, immersed in the sea water, suspended from the floating unit to the seabed. The suspended part of these elements is named "riser" and is subjected to the ocean environment loads, such as waves and sea current. This work presents a structural geometrically-exact 3D beam model, discretized using the finite element method for riser modeling. An updated Lagrangian framework for the rotation parameterization has been used for the description of the exact kinematics. The goal is to perform a complete static analysis, considering the oceanic loads and the unilateral contact with the seabed, extending the current standard analysis for situations in which very large rotations occurs, in particular, large torsion. Details of the nonlinear 3D model and loads from oceanic environment are discussed, including the contact unilateral constraint.
Dean, David S.; Horgan, Ron R.; Naji, Ali; Podgornik, Rudolf
2009-01-01
We evaluate exactly the statistical integral for an inhomogeneous one-dimensional (1D) counterion-only Coulomb gas between two charged boundaries and from this compute the effective interaction, or disjoining pressure, between the bounding surfaces. Our exact results are compared to the limiting cases of weak and strong couplings which are the same for 1D and three-dimensional (3D) systems. For systems with a large number of counterions it is found that the weak-coupling (mean-field) approximation for the disjoining pressure works perfectly and that fluctuations around the mean-field in 1D are much smaller than in 3D. In the case of few counterions it works less well and strong-coupling approximation performs much better as it takes into account properly the discreteness of the counterion charges. PMID:19275406
Discretization vs. Rounding Error in Euler's Method
ERIC Educational Resources Information Center
Borges, Carlos F.
2011-01-01
Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…
Discrete/PWM Ballast-Resistor Controller
NASA Technical Reports Server (NTRS)
King, Roger J.
1994-01-01
Circuit offers low switching loss and automatic compensation for failure of ballast resistor. Discrete/PWM ballast-resistor controller improved shunt voltage-regulator circuit designed to supply power from high-resistance source to low-impedance bus. Provides both coarse discrete voltage levels (by switching of ballast resistors) and continuous fine control of voltage via pulse-width modulation.
Discreteness and Gradience in Intonational Contrasts.
ERIC Educational Resources Information Center
Gussenhoven, Carlos
1999-01-01
Three experimental techniques that can be used to investigate the gradient of discrete nature of intonational differences, the semantic task, the imitation task, and the pitch range task are discussed and evaluated. It is pointed out that categorical perception is a sufficient but not a necessary, property of phonological discreteness. (Author/VWL)
Current Density and Continuity in Discretized Models
ERIC Educational Resources Information Center
Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard
2010-01-01
Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…
Discrete Fractional Diffusion Equation of Chaotic Order
NASA Astrophysics Data System (ADS)
Wu, Guo-Cheng; Baleanu, Dumitru; Xie, He-Ping; Zeng, Sheng-Da
Discrete fractional calculus is suggested in diffusion modeling in porous media. A variable-order fractional diffusion equation is proposed on discrete time scales. A function of the variable order is constructed by a chaotic map. The model shows some new random behaviors in comparison with other variable-order cases.
Discrete elements method of neutral particle transport
Mathews, K.A.
1983-01-01
A new discrete elements (L/sub N/) transport method is derived and compared to the discrete ordinates S/sub N/ method, theoretically and by numerical experimentation. The discrete elements method is more accurate than discrete ordinates and strongly ameliorates ray effects for the practical problems studied. The discrete elements method is shown to be more cost effective, in terms of execution time with comparable storage to attain the same accuracy, for a one-dimensional test case using linear characteristic spatial quadrature. In a two-dimensional test case, a vacuum duct in a shield, L/sub N/ is more consistently convergent toward a Monte Carlo benchmark solution than S/sub N/, using step characteristic spatial quadrature. An analysis of the interaction of angular and spatial quadrature in xy-geometry indicates the desirability of using linear characteristic spatial quadrature with the L/sub N/ method.
Active control of turbomachine discrete tones
NASA Astrophysics Data System (ADS)
Fleeter, Sanford
This paper was directed at active control of discrete frequency noise generated by subsonic blade rows through cancellation of the blade row interaction generated propagating acoustic waves. First discrete frequency noise generated by a rotor and stator in a duct was analyzed to determine the propagating acoustic pressure waves. Then a mathematical model was developed to analyze and predict the active control of discrete frequency noise generated by subsonic blade rows through cancellation of the propagating acoustic waves, accomplished by utilizing oscillating airfoil surfaces to generate additional control propagating pressure waves. These control waves interact with the propagating acoustic waves, thereby, in principle, canceling the acoustic waves and thus, the far field discrete frequency tones. This model was then applied to a fan exit guide vane to investigate active airfoil surface techniques for control of the propagating acoustic waves, and thus the far field discrete frequency tones, generated by blade row interactions.
MULTISCALE DISCRETIZATION OF SHAPE CONTOURS
Prasad, L.; Rao, R.
2000-09-01
We present an efficient multi-scale scheme to adaptively approximate the continuous (or densely sampled) contour of a planar shape at varying resolutions. The notion of shape is intimately related to the notion of contour, and the efficient representation of the contour of a shape is vital to a computational understanding of the shape. Any polygonal approximation of a planar smooth curve is equivalent to a piecewise constant approximation of the parameterized X and Y coordinate functions of a discrete point set obtained by densely sampling the curve. Using the Haar wavelet transform for the piecewise approximation yields a hierarchical scheme in which the size of the approximating point set is traded off against the morphological accuracy of the approximation. Our algorithm compresses the representation of the initial shape contour to a sparse sequence of points in the plane defining the vertices of the shape's polygonal approximation. Furthermore, it is possible to control the overall resolution of the approximation by a single, scale-independent parameter.
Seipin Is a Discrete Homooligomer†
Binns, Derk; Lee, SungKyung; Hilton, Christopher L.; Jiang, Qiu-Xing; Goodman, Joel M.
2011-01-01
Seipin is a transmembrane protein that resides in the endoplasmic reticulum and concentrates at junctions between the ER and cytosolic lipid droplets. Mutations in the human seipin gene, including the missense mutation A212P, lead to congenital generalized lipodystrophy (CGL), characterized by the lack of normal adipose tissue and accumulation of fat in liver and muscles. In both yeast and CGL patient fibroblasts, seipin is required for normal lipid droplet morphology; in its absence droplets appear to bud abnormally from the ER. Here we report the first purification and physical characterization of seipin. Yeast seipin is in a large discrete protein complex. Affinity purification demonstrated that seipin is the main if not exclusive protein in the complex. Detergent sucrose gradients in H2O, and D2O and gel filtration were used to determine the size of the seipin complex and account for detergent binding. Both seipin-myc13 (seipin fused to 13 tandem copies of the myc epitope) expressed from the endogenous promoter and overexpressed seipin-mCherry form ~500 kDa proteins consisting of about 9 copies of seipin. The yeast orthologue of the human A212P allele forms only smaller complexes and is unstable; we hypothesize that this accounts for its null phenotype in humans. Seipin appears as a toroid by negative staining electron microscopy. We speculate that seipin plays at least a structural role in organizing droplets or in communication between droplets and ER. PMID:21062080
NASA Technical Reports Server (NTRS)
Dlugach, Janna M.; Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.
2011-01-01
Direct computer simulations of electromagnetic scattering by discrete random media have become an active area of research. In this progress review, we summarize and analyze our main results obtained by means of numerically exact computer solutions of the macroscopic Maxwell equations. We consider finite scattering volumes with size parameters in the range, composed of varying numbers of randomly distributed particles with different refractive indices. The main objective of our analysis is to examine whether all backscattering effects predicted by the low-density theory of coherent backscattering (CB) also take place in the case of densely packed media. Based on our extensive numerical data we arrive at the following conclusions: (i) all backscattering effects predicted by the asymptotic theory of CB can also take place in the case of densely packed media; (ii) in the case of very large particle packing density, scattering characteristics of discrete random media can exhibit behavior not predicted by the low-density theories of CB and radiative transfer; (iii) increasing the absorptivity of the constituent particles can either enhance or suppress typical manifestations of CB depending on the particle packing density and the real part of the refractive index. Our numerical data strongly suggest that spectacular backscattering effects identified in laboratory experiments and observed for a class of high-albedo Solar System objects are caused by CB.
NASA Astrophysics Data System (ADS)
Dai, Fengzhao; Li, Jie; Wang, Xiangzhao; Bu, Yang
2016-05-01
A novel zonal method is proposed for exact discrete reconstruction of a two-dimensional wavefront with high spatial resolution for lateral shearing interferometry. Four difference wavefronts measured in the x and y shear directions are required. Each of the two shear directions is measured twice with different shear amounts. The shear amounts of the second measurements of the x and y directions are Sx+1 pixels and Sy+1 pixels, where Sx pixels and Sy pixels are the shear amounts of the first measurements in the x and y directions, respectively. The shear amount in each direction can be chosen freely, provided that it is below a maximum value determined by the pupil shape and the number of samples N in that direction; thus, the choices are not limited by the more stringent condition required by previous methods, namely, that the shear amounts must be divisors of N. This method can exactly reconstruct any wavefront at evaluation points up to an arbitrary constant if the data is noiseless, and high spatial resolution can be achieved even with large shear amounts. The method is applicable not only to square pupils, but also to general pupil shapes if a sufficient number of Gerchberg iterations are employed. In this study, the validity and capability of the method were confirmed by numerical experiments. In addition, the experiments demonstrated that the method is stable with respect to noise in the difference wavefronts.
Multidimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations
NASA Astrophysics Data System (ADS)
Chacon, Luis
2015-09-01
We discuss a new, conservative, fully implicit 2D-3V particle-in-cell algorithm for non-radiative, electromagnetic kinetic plasma simulations, based on the Vlasov-Darwin model. Unlike earlier linearly implicit PIC schemes and standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. This has been demonstrated in 1D electrostatic and electromagnetic contexts. In this study, we build on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the Darwin field and particle orbit equations for multiple species in multiple dimensions. The Vlasov-Darwin model is very attractive for PIC simulations because it avoids radiative noise issues in non-radiative electromagnetic regimes. The algorithm conserves global energy, local charge, and particle canonical-momentum exactly, even with grid packing. The nonlinear iteration is effectively accelerated with a fluid preconditioner, which allows efficient use of large timesteps, O(√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D and 2D. Support from the LANL LDRD program and the DOE-SC ASCR office.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
Nieto, M.M.; Daboul, J.
1994-07-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = {minus}{gamma}/r{sup {nu}}, {gamma} > 0 and {minus}{infinity} < {nu} < {infinity}. When the angular momentum is non-zero, these solutions lead to the classical orbits {rho}(t) = [cos {mu}({var_phi}(t) {minus} {var_phi}{sub 0}(t))]{sup 1/{mu}}, with {mu} = {nu}/2 {minus} 1 {ne} 0. For {nu} > 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when {nu} > 2 the solutions are normalizable (bound), as in the classical case. Also, there are normalizable discrete, yet unbound, state which correspond to unbound classical particles which reach infinity in a finite time. These and other interesting comparisons to the classical system will be discussed.
Exact, E = 0, classical and quantum solutions for general power-law oscillators
NASA Technical Reports Server (NTRS)
Nieto, Michael Martin; Daboul, Jamil
1995-01-01
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
The exact density functional for two electrons in one dimension
NASA Astrophysics Data System (ADS)
Cohen, Aron; Mori-Sanchez, Paula
The exact universal density functional F [ ρ ] is calculated for real space two-electron densities in one dimension ρ (x) with a soft-Coulomb interaction. It is calculated by the Levy constrained search F [ ρ ] =minΨ-->ρ < Ψ | \\Tcirc +\\Vcircee | Ψ > over wavefunctions of a two-dimensional Hilbert space Ψ (x1 ,x2) --> ρ (x1) and can be directly visualized. We do an approximate constrained search via density matrices and a direct approximation to natural orbitals. This allows us to make an accurate approximation to the exact functional that is calculated using a search over potentials. We investigate the exact functional and the performance of many approximations on some of the most challenging electronic structure in two-electron systems, from strongly-correlated electron transfer to the description of a localized-delocalized transition. The exact Kohn-Sham potential, vs (x) , and exact Kohn-Sham eigenvalues, ɛi, are calculated and this allows us to discuss the band-gap problem versus the perspective of the exact density functional F [ ρ ] for all numbers of electrons. We calculate the derivative discontinuity of the exact functional in an example of a Mott-Insulator, one-dimensional stretched H2.
Dissociation between exact and approximate addition in developmental dyslexia.
Yang, Xiujie; Meng, Xiangzhi
2016-09-01
Previous research has suggested that number sense and language are involved in number representation and calculation, in which number sense supports approximate arithmetic, and language permits exact enumeration and calculation. Meanwhile, individuals with dyslexia have a core deficit in phonological processing. Based on these findings, we thus hypothesized that children with dyslexia may exhibit exact calculation impairment while doing mental arithmetic. The reaction time and accuracy while doing exact and approximate addition with symbolic Arabic digits and non-symbolic visual arrays of dots were compared between typically developing children and children with dyslexia. Reaction time analyses did not reveal any differences across two groups of children, the accuracies, interestingly, revealed a distinction of approximation and exact addition across two groups of children. Specifically, two groups of children had no differences in approximation. Children with dyslexia, however, had significantly lower accuracy in exact addition in both symbolic and non-symbolic tasks than that of typically developing children. Moreover, linguistic performances were selectively associated with exact calculation across individuals. These results suggested that children with dyslexia have a mental arithmetic deficit specifically in the realm of exact calculation, while their approximation ability is relatively intact. PMID:27310366
Compatible Spatial Discretizations for Partial Differential Equations
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
Exact propagators on the lattice with applications to diffractive effects
NASA Astrophysics Data System (ADS)
Sadurní, E.
2012-11-01
The propagator of the discrete Schrödinger equation is computed and its properties are revealed through a Feynman path summation in discrete space. Initial data problems such as diffraction in discrete space and continuous time are studied analytically by the application of the new propagator. In the second part of this paper, the analogy between time propagation and 2D scattering by 1D obstacles is explored. New results are given in the context of diffraction by edges within a periodic medium. A connection with tight-binding arrays and photonic crystals is indicated.
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Kutler, Paul (Technical Monitor)
1998-01-01
Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.
Impedance Matching for Discrete, Periodic Media and Application to Two-Scale Wave Propagation Models
NASA Astrophysics Data System (ADS)
Thirunavukkarasu, Senganal
also be very useful for numerical simulation of dynamics of crystal lattices, for both MD simulations and AtC coupling. A critical problem that needs to be resolved in this context is the well-posedness of the discrete PMDL formulation. The proposed ECM facilitates direct extension of well-posedness criteria from continuous ABCs to discrete ABCs, and thus to discrete PMDL. This criterion is then used to develop a well-posed discrete PMDL formulation for a diatomic lattice, a simple but representative complex lattice, which is numerically verified to be stable. The methodology can be extended to more complex lattices, but at the expense of increased algebraic complexity, and perhaps significant increase in computational cost. Time-harmonic discrete PMDL can play an important role in numerical simulation of wave propagation in continuous periodic media, e.g. photonic crystals. ECM provides an alternate viewpoint for developing effective ABCs for periodic media. For instance, using ECM we derive an alternative expression for the exact Dirichlet-to-Neumann (DtN) operator of an unbounded periodic waveguide. While it is not yet clear if this alternative expression is computationally advantageous, it is nevertheless an interesting alternative. More significantly, we build on the existing idea of recursive doubling to propose a new and efficient method, based on discrete PMDL, to compute the DtN operator of an unbounded periodic waveguide. Compared to the original method, applicable only to dissipative media, the proposed method is more general and applicable to both dissipative and non-dissipative media. Based on the observations, it appears that discrete PMDL, and more generally the idea of equivalent continuous media, offers additional flexibility towards developing accurate methods for modeling wave propagation in a variety of application problems.
Fast and Exact Continuous Collision Detection with Bernstein Sign Classification
Tang, Min; Tong, Ruofeng; Wang, Zhendong; Manocha, Dinesh
2014-01-01
We present fast algorithms to perform accurate CCD queries between triangulated models. Our formulation uses properties of the Bernstein basis and Bézier curves and reduces the problem to evaluating signs of polynomials. We present a geometrically exact CCD algorithm based on the exact geometric computation paradigm to perform reliable Boolean collision queries. Our algorithm is more than an order of magnitude faster than prior exact algorithms. We evaluate its performance for cloth and FEM simulations on CPUs and GPUs, and highlight the benefits. PMID:25568589
Phase retrieval from exactly oversampled diffraction intensity through deconvolution
Song Changyong; Ramunno-Johnson, Damien; Miao Jianwei; Nishino, Yoshinori; Kohmura, Yoshiki; Ishikawa, Tetsuya
2007-01-01
We have shown that, when the linear oversampling ratio {>=}2, exactly oversampled diffraction patterns can be directly obtained from measured data through deconvolution. By using computer simulations and experimental data, we have demonstrated that exact oversampling of diffraction patterns distinctively improves the quality of phase retrieval. Furthermore, phase retrieval based on the exact sampling scheme is independent of the oversampling ratio, which can significantly reduce the radiation dosage to the samples. We believe that the present work will contribute to high-quality image reconstruction of materials science samples and biological structures using x-ray diffraction microscopy.
NASA Astrophysics Data System (ADS)
Hoffmann, Tim
2000-01-01
The equivalence of the discrete isotropic Heisenberg magnet (IHM) model and the discrete nonlinear Schrödinger equation (NLSE) given by Ablowitz and Ladik is shown. This is used to derive the equivalence of their discretization with the one by Izgerin and Korepin. Moreover a doubly discrete IHM is presented that is equivalent to Ablowitz' and Ladiks doubly discrete NLSE.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Discrete flavour symmetries from the Heisenberg group
NASA Astrophysics Data System (ADS)
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
High-accuracy discrete positioning device
NASA Technical Reports Server (NTRS)
Brooks, John J. (Inventor)
1994-01-01
An article (30) is controllably and precisely positioned at one of three discrete locations defined by a linkage. The positioning apparatus includes two independently driven cranks (34, 42), with a link (50) pivotably connected between the two cranks (34, 42). Another connector (44) is pivotably connected between one of the cranks (34 or 42) and the article (30) to be positioned. The cranks (34, 42) are rotationally adjusted so that the pivot points (52, 54) of the link (50) are collinear with the axes of rotation of the cranks (40, 48), thereby defining one of the three discrete locations. Additional cranks and links can be provided to define additional discrete locations.
Exact and Explicit Internal Equatorial Water Waves with Underlying Currents
NASA Astrophysics Data System (ADS)
Kluczek, Mateusz
2016-07-01
In this paper we present an exact and explicit solution to the geophysical governing equations in the Equatorial region, which represents internal oceanic waves in the presence of a constant underlying current.
Novel quasi-exactly solvable models with anharmonic singular potentials
Agboola, Davids Zhang, Yao-Zhong
2013-03-15
We present new quasi-exactly solvable models with inverse quartic, sextic, octic and decatic power potentials, respectively. We solve these models exactly by means of the functional Bethe ansatz method. For each case, we give closed-form solutions for the energies and the wave functions as well as analytical expressions for the allowed potential parameters in terms of the roots of a set of algebraic equations. - Highlights: Black-Right-Pointing-Pointer The quasi-exactly solvable treatments of a class of singular anharmonic models. Black-Right-Pointing-Pointer Exact solutions to a class of integer power singular potential. Black-Right-Pointing-Pointer Solutions obtained in terms of the roots to the Bethe ansatz equations. Black-Right-Pointing-Pointer Results useful in describing diatomic molecules and elastic differential cross sections for high energy scattering.
Exact theory of intermediate phases in two dimensions
Delfino, Gesualdo Squarcini, Alessio
2014-03-15
We show how field theory yields the exact description of intermediate phases in the scaling limit of two-dimensional statistical systems at a first order phase transition point. The ability of a third phase to form an intermediate wetting layer or only isolated bubbles is explicitly related to the spectrum of excitations of the field theory. The order parameter profiles are determined and interface properties such as passage probabilities and internal structure are deduced from them. The theory is illustrated through the application to the q-state Potts model and the Ashkin–Teller model. The latter is shown to provide the first exact solution of a bulk wetting transition. -- Highlights: •Phase separation with appearance of a third phase is studied exactly. •Interfacial properties are derived from field theory. •Exact solution of bulk wetting transition is provided.
Exact correspondence between Renyi entropy flows and physical flows
NASA Astrophysics Data System (ADS)
Ansari, Mohammad H.; Nazarov, Yuli V.
2015-05-01
We present a universal relation between the flow of a Renyi entropy and the full counting statistics of energy transfers. We prove the exact relation for a flow to a system in thermal equilibrium that is weakly coupled to an arbitrary time-dependent and nonequilibrium system. The exact correspondence, given by this relation, provides a simple protocol to quantify the flows of Shannon and Renyi entropies from the measurements of energy transfer statistics.
Exact Magnetic Diffusion Solutions for Magnetohydrodynamic Code Verification
Miller, D S
2010-12-03
In this paper, the authors present several new exact analytic space and time dependent solutions to the problem of magnetic diffusion in R-Z geometry. These problems serve to verify several different elements of an MHD implementation: magnetic diffusion, external circuit time integration, current and voltage energy sources, spatially dependent conductivities, and ohmic heating. The exact solutions are shown in comparison with 2D simulation results from the Ares code.
The discrete-time compensated Kalman filter
NASA Technical Reports Server (NTRS)
Lee, W. H.; Athans, M.
1978-01-01
A suboptimal dynamic compensator to be used in conjunction with the ordinary discrete time Kalman filter was derived. The resultant compensated Kalman Filter has the property that steady state bias estimation errors, resulting from modelling errors, were eliminated.
Running Parallel Discrete Event Simulators on Sierra
Barnes, P. D.; Jefferson, D. R.
2015-12-03
In this proposal we consider porting the ROSS/Charm++ simulator and the discrete event models that run under its control so that they run on the Sierra architecture and make efficient use of the Volta GPUs.
Motion of Discrete Interfaces Through Mushy Layers
NASA Astrophysics Data System (ADS)
Braides, Andrea; Solci, Margherita
2016-04-01
We study the geometric motion of sets in the plane derived from the homogenization of discrete ferromagnetic energies with weak inclusions. We show that the discrete sets are composed by a `bulky' part and an external `mushy region' composed only of weak inclusions. The relevant motion is that of the bulky part, which asymptotically obeys to a motion by crystalline mean curvature with a forcing term, due to the energetic contribution of the mushy layers, and pinning effects, due to discreteness. From an analytical standpoint, it is interesting to note that the presence of the mushy layers implies only a weak and not strong convergence of the discrete motions, so that the convergence of the energies does not commute with the evolution. From a mechanical standpoint it is interesting to note the geometrical similarity of some phenomena in the cooling of binary melts.
A discrete control model of PLANT
NASA Technical Reports Server (NTRS)
Mitchell, C. M.
1985-01-01
A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.
Motion of Discrete Interfaces Through Mushy Layers
NASA Astrophysics Data System (ADS)
Braides, Andrea; Solci, Margherita
2016-08-01
We study the geometric motion of sets in the plane derived from the homogenization of discrete ferromagnetic energies with weak inclusions. We show that the discrete sets are composed by a `bulky' part and an external `mushy region' composed only of weak inclusions. The relevant motion is that of the bulky part, which asymptotically obeys to a motion by crystalline mean curvature with a forcing term, due to the energetic contribution of the mushy layers, and pinning effects, due to discreteness. From an analytical standpoint, it is interesting to note that the presence of the mushy layers implies only a weak and not strong convergence of the discrete motions, so that the convergence of the energies does not commute with the evolution. From a mechanical standpoint it is interesting to note the geometrical similarity of some phenomena in the cooling of binary melts.
Discrete Element Modeling of Drop Tests
NASA Astrophysics Data System (ADS)
Wang, Yuannian; Tonon, Fulvio
2012-09-01
A discrete element code with impact model has been developed and calibrated to simulate the dynamic behavior of rock materials, with special regard to rock fragmentation upon impact during rock-fall analysis. The paper summarizes the discrete element code, the calibration algorithms developed to identify the model microparameters, and the impact model. Experimental work on drop tests is then used to validate the code on modeling impact fragmentation. It has been found that the developed discrete element code and impact model can reasonably simulate rock fragmentation in drop tests. The use of the discrete element code and impact model can provide good reference results in evaluating impact fragmentation in rock-fall analysis.
Comparing the Discrete and Continuous Logistic Models
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2008-01-01
The solutions of the discrete logistic growth model based on a difference equation and the continuous logistic growth model based on a differential equation are compared and contrasted. The investigation is conducted using a dynamic interactive spreadsheet. (Contains 5 figures.)
Reducing Neuronal Networks to Discrete Dynamics
Terman, David; Ahn, Sungwoo; Wang, Xueying; Just, Winfried
2008-01-01
We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [1], we analyze the discrete model. PMID:18443649
Dynamic discretization method for solving Kepler's equation
NASA Astrophysics Data System (ADS)
Feinstein, Scott A.; McLaughlin, Craig A.
2006-09-01
Kepler’s equation needs to be solved many times for a variety of problems in Celestial Mechanics. Therefore, computing the solution to Kepler’s equation in an efficient manner is of great importance to that community. There are some historical and many modern methods that address this problem. Of the methods known to the authors, Fukushima’s discretization technique performs the best. By taking more of a system approach and combining the use of discretization with the standard computer science technique known as dynamic programming, we were able to achieve even better performance than Fukushima. We begin by defining Kepler’s equation for the elliptical case and describe existing solution methods. We then present our dynamic discretization method and show the results of a comparative analysis. This analysis will demonstrate that, for the conditions of our tests, dynamic discretization performs the best.
NASA Astrophysics Data System (ADS)
Moon, Haksu; Teixeira, Fernando L.; Omelchenko, Yuri A.
2015-09-01
We describe a charge-conserving scatter-gather algorithm for particle-in-cell simulations on unstructured grids. Charge conservation is obtained from first principles, i.e., without the need for any post-processing or correction steps. This algorithm recovers, at a fundamental level, the scatter-gather algorithms presented recently by Campos-Pinto et al. (2014) (to first-order) and by Squire et al. (2012), but it is derived here in a streamlined fashion from a geometric viewpoint. Some ingredients reflecting this viewpoint are (1) the use of (discrete) differential forms of various degrees to represent fields, currents, and charged particles and provide localization rules for the degrees of freedom thereof on the various grid elements (nodes, edges, facets), (2) use of Whitney forms as basic interpolants from discrete differential forms to continuum space, and (3) use of a Galerkin formula for the discrete Hodge star operators (i.e., "mass matrices" incorporating the metric datum of the grid) applicable to generally irregular, unstructured grids. The expressions obtained for the scatter charges and scatter currents are very concise and do not involve numerical quadrature rules. Appropriate fractional areas within each grid element are identified that represent scatter charges and scatter currents within the element, and a simple geometric representation for the (exact) charge conservation mechanism is obtained by such identification. The field update is based on the coupled first-order Maxwell's curl equations to avoid spurious modes with secular growth (otherwise present in formulations that discretize the second-order wave equation). Examples are provided to verify preservation of discrete Gauss' law for all times.
NASA Astrophysics Data System (ADS)
Houdayer, Cyril; Isono, Yusuke
2016-05-01
We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras {M = B rtimes Γ} arising from arbitrary actions {Γ &ucedil;rvearrowright B} of bi-exact discrete groups (e.g. free groups) on amenable von Neumann algebras. We prove a spectral gap rigidity result for the central sequence algebra {N' \\cap M^ω} of any nonamenable von Neumann subalgebra with normal expectation {N subset M} . We use this result to show that for any strongly ergodic essentially free nonsingular action {Γ &ucedil;rvearrowright (X, μ)} of any bi-exact countable discrete group on a standard probability space, the corresponding group measure space factor {L^∞(X) rtimes Γ} has no nontrivial central sequence. Using recent results of Boutonnet et al. (Local spectral gap in simple Lie groups and applications, 2015), we construct, for every {0 < λ ≤ 1} , a type {III_λ} strongly ergodic essentially free nonsingular action F_∞ &ucedil;rvearrowright (X_λ, μ_λ) of the free group F_∞ on a standard probability space so that the corresponding group measure space type {III_λ} factor {L^∞(X_λ, μ_λ) rtimes F_∞ has no nontrivial central sequence by our main result. In particular, we obtain the first examples of group measure space type {III} factors with no nontrivial central sequence.
Eigenforms, Discrete Processes and Quantum Processes
NASA Astrophysics Data System (ADS)
Kauffman, Louis H.
2012-05-01
This essay is a discussion of the concept of eigenform, due to Heinz von Foerster, and its relationship with discrete physics and quantum mechanics. We interpret the square root of minus one as a simple oscillatory process - a clock, and as an eigenform. By taking a generalization of this identification of i as a clock and eigenform, we show how quantum mechanics emerges from discrete physics.
Separable two-dimensional discrete Hartley transform
NASA Technical Reports Server (NTRS)
Watson, Andrew B.; Poirson, Allen
1986-01-01
Bracewell has proposed the Discrete Hartley Transform (DHT) as a substitute for the Discrete Fourier Transform (DFT), particularly as a means of convolution. Here, it is shown that the most natural extension of the DHT to two dimensions fails to be separate in the two dimensions, and is therefore inefficient. An alternative separable form is considered, corresponding convolution theorem is derived. That the DHT is unlikely to provide faster convolution than the DFT is also discussed.
`t Hooft anomaly matching for discrete symmetries
Csaki, C.; Murayama, Hitoshi |
1998-05-01
The authors show how to extend the `t Hooft anomaly matching conditions to discrete symmetries. They check these discrete anomally matching conditions on several proposed low-energy spectra of certain strongly interacting gauge theories. The excluded examples include the proposed chirally symmetric vacuum of pure N = 1 supersymmetric yang-Mills theories, certain non-supersymmetric confining theories and some self-dual N = 1 supersymmetric theories based on exceptional groups.
Terminal Dynamics Approach to Discrete Event Systems
NASA Technical Reports Server (NTRS)
Zak, Michail; Meyers, Ronald
1995-01-01
This paper presents and discusses a mathematical formalism for simulation of discrete event dynamic (DED)-a special type of 'man-made' systems to serve specific purposes of information processing. The main objective of this work is to demonstrate that the mathematical formalism for DED can be based upon a terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.!.
Discrete wavelet analysis of power system transients
Wilkinson, W.A.; Cox, M.D.
1996-11-01
Wavelet analysis is a new method for studying power system transients. Through wavelet analysis, transients are decomposed into a series of wavelet components, each of which is a time-domain signal that covers a specific octave frequency band. This paper presents the basic ideas of discrete wavelet analysis. A variety of actual and simulated transient signals are then analyzed using the discrete wavelet transform that help demonstrate the power of wavelet analysis.
NASA Astrophysics Data System (ADS)
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2016-05-01
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equations are first rewritten using the exterior calculus notation, replacing vector calculus differential operators by the exterior derivative, Hodge star and wedge product operators. The discretization is then carried out by substituting with the corresponding discrete operators based on the DEC framework. Numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured-triangular meshes, and first order accuracy for otherwise unstructured meshes. By construction, the method is conservative in that both mass and vorticity are conserved up to machine precision. The relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step.
Practical method to make a discrete memristor based on the aqueous solution of copper sulfate
NASA Astrophysics Data System (ADS)
Merrikh-Bayat, Farshad; Parvizi, Meysam
2016-06-01
A new method to realize a discrete memristor is proposed. The device under study consists of a tube filled of aqueous saturated solution of copper sulfate which can be electrolyzed by using two asymmetric copper electrodes, one of which has a considerably smaller cross-sectional area than to the other one. It is shown both theoretically and experimentally that this device has exactly the properties of a memristor if it is designed such that the electrical field and the current density on the thinner electrode when it acts as anode are sufficiently large. Different aspects of the proposed discrete memristor, including pinched hysteresis loop, on-off resistance ratio and memory volatilization, are studied and experimental results are presented.
Fermionic Renormalization Group Flow at All Scales: Breaking a Discrete Symmetry
NASA Astrophysics Data System (ADS)
Gersch, Roland; Honerkamp, Carsten; Rohe, Daniel; Metzner, Walter
2006-07-01
We extend the functional renormalization group technique in a modi cation of the one-particle irreducible scheme to study discrete symmetry breaking at nite temperature. As an instructive example, we employ the technique to access both the symmetric and the symmetry-broken phase of a charge-density wave mean- eld model. We study the half- lled case, and thus the breaking of a discrete symmetry, at nite temperature. A small external symmetry-breaking eld allows us to access the symmetry-broken state without encountering any divergence in the o w. We show diagrammatically that our method is equivalent to an exact resummation treatment. We numerically study the dependence of the o w on the external eld and on temperature.
How to discretize a quantum bath for real-time evolution
NASA Astrophysics Data System (ADS)
de Vega, Inés; Schollwöck, Ulrich; Wolf, F. Alexander
2015-10-01
Many numerical techniques for the description of quantum systems that are coupled to a continuous bath require the discretization of the latter. To this end, a wealth of methods has been developed in the literature, which we classify as (i) direct discretization, (ii) orthogonal polynomial, and (iii) numerical optimization strategies. We recapitulate strategies (i) and (ii) to clarify their relation. For quadratic Hamiltonians, we show that (ii) is the best strategy in the sense that it gives the numerically exact time evolution up to a maximum time tmax, for which we give a simple expression. For nonquadratic Hamiltonians, we show that no such best strategy exists. We present numerical examples relevant to open quantum systems and strongly correlated systems, as treated by dynamical mean-field theory (DMFT).
Keyes, D.E. . Dept. of Mechanical Engineering); Gropp, W.D. )
1990-01-01
Discrete systems arising in computational fluid dynamics applications often require wide stencils adapted to the local convective direction in order to accommodate higher-order upwind differencing, and involve multiple components perhaps coupling strongly at each point. Conventional exactly or approximately factored inverses of such operators are burdensome to apply globally, especially in problems complicated by non-tensor-product domain geometry or adaptive refinement, though their forward'' action is not. Such problems can be solved by iterative methods by using either point-block preconditioners or combination space-decoupled/component-decoupled preconditioners that are based on lower-order discretizations. Except for a global implicit solve on a coarse grid, each phase in the application of such preconditioners has simple locally exploitable structure. 16 refs., 2 figs., 3 tabs.
Lyapunov Schmidt reduction algorithm for three-dimensional discrete vortices
NASA Astrophysics Data System (ADS)
Lukas, Mike; Pelinovsky, Dmitry; Kevrekidis, P. G.
2008-03-01
We address the persistence and stability of three-dimensional vortex configurations in the discrete nonlinear Schrödinger equation and develop a symbolic package based on Wolfram’s MATHEMATICA for computations of the Lyapunov-Schmidt reduction method. The Lyapunov-Schmidt reduction method is a theoretical tool which enables us to study continuations and terminations of the discrete vortices for small coupling between lattice nodes as well as the spectral stability of the persistent configurations. The method was developed earlier in the context of the two-dimensional lattice and applied to the onsite and offsite configurations (called the vortex cross and the vortex cell) by using semianalytical computations [D.E. Pelinovsky, P.G. Kevrekidis, D. Frantzeskakis, Physica D 212 (2005) 20-53; P.G. Kevrekidis, D.E. Pelinovsky, Proc. R. Soc. A 462 (2006) 2671-2694]. The present treatment develops a full symbolic computational package which takes a desired waveform at the anticontinuum limit of uncoupled sites, performs a required number of Lyapunov-Schmidt reductions and outputs the predictions on whether the configuration persists, for finite coupling, in the three-dimensional lattice and whether it is stable or unstable. It also provides approximations for the eigenvalues of the linearized stability problem. We report a number of applications of the algorithm to important multisite three-dimensional configurations, such as the simple cube, the double cross and the diamond. For each configuration, we identify exactly one solution, which is stable for small coupling between lattice nodes.
An implicit finite element method for discrete dynamic fracture
Jobie M. Gerken
1999-12-01
A method for modeling the discrete fracture of two-dimensional linear elastic structures with a distribution of small cracks subject to dynamic conditions has been developed. The foundation for this numerical model is a plane element formulated from the Hu-Washizu energy principle. The distribution of small cracks is incorporated into the numerical model by including a small crack at each element interface. The additional strain field in an element adjacent to this crack is treated as an externally applied strain field in the Hu-Washizu energy principle. The resulting stiffness matrix is that of a standard plane element. The resulting load vector is that of a standard plane element with an additional term that includes the externally applied strain field. Except for the crack strain field equations, all terms of the stiffness matrix and load vector are integrated symbolically in Maple V so that fully integrated plane stress and plane strain elements are constructed. The crack strain field equations are integrated numerically. The modeling of dynamic behavior of simple structures was demonstrated within acceptable engineering accuracy. In the model of axial and transverse vibration of a beam and the breathing mode of vibration of a thin ring, the dynamic characteristics were shown to be within expected limits. The models dominated by tensile forces (the axially loaded beam and the pressurized ring) were within 0.5% of the theoretical values while the shear dominated model (the transversely loaded beam) is within 5% of the calculated theoretical value. The constant strain field of the tensile problems can be modeled exactly by the numerical model. The numerical results should therefore, be exact. The discrepancies can be accounted for by errors in the calculation of frequency from the numerical results. The linear strain field of the transverse model must be modeled by a series of constant strain elements. This is an approximation to the true strain field, so some
Discrete geometric analysis of message passing algorithm on graphs
NASA Astrophysics Data System (ADS)
Watanabe, Yusuke
2010-04-01
We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.
Discrete Ordinate Quadrature Selection for Reactor-based Eigenvalue Problems
Jarrell, Joshua J; Evans, Thomas M; Davidson, Gregory G
2013-01-01
In this paper we analyze the effect of various quadrature sets on the eigenvalues of several reactor-based problems, including a two-dimensional (2D) fuel pin, a 2D lattice of fuel pins, and a three-dimensional (3D) reactor core problem. While many quadrature sets have been applied to neutral particle discrete ordinate transport calculations, the Level Symmetric (LS) and the Gauss-Chebyshev product (GC) sets are the most widely used in production-level reactor simulations. Other quadrature sets, such as Quadruple Range (QR) sets, have been shown to be more accurate in shielding applications. In this paper, we compare the LS, GC, QR, and the recently developed linear-discontinuous finite element (LDFE) sets, as well as give a brief overview of other proposed quadrature sets. We show that, for a given number of angles, the QR sets are more accurate than the LS and GC in all types of reactor problems analyzed (2D and 3D). We also show that the LDFE sets are more accurate than the LS and GC sets for these problems. We conclude that, for problems where tens to hundreds of quadrature points (directions) per octant are appropriate, QR sets should regularly be used because they have similar integration properties as the LS and GC sets, have no noticeable impact on the speed of convergence of the solution when compared with other quadrature sets, and yield more accurate results. We note that, for very high-order scattering problems, the QR sets exactly integrate fewer angular flux moments over the unit sphere than the GC sets. The effects of those inexact integrations have yet to be analyzed. We also note that the LDFE sets only exactly integrate the zeroth and first angular flux moments. Pin power comparisons and analyses are not included in this paper and are left for future work.
Nonrecurrent quantum states: Systems with singular-continuous and discrete spectra
Lahiri, A. )
1993-03-15
The energy spectrum for a tight binding model with on-site potentials forming a Cantor set is seen to have a globally self-similar structure, and an exact correlation of the wave functions with the energies is pointed out. With periodic driving the quasienergy spectrum is obtained from an equivalent lattice problem and is seen to imply nonrecurrent time evolution of states. A model system with a discrete spectrum shows similar behavior. Implications for the problem of microwave ionization of hydrogen atoms are indicated.
Stochastic Event Counter for Discrete-Event Systems Under Unreliable Observations
Tae-Sic Yoo; Humberto E. Garcia
2008-06-01
This paper addresses the issues of counting the occurrence of special events in the framework of partiallyobserved discrete-event dynamical systems (DEDS). First, we develop a noble recursive procedure that updates active counter information state sequentially with available observations. In general, the cardinality of active counter information state is unbounded, which makes the exact recursion infeasible computationally. To overcome this difficulty, we develop an approximated recursive procedure that regulates and bounds the size of active counter information state. Using the approximated active counting information state, we give an approximated minimum mean square error (MMSE) counter. The developed algorithms are then applied to count special routing events in a material flow system.
Exact solutions and spacetime singularities in nonlocal gravity
NASA Astrophysics Data System (ADS)
Li, Yao-Dong; Modesto, Leonardo; Rachwał, Lesław
2015-12-01
We hereby study exact solutions in a wide range of local higher-derivative and weakly nonlocal gravitational theories. In particular, we give a list of exact classical solutions for two classes of gravitational theories both weakly nonlocal, unitary, and super-renormalizable (or finite) at quantum level. We prove that maximally symmetric spacetimes are exact solutions in both classes, while in dimension higher than four we can also have Anti-de Sitter solutions in the presence of positive cosmological constant. It is explicitly shown under which conditions flat and Ricci-flat spacetimes are exact solutions of the equation of motion (EOM) for the first class of theories not involving the Weyl tensor in the action. We find that the well-known physical spacetimes like Schwarzschild, Kerr, (Anti-) de Sitter serve as solutions for standard matter content, when the EOM does not contain the Riemann tensor alone (operators made out of only the Riemann tensor.) We pedagogically show how to obtain these exact solutions. Furthermore, for the second class of gravity theories, with terms in the Lagrangian written using Weyl tensors, the Friedmann-Robertson-Walker (FRW) spacetimes are also exact solutions (exactly in the same way like in Einstein theory), when the matter content is given by conformal matter (radiation). We also comment on rather inevitable presence and universality of singularities and possible resolution of them in finite and conformally invariant theories. "Delocalization" is proposed as a way to solve the black hole singularity problem in the first class. In order to solve the problem of cosmological singularities in the second class, it seems crucial to have a conformally invariant or asymptotically free quantum gravitational theory.
Exact-Differential Large-Scale Traffic Simulation
Hanai, Masatoshi; Suzumura, Toyotaro; Theodoropoulos, Georgios; Perumalla, Kalyan S
2015-01-01
Analyzing large-scale traffics by simulation needs repeating execution many times with various patterns of scenarios or parameters. Such repeating execution brings about big redundancy because the change from a prior scenario to a later scenario is very minor in most cases, for example, blocking only one of roads or changing the speed limit of several roads. In this paper, we propose a new redundancy reduction technique, called exact-differential simulation, which enables to simulate only changing scenarios in later execution while keeping exactly same results as in the case of whole simulation. The paper consists of two main efforts: (i) a key idea and algorithm of the exact-differential simulation, (ii) a method to build large-scale traffic simulation on the top of the exact-differential simulation. In experiments of Tokyo traffic simulation, the exact-differential simulation shows 7.26 times as much elapsed time improvement in average and 2.26 times improvement even in the worst case as the whole simulation.
Seleson, Pablo; Du, Qiang; Parks, Michael L.
2016-08-16
The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. While nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of suchmore » discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest
PREFACE: 4th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE2014)
NASA Astrophysics Data System (ADS)
Di Domenico, Antonio; Mavromatos, Nick E.; Mitsou, Vasiliki A.; Skliros, Dimitri P.
2015-07-01
The DISCRETE 2014: Fourth Symposium in the Physics of Discrete Symmetries took place at King's College London, Strand Campus, London WC2R 2LS, from Tuesday, December 2 2014 till Saturday, December 6 2014. This is the fourth Edition of the DISCRETE conference series, which is a biannual event, having been held previously in Valencia (Discrete'08), Rome (Discrete2010) and Lisbon (Discrete2012). The topics covered at the DISCRETE series of conferences are: T, C, P, CP symmetries; accidental symmetries (B, L conservation); CPT symmetry, decoherence and entangled states, Lorentz symmetry breaking (phenomenology and current bounds); neutrino mass and mixing; implications for cosmology and astroparticle physics, dark matter searches; experimental prospects at LHC, new facilities. In DISCRETE 2014 we have also introduced two new topics: cosmological aspects of non-commutative space-times as well as PT symmetric Hamiltonians (non-Hermitian but with real eigenvalues), a topic that has wide applications in particle physics and beyond. The conference was opened by the King's College London Vice Principal on Research and Innovation, Mr Chris Mottershead, followed by a welcome address by the Chair of DISCRETE 2014 (Professor Nick E. Mavromatos). After these introductory talks, the scientific programme of the DISCRETE 2014 symposium started. Following the tradition of DISCRETE series of conferences, the talks (138 in total) were divided into plenary-review talks (25), invited research talks (50) and shorter presentations (63) — selected by the conveners of each session in consultation with the organisers — from the submitted abstracts. We have been fortunate to have very high-quality, thought stimulating and interesting talks at all levels, which, together with the discussions among the participants, made the conference quite enjoyable. There were 152 registered participants for the event.
Discrete Nonholonomic Lagrangian Systems on Lie Groupoids
NASA Astrophysics Data System (ADS)
Iglesias, David; Marrero, Juan C.; de Diego, David Martín; Martínez, Eduardo
2008-06-01
This paper studies the construction of geometric integrators for nonholonomic systems. We develop a formalism for nonholonomic discrete Euler Lagrange equations in a setting that permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).
An exact zooming method for finite element analyses
NASA Technical Reports Server (NTRS)
Hirai, I.; Wang, B. P.; Pilkey, W. D.
1982-01-01
An exact zooming technique which employs static condensation and exact structural reanalysis methods was developed. Successive application of static condensation reduces the system to one that is only associated with the degrees of freedom (dof) of the original model. Application of an exact static reanalysis technique permits the displacements at the dof of the original model that are contained in the zoomed portion of the structure to be obtained first. The response external to the zoom, as well as the response of additional dof within various levels of zooming, is computed. With the triangular factor of the stiffness matrix of the original system available, this approach involves only the solution of a system of equations of small order.
Universality in exact quantum state population dynamics and control
Wu, Lian-Ao; Segal, Dvira; Brumer, Paul; Egusquiza, Inigo L.
2010-09-15
We consider an exact population transition, defined as the probability of finding a state at a final time that is exactly equal to the probability of another state at the initial time. We prove that, given a Hamiltonian, there always exists a complete set of orthogonal states that can be employed as time-zero states for which this exact population transition occurs. The result is general: It holds for arbitrary systems, arbitrary pairs of initial and final states, and for any time interval. The proposition is illustrated with several analytic models. In particular, we demonstrate that in some cases, by tuning the control parameters, a complete transition might occur, where a target state, vacant at t=0, is fully populated at time {tau}.
Exact Interior Reconstruction from Truncated Limited-Angle Projection Data
Ye, Yangbo; Yu, Hengyong; Wang, Ge
2008-01-01
Using filtered backprojection (FBP) and an analytic continuation approach, we prove that exact interior reconstruction is possible and unique from truncated limited-angle projection data, if we assume a prior knowledge on a subregion or subvolume within an object to be reconstructed. Our results show that (i) the interior region-of-interest (ROI) problem and interior volume-of-interest (VOI) problem can be exactly reconstructed from a limited-angle scan of the ROI/VOI and a 180 degree PI-scan of the subregion or subvolume and (ii) the whole object function can be exactly reconstructed from nontruncated projections from a limited-angle scan. These results improve the classical theory of Hamaker et al. (1980). PMID:18490957
Electron transfer dynamics: Zusman equation versus exact theory.
Shi, Qiang; Chen, Liping; Nan, Guangjun; Xu, Ruixue; Yan, YiJing
2009-04-28
The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations. PMID:19405605
Exact blocking formulas for spin and gauge models
NASA Astrophysics Data System (ADS)
Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Unmuth-Yockey, J.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan
2013-09-01
Using the example of the two-dimensional (2D) Ising model, we show that in contrast to what can be done in configuration space, the tensor renormalization group formulation allows one to write exact, compact, and manifestly local blocking formulas and exact coarse-grained expressions for the partition function. We argue that similar results should hold for most models studied by lattice gauge theorists. We provide exact blocking formulas for several 2D spin models [the O(2) and O(3) sigma models and the SU(2) principal chiral model] and for the three-dimensional gauge theories with groups Z2, U(1) and SU(2). We briefly discuss generalizations to other groups, higher dimensions and practical implementations.
ERIC Educational Resources Information Center
Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.
This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major effort now underway to…
Exact score distribution computation for ontological similarity searches
2011-01-01
Background Semantic similarity searches in ontologies are an important component of many bioinformatic algorithms, e.g., finding functionally related proteins with the Gene Ontology or phenotypically similar diseases with the Human Phenotype Ontology (HPO). We have recently shown that the performance of semantic similarity searches can be improved by ranking results according to the probability of obtaining a given score at random rather than by the scores themselves. However, to date, there are no algorithms for computing the exact distribution of semantic similarity scores, which is necessary for computing the exact P-value of a given score. Results In this paper we consider the exact computation of score distributions for similarity searches in ontologies, and introduce a simple null hypothesis which can be used to compute a P-value for the statistical significance of similarity scores. We concentrate on measures based on Resnik's definition of ontological similarity. A new algorithm is proposed that collapses subgraphs of the ontology graph and thereby allows fast score distribution computation. The new algorithm is several orders of magnitude faster than the naive approach, as we demonstrate by computing score distributions for similarity searches in the HPO. It is shown that exact P-value calculation improves clinical diagnosis using the HPO compared to approaches based on sampling. Conclusions The new algorithm enables for the first time exact P-value calculation via exact score distribution computation for ontology similarity searches. The approach is applicable to any ontology for which the annotation-propagation rule holds and can improve any bioinformatic method that makes only use of the raw similarity scores. The algorithm was implemented in Java, supports any ontology in OBO format, and is available for non-commercial and academic usage under: https://compbio.charite.de/svn/hpo/trunk/src/tools/significance/ PMID:22078312
Exact maps in density functional theory for lattice models
NASA Astrophysics Data System (ADS)
Dimitrov, Tanja; Appel, Heiko; Fuks, Johanna I.; Rubio, Angel
2016-08-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg–Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
NASA Astrophysics Data System (ADS)
Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.
2015-03-01
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space-time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge-Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that its
A practical discrete-adjoint method for high-fidelity compressible turbulence simulations
Vishnampet, Ramanathan; Bodony, Daniel J.; Freund, Jonathan B.
2015-03-15
Methods and computing hardware advances have enabled accurate predictions of complex compressible turbulence phenomena, such as the generation of jet noise that motivates the present effort. However, limited understanding of underlying physical mechanisms restricts the utility of such predictions since they do not, by themselves, indicate a route to design improvements. Gradient-based optimization using adjoints can circumvent the flow complexity to guide designs, though this is predicated on the availability of a sufficiently accurate solution of the forward and adjoint systems. These are challenging to obtain, since both the chaotic character of the turbulence and the typical use of discretizations near their resolution limits in order to efficiently represent its smaller scales will amplify any approximation errors made in the adjoint formulation. Formulating a practical exact adjoint that avoids such errors is especially challenging if it is to be compatible with state-of-the-art simulation methods used for the turbulent flow itself. Automatic differentiation (AD) can provide code to calculate a nominally exact adjoint, but existing general-purpose AD codes are inefficient to the point of being prohibitive for large-scale turbulence simulations. Here, we analyze the compressible flow equations as discretized using the same high-order workhorse methods used for many high-fidelity compressible turbulence simulations, and formulate a practical space–time discrete-adjoint method without changing the basic discretization. A key step is the definition of a particular discrete analog of the continuous norm that defines our cost functional; our selection leads directly to an efficient Runge–Kutta-like scheme, though it would be just first-order accurate if used outside the adjoint formulation for time integration, with finite-difference spatial operators for the adjoint system. Its computational cost only modestly exceeds that of the flow equations. We confirm that
Aesthetic Responses to Exact Fractals Driven by Physical Complexity
Bies, Alexander J.; Blanc-Goldhammer, Daryn R.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.
2016-01-01
Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a
Aesthetic Responses to Exact Fractals Driven by Physical Complexity.
Bies, Alexander J; Blanc-Goldhammer, Daryn R; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E
2016-01-01
Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a
Symmetrized quartic polynomial oscillators and their partial exact solvability
NASA Astrophysics Data System (ADS)
Znojil, Miloslav
2016-04-01
Sextic polynomial oscillator is probably the best known quantum system which is partially exactly alias quasi-exactly solvable (QES), i.e., which possesses closed-form, elementary-function bound states ψ (x) at certain couplings and energies. In contrast, the apparently simpler and phenomenologically more important quartic polynomial oscillator is not QES. A resolution of the paradox is proposed: The one-dimensional Schrödinger equation is shown QES after the analyticity-violating symmetrization V (x) = A | x | + Bx2 + C | x|3 +x4 of the quartic polynomial potential.
Exact Distribution of the Maximal Height of p Vicious Walkers
NASA Astrophysics Data System (ADS)
Schehr, Grégory; Majumdar, Satya N.; Comtet, Alain; Randon-Furling, Julien
2008-10-01
Using path-integral techniques, we compute exactly the distribution of the maximal height Hp of p nonintersecting Brownian walkers over a unit time interval in one dimension, both for excursions p watermelons with a wall, and bridges p watermelons without a wall, for all integer p≥1. For large p, we show that ⟨Hp⟩˜2p (excursions) whereas ⟨Hp⟩˜p (bridges). Our exact results prove that previous numerical experiments only measured the preasymptotic behaviors and not the correct asymptotic ones. In addition, our method establishes a physical connection between vicious walkers and random matrix theory.
Exact asymmetric Skyrmion in anisotropic ferromagnet and its helimagnetic application
NASA Astrophysics Data System (ADS)
Kundu, Anjan
2016-08-01
Topological Skyrmions as intricate spin textures were observed experimentally in helimagnets on 2d plane. Theoretical foundation of such solitonic states to appear in pure ferromagnetic model, as exact solutions expressed through any analytic function, was made long ago by Belavin and Polyakov (BP). We propose an innovative generalization of the BP solution for an anisotropic ferromagnet, based on a physically motivated geometric (in-)equality, which takes the exact Skyrmion to a new class of functions beyond analyticity. The possibility of stabilizing such metastable states in helimagnets is discussed with the construction of individual Skyrmion, Skyrmion crystal and lattice with asymmetry, likely to be detected in precision experiments.
Exact force-free electrodynamic solutions and their perturbations
NASA Astrophysics Data System (ADS)
Zhang, Fan; Lehner, Luis; McWilliams, Sean; Pfeiffer, Harald; Yang, Huan
2015-04-01
This talk is an amalgamation of several works relating to finding exact force-free electrodynamic (FFE) solutions and examining their behaviour under perturbations, both analytically and numerically. The talk will briefly discuss technical points such as the choice of numerical FFE evolution systems and challenges posed by light surfaces when seeking analytical FFE solutions, presenting along the way a couple of new solutions in the near horizon extreme Kerr spacetime. It will then move on to present the mode structure of the perturbed Blandford-Znajek solution and some results concerning the stability of a family of exact propagating FFE solutions. Supported in part by NSFC Grant No. 11443008.
Constant pressure and temperature discrete-time Langevin molecular dynamics.
Grønbech-Jensen, Niels; Farago, Oded
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation. PMID:25416875
Constant pressure and temperature discrete-time Langevin molecular dynamics
Grønbech-Jensen, Niels; Farago, Oded
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems—a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.
A discrete convolution kernel for No-DC MRI
NASA Astrophysics Data System (ADS)
Zeng, Gengsheng L.; Li, Ya
2015-08-01
An analytical inversion formula for the exponential Radon transform with an imaginary attenuation coefficient was developed in 2007 (2007 Inverse Problems 23 1963-71). The inversion formula in that paper suggested that it is possible to obtain an exact MRI (magnetic resonance imaging) image without acquiring low-frequency data. However, this un-measured low-frequency region (ULFR) in the k-space (which is the two-dimensional Fourier transform space in MRI terminology) must be very small. This current paper derives a FBP (filtered backprojection) algorithm based on You’s formula by suggesting a practical discrete convolution kernel. A point spread function is derived for this FBP algorithm. It is demonstrated that the derived FBP algorithm can have a larger ULFR than that in the 2007 paper. The significance of this paper is that we present a closed-form reconstruction algorithm for a special case of under-sampled MRI data. Usually, under-sampled MRI data requires iterative (instead of analytical) algorithms with L1-norm or total variation norm to reconstruct the image.
The Cauchy-Kovalevskaya Extension Theorem in Discrete Clifford Analysis
NASA Astrophysics Data System (ADS)
De Ridder, H.; De Schepper, H.; Sommen, F.
2010-09-01
Discrete Clifford analysis is a higher dimensional discrete function theory based on skew Weyl relations. It is centered around the study of Clifford algebra valued null solutions, called discrete monogenic functions, of a discrete Dirac operator, i.e. a first order, Clifford vector valued difference operator. In this contribution, we establish a Cauchy-Kovalevskaya extension theorem for discrete monogenic functions defined on the grid Zhm of m-tuples of integer multiples of a variable mesh width h. Convergence to the continuous case is investigated. As illustrative examples we explicitly construct the Cauchy-Kovalevskaya extensions of the discrete delta function and of a discretized exponential.
The ultimatum game: Discrete vs. continuous offers
NASA Astrophysics Data System (ADS)
Dishon-Berkovits, Miriam; Berkovits, Richard
2014-09-01
In many experimental setups in social-sciences, psychology and economy the subjects are requested to accept or dispense monetary compensation which is usually given in discrete units. Using computer and mathematical modeling we show that in the framework of studying the dynamics of acceptance of proposals in the ultimatum game, the long time dynamics of acceptance of offers in the game are completely different for discrete vs. continuous offers. For discrete values the dynamics follow an exponential behavior. However, for continuous offers the dynamics are described by a power-law. This is shown using an agent based computer simulation as well as by utilizing an analytical solution of a mean-field equation describing the model. These findings have implications to the design and interpretation of socio-economical experiments beyond the ultimatum game.
Numerical discretization for nonlinear diffusion filter
NASA Astrophysics Data System (ADS)
Mustaffa, I.; Mizuar, I.; Aminuddin, M. M. M.; Dasril, Y.
2015-05-01
Nonlinear diffusion filters are famously used in machine vision for image denoising and restoration. This paper presents a study on the effects of different numerical discretization of nonlinear diffusion filter. Several numerical discretization schemes are presented; namely semi-implicit, AOS, and fully implicit schemes. The results of these schemes are compared by visual results, objective measurement e.g. PSNR and MSE. The results are also compared to a Daubechies wavelet denoising method. It is acknowledged that the two preceding scheme have already been discussed in literature, however comparison to the latter scheme has not been made. The semi-implicit scheme uses an additive operator splitting (AOS) developed to overcome the shortcoming of the explicit scheme i.e., stability for very small time steps. Although AOS has proven to be efficient, from the nonlinear diffusion filter results with different discretization schemes, examples shows that implicit schemes are worth pursuing.
Discrete photon statistics from continuous microwave measurements
NASA Astrophysics Data System (ADS)
Virally, Stéphane; Simoneau, Jean Olivier; Lupien, Christian; Reulet, Bertrand
2016-04-01
Photocount statistics are an important tool for the characterization of electromagnetic fields, especially for fields with an irrelevant phase. In the microwave domain, continuous rather than discrete measurements are the norm. Using a different approach, we recover discrete photon statistics from the cumulants of a continuous distribution of field quadrature measurements. The use of cumulants allows the separation between the signal of interest and experimental noise. Using a parametric amplifier as the first stage of the amplification chain, we extract useful data from up to the sixth cumulant of the continuous distribution of a coherent field, hence recovering up to the third moment of the discrete statistics associated with a signal with much less than one average photon.
Discrete Roughness Transition for Hypersonic Flight Vehicles
NASA Technical Reports Server (NTRS)
Berry, Scott A.; Horvath, Thomas J.
2007-01-01
The importance of discrete roughness and the correlations developed to predict the onset of boundary layer transition on hypersonic flight vehicles are discussed. The paper is organized by hypersonic vehicle applications characterized in a general sense by the boundary layer: slender with hypersonic conditions at the edge of the boundary layer, moderately blunt with supersonic, and blunt with subsonic. This paper is intended to be a review of recent discrete roughness transition work completed at NASA Langley Research Center in support of agency flight test programs. First, a review is provided of discrete roughness wind tunnel data and the resulting correlations that were developed. Then, results obtained from flight vehicles, in particular the recently flown Hyper-X and Shuttle missions, are discussed and compared to the ground-based correlations.
Tree Ensembles on the Induced Discrete Space.
Yildiz, Olcay Taner
2016-05-01
Decision trees are widely used predictive models in machine learning. Recently, K -tree is proposed, where the original discrete feature space is expanded by generating all orderings of values of k discrete attributes and these orderings are used as the new attributes in decision tree induction. Although K -tree performs significantly better than the proper one, their exponential time complexity can prohibit their use. In this brief, we propose K -forest, an extension of random forest, where a subset of features is selected randomly from the induced discrete space. Simulation results on 17 data sets show that the novel ensemble classifier has significantly lower error rate compared with the random forest based on the original feature space. PMID:26011897
An algebra of discrete event processes
NASA Technical Reports Server (NTRS)
Heymann, Michael; Meyer, George
1991-01-01
This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.
Discrete-time Markovian stochastic Petri nets
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco
1995-01-01
We revisit and extend the original definition of discrete-time stochastic Petri nets, by allowing the firing times to have a 'defective discrete phase distribution'. We show that this formalism still corresponds to an underlying discrete-time Markov chain. The structure of the state for this process describes both the marking of the Petri net and the phase of the firing time for each transition, resulting in a large state space. We then modify the well-known power method to perform a transient analysis even when the state space is infinite, subject to the condition that only a finite number of states can be reached in a finite amount of time. Since the memory requirements might still be excessive, we suggest a bounding technique based on truncation.
Uncertainty relation for the discrete Fourier transform.
Massar, Serge; Spindel, Philippe
2008-05-16
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=e(i phi) VU. Its most important application is to constrain how much a quantum state can be localized simultaneously in two mutually unbiased bases related by a discrete fourier transform. It provides an uncertainty relation which smoothly interpolates between the well-known cases of the Pauli operators in two dimensions and the continuous variables position and momentum. This work also provides an uncertainty relation for modular variables, and could find applications in signal processing. In the finite dimensional case the minimum uncertainty states, discrete analogues of coherent and squeezed states, are minimum energy solutions of Harper's equation, a discrete version of the harmonic oscillator equation. PMID:18518426
The discrete regime of flame propagation
NASA Astrophysics Data System (ADS)
Tang, Francois-David; Goroshin, Samuel; Higgins, Andrew
The propagation of laminar dust flames in iron dust clouds was studied in a low-gravity envi-ronment on-board a parabolic flight aircraft. The elimination of buoyancy-induced convection and particle settling permitted measurements of fundamental combustion parameters such as the burning velocity and the flame quenching distance over a wide range of particle sizes and in different gaseous mixtures. The discrete regime of flame propagation was observed by substitut-ing nitrogen present in air with xenon, an inert gas with a significantly lower heat conductivity. Flame propagation in the discrete regime is controlled by the heat transfer between neighbor-ing particles, rather than by the particle burning rate used by traditional continuum models of heterogeneous flames. The propagation mechanism of discrete flames depends on the spa-tial distribution of particles, and thus such flames are strongly influenced by local fluctuations in the fuel concentration. Constant pressure laminar dust flames were observed inside 70 cm long, 5 cm diameter Pyrex tubes. Equally-spaced plate assemblies forming rectangular chan-nels were placed inside each tube to determine the quenching distance defined as the minimum channel width through which a flame can successfully propagate. High-speed video cameras were used to measure the flame speed and a fiber optic spectrometer was used to measure the flame temperature. Experimental results were compared with predictions obtained from a numerical model of a three-dimensional flame developed to capture both the discrete nature and the random distribution of particles in the flame. Though good qualitative agreement was obtained between model predictions and experimental observations, residual g-jitters and the short reduced-gravity periods prevented further investigations of propagation limits in the dis-crete regime. The full exploration of the discrete flame phenomenon would require high-quality, long duration reduced gravity environment
Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
1997-01-01
This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.
Model reduction for discrete bilinear systems
NASA Technical Reports Server (NTRS)
King, A. M.; Skelton, R. E.
1987-01-01
A model reduction method for discrete bilinear systems is developed which matches q sets of Volterra and covariance parameters. These parameters are shown to represent both deterministic and stochastic attributes of the discrete bilinear system. A reduced order model which matches these q sets of parameters is defined to be a q-Volterra covariance equivalent realization (q-Volterra COVER). An algorithm is presented which constructs a class of q-Volterra COVERs parameterized by solutions to a Hermitian, quadratic, matrix equation. The algorithm is applied to a bilinear model of a robot manipulator.
1-D EQUILIBRIUM DISCRETE DIFFUSION MONTE CARLO
T. EVANS; ET AL
2000-08-01
We present a new hybrid Monte Carlo method for 1-D equilibrium diffusion problems in which the radiation field coexists with matter in local thermodynamic equilibrium. This method, the Equilibrium Discrete Diffusion Monte Carlo (EqDDMC) method, combines Monte Carlo particles with spatially discrete diffusion solutions. We verify the EqDDMC method with computational results from three slab problems. The EqDDMC method represents an incremental step toward applying this hybrid methodology to non-equilibrium diffusion, where it could be simultaneously coupled to Monte Carlo transport.
Discrete Gabor Filters For Binocular Disparity Measurement
NASA Technical Reports Server (NTRS)
Weiman, Carl F. R.
1995-01-01
Discrete Gabor filters proposed for use in determining binocular disparity - difference between positions of same feature or object depicted in stereoscopic images produced by two side-by-side cameras aimed in parallel. Magnitude of binocular disparity used to estimate distance from cameras to feature or object. In one potential application, cameras charge-coupled-device video cameras in robotic vision system, and binocular disparities and distance estimates used as control inputs - for example, to control approaches to objects manipulated or to maintain safe distances from obstacles. Binocular disparities determined from phases of discretized Gabor transforms.
Hybrid Discrete-Continuous Markov Decision Processes
NASA Technical Reports Server (NTRS)
Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich
2003-01-01
This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.
Discrete-Layer Piezoelectric Plate and Shell Models for Active Tip-Clearance Control
NASA Technical Reports Server (NTRS)
Heyliger, P. R.; Ramirez, G.; Pei, K. C.
1994-01-01
The objectives of this work were to develop computational tools for the analysis of active-sensory composite structures with added or embedded piezoelectric layers. The targeted application for this class of smart composite laminates and the analytical development is the accomplishment of active tip-clearance control in turbomachinery components. Two distinct theories and analytical models were developed and explored under this contract: (1) a discrete-layer plate theory and corresponding computational models, and (2) a three dimensional general discrete-layer element generated in curvilinear coordinates for modeling laminated composite piezoelectric shells. Both models were developed from the complete electromechanical constitutive relations of piezoelectric materials, and incorporate both displacements and potentials as state variables. This report describes the development and results of these models. The discrete-layer theories imply that the displacement field and electrostatic potential through-the-thickness of the laminate are described over an individual layer rather than as a smeared function over the thickness of the entire plate or shell thickness. This is especially crucial for composites with embedded piezoelectric layers, as the actuating and sensing elements within these layers are poorly represented by effective or smeared properties. Linear Lagrange interpolation polynomials were used to describe the through-thickness laminate behavior. Both analytic and finite element approximations were used in the plane or surface of the structure. In this context, theoretical developments are presented for the discrete-layer plate theory, the discrete-layer shell theory, and the formulation of an exact solution for simply-supported piezoelectric plates. Finally, evaluations and results from a number of separate examples are presented for the static and dynamic analysis of the plate geometry. Comparisons between the different approaches are provided when
Exact Faraday rotation in the cylindrical Einstein-Maxwell waves
Arafah, M.R.; Fakioglu, S.; Halilsoy, M. )
1990-07-15
We obtain the exact behavior of the cross-polarized cylindrical Einstein-Maxwell waves that generalizes the well-known Einstein-Rosen waves. In the presence of the second mode of polarization the outgoing waves interact with the incoming ones to exhibit an analogous effect of the Faraday rotation.
Exact Controllability and Perturbation Analysis for Elastic Beams
Moreles, Miguel Angel
2004-05-15
The Rayleigh beam is a perturbation of the Bernoulli-Euler beam. We establish convergence of the solution of the Exact Controllability Problem for the Rayleigh beam to the corresponding solution of the Bernoulli-Euler beam. Convergence is related to a Singular Perturbation Problem. The main tool in solving this perturbation problem is a weak version of a lower bound for hyperbolic polynomials.
Exact geometric optics in a Morris-Thorne wormhole spacetime
Mueller, Thomas
2008-02-15
The simplicity of the Morris-Thorne wormhole spacetime permits us to determine null and timelike geodesics by means of elliptic integral functions and Jacobian elliptic functions. This analytic solution makes it possible to find a geodesic which connects two distant events. An exact gravitational lensing, an illumination calculation, and even an interactive visualization become possible.
Exact Nonlinear Internal Equatorial Waves in the f-plane
NASA Astrophysics Data System (ADS)
Hsu, Hung-Chu
2016-07-01
We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline.
Exact Chord-Length Distribution For SEU Calculations
NASA Technical Reports Server (NTRS)
Buehler, Martin G.; Luke, Keung L.
1990-01-01
Computed rates of SEU's more accurate. Exact integral chord-length distribution derived for use in calculations of rates of single-event upsets (SEU's) (changes in logic states) caused by impingement of cosmic rays or other ionizing radiation on electronic logic circuits.
Exact stochastic simulation of coupled chemical reactions with delays
NASA Astrophysics Data System (ADS)
Cai, Xiaodong
2007-03-01
Gillespie's exact stochastic simulation algorithm (SSA) [J. Phys. Chem. 81, 2350 (1977)] has been widely used to simulate the stochastic dynamics of chemically reacting systems. In this algorithm, it is assumed that all reactions occur instantly. While this is true in many cases, it is also possible that some chemical reactions, such as gene transcription and translation in living cells, take certain time to finish after they are initiated. Thus, the product of such reactions will emerge after certain delays. Apparently, Gillespie's SSA is not an exact algorithm for chemical reaction systems with delays. In this paper, the author develops an exact SSA for chemical reaction systems with delays, based upon the same fundamental premise of stochastic kinetics used by Gillespie in the development of his SSA. He then shows that an algorithm modified from Gillespie's SSA by Barrio et al. [PLOS Comput. Biol. 2, 1017 (2006)] is also an exact SSA for chemical reaction systems with delays, but it needs to generate more random variables than the author's algorithm.
Exact solutions of the generalized Sinh-Gordon equation
NASA Astrophysics Data System (ADS)
Neirameh, A.
2016-07-01
In this paper, we successfully derive a new exact traveling wave solutions of the generalized Sinh-Gordon equation by new application of the homogeneous balance method. This method could be used in further works to establish more entirely new solutions for other kinds of nonlinear evolution equations arising in physics.
Exact solution for a one-dimensional model for reptation
NASA Astrophysics Data System (ADS)
Drzewiński, Andrzej; van Leeuwen, J. M. J.
2006-05-01
We discuss the exact solution for the properties of the recently introduced “necklace” model for reptation. The solution gives the drift velocity, diffusion constant, and renewal time for asymptotically long chains. Its properties are also related to a special case of the Rubinstein-Duke model in one dimension.
Exact vibration amplitude derivative measurement with TV shearography
NASA Astrophysics Data System (ADS)
Valera, J. D. R.; Jones, J. D. C.; Løkberg, O. J.
1996-06-01
An electronic speckle shearing interferometer, or TV shearometer, characterized by a very small shear, has been used to measure the exact vibration amplitude derivative of a vibrating object. The technique is based on a heterodyne speckle shearing interferometer and uses fringe analysis methods appropriate when less than one fringe is observed on the vibrating object.
The Fisher-Yates Exact Test and Unequal Sample Sizes
ERIC Educational Resources Information Center
Johnson, Edgar M.
1972-01-01
A computational short cut suggested by Feldman and Klinger for the one-sided Fisher-Yates exact test is clarified and is extended to the calculation of probability values for certain two-sided tests when sample sizes are unequal. (Author)
Exactly Solvable Quantum Mechanical Potentials: An Alternative Approach.
ERIC Educational Resources Information Center
Pronchik, Jeremy N.; Williams, Brian W.
2003-01-01
Describes an alternative approach to finding exactly solvable, one-dimensional quantum mechanical potentials. Differs from the usual approach in that instead of starting with a particular potential and seeking solutions to the related Schrodinger equations, it begins with known solutions to second-order ordinary differential equations and seeks to…
Exact Results for One Dimensional Fluids Through Functional Integration
NASA Astrophysics Data System (ADS)
Fantoni, Riccardo
2016-06-01
We review some of the exactly solvable one dimensional continuum fluid models of equilibrium classical statistical mechanics under the unified setting of functional integration in one dimension. We make some further developments and remarks concerning fluids with penetrable particles. We then apply our developments to the study of the Gaussian core model for which we are unable to find a well defined thermodynamics.
Exact solutions, energy, and charge of stable Q-balls
NASA Astrophysics Data System (ADS)
Bazeia, D.; Marques, M. A.; Menezes, R.
2016-05-01
In this work we deal with nontopological solutions of the Q-ball type in two spacetime dimensions. We study models of current interest, described by a Higgs-like and other, similar potentials which unveil the presence of exact solutions. We use the analytic results to investigate how to control the energy and charge to make the Q-balls stable.
An Exactly Solvable Model for the Spread of Disease
ERIC Educational Resources Information Center
Mickens, Ronald E.
2012-01-01
We present a new SIR epidemiological model whose exact analytical solution can be calculated. In this model, unlike previous models, the infective population becomes zero at a finite time. Remarkably, these results can be derived from only an elementary knowledge of differential equations.
A new classical conjugate gradient coefficient with exact line search
NASA Astrophysics Data System (ADS)
Shapiee, Norrlaili; Rivaie, Mohd.; Mamat, Mustafa
2016-06-01
In this paper, we proposed a new classical conjugate gradient method. The global convergence is established using exact line search. Numerical results are presented based on number of iterations and CPU time. This numerical result shows that our method is performs better than classical CG method for a given standard test problems.
Exact Bremsstrahlung Function in N=2 Superconformal Field Theories.
Fiol, Bartomeu; Gerchkovitz, Efrat; Komargodski, Zohar
2016-02-26
We propose an exact formula for the energy radiated by an accelerating quark in N=2 superconformal theories in four dimensions. This formula reproduces the known bremsstrahlung function for N=4 theories and provides a prediction for all the perturbative and instanton corrections in N=2 theories. We perform a perturbative check of our proposal up to three loops. PMID:26967407
Exact Repetition as Input Enhancement in Second Language Acquisition.
ERIC Educational Resources Information Center
Jensen, Eva Dam; Vinther, Thora
2003-01-01
Reports on two studies on input enhancement used to support learners' selection of focus of attention in Spanish second language listening material. Input consisted of video recordings of dialogues between native speakers. Exact repetition and speech rate reduction were examined for effect on comprehension, acquisition of decoding strategies, and…
NASA Astrophysics Data System (ADS)
Käppeli, R.; Mishra, S.
2016-03-01
Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims: We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods: A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved. Results: The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.
Exact Averaging of Stochastic Equations for Flow in Porous Media
Karasaki, Kenzi; Shvidler, Mark; Karasaki, Kenzi
2008-03-15
It is well known that at present, exact averaging of the equations for flow and transport in random porous media have been proposed for limited special fields. Moreover, approximate averaging methods--for example, the convergence behavior and the accuracy of truncated perturbation series--are not well studied, and in addition, calculation of high-order perturbations is very complicated. These problems have for a long time stimulated attempts to find the answer to the question: Are there in existence some, exact, and sufficiently general forms of averaged equations? Here, we present an approach for finding the general exactly averaged system of basic equations for steady flow with sources in unbounded stochastically homogeneous fields. We do this by using (1) the existence and some general properties of Green's functions for the appropriate stochastic problem, and (2) some information about the random field of conductivity. This approach enables us to find the form of the averaged equations without directly solving the stochastic equations or using the usual assumption regarding any small parameters. In the common case of a stochastically homogeneous conductivity field we present the exactly averaged new basic nonlocal equation with a unique kernel-vector. We show that in the case of some type of global symmetry (isotropy, transversal isotropy, or orthotropy), we can for three-dimensional and two-dimensional flow in the same way derive the exact averaged nonlocal equations with a unique kernel-tensor. When global symmetry does not exist, the nonlocal equation with a kernel-tensor involves complications and leads to an ill-posed problem.
Electrolytic plating apparatus for discrete microsized particles
Mayer, Anton
1976-11-30
Method and apparatus are disclosed for electrolytically producing very uniform coatings of a desired material on discrete microsized particles. Agglomeration or bridging of the particles during the deposition process is prevented by imparting a sufficiently random motion to the particles that they are not in contact with a powered cathode for a time sufficient for such to occur.
Electroless plating apparatus for discrete microsized particles
Mayer, Anton
1978-01-01
Method and apparatus are disclosed for producing very uniform coatings of a desired material on discrete microsized particles by electroless techniques. Agglomeration or bridging of the particles during the deposition process is prevented by imparting a sufficiently random motion to the particles that they are not in contact with each other for a time sufficient for such to occur.
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Neutrino mass and mixing with discrete symmetry
NASA Astrophysics Data System (ADS)
King, Stephen F.; Luhn, Christoph
2013-05-01
This is a review paper about neutrino mass and mixing and flavour model building strategies based on discrete family symmetry. After a pedagogical introduction and overview of the whole of neutrino physics, we focus on the PMNS mixing matrix and the latest global fits following the Daya Bay and RENO experiments which measure the reactor angle. We then describe the simple bimaximal, tri-bimaximal and golden ratio patterns of lepton mixing and the deviations required for a non-zero reactor angle, with solar or atmospheric mixing sum rules resulting from charged lepton corrections or residual trimaximal mixing. The different types of see-saw mechanism are then reviewed as well as the sequential dominance mechanism. We then give a mini-review of finite group theory, which may be used as a discrete family symmetry broken by flavons either completely, or with different subgroups preserved in the neutrino and charged lepton sectors. These two approaches are then reviewed in detail in separate chapters including mechanisms for flavon vacuum alignment and different model building strategies that have been proposed to generate the reactor angle. We then briefly review grand unified theories (GUTs) and how they may be combined with discrete family symmetry to describe all quark and lepton masses and mixing. Finally, we discuss three model examples which combine an SU(5) GUT with the discrete family symmetries A4, S4 and Δ(96).
Discrete Gust Model for Launch Vehicle Assessments
NASA Technical Reports Server (NTRS)
Leahy, Frank B.
2008-01-01
Analysis of spacecraft vehicle responses to atmospheric wind gusts during flight is important in the establishment of vehicle design structural requirements and operational capability. Typically, wind gust models can be either a spectral type determined by a random process having a wide range of wavelengths, or a discrete type having a single gust of predetermined magnitude and shape. Classical discrete models used by NASA during the Apollo and Space Shuttle Programs included a 9 m/sec quasi-square-wave gust with variable wavelength from 60 to 300 m. A later study derived discrete gust from a military specification (MIL-SPEC) document that used a "1-cosine" shape. The MIL-SPEC document contains a curve of non-dimensional gust magnitude as a function of non-dimensional gust half-wavelength based on the Dryden spectral model, but fails to list the equation necessary to reproduce the curve. Therefore, previous studies could only estimate a value of gust magnitude from the curve, or attempt to fit a function to it. This paper presents the development of the MIL-SPEC curve, and provides the necessary information to calculate discrete gust magnitudes as a function of both gust half-wavelength and the desired probability level of exceeding a specified gust magnitude.
Fast mix table construction for material discretization
Johnson, S. R.
2013-07-01
An effective hybrid Monte Carlo-deterministic implementation typically requires the approximation of a continuous geometry description with a discretized piecewise-constant material field. The inherent geometry discretization error can be reduced somewhat by using material mixing, where multiple materials inside a discrete mesh voxel are homogenized. Material mixing requires the construction of a 'mix table,' which stores the volume fractions in every mixture so that multiple voxels with similar compositions can reference the same mixture. Mix table construction is a potentially expensive serial operation for large problems with many materials and voxels. We formulate an efficient algorithm to construct a sparse mix table in O(number of voxels x log number of mixtures) time. The new algorithm is implemented in ADVANTG and used to discretize continuous geometries onto a structured Cartesian grid. When applied to an end-of-life MCNP model of the High Flux Isotope Reactor with 270 distinct materials, the new method improves the material mixing time by a factor of 100 compared to a naive mix table implementation. (authors)