NASA Astrophysics Data System (ADS)
Frank, T. D.
2008-06-01
Some elementary properties and examples of Markov processes are reviewed. It is shown that the definition of the Markov property naturally leads to a classification of Markov processes into linear and nonlinear ones.
NASA Astrophysics Data System (ADS)
Saakian, David B.
2012-03-01
We map the Markov-switching multifractal model (MSM) onto the random energy model (REM). The MSM is, like the REM, an exactly solvable model in one-dimensional space with nontrivial correlation functions. According to our results, four different statistical physics phases are possible in random walks with multifractal behavior. We also introduce the continuous branching version of the model, calculate the moments, and prove multiscaling behavior. Different phases have different multiscaling properties.
Computer model of one-dimensional equilibrium controlled sorption processes
Grove, D.B.; Stollenwerk, K.G.
1984-01-01
A numerical solution to the one-dimensional solute-transport equation with equilibrium-controlled sorption and a first-order irreversible-rate reaction is presented. The computer code is written in FORTRAN language, with a variety of options for input and output for user ease. Sorption reactions include Langmuir, Freundlich, and ion-exchange, with or without equal valance. General equations describing transport and reaction processes are solved by finite-difference methods, with nonlinearities accounted for by iteration. Complete documentation of the code, with examples, is included. (USGS)
NASA Technical Reports Server (NTRS)
Smith, R. M.
1991-01-01
Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.
A fast and flexible one-dimensional image processing implementation for visual feedback control
NASA Technical Reports Server (NTRS)
Richardson, Richard W.; Penix, Wayne A.; Richardson, Russell D.
1988-01-01
A simple and efficient image processing system is described which can provide one-dimensional image processing for sample rates approaching video rates. The system is utilized for visual feedback where guidance and process controls are required, such as for arc-welding robots.
Fluctuations and Stochastic Processes in One-Dimensional Many-Body Quantum Systems
Stimming, H.-P.; Mauser, N. J.; Mazets, I. E.
2010-07-02
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.
Modelling and calculation of flotation process in one-dimensional formulation
NASA Astrophysics Data System (ADS)
Amanbaev, Tulegen; Tilleuov, Gamidulla; Tulegenova, Bibigul
2016-08-01
In the framework of the assumptions of the mechanics of the multiphase media is constructed a mathematical model of the flotation process in the dispersed mixture of liquid, solid and gas phases, taking into account the degree of mineralization of the surface of the bubbles. Application of the constructed model is demonstrated on the example of one-dimensional stationary flotation and it is shown that the equations describing the process of ascent of the bubbles are singularly perturbed ("rigid"). The effect of size and concentration of bubbles and the volumetric content of dispersed particles on the flotation process are analyzed.
Itu, Lucian; Sharma, Puneet; Kamen, Ali; Suciu, Constantin; Comaniciu, Dorin
2013-12-01
One-dimensional blood flow models have been used extensively for computing pressure and flow waveforms in the human arterial circulation. We propose an improved numerical implementation based on a graphics processing unit (GPU) for the acceleration of the execution time of one-dimensional model. A novel parallel hybrid CPU-GPU algorithm with compact copy operations (PHCGCC) and a parallel GPU only (PGO) algorithm are developed, which are compared against previously introduced PHCG versions, a single-threaded CPU only algorithm and a multi-threaded CPU only algorithm. Different second-order numerical schemes (Lax-Wendroff and Taylor series) are evaluated for the numerical solution of one-dimensional model, and the computational setups include physiologically motivated non-periodic (Windkessel) and periodic boundary conditions (BC) (structured tree) and elastic and viscoelastic wall laws. Both the PHCGCC and the PGO implementations improved the execution time significantly. The speed-up values over the single-threaded CPU only implementation range from 5.26 to 8.10 × , whereas the speed-up values over the multi-threaded CPU only implementation range from 1.84 to 4.02 × . The PHCGCC algorithm performs best for an elastic wall law with non-periodic BC and for viscoelastic wall laws, whereas the PGO algorithm performs best for an elastic wall law with periodic BC. PMID:24009129
NASA Technical Reports Server (NTRS)
Turco, R. P.; Toon, O. B.; Whitten, R. C.; Keesee, R. G.; Hamill, P.
1982-01-01
A one-dimensional, time-dependent model of tropospheric air composition is developed which incorporates several heterogeneous physical and chemical processes. The model includes the interaction of gases, aerosols, and hydrometeors through the physical mechanisms of nucleation, condensation, evaporation, coagulation, coalescence, and deliquescence. Precipitation, sedimentation, and dry deposition act to remove material from the atmosphere, while chemical transformations occur both in the vapor and the condensed phases. The model also incorporates the sources and vertical diffusion of gases and particles, as well as changes in the solar intensity caused by light-scattering from aerosols and clouds. Preliminary simulations made using this model indicate that rainout and washout processes strongly influence the distributions of tropospheric gases and aerosols under certain conditions.
Few-boson processes in the presence of an attractive impurity under one-dimensional confinement
NASA Astrophysics Data System (ADS)
Mehta, Nirav; Morehead, Connor
2016-05-01
We consider the universal few-body physics of a single light impurity atom (L) interacting with a few heavier atoms (H) under strict one-dimensional confinement with zero-range interactions. Due to the mass imbalance, the system is non-integrable. All universal properties are specified by the mass ratio β =mL /mH and the coupling ratio λ =gHH /gHL , enabling the calculation of few-body ``phase diagrams'' on the λ- β plane. Because the three-body and four-body eigenenergies determine the energy thresholds for inelastic scattering processes involving HL , HHL and HHHL collision partners, we are able to partition the λ- β phase space into regions according to whether or not particular inelastic processes are energetically allowed.
NASA Astrophysics Data System (ADS)
Masugata, Yoshimitsu; Iizuka, Hideyuki; Sato, Kosuke; Nakayama, Takashi
2016-08-01
Fundamental processes of exciton scattering at organic solar-cell interfaces were studied using a one-dimensional tight-binding model and by performing a time-evolution simulation of electron–hole pair wave packets. We found the fundamental features of exciton scattering: the scattering promotes not only the dissociation of excitons and the generation of interface-bound (charge-transferred) excitons but also the transmission and reflection of excitons depending on the electron and hole interface offsets. In particular, the dissociation increases in a certain region of an interface offset, while the transmission shows resonances with higher-energy bound-exciton and interface bound-exciton states. We also studied the effects of carrier-transfer and potential modulations at the interface and the scattering of charged excitons, and we found trap dissociations where one of the carriers is trapped around the interface after the dissociation.
Phase transition of the one-dimensional coagulation-production process
Odor, Geza
2001-06-01
Recently an exact solution has been found by M. Henkel and H. Hinrichsen [J. Phys. A >34, 1561 (2001)] for the one-dimensional coagulation-production process: 2A{r_arrow}A, A0A{r_arrow}3A with equal diffusion and coagulation rates. This model evolves into the inactive phase independently of the production rate with t{sup {minus}1/2} density decay law. This paper shows that cluster mean-field approximations and Monte Carlo simulations predict a continuous phase transition for higher diffusion/coagulation rates as considered by the exact solution. Numerical evidence is given that the phase transition universality agrees with that of the annihilation-fission model with low diffusions.
A compositional framework for Markov processes
NASA Astrophysics Data System (ADS)
Baez, John C.; Fong, Brendan; Pollard, Blake S.
2016-03-01
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.
COCIS: Markov processes in single molecule fluorescence
Talaga, David S.
2009-01-01
This article examines the current status of Markov processes in single molecule fluorescence. For molecular dynamics to be described by a Markov process, the Markov process must include all states involved in the dynamics and the FPT distributions out of those states must be describable by a simple exponential law. The observation of non-exponential first-passage time distributions or other evidence of non-Markovian dynamics is common in single molecule studies and offers an opportunity to expand the Markov model to include new dynamics or states that improve understanding of the system. PMID:19543444
Liang, Hai-Wei; Liu, Jian-Wei; Qian, Hai-Sheng; Yu, Shu-Hong
2013-07-16
Since their detection 20 years ago, carbon nanotubes (CNTs) have captured the interest of scientists, because one-dimensional (1D) nanostructures (nanowires, nanotubes, and nanoribbons) have fascinating physical properties and many potential technological applications. These are materials with structural features limited to the range of 1-100 nm in one dimension, and unlimited in the others. When their size goes down to certain characteristic lengths, such as the Bohr radius, the wavelength of incandescent light, and the phonon mean-free path, quantum mechanical effects can occur. This results in novel optical, magnetic, and electronic characteristics. These physical properties, along with unique transport features in the longitudinal direction and large surface-to-volume ratio, make 1D nanostructures attract extensive attention in both fundamental research and engineering applications. From a synthetic point of view, it is highly desirable to develop a simple route for fabricating 1D nanostructures in large scale at low cost. On the other hand, in order to transfer the intrinsic features of individual 1D nanostructures into macroscopic scale and realize practical applications, we need to explore highly efficient and scalable assembly methods to integrate 1D nanostructures into functional macroscopic architectures. In 2006, our group developed a simple hydrothermal method for synthesizing ultrathin Te nanowires (TeNWs) using conventional chemicals. As we found through systematic study over the past several years, we can use the ultrathin TeNWs as a versatile templating material to fabricate a series of high-quality 1D nanostructures by taking the unique advantages of TeNWs, such as large-scale synthesis, high processability, and high reactivity. The obtained 1D products inherit the dimensional (high aspect ratio) and mechanical (high flexibility) features of the original TeNW templates, thus allowing us to construct macroscopic architectures by using them as
One-dimensional structures of Bi 2O 3 synthesized via metalorganic chemical vapor deposition process
NASA Astrophysics Data System (ADS)
Kim, Hyoun Woo; Myung, Ju Hyun; Shim, Seung Hyun
2006-01-01
We have demonstrated the synthesis of one-dimensional (1D) structures of bismuth oxide (Bi 2O 3) by a reaction of a trimethylbismuth (TMBi) and oxygen (O 2) mixture at 450 °C. Scanning electron microscopy showed that the product consisted of 1D materials with width or diameters less than 1 μm and lengths up to several tens of micrometers. The X-ray energy dispersive spectroscopy revealed that the materials contained elements of Bi and O. The results of X-ray diffraction and selected area electron diffraction pattern indicated that the obtained Bi 2O 3 were crystalline with monoclinic structure.
NASA Astrophysics Data System (ADS)
Grinfeld, Michael; Knight, Philip A.; Wade, Andrew R.
2012-01-01
We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspired by variants of the Bak-Sneppen model of evolution, in which the system represents an evolutionary `fitness landscape' and which is famous as a simple model displaying self-organized criticality. Our main results are concerned with long-time large- N asymptotics for the general model in which, at each time step, K randomly chosen elements are discarded and replaced by independent U[0,1] variables, where the ranks of the elements to be replaced are chosen, independently at each time step, according to a distribution κ N on {1,2,…, N} K . Our main results are that, under appropriate conditions on κ N , the system exhibits threshold behavior at s ∗∈[0,1], where s ∗ is a function of κ N , and the marginal distribution of a randomly selected element converges to U[ s ∗,1] as t→∞ and N→∞. Of this class of models, results in the literature have previously been given for special cases only, namely the `mean-field' or `random neighbor' Bak-Sneppen model. Our proofs avoid the heuristic arguments of some of the previous work and use Foster-Lyapunov ideas. Our results extend existing results and establish their natural, more general context. We derive some more specialized results for the particular case where K=2. One of our technical tools is a result on convergence of stationary distributions for families of uniformly ergodic Markov chains on increasing state-spaces, which may be of independent interest.
Kerstein, A.R.
1996-12-31
One-Dimensional Turbulence is a new turbulence modeling strategy involving an unsteady simulation implemented in one spatial dimension. In one dimension, fine scale viscous and molecular-diffusive processes can be resolved affordably in simulations at high turbulence intensity. The mechanistic distinction between advective and molecular processes is thereby preserved, in contrast to turbulence models presently employed. A stochastic process consisting of mapping {open_quote}events{close_quote} applied to a one-dimensional velocity profile represents turbulent advection. The local event rate for given eddy size is proportional to the velocity difference across the eddy. These properties cause an imposed shear to induce an eddy cascade analogous in many respects to the eddy cascade in turbulent flow. Many scaling and fluctuation properties of self-preserving flows, and of passive scalars introduced into these flows, are reproduced.
Exact Results for a Diffusion-Limited Pair Annihilation Process on a One-Dimensional Lattice
NASA Astrophysics Data System (ADS)
Sasaki, Kazuo; Nakagawa, Tomohiro
2000-05-01
The process of pair annihilation of particles diffusing on a ring ofone-dimensional lattice is studied analytically.A set of master equations for the distribution functions of particlesare solved exactly for the initial condition of uniform, randomdistribution of particles.An explicit expression for the time dependence of the densityof particles is derived from the distribution functions.In the limit of infinite lattice, the present result agreeswith the one obtained by [Balding, Clifford and Green:Phys. Lett. A 126 (1988) 481].
Few-boson processes in the presence of an attractive impurity under one-dimensional confinement
NASA Astrophysics Data System (ADS)
Mehta, N. P.; Morehead, Connor D.
2015-10-01
We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with δ functions, but due to the mass imbalance the problem is nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer scattering lengths, are all calculated in terms of two parameters, namely the mass ratio mL/mH , and ratio gHH/gHL of the δ -function couplings. We specifically identify the values of these ratios for which the atom-dimer or atom-trimer scattering lengths vanish or diverge. We identify regions in this parameter space in which various few-body inelastic processes become energetically allowed. In the Tonks-Girardeau limit (gHH→∞ ), our results are relevant to experiments involving trapped fermions with an impurity atom.
Equivalent Markov processes under gauge group
NASA Astrophysics Data System (ADS)
Caruso, M.; Jarne, C.
2015-11-01
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method to resolve equations, included the case in a previous work in which the sample space is time-dependent [Phys. Rev. E 90, 022125 (2014), 10.1103/PhysRevE.90.022125]. We found a general solution through dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to that in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work, we show how the Markov process in general could be linked via gauge (local) transformations, and we present some illustrative examples for this result.
Equivalent Markov processes under gauge group.
Caruso, M; Jarne, C
2015-11-01
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method to resolve equations, included the case in a previous work in which the sample space is time-dependent [Phys. Rev. E 90, 022125 (2014)]. We found a general solution through dilation of the state space, although the prior probability distribution of the states defined in this new space takes smaller values with respect to that in the initial problem. The gauge (local) group of dilations modifies the distribution on the dilated space to restore the original process. In this work, we show how the Markov process in general could be linked via gauge (local) transformations, and we present some illustrative examples for this result. PMID:26651671
Large deviations for Markov processes with resetting.
Meylahn, Janusz M; Sabhapandit, Sanjib; Touchette, Hugo
2015-12-01
Markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches, foraging, and population dynamics. Here we study the large deviations of time-additive functions or observables of Markov processes with resetting. By deriving a renewal formula linking generating functions with and without resetting, we are able to obtain the rate function of such observables, characterizing the likelihood of their fluctuations in the long-time limit. We consider as an illustration the large deviations of the area of the Ornstein-Uhlenbeck process with resetting. Other applications involving diffusions, random walks, and jump processes with resetting or catastrophes are discussed. PMID:26764673
Emel'yanov, V.S.; Klemin, A.I.; Rabchun, A.V.
1987-06-01
The authors construct a statistical model based on the Markov diffusion process and the Fokker-Planck-Kolmogorov equation for forecasting the remaining service life of reactor components. The model is one-dimensional and allows changes in the probabilistic characteristics of random aging processes of individual mechanical systems to be predicted with sufficient accuracy for engineering purposes.
Markov Processes: Linguistics and Zipf's Law
NASA Astrophysics Data System (ADS)
Kanter, I.; Kessler, D. A.
1995-05-01
It is shown that a 2-parameter random Markov process constructed with N states and biased random transitions gives rise to a stationary distribution where the probabilities of occurrence of the states, P\\(k\\), k = 1,...,N, exhibit the following three universal behaviors which characterize biological sequences and texts in natural languages: (a) the rank-ordered frequencies of occurrence of words are given by Zipf's law P\\(k\\)~1/kρ, where ρ\\(k\\) is slowly increasing for small k; (b) the frequencies of occurrence of letters are given by P\\(k\\) = A-Dln\\(k\\); and (c) long-range correlations are observed over long but finite intervals, as a result of the quasiergodicity of the Markov process.
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.
Generator estimation of Markov jump processes
NASA Astrophysics Data System (ADS)
Metzner, P.; Dittmer, E.; Jahnke, T.; Schütte, Ch.
2007-11-01
Estimating the generator of a continuous-time Markov jump process based on incomplete data is a problem which arises in various applications ranging from machine learning to molecular dynamics. Several methods have been devised for this purpose: a quadratic programming approach (cf. [D.T. Crommelin, E. Vanden-Eijnden, Fitting timeseries by continuous-time Markov chains: a quadratic programming approach, J. Comp. Phys. 217 (2006) 782-805]), a resolvent method (cf. [T. Müller, Modellierung von Proteinevolution, PhD thesis, Heidelberg, 2001]), and various implementations of an expectation-maximization algorithm ([S. Asmussen, O. Nerman, M. Olsson, Fitting phase-type distributions via the EM algorithm, Scand. J. Stat. 23 (1996) 419-441; I. Holmes, G.M. Rubin, An expectation maximization algorithm for training hidden substitution models, J. Mol. Biol. 317 (2002) 753-764; U. Nodelman, C.R. Shelton, D. Koller, Expectation maximization and complex duration distributions for continuous time Bayesian networks, in: Proceedings of the twenty-first conference on uncertainty in AI (UAI), 2005, pp. 421-430; M. Bladt, M. Sørensen, Statistical inference for discretely observed Markov jump processes, J.R. Statist. Soc. B 67 (2005) 395-410]). Some of these methods, however, seem to be known only in a particular research community, and have later been reinvented in a different context. The purpose of this paper is to compile a catalogue of existing approaches, to compare the strengths and weaknesses, and to test their performance in a series of numerical examples. These examples include carefully chosen model problems and an application to a time series from molecular dynamics.
Yan, Yongli; Zhang, Chuang; Yao, Jiannian; Zhao, Yong Sheng
2013-07-19
Many recent activities in the use of one-dimensional nanostructures as photonic elements for optical information processing are explained by huge advantages that photonic circuits possess over traditional silicon-based electronic ones in bandwidth, heat dissipation, and resistance to electromagnetic wave interference. Organic materials are a promising candidate to support these optical-related applications, as they combine the properties of plastics with broad spectral tunability, high optical cross-section, easy fabrication, as well as low cost. Their outstanding compatibility allows organic composite structures which are made of two or more kinds of materials combined together, showing great superiority to single-component materials due to the introduced interactions among multiple constituents, such as energy transfer, electron transfer, exciton coupling, etc. The easy processability of organic 1D crystalline heterostructures enables a fine topological control of both composition and geometry, which offsets the intrinsic deficiencies of individual material. At the same time, the strong exciton-photon coupling and exciton-exciton interaction impart the excellent confinement of photons in organic microstructures, thus light can be manipulated according to our intention to realize specific functions. These collective properties indicate a potential utility of organic heterogeneous material for miniaturized photonic circuitry. Herein, focus is given on recent advances of 1D organic crystalline heterostructures, with special emphasis on the novel design, controllable construction, diverse performance, as well as wide applications in isolated photonic elements for integration. It is proposed that the highly coupled, hybrid optical networks would be an important material basis towards the creation of on-chip optical information processing. PMID:23703829
Non-Markov stochastic processes satisfying equations usually associated with a Markov process
NASA Astrophysics Data System (ADS)
McCauley, J. L.
2012-04-01
There are non-Markov Ito processes that satisfy the Fokker-Planck, backward time Kolmogorov, and Chapman-Kolmogorov equations. These processes are non-Markov in that they may remember an initial condition formed at the start of the ensemble. Some may even admit 1-point densities that satisfy a nonlinear 1-point diffusion equation. However, these processes are linear, the Fokker-Planck equation for the conditional density (the 2-point density) is linear. The memory may be in the drift coefficient (representing a flow), in the diffusion coefficient, or in both. We illustrate the phenomena via exactly solvable examples. In the last section we show how such memory may appear in cooperative phenomena.
Transition-Independent Decentralized Markov Decision Processes
NASA Technical Reports Server (NTRS)
Becker, Raphen; Silberstein, Shlomo; Lesser, Victor; Goldman, Claudia V.; Morris, Robert (Technical Monitor)
2003-01-01
There has been substantial progress with formal models for sequential decision making by individual agents using the Markov decision process (MDP). However, similar treatment of multi-agent systems is lacking. A recent complexity result, showing that solving decentralized MDPs is NEXP-hard, provides a partial explanation. To overcome this complexity barrier, we identify a general class of transition-independent decentralized MDPs that is widely applicable. The class consists of independent collaborating agents that are tied up by a global reward function that depends on both of their histories. We present a novel algorithm for solving this class of problems and examine its properties. The result is the first effective technique to solve optimally a class of decentralized MDPs. This lays the foundation for further work in this area on both exact and approximate solutions.
NASA Astrophysics Data System (ADS)
Ding, Hanqin; Zhang, Jun
2016-05-01
Motivated by recent experimental realization of the tunability of many-body interactions in ultracold fermionic gases trapped in optical lattices, we investigate analytically effects of nearest-neighboring diagonal three-body (T) and four-body (F) couplings on the one-dimensional conventional extended Hubbard model with on-site (U) and inter-site (V) interactions. Applying the bosonization and renormalization-group techniques, we present quantum phase diagrams at half filling and in the weak-coupling regime. The result shows that, whether the three-body or four-body effective attraction may give rise to superconducting phases in the region for repulsive U and V. Besides, the four-body coupling can lead to a bond-spin-density-wave phase for F > 0 and a bond-charge-density-wave phase for F < 0.
Performability analysis using semi-Markov reward processes
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco; Marie, Raymond A.; Sericola, Bruno; Trivedi, Kishor S.
1990-01-01
Beaudry (1978) proposed a simple method of computing the distribution of performability in a Markov reward process. Two extensions of Beaudry's approach are presented. The method is generalized to a semi-Markov reward process by removing the restriction requiring the association of zero reward to absorbing states only. The algorithm proceeds by replacing zero-reward nonabsorbing states by a probabilistic switch; it is therefore related to the elimination of vanishing states from the reachability graph of a generalized stochastic Petri net and to the elimination of fast transient states in a decomposition approach to stiff Markov chains. The use of the approach is illustrated with three applications.
NonMarkov Ito Processes with 1- state memory
NASA Astrophysics Data System (ADS)
McCauley, Joseph L.
2010-08-01
A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.
MODELING PAVEMENT DETERIORATION PROCESSES BY POISSON HIDDEN MARKOV MODELS
NASA Astrophysics Data System (ADS)
Nam, Le Thanh; Kaito, Kiyoyuki; Kobayashi, Kiyoshi; Okizuka, Ryosuke
In pavement management, it is important to estimate lifecycle cost, which is composed of the expenses for repairing local damages, including potholes, and repairing and rehabilitating the surface and base layers of pavements, including overlays. In this study, a model is produced under the assumption that the deterioration process of pavement is a complex one that includes local damages, which occur frequently, and the deterioration of the surface and base layers of pavement, which progresses slowly. The variation in pavement soundness is expressed by the Markov deterioration model and the Poisson hidden Markov deterioration model, in which the frequency of local damage depends on the distribution of pavement soundness, is formulated. In addition, the authors suggest a model estimation method using the Markov Chain Monte Carlo (MCMC) method, and attempt to demonstrate the applicability of the proposed Poisson hidden Markov deterioration model by studying concrete application cases.
Sakai, Hayato; Ohkubo, Kei; Fukuzumi, Shunichi; Hasobe, Taku
2016-02-18
One-dimensional supramolecular columnar phases composed of porphyrins (electron donor: D) and benzo[ghi]perylenetriimides (electron acceptor: A) through triple hydrogen bonds have been successfully constructed to perform sequential light-harvesting and electron-transfer processes. A series of benzo[ghi]peryleneimide derivatives have been synthesized to examine the substituent effects such as imide and nitrile groups on the spectroscopic and electrochemical properties. Then, formation of the 1:1 supramolecular complex between zinc porphyrin and benzo[ghi]perylenetriimide derivatives through triple hydrogen bonds was confirmed by Job's plot of (1) H NMR titration. Next, the one-dimensional supramolecular nanoarrays were successfully prepared in a mixed solvent. X-ray diffraction (XRD) measurement suggested that these nanoarrays contained one-dimensional columnar phases composed of stacked donor and acceptor layers. Finally, femtosecond transient absorption and electron spin resonance (ESR) measurements clearly indicated that photoinduced electron transfer occurred via the singlet excited states in the supramolecular columns. PMID:26766519
NASA Astrophysics Data System (ADS)
Uchiyama, Yusuke; Konno, Hidetoshi
2014-04-01
Defect turbulence described by the one-dimensional complex Ginzburg-Landau equation is investigated and analyzed via a birth-death process of the local structures composed of defects, holes, and modulated amplitude waves (MAWs). All the number statistics of each local structure, in its stationary state, are subjected to Poisson statistics. In addition, the probability density functions of interarrival times of defects, lifetimes of holes, and MAWs show the existence of long-memory and some characteristic time scales caused by zigzag motions of oscillating traveling holes. The corresponding stochastic process for these observations is fully described by a non-Markovian master equation.
One-Dimensionality and Whiteness
ERIC Educational Resources Information Center
Calderon, Dolores
2006-01-01
This article is a theoretical discussion that links Marcuse's concept of one-dimensional society and the Great Refusal with critical race theory in order to achieve a more robust interrogation of whiteness. The author argues that in the context of the United States, the one-dimensionality that Marcuse condemns in "One-Dimensional Man" is best…
NASA Astrophysics Data System (ADS)
Papadimitriou, P.; Skorek, T.
THESUS is a thermohydraulic code for the calculation of steady state and transient processes of two-phase cryogenic flows. The physical model is based on four conservation equations with separate liquid and gas phase mass conservation equations. The thermohydraulic non-equilibrium is calculated by means of evaporation and condensation models. The mechanical non-equilibrium is modeled by a full-range drift-flux model. Also heat conduction in solid structures and heat exchange for the full spectrum of heat transfer regimes can be simulated. Test analyses of two-channel chilldown experiments and comparisons with the measured data have been performed.
Efficient maximum likelihood parameterization of continuous-time Markov processes
McGibbon, Robert T.; Pande, Vijay S.
2015-01-01
Continuous-time Markov processes over finite state-spaces are widely used to model dynamical processes in many fields of natural and social science. Here, we introduce a maximum likelihood estimator for constructing such models from data observed at a finite time interval. This estimator is dramatically more efficient than prior approaches, enables the calculation of deterministic confidence intervals in all model parameters, and can easily enforce important physical constraints on the models such as detailed balance. We demonstrate and discuss the advantages of these models over existing discrete-time Markov models for the analysis of molecular dynamics simulations. PMID:26203016
NASA Astrophysics Data System (ADS)
Jin, Changhyun; Kim, Hyunsu; Park, Sunghoon; An, Soyeon; Lee, Chongmu
2013-11-01
Zinc sulfide (ZnS) nanostructures with different morphologies and microstructures were synthesized using a single thermal evaporation process. The microstructure and photoluminescence properties of the ZnS nanowires produced in four different temperature zones were examined. Scanning electron microscopy showed that as the substrate temperature decreased, the morphology of the ZnS nanowires changed from a longer curved morphology to a shorter earthworm-like morphology. X-ray diffraction (XRD) shows that all samples were mixtures of a zincblende-structured ZnS phase and a wurtzite-structured ZnS phase and that dominance of the zincblende phase tends to increase with decreasing substrate temperature. The zincblende phase appeared to be dominant regardless of the substrate temperature. A closer comparison of the XRD patterns of the products in the different temperature zones showed that dominance of the zincblende phase tends to increase with decreasing substrate temperature. Photoluminescence spectroscopy revealed a decrease in emission intensity with decreasing substrate temperature. ZnS nanostructures synthesized in temperature zones 2, 3 and 4 (∼ 900, ∼ 800 and ∼ 700 °C, respectively) showed green emission, whereas those synthesized in temperature zone 5 (∼ 600 °C) showed yellow emission. The origins of the emissions are also discussed.
NASA Astrophysics Data System (ADS)
Fang, Cheng; Butler, David Lee
2013-05-01
In this paper, an innovative method for CMM (Coordinate Measuring Machine) self-calibration is proposed. In contrast to conventional CMM calibration that relies heavily on a high precision reference standard such as a laser interferometer, the proposed calibration method is based on a low-cost artefact which is fabricated with commercially available precision ball bearings. By optimizing the mathematical model and rearranging the data sampling positions, the experimental process and data analysis can be simplified. In mathematical expression, the samples can be minimized by eliminating the redundant equations among those configured by the experimental data array. The section lengths of the artefact are measured at arranged positions, with which an equation set can be configured to determine the measurement errors at the corresponding positions. With the proposed method, the equation set is short of one equation, which can be supplemented by either measuring the total length of the artefact with a higher-precision CMM or calibrating the single point error at the extreme position with a laser interferometer. In this paper, the latter is selected. With spline interpolation, the error compensation curve can be determined. To verify the proposed method, a simple calibration system was set up on a commercial CMM. Experimental results showed that with the error compensation curve uncertainty of the measurement can be reduced to 50%.
Markov and non-Markov processes in complex systems by the dynamical information entropy
NASA Astrophysics Data System (ADS)
Yulmetyev, R. M.; Gafarov, F. M.
1999-12-01
We consider the Markov and non-Markov processes in complex systems by the dynamical information Shannon entropy (DISE) method. The influence and important role of the two mutually dependent channels of entropy alternation (creation or generation of correlation) and anti-correlation (destroying or annihilation of correlation) have been discussed. The developed method has been used for the analysis of the complex systems of various natures: slow neutron scattering in liquid cesium, psychology (short-time numeral and pattern human memory and effect of stress on the dynamical taping-test), random dynamics of RR-intervals in human ECG (problem of diagnosis of various disease of the human cardio-vascular systems), chaotic dynamics of the parameters of financial markets and ecological systems.
NASA Astrophysics Data System (ADS)
Fletcher, S.
1983-02-01
In this paper we discuss irreversible kinetics on a one-dimensional lattice. We compare the expectation value of the coverage of the lattice, as a function of time, with that predicted by a point-process nucleation-growth-collision model. We conclude that the nucleation-growth-collision model is only applicable to lattice kinetics when the spreading rate of clusters is much greater than their nucleation rate. Although the kinetics of coverage of a one-dimensional lattice are known exactly, the complete solution turns out to be rather complex. In order to facilitate comparison with the point-process nucleation and growth model, we calculate an approximation to the lattice kinetics which is valid when the collision rate of clusters is very fast. The result is complementary to an earlier approximation of McQuarrie, McTague and Reiss, which described the case when the collision rate of clusters was comparable with the spreading rate. We also consider an integral geometrical approach to discreteness effects in lattice models. The general approach which we suggest is to calculate coefficients of variation of the numbers of lattice sites covered by various geometric shapes as a measure of "discreteness". This method uses some mathematical results of Kendall et al.
Inferring parental genomic ancestries using pooled semi-Markov processes
Zou, James Y.; Halperin, Eran; Burchard, Esteban; Sankararaman, Sriram
2015-01-01
Motivation: A basic problem of broad public and scientific interest is to use the DNA of an individual to infer the genomic ancestries of the parents. In particular, we are often interested in the fraction of each parent’s genome that comes from specific ancestries (e.g. European, African, Native American, etc). This has many applications ranging from understanding the inheritance of ancestry-related risks and traits to quantifying human assortative mating patterns. Results: We model the problem of parental genomic ancestry inference as a pooled semi-Markov process. We develop a general mathematical framework for pooled semi-Markov processes and construct efficient inference algorithms for these models. Applying our inference algorithm to genotype data from 231 Mexican trios and 258 Puerto Rican trios where we have the true genomic ancestry of each parent, we demonstrate that our method accurately infers parameters of the semi-Markov processes and parents’ genomic ancestries. We additionally validated the method on simulations. Our model of pooled semi-Markov process and inference algorithms may be of independent interest in other settings in genomics and machine learning. Contact: jazo@microsoft.com PMID:26072482
J. E. O'Brien; M. G. McKellar; G. L. Hawkes; C. M. Stoots
2007-07-01
A one-dimensional chemical equilibrium model has been developed for analysis of simultaneous high-temperature electrolysis of steam and carbon dioxide (coelectrolysis) for the direct production of syngas, a mixture of hydrogen and carbon monoxide. The model assumes local chemical equilibrium among the four process-gas species via the shift reaction. For adiabatic or specified-heat-transfer conditions, the electrolyzer model allows for the determination of coelectrolysis outlet temperature, composition (anode and cathode sides), mean Nernst potential, operating voltage and electrolyzer power based on specified inlet gas flow rates, heat loss or gain, current density, and cell area-specific resistance. Alternately, for isothermal operation, it allows for determination of outlet composition, mean Nernst potential, operating voltage, electrolyzer power, and the isothermal heat requirement for specified inlet gas flow rates, operating temperature, current density and area-specific resistance. This model has been developed for incorporation into a system-analysis code from which the overall performance of large-scale coelectrolysis plants can be evaluated. The one-dimensional co-electrolysis model has been validated by comparison with results obtained from a 3-D computational fluid dynamics model and by comparison with experimental results.
Predictive Rate-Distortion for Infinite-Order Markov Processes
NASA Astrophysics Data System (ADS)
Marzen, Sarah E.; Crutchfield, James P.
2016-05-01
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.
Predictive Rate-Distortion for Infinite-Order Markov Processes
NASA Astrophysics Data System (ADS)
Marzen, Sarah E.; Crutchfield, James P.
2016-06-01
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on finite sequences cannot capture all of their past dependencies. Spectral arguments confirm a popular intuition: algorithms that cluster finite-length sequences fail dramatically when the underlying process has long-range temporal correlations and can fail even for processes generated by finite-memory hidden Markov models. We circumvent the curse of dimensionality in rate-distortion analysis of finite- and infinite-order processes by casting predictive rate-distortion objective functions in terms of the forward- and reverse-time causal states of computational mechanics. Examples demonstrate that the resulting algorithms yield substantial improvements.
MARKOV: A methodology for the solution of infinite time horizon MARKOV decision processes
Williams, B.K.
1988-01-01
Algorithms are described for determining optimal policies for finite state, finite action, infinite discrete time horizon Markov decision processes. Both value-improvement and policy-improvement techniques are used in the algorithms. Computing procedures are also described. The algorithms are appropriate for processes that are either finite or infinite, deterministic or stochastic, discounted or undiscounted, in any meaningful combination of these features. Computing procedures are described in terms of initial data processing, bound improvements, process reduction, and testing and solution. Application of the methodology is illustrated with an example involving natural resource management. Management implications of certain hypothesized relationships between mallard survival and harvest rates are addressed by applying the optimality procedures to mallard population models.
Symbolic Heuristic Search for Factored Markov Decision Processes
NASA Technical Reports Server (NTRS)
Morris, Robert (Technical Monitor); Feng, Zheng-Zhu; Hansen, Eric A.
2003-01-01
We describe a planning algorithm that integrates two approaches to solving Markov decision processes with large state spaces. State abstraction is used to avoid evaluating states individually. Forward search from a start state, guided by an admissible heuristic, is used to avoid evaluating all states. We combine these two approaches in a novel way that exploits symbolic model-checking techniques and demonstrates their usefulness for decision-theoretic planning.
Indexed semi-Markov process for wind speed modeling.
NASA Astrophysics Data System (ADS)
Petroni, F.; D'Amico, G.; Prattico, F.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. In a previous work we proposed different semi-Markov models, showing their ability to reproduce the autocorrelation structures of wind speed data. In that paper we showed also that the autocorrelation is higher with respect to the Markov model. Unfortunately this autocorrelation was still too small compared to the empirical one. In order to overcome the problem of low autocorrelation, in this paper we propose an indexed semi-Markov model. More precisely we assume that wind speed is described by a discrete time homogeneous semi-Markov process. We introduce a memory index which takes into account the periods of different wind activities. With this model the statistical characteristics of wind speed are faithfully reproduced. The wind is a very unstable phenomenon characterized by a sequence of lulls and sustained speeds, and a good wind generator must be able to reproduce such sequences. To check the validity of the predictive semi-Markovian model, the persistence of synthetic winds were calculated, then averaged and computed. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and the time lagged autocorrelation is used to compare statistical properties of the proposed models with those of real data and also with a time series generated though a simple Markov chain. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic generation of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating
Markov decision processes in natural resources management: Observability and uncertainty
Williams, B.K.
2009-01-01
The breadth and complexity of stochastic decision processes in natural resources presents a challenge to analysts who need to understand and use these approaches. The objective of this paper is to describe a class of decision processes that are germane to natural resources conservation and management, namely Markov decision processes, and to discuss applications and computing algorithms under different conditions of observability and uncertainty. A number of important similarities are developed in the framing and evaluation of different decision processes, which can be useful in their applications in natural resources management. The challenges attendant to partial observability are highlighted, and possible approaches for dealing with it are discussed.
Markov decision processes in natural resources management: observability and uncertainty
Williams, Byron K.
2015-01-01
The breadth and complexity of stochastic decision processes in natural resources presents a challenge to analysts who need to understand and use these approaches. The objective of this paper is to describe a class of decision processes that are germane to natural resources conservation and management, namely Markov decision processes, and to discuss applications and computing algorithms under different conditions of observability and uncertainty. A number of important similarities are developed in the framing and evaluation of different decision processes, which can be useful in their applications in natural resources management. The challenges attendant to partial observability are highlighted, and possible approaches for dealing with it are discussed.
Heredity in one-dimensional quadratic maps
NASA Astrophysics Data System (ADS)
Romera, M.; Pastor, G.; Alvarez, G.; Montoya, F.
1998-12-01
In an iterative process, as is the case of a one-dimensional quadratic map, heredity has never been mentioned. In this paper we show that the pattern of a superstable orbit of a one-dimensional quadratic map can be expressed as the sum of the gene of the chaotic band where the pattern is to be found, and the ancestral path that joins all its ancestors. The ancestral path holds all the needed genetic information to calculate the descendants of the pattern. The ancestral path and successive descendant generations of the pattern constitute the family tree of the pattern, which is important to study and understand the orbit's ordering.
NASA Astrophysics Data System (ADS)
Hanesiak, John Michael
Snow covered sea ice plays a crucial role in the earth's climate. This includes polar biology, local, regional and world weather and ocean circulations as well as indigenous people's way of life. Recent research has indicated significant climate change in the polar regions, especially the Canadian arctic. Polar climate processes are also among the most poorly misrepresented within global circulation models (GCMs). The goal of this thesis is to improve our understanding and capability to simulate arctic climate processes in a predictive sense. An electro-thermophysical relationship exists between the thermophysical characteristics (climate variables and processes) and electrical properties (dielectrics) that control microwave remote sensing of snow-covered first- year sea ice (FYI). This work explicitly links microwave dielectrics and a thermodynamic model of snow and sea ice by addressing four key issues. These includes: (1)ensure the existing one-dimensional sea ice models treat the surface energy balance (SEB) and snow/ice thermodynamics in the appropriate time scales we see occurring in field experiments, (2)ensure the snow/ice thermodynamics are not compromised by differences in environmental and spatial representation within components of the SEB, (3)ensure the snow layer is properly handled in the modeling environment, and (4)how we can make use of satellite microwave remote sensing data within the model environment. Results suggest that diurnal processes are critical and need to be accounted for in modeling snow-covered FYI, similar to time scales acting in microwave remote sensing signatures. Output from the coupled snow sea-ice model provides the required input to microwave dielectric models of snow and sea ice to predict microwave penetration depths within the snow and sea ice (an Electro-Thermophysical model of the Snow Sea Ice System (ETSSIS)). Results suggest ETSSIS can accurately simulate microwave penetration depths in the cold dry snow season and
One-Dimensional Grid Turbulence
NASA Astrophysics Data System (ADS)
Kerstein, Alan R.; Nilsen, Vebjørn
1998-11-01
To capture molecular mixing and other small scale phenomena such as chemical reactions and differential diffusion, it is essential to resolve all the length (and time) scales. For large Reynolds number flows this is impossible to do in three-dimensional turbulence simulations with the current and foreseeable future computer technology. To circumvent this problem the one-dimensional turbulence (ODT) model, as the name implies, considers only one spatial dimension in which all the length scales can be resolved even at very large Reynolds numbers. To incorporate the effect of advection on a one-dimensional domain, the evolution of the velocity and scalar profiles is randomly interrupted by a sequence of profile rearrangements representing the effect of turbulent eddies. Results obtained from ODT simulations of grid turbulence with a passive scalar are presented. The decay exponents for the velocity and passive scalar fluctuations, as predicted by ODT, compare favorably with experimental data.
Inferring phenomenological models of Markov processes from data
NASA Astrophysics Data System (ADS)
Rivera, Catalina; Nemenman, Ilya
Microscopically accurate modeling of stochastic dynamics of biochemical networks is hard due to the extremely high dimensionality of the state space of such networks. Here we propose an algorithm for inference of phenomenological, coarse-grained models of Markov processes describing the network dynamics directly from data, without the intermediate step of microscopically accurate modeling. The approach relies on the linear nature of the Chemical Master Equation and uses Bayesian Model Selection for identification of parsimonious models that fit the data. When applied to synthetic data from the Kinetic Proofreading process (KPR), a common mechanism used by cells for increasing specificity of molecular assembly, the algorithm successfully uncovers the known coarse-grained description of the process. This phenomenological description has been notice previously, but this time it is derived in an automated manner by the algorithm. James S. McDonnell Foundation Grant No. 220020321.
Intracellular Ca(2+) release as irreversible Markov process.
Rengifo, Juliana; Rosales, Rafael; González, Adom; Cheng, Heping; Stern, Michael D; Ríos, Eduardo
2002-01-01
In striated muscles, intracellular Ca(2+) release is tightly controlled by the membrane voltage sensor. Ca(2+) ions are necessary mediators of this control in cardiac but not in skeletal muscle, where their role is ill-understood. An intrinsic gating oscillation of Ca(2+) release-not involving the voltage sensor-is demonstrated in frog skeletal muscle fibers under voltage clamp. A Markov model of the Ca(2+) release units is shown to reproduce the oscillations, and it is demonstrated that for Markov processes to have oscillatory transients, its transition rates must violate thermodynamic reversibility. Such irreversibility results in permanent cycling of the units through a ring of states, which requires a source of free energy. Inhibition of the oscillation by 20 to 40 mM EGTA or partial depletion of Ca(2+) in the sarcoplasmic reticulum (SR) identifies the SR [Ca(2+)] gradient as the energy source, and indicates a location of the critical Ca(2+)-sensing site at distances greater than 35 nm from the open channel. These results, which are consistent with a recent demonstration of irreversibility in gating of cardiac Ca(2+) sparks, (Wang, S.-Q., L.-S. Song, L. Xu, G. Meissner, E. G. Lakatta, E. Ríos, M. D. Stern, and H. Cheng. 2002. Biophys. J. 83:242-251) exemplify a cell-wide oscillation caused by coupling between ion permeation and channel gating. PMID:12414685
The exit-time problem for a Markov jump process
Burch, N.; D'Elia, Marta; Lehoucq, Richard B.
2014-12-15
The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.
The exit-time problem for a Markov jump process
NASA Astrophysics Data System (ADS)
Burch, N.; D'Elia, M.; Lehoucq, R. B.
2014-12-01
The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.
One-Dimensional Heat Conduction
Sutton, Steven B.
1992-03-09
ICARUS-LLNL was developed to solve one-dimensional planar, cylindrical, or spherical conduction heat transfer problems. The IBM PC version is a family of programs including ICARUSB, an interactive BASIC heat conduction program; ICARUSF, a FORTRAN heat conduction program; PREICAR, a BASIC preprocessor for ICARUSF; and PLOTIC and CPLOTIC, interpretive BASIC and compiler BASIC plot postprocessor programs. Both ICARUSB and ICARUSF account for multiple material regions and complex boundary conditions, such as convection or radiation. In addition, ICARUSF accounts for temperature-dependent material properties and time or temperature-dependent boundary conditions. PREICAR is a user-friendly preprocessor used to generate or modify ICARUSF input data. PLOTIC and CPLOTIC generate plots of the temperature or heat flux profile at specified times, plots of the variation of temperature or heat flux with time at selected nodes, or plots of the solution grid. First developed in 1974 to allow easy modeling of complex one-dimensional systems, its original application was in the nuclear explosive testing program. Since then it has undergone extensive revision and been applied to problems dealing with laser fusion target fabrication, heat loads on underground tests, magnetic fusion switching tube anodes, and nuclear waste isolation canisters.
One-Dimensional Heat Conduction
Energy Science and Technology Software Center (ESTSC)
1992-03-09
ICARUS-LLNL was developed to solve one-dimensional planar, cylindrical, or spherical conduction heat transfer problems. The IBM PC version is a family of programs including ICARUSB, an interactive BASIC heat conduction program; ICARUSF, a FORTRAN heat conduction program; PREICAR, a BASIC preprocessor for ICARUSF; and PLOTIC and CPLOTIC, interpretive BASIC and compiler BASIC plot postprocessor programs. Both ICARUSB and ICARUSF account for multiple material regions and complex boundary conditions, such as convection or radiation. In addition,more » ICARUSF accounts for temperature-dependent material properties and time or temperature-dependent boundary conditions. PREICAR is a user-friendly preprocessor used to generate or modify ICARUSF input data. PLOTIC and CPLOTIC generate plots of the temperature or heat flux profile at specified times, plots of the variation of temperature or heat flux with time at selected nodes, or plots of the solution grid. First developed in 1974 to allow easy modeling of complex one-dimensional systems, its original application was in the nuclear explosive testing program. Since then it has undergone extensive revision and been applied to problems dealing with laser fusion target fabrication, heat loads on underground tests, magnetic fusion switching tube anodes, and nuclear waste isolation canisters.« less
One-dimensional Quantum Fluids
NASA Astrophysics Data System (ADS)
Gervais, Guillaume
2015-03-01
Fifty year ago, Joachim Mazdak Luttinger generalized the Tomonaga theory of interactions in a one-dimensional metal and show that the prior restrictions imposed by Tomonaga were not necessary. This model is now known as the Tomonaga- Luttinger liquid model (TLL) and most remarkably it does have mathematically exact solutions. In the case of electrons, it predicts that the spin and charge sector should separate, with each of them propagating with their own velocities. While there has been many attempts (some with great success) to observe TLL behaviour in clean quantum wires designed on an ultra-clean semiconductor platform, overall the Luttinger physics is experimentally still in its infancy. For instance, little is known regarding the 1D physics in a strongly-interacting neutral system, whether from the point-of-view of TLL theory or even localization physics. Helium-4, the paradigm superfluid, and Helium-3, the paradigm Fermi liquid, should in principleboth become Luttinger liquids if taken to the one-dimensional limit. In the bosonic case, this is supported by large-scale Quantum Monte Carlo simulations which found that a lengthscale of ~ 2 nm is sufficient for the system to crossover to the 1D regime and display universal Luttinger scaling. At McGill University, an experiment has been constructed to measure the liquid helium mass flow through a single nanopore. The technique consists of drilling a single nanopore in a SiN membrane using a TEM, and then applying a pressure gradient across the membrane. Previously published data in 45nm diameter hole determined the superfluid critical velocity to be close to the limit set by the Feynman vortex rings model. More recent work performed on nanopores with radii as small as 3 nm (and a length of 30nm) show the critical exponent for superfluid velocity to significantly deviate from its bulk value, 2/3. This is an important hint for the crossing over to the one-dimensional state in a strongly-correlated bosonic liquid.
From empirical data to time-inhomogeneous continuous Markov processes.
Lencastre, Pedro; Raischel, Frank; Rogers, Tim; Lind, Pedro G
2016-03-01
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than 60% of tested matrices, typically 80% to 90%, and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed. PMID:27078320
From empirical data to time-inhomogeneous continuous Markov processes
NASA Astrophysics Data System (ADS)
Lencastre, Pedro; Raischel, Frank; Rogers, Tim; Lind, Pedro G.
2016-03-01
We present an approach for testing for the existence of continuous generators of discrete stochastic transition matrices. Typically, existing methods to ascertain the existence of continuous Markov processes are based on the assumption that only time-homogeneous generators exist. Here a systematic extension to time inhomogeneity is presented, based on new mathematical propositions incorporating necessary and sufficient conditions, which are then implemented computationally and applied to numerical data. A discussion concerning the bridging between rigorous mathematical results on the existence of generators to its computational implementation is presented. Our detection algorithm shows to be effective in more than 60 % of tested matrices, typically 80 % to 90 % , and for those an estimate of the (nonhomogeneous) generator matrix follows. We also solve the embedding problem analytically for the particular case of three-dimensional circulant matrices. Finally, a discussion of possible applications of our framework to problems in different fields is briefly addressed.
Hidden Markov model using Dirichlet process for de-identification.
Chen, Tao; Cullen, Richard M; Godwin, Marshall
2015-12-01
For the 2014 i2b2/UTHealth de-identification challenge, we introduced a new non-parametric Bayesian hidden Markov model using a Dirichlet process (HMM-DP). The model intends to reduce task-specific feature engineering and to generalize well to new data. In the challenge we developed a variational method to learn the model and an efficient approximation algorithm for prediction. To accommodate out-of-vocabulary words, we designed a number of feature functions to model such words. The results show the model is capable of understanding local context cues to make correct predictions without manual feature engineering and performs as accurately as state-of-the-art conditional random field models in a number of categories. To incorporate long-range and cross-document context cues, we developed a skip-chain conditional random field model to align the results produced by HMM-DP, which further improved the performance. PMID:26407642
One-dimensional wave turbulence
NASA Astrophysics Data System (ADS)
Zakharov, Vladimir; Dias, Frédéric; Pushkarev, Andrei
2004-08-01
The problem of turbulence is one of the central problems in theoretical physics. While the theory of fully developed turbulence has been widely studied, the theory of wave turbulence has been less studied, partly because it developed later. Wave turbulence takes place in physical systems of nonlinear dispersive waves. In most applications nonlinearity is small and dispersive wave interactions are weak. The weak turbulence theory is a method for a statistical description of weakly nonlinear interacting waves with random phases. It is not surprising that the theory of weak wave turbulence began to develop in connection with some problems of plasma physics as well as of wind waves. The present review is restricted to one-dimensional wave turbulence, essentially because finer computational grids can be used in numerical computations. Most of the review is devoted to wave turbulence in various wave equations, and in particular in a simple one-dimensional model of wave turbulence introduced by Majda, McLaughlin and Tabak in 1997. All the considered equations are model equations, but consequences on physical systems such as ocean waves are discussed as well. The main conclusion is that the range in which the theory of pure weak turbulence is valid is narrow. In general, wave turbulence is not completely weak. Together with the weak turbulence component, it can include coherent structures, such as solitons, quasisolitons, collapses or broad collapses. As a result, weak and strong turbulence coexist. In situations where coherent structures cannot develop, weak turbulence dominates. Even though this is primarily a review paper, new results are presented as well, especially on self-organized criticality and on quasisolitonic turbulence.
Bayesian inference for Markov jump processes with informative observations.
Golightly, Andrew; Wilkinson, Darren J
2015-04-01
In this paper we consider the problem of parameter inference for Markov jump process (MJP) representations of stochastic kinetic models. Since transition probabilities are intractable for most processes of interest yet forward simulation is straightforward, Bayesian inference typically proceeds through computationally intensive methods such as (particle) MCMC. Such methods ostensibly require the ability to simulate trajectories from the conditioned jump process. When observations are highly informative, use of the forward simulator is likely to be inefficient and may even preclude an exact (simulation based) analysis. We therefore propose three methods for improving the efficiency of simulating conditioned jump processes. A conditioned hazard is derived based on an approximation to the jump process, and used to generate end-point conditioned trajectories for use inside an importance sampling algorithm. We also adapt a recently proposed sequential Monte Carlo scheme to our problem. Essentially, trajectories are reweighted at a set of intermediate time points, with more weight assigned to trajectories that are consistent with the next observation. We consider two implementations of this approach, based on two continuous approximations of the MJP. We compare these constructs for a simple tractable jump process before using them to perform inference for a Lotka-Volterra system. The best performing construct is used to infer the parameters governing a simple model of motility regulation in Bacillus subtilis. PMID:25720091
Markov vs. Hurst-Kolmogorov behaviour identification in hydroclimatic processes
NASA Astrophysics Data System (ADS)
Dimitriadis, Panayiotis; Gournari, Naya; Koutsoyiannis, Demetris
2016-04-01
Hydroclimatic processes are usually modelled either by exponential decay of the autocovariance function, i.e., Markovian behaviour, or power type decay, i.e., long-term persistence (or else Hurst-Kolmogorov behaviour). For the identification and quantification of such behaviours several graphical stochastic tools can be used such as the climacogram (i.e., plot of the variance of the averaged process vs. scale), autocovariance, variogram, power spectrum etc. with the former usually exhibiting smaller statistical uncertainty as compared to the others. However, most methodologies including these tools are based on the expected value of the process. In this analysis, we explore a methodology that combines both the practical use of a graphical representation of the internal structure of the process as well as the statistical robustness of the maximum-likelihood estimation. For validation and illustration purposes, we apply this methodology to fundamental stochastic processes, such as Markov and Hurst-Kolmogorov type ones. Acknowledgement: This research is conducted within the frame of the undergraduate course "Stochastic Methods in Water Resources" of the National Technical University of Athens (NTUA). The School of Civil Engineering of NTUA provided moral support for the participation of the students in the Assembly.
Hybrid Nanomaterials: One Dimensional Nanoparticle Assemblies
NASA Astrophysics Data System (ADS)
Sharma, Nikhil; Pochan, Darrin
2007-03-01
One-dimensional nanoparticle assemblies have potential applications in sensing, as plasmon and energy waveguides and in the conduction of novel signals such as phonons and spin states. Herein we present two strategies for the fabrication of such assemblies. Micro and meso-scale particle assemblies have been produced via a coaxial electrospinning process that results in assemblies of particles (silica and silver) encapsulated within a polymer nanofiber (polyethylene oxide). The method has been demonstrated successfully in the creation of 1D assemblies of differently sized silica particles. The effect of change in solution concentrations and relative flow rates in internal and external channels of the coaxial electrospinning apparatus on the structure of these assemblies has been investigated. Nano-scale assemblies of gold particles have been prepared by templating gold nanoparticles on a 20 amino acid peptide that displays laminated morphology. These assemblies are formed as laterally spaced one-dimensional nanoparticle assemblies.
NASA Technical Reports Server (NTRS)
Turco, R. P.; Hamill, P.; Toon, O. B.; Whitten, R. C.; Kiang, C. S.
1979-01-01
A new time-dependent one-dimensional model of the stratospheric sulfate aerosol layer is developed. The model treats atmospheric photochemistry and aerosol physics in detail and includes the interaction between gases and particles explicitly. It is shown that the numerical algorithms used in the model are quite precise. Sensitivity studies and comparison with observations are made. The simulated aerosol physics generates a particle layer with most of the observed properties. The sensitivity of the calculated properties to changes in a large number of aeronomic aerosol parameters is discussed in some detail. The sensitivity analysis reveals areas where the aerosol model is most uncertain. New observations are suggested that might help resolve important questions about the origin of the stratospheric aerosol layer.
Volatility: a hidden Markov process in financial time series.
Eisler, Zoltán; Perelló, Josep; Masoliver, Jaume
2007-11-01
Volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is a time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data by assuming that it is described by a hidden Markov process which together with the price forms a two-dimensional diffusion process. We derive a maximum-likelihood estimate of the volatility path valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are that (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model, (ii) the estimated volatility is related to trading volume by a power law of the form sigma proportional, variant V0.55, and (iii) future returns are proportional to the current volatility, which suggests some degree of predictability for the size of future returns. PMID:18233716
Volatility: A hidden Markov process in financial time series
NASA Astrophysics Data System (ADS)
Eisler, Zoltán; Perelló, Josep; Masoliver, Jaume
2007-11-01
Volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, volatility is unobservable and only the price is known. Diffusion theory has many common points with the research on volatility, the key of the analogy being that volatility is a time-dependent diffusion coefficient of the random walk for the price return. We present a formal procedure to extract volatility from price data by assuming that it is described by a hidden Markov process which together with the price forms a two-dimensional diffusion process. We derive a maximum-likelihood estimate of the volatility path valid for a wide class of two-dimensional diffusion processes. The choice of the exponential Ornstein-Uhlenbeck (expOU) stochastic volatility model performs remarkably well in inferring the hidden state of volatility. The formalism is applied to the Dow Jones index. The main results are that (i) the distribution of estimated volatility is lognormal, which is consistent with the expOU model, (ii) the estimated volatility is related to trading volume by a power law of the form σ∝V0.55 , and (iii) future returns are proportional to the current volatility, which suggests some degree of predictability for the size of future returns.
Dynamical symmetries of Markov processes with multiplicative white noise
NASA Astrophysics Data System (ADS)
Aron, Camille; Barci, Daniel G.; Cugliandolo, Leticia F.; González Arenas, Zochil; Lozano, Gustavo S.
2016-05-01
We analyse various properties of stochastic Markov processes with multiplicative white noise. We take a single-variable problem as a simple example, and we later extend the analysis to the Landau–Lifshitz–Gilbert equation for the stochastic dynamics of a magnetic moment. In particular, we focus on the non-equilibrium transfer of angular momentum to the magnetization from a spin-polarised current of electrons, a technique which is widely used in the context of spintronics to manipulate magnetic moments. We unveil two hidden dynamical symmetries of the generating functionals of these Markovian multiplicative white-noise processes. One symmetry only holds in equilibrium and we use it to prove generic relations such as the fluctuation-dissipation theorems. Out of equilibrium, we take profit of the symmetry-breaking terms to prove fluctuation theorems. The other symmetry yields strong dynamical relations between correlation and response functions which can notably simplify the numerical analysis of these problems. Our construction allows us to clarify some misconceptions on multiplicative white-noise stochastic processes that can be found in the literature. In particular, we show that a first-order differential equation with multiplicative white noise can be transformed into an additive-noise equation, but that the latter keeps a non-trivial memory of the discretisation prescription used to define the former.
One-dimensional silicone nanofilaments.
Artus, Georg R J; Seeger, Stefan
2014-07-01
A decade ago one-dimensional silicone nanofilaments (1D-SNF) such as fibres and wires were described for the first time. Since then, the exploration of 1D-SNF has led to remarkable advancements with respect to material science and surface science: one-, two- and three-dimensional nanostructures of silicone were unknown before. The discovery of silicone nanostructures marks a turning point in the research on the silicone material at the nanoscale. Coatings made of 1D-SNF are among the most superhydrophobic surfaces known today. They are free of fluorine, can be applied to a large range of technologically important materials and their properties can be modified chemically. This opens the way to many interesting applications such as water harvesting, superoleophobicity, separation of oil and water, patterned wettability and storage and manipulation of data on a surface. Because of their high surface area, coatings consisting of 1D-SNF are used for protein adsorption experiments and as carrier systems for catalytically active nanoparticles. This paper reviews the current knowledge relating to the broad development of 1D-SNF technologies. Common preparation and coating techniques are presented along with a comparison and discussion of the published coating parameters to provide an insight on how these affect the topography of the 1D-SNF or coating. The proposed mechanisms of growth are presented, and their potentials and shortcomings are discussed. We introduce all explored applications and finally identify future prospects and potentials of 1D-SNF with respect to applications in material science and surface science. PMID:24742356
Optimal Control of Markov Processes with Age-Dependent Transition Rates
Ghosh, Mrinal K. Saha, Subhamay
2012-10-15
We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite horizon average cost problems. Our approach is via the construction of an equivalent semi-Markov decision process. We characterise the value function and optimal controls for both discounted and average cost cases.
Modeling sediment transport as a spatio-temporal Markov process.
NASA Astrophysics Data System (ADS)
Heyman, Joris; Ancey, Christophe
2014-05-01
Despite a century of research about sediment transport by bedload occuring in rivers, its constitutive laws remain largely unknown. The proof being that our ability to predict mid-to-long term transported volumes within reasonable confidence interval is almost null. The intrinsic fluctuating nature of bedload transport may be one of the most important reasons why classical approaches fail. Microscopic probabilistic framework has the advantage of taking into account these fluctuations at the particle scale, to understand their effect on the macroscopic variables such as sediment flux. In this framework, bedload transport is seen as the random motion of particles (sand, gravel, pebbles...) over a two-dimensional surface (the river bed). The number of particles in motion, as well as their velocities, are random variables. In this talk, we show how a simple birth-death Markov model governing particle motion on a regular lattice accurately reproduces the spatio-temporal correlations observed at the macroscopic level. Entrainment, deposition and transport of particles by the turbulent fluid (air or water) are supposed to be independent and memoryless processes that modify the number of particles in motion. By means of the Poisson representation, we obtained a Fokker-Planck equation that is exactly equivalent to the master equation and thus valid for all cell sizes. The analysis shows that the number of moving particles evolves locally far from thermodynamic equilibrium. Several analytical results are presented and compared to experimental data. The index of dispersion (or variance over mean ratio) is proved to grow from unity at small scales to larger values at larger scales confirming the non Poisonnian behavior of bedload transport. Also, we study the one and two dimensional K-function, which gives the average number of moving particles located in a ball centered at a particle centroid function of the ball's radius.
Students' Progress throughout Examination Process as a Markov Chain
ERIC Educational Resources Information Center
Hlavatý, Robert; Dömeová, Ludmila
2014-01-01
The paper is focused on students of Mathematical methods in economics at the Czech university of life sciences (CULS) in Prague. The idea is to create a model of students' progress throughout the whole course using the Markov chain approach. Each student has to go through various stages of the course requirements where his success depends on the…
Lee, Lee-Min; Jean, Fu-Rong
2016-08-01
The hidden Markov models have been widely applied to systems with sequential data. However, the conditional independence of the state outputs will limit the output of a hidden Markov model to be a piecewise constant random sequence, which is not a good approximation for many real processes. In this paper, a high-order hidden Markov model for piecewise linear processes is proposed to better approximate the behavior of a real process. A parameter estimation method based on the expectation-maximization algorithm was derived for the proposed model. Experiments on speech recognition of noisy Mandarin digits were conducted to examine the effectiveness of the proposed method. Experimental results show that the proposed method can reduce the recognition error rate compared to a baseline hidden Markov model. PMID:27586781
NASA Astrophysics Data System (ADS)
Janson, N. B.; Balanov, A. G.; Anishchenko, V. S.; McClintock, P. V.
2002-03-01
The recently proposed approach to detect synchronization from univariate data is applied to heart-rate-variability (HRV) data from ten healthy humans. The approach involves introducing angles for return times map and studying their behavior. For filtered human HRV data, it is demonstrated that: (i) in many of the subjects studied, interactions between different processes within the cardiovascular system can be considered as weak, and the angles can be well described by the derived model; (ii) in some of the subjects the strengths of the interactions between the processes are sufficiently large that the angles map has a distinctive structure, which is not captured by our model; (iii) synchronization between the processes involved can often be detected; (iv) the instantaneous radii are rather disordered.
Wang, Yu; Li, Yang; Zhu, Weigang; Liu, Jinyu; Zhang, Xiaotao; Li, Rongjin; Zhen, Yonggang; Dong, Huanli; Hu, Wenping
2016-08-11
In this study, 1D nanocrystals composed of C60 and corannulene were synthesized efficiently through cocrystallization by a solution process. These 1D nanocrystals display high electron transport characteristics of up to 0.11 cm(2) V(-1) s(-1) and good photoresponse of 0.09 A W(-1), indicating their potential applications in optoelectronics. The results suggest that co-crystal engineering provides a novel strategy for the rational design of new carbon-based crystalline nanomaterials. PMID:27480136
One-Dimensional Photonic Crystal Superprisms
NASA Technical Reports Server (NTRS)
Ting, David
2005-01-01
Theoretical calculations indicate that it should be possible for one-dimensional (1D) photonic crystals (see figure) to exhibit giant dispersions known as the superprism effect. Previously, three-dimensional (3D) photonic crystal superprisms have demonstrated strong wavelength dispersion - about 500 times that of conventional prisms and diffraction gratings. Unlike diffraction gratings, superprisms do not exhibit zero-order transmission or higher-order diffraction, thereby eliminating cross-talk problems. However, the fabrication of these 3D photonic crystals requires complex electron-beam substrate patterning and multilayer thin-film sputtering processes. The proposed 1D superprism is much simpler in structural complexity and, therefore, easier to design and fabricate. Like their 3D counterparts, the 1D superprisms can exhibit giant dispersions over small spectral bands that can be tailored by judicious structure design and tuned by varying incident beam direction. Potential applications include miniature gas-sensing devices.
One-Dimensional Czedli-Type Islands
ERIC Educational Resources Information Center
Horvath, Eszter K.; Mader, Attila; Tepavcevic, Andreja
2011-01-01
The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.
One dimensional representations in quantum optics
NASA Technical Reports Server (NTRS)
Janszky, J.; Adam, P.; Foldesi, I.; Vinogradov, An. V.
1993-01-01
The possibility of representing the quantum states of a harmonic oscillator not on the whole alpha-plane but on its one dimensional manifolds is considered. It is shown that a simple Gaussian distribution along a straight line describes a quadrature squeezed state while a similar Gaussian distribution along a circle leads to the amplitude squeezed state. The connection between the one dimensional representations and the usual Glauber representation is discussed.
Likelihood free inference for Markov processes: a comparison.
Owen, Jamie; Wilkinson, Darren J; Gillespie, Colin S
2015-04-01
Approaches to Bayesian inference for problems with intractable likelihoods have become increasingly important in recent years. Approximate Bayesian computation (ABC) and "likelihood free" Markov chain Monte Carlo techniques are popular methods for tackling inference in these scenarios but such techniques are computationally expensive. In this paper we compare the two approaches to inference, with a particular focus on parameter inference for stochastic kinetic models, widely used in systems biology. Discrete time transition kernels for models of this type are intractable for all but the most trivial systems yet forward simulation is usually straightforward. We discuss the relative merits and drawbacks of each approach whilst considering the computational cost implications and efficiency of these techniques. In order to explore the properties of each approach we examine a range of observation regimes using two example models. We use a Lotka-Volterra predator-prey model to explore the impact of full or partial species observations using various time course observations under the assumption of known and unknown measurement error. Further investigation into the impact of observation error is then made using a Schlögl system, a test case which exhibits bi-modal state stability in some regions of parameter space. PMID:25720092
Post processing with first- and second-order hidden Markov models
NASA Astrophysics Data System (ADS)
Taghva, Kazem; Poudel, Srijana; Malreddy, Spandana
2013-01-01
In this paper, we present the implementation and evaluation of first order and second order Hidden Markov Models to identify and correct OCR errors in the post processing of books. Our experiments show that the first order model approximately corrects 10% of the errors with 100% precision, while the second order model corrects a higher percentage of errors with much lower precision.
One-dimensional Gromov minimal filling problem
Ivanov, Alexandr O; Tuzhilin, Alexey A
2012-05-31
The paper is devoted to a new branch in the theory of one-dimensional variational problems with branching extremals, the investigation of one-dimensional minimal fillings introduced by the authors. On the one hand, this problem is a one-dimensional version of a generalization of Gromov's minimal fillings problem to the case of stratified manifolds. On the other hand, this problem is interesting in itself and also can be considered as a generalization of another classical problem, the Steiner problem on the construction of a shortest network connecting a given set of terminals. Besides the statement of the problem, we discuss several properties of the minimal fillings and state several conjectures. Bibliography: 38 titles.
One-Dimensional Oscillator in a Box
ERIC Educational Resources Information Center
Amore, Paolo; Fernandez, Francisco M.
2010-01-01
We discuss a quantum-mechanical model of two particles that interact by means of a harmonic potential and are confined to a one-dimensional box with impenetrable walls. We apply perturbation theory to the cases of different and equal masses and analyse the symmetry of the states in the latter case. We compare the approximate perturbation results…
One-Dimensional Wavefront Sensor Analysis
Energy Science and Technology Software Center (ESTSC)
1996-04-25
This software analyzes one-dimensional wavefront sensor data acquired with any of several data acquisition systems. It analyzes the data to determine centroids, wavefront slopes and overall wavefront error. The data can be displayed in many formats, with plots of various parameters vs time and position, including computer generated movies. Data can also be exported for use by other programs.
Hybrid surface-relief/volume one dimensional holographic gratings
NASA Astrophysics Data System (ADS)
Lucchetta, D. E.; Spegni, P.; Di Donato, A.; Simoni, F.; Castagna, R.
2015-04-01
Many one dimensional optically patterned photopolymers exist as surface relief or volume phase gratings. However, as far as we know, holographically recorded acrylate-based gratings in which both configurations are present are not described in literature. In this work we report a two steps fabrication process in which a large-area high-resolution hybrid volume/surface relief grating phase gratings is created in a thin film of multiacrylate material spinned on a proper designed substrate. Optical and morphological investigations, made on the optically patterned area, confirm the presence of a one dimensional double (surface relief and Bragg volume phase) periodic structure.
One-Dimensional SO2 Predictions for Duct Injection
Energy Science and Technology Software Center (ESTSC)
1993-10-05
DIAN1D is a one-dimensional model that predicts SO2 absorption by slurry droplets injected into a flue gas stream with two-fluid atomizers. DIANUI is an interactive user interface for DIAN1D. It prepares the input file for DIAN1D from plant design specifications and process requirements.
Transition density of one-dimensional diffusion with discontinuous drift
NASA Technical Reports Server (NTRS)
Zhang, Weijian
1990-01-01
The transition density of a one-dimensional diffusion process with a discontinuous drift coefficient is studied. A probabilistic representation of the transition density is given, illustrating the close connections between discontinuities of the drift and Brownian local times. In addition, some explicit results are obtained based on the trivariate density of Brownian motion, its occupation, and local times.
Transient One-dimensional Pipe Flow Analyzer
Energy Science and Technology Software Center (ESTSC)
1986-04-08
TOPAZ-SNLL, the Transient One- dimensional Pipe flow AnalyZer code, is a user-friendly computer program for modeling the heat transfer, fluid mechanics, and thermodynamics of multi-species gas transfer in arbitrary arrangements of pipes, valves, vessels, and flow branches. Although the flow conservation equations are assumed to be one-dimensional and transient, multidimensional features of internal fluid flow and heat transfer may be accounted for using the available quasi-steady flow correlations (e.g., Moody friction factor correlation and variousmore » form loss and heat transfer correlations). Users may also model the effects of moving system boundaries such as pistons, diaphragms, and bladders. The features of fully compressible flow are modeled, including the propagation of shocks and rarefaction waves, as well as the establishment of multiple choke points along the flow path.« less
Transient One-dimensional Pipe Flow Analyzer
1986-04-08
TOPAZ-SNLL, the Transient One- dimensional Pipe flow AnalyZer code, is a user-friendly computer program for modeling the heat transfer, fluid mechanics, and thermodynamics of multi-species gas transfer in arbitrary arrangements of pipes, valves, vessels, and flow branches. Although the flow conservation equations are assumed to be one-dimensional and transient, multidimensional features of internal fluid flow and heat transfer may be accounted for using the available quasi-steady flow correlations (e.g., Moody friction factor correlation and various form loss and heat transfer correlations). Users may also model the effects of moving system boundaries such as pistons, diaphragms, and bladders. The features of fully compressible flow are modeled, including the propagation of shocks and rarefaction waves, as well as the establishment of multiple choke points along the flow path.
NASA Astrophysics Data System (ADS)
Kubo, Hisahiko; Dhakal, Yadab P.; Suzuki, Wataru; Kunugi, Takashi; Aoi, Shin; Fujiwara, Hiroyuki
2016-02-01
The source rupture process of the 2015 Gorkha, Nepal, earthquake was estimated by the joint kinematic source inversion with near-field waveforms, teleseismic waveforms, and geodetic data. The estimated seismic moment and maximum slip are 7.5 × 1020 Nm ( M w 7.9) and 7.3 m, respectively. The total source duration is approximately 50 s. The derived source model has a unilateral rupture toward the east and a large-slip area north of Kathmandu with the maximum slip. Using the estimated source model together with a one-dimensional (1-D) velocity basin structure model, long-period (> 4 s) ground motions were simulated at a site located in the Kathmandu basin, where strong ground motions with predominant components in a 4-5s period were observed during the 2015 Gorkha earthquake. This simulation demonstrated that the major features of the observed waveforms can be reproduced by our source model and the 1-D basin structure model.
A fast exact simulation method for a class of Markov jump processes
Li, Yao; Hu, Lili
2015-11-14
A new method of the stochastic simulation algorithm (SSA), named the Hashing-Leaping method (HLM), for exact simulations of a class of Markov jump processes, is presented in this paper. The HLM has a conditional constant computational cost per event, which is independent of the number of exponential clocks in the Markov process. The main idea of the HLM is to repeatedly implement a hash-table-like bucket sort algorithm for all times of occurrence covered by a time step with length τ. This paper serves as an introduction to this new SSA method. We introduce the method, demonstrate its implementation, analyze its properties, and compare its performance with three other commonly used SSA methods in four examples. Our performance tests and CPU operation statistics show certain advantages of the HLM for large scale problems.
NASA Astrophysics Data System (ADS)
Nguyen, Tuyen Van; Liu, Yuedan; Jung, Il-Hyo; Chon, Tae-Soo; Lee, Sang-Hee
Revealing biological responses of organisms in responding to environmental stressors is the critical issue in contemporary ecological sciences. Markov processes in behavioral data were unraveled by utilizing the hidden Markov model (HMM). Individual organisms of daphnia (Daphnia magna) and zebrafish (Danio rerio) were exposed to diazinon at low concentrations. The transition probability matrix (TPM) and the emission probability matrix (EPM) were accordingly estimated by training with the HMM and were verified before and after the treatments with 10-6 tolerance in 103 iterations. Structured property in behavioral changes was accordingly revealed to characterize dynamic processes in movement patterns. Parameters and sequences produced through the HMM training could be a suitable means of monitoring toxic chemicals in environment.
An Overview of Markov Chain Methods for the Study of Stage-Sequential Developmental Processes
ERIC Educational Resources Information Center
Kapland, David
2008-01-01
This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model.…
Wave turbulence in one-dimensional models
NASA Astrophysics Data System (ADS)
Zakharov, V. E.; Guyenne, P.; Pushkarev, A. N.; Dias, F.
2001-05-01
A two-parameter nonlinear dispersive wave equation proposed by Majda, McLaughlin and Tabak is studied analytically and numerically as a model for the study of wave turbulence in one-dimensional systems. Our ultimate goal is to test the validity of weak turbulence theory. Although weak turbulence theory is independent on the sign of the nonlinearity of the model, the numerical results show a strong dependence on the sign of the nonlinearity. A possible explanation for this discrepancy is the strong influence of coherent structures - wave collapses and quasisolitons - in wave turbulence.
One-dimensional hypersonic phononic crystals.
Gomopoulos, N; Maschke, D; Koh, C Y; Thomas, E L; Tremel, W; Butt, H-J; Fytas, G
2010-03-10
We report experimental observation of a normal incidence phononic band gap in one-dimensional periodic (SiO(2)/poly(methyl methacrylate)) multilayer film at gigahertz frequencies using Brillouin spectroscopy. The band gap to midgap ratio of 0.30 occurs for elastic wave propagation along the periodicity direction, whereas for inplane propagation the system displays an effective medium behavior. The phononic properties are well captured by numerical simulations. The porosity in the silica layers presents a structural scaffold for the introduction of secondary active media for potential coupling between phonons and other excitations, such as photons and electrons. PMID:20141118
A mixed model for two-state Markov processes under panel observation.
Cook, R J
1999-09-01
Many chronic medical conditions can be meaningfully characterized in terms of a two-state stochastic process. Here we consider the problem in which subjects make transitions among two such states in continuous time but are only observed at discrete, irregularly spaced time points that are possibly unique to each subject. Data arising from such an observation scheme are called panel data, and methods for related analyses are typically based on Markov assumptions. The purpose of this article is to present a conditionally Markov model that accommodates subject-to-subject variation in the model parameters by the introduction of random effects. We focus on a particular random effects formulation that generates a closed-form expression for the marginal likelihood. The methodology is illustrated by application to a data set from a parasitic field infection survey. PMID:11315028
NASA Astrophysics Data System (ADS)
Gosavi, Abhijit
2014-08-01
In control systems theory, the Markov decision process (MDP) is a widely used optimization model involving selection of the optimal action in each state visited by a discrete-event system driven by Markov chains. The classical MDP model is suitable for an agent/decision-maker interested in maximizing expected revenues, but does not account for minimizing variability in the revenues. An MDP model in which the agent can maximize the revenues while simultaneously controlling the variance in the revenues is proposed. This work is rooted in machine learning/neural network concepts, where updating is based on system feedback and step sizes. First, a Bellman equation for the problem is proposed. Thereafter, convergent dynamic programming and reinforcement learning techniques for solving the MDP are provided along with encouraging numerical results on a small MDP and a preventive maintenance problem.
A reward semi-Markov process with memory for wind speed modeling
NASA Astrophysics Data System (ADS)
Petroni, F.; D'Amico, G.; Prattico, F.
2012-04-01
-order Markov chain with different number of states, and Weibull distribution. All this model use Markov chains to generate synthetic wind speed time series but the search for a better model is still open. Approaching this issue, we applied new models which are generalization of Markov models. More precisely we applied semi-Markov models to generate synthetic wind speed time series. The primary goal of this analysis is the study of the time history of the wind in order to assess its reliability as a source of power and to determine the associated storage levels required. In order to assess this issue we use a probabilistic model based on indexed semi-Markov process [4] to which a reward structure is attached. Our model is used to calculate the expected energy produced by a given turbine and its variability expressed by the variance of the process. Our results can be used to compare different wind farms based on their reward and also on the risk of missed production due to the intrinsic variability of the wind speed process. The model is used to generate synthetic time series for wind speed by means of Monte Carlo simulations and backtesting procedure is used to compare results on first and second oder moments of rewards between real and synthetic data. [1] A. Shamshad, M.A. Bawadi, W.M.W. Wan Hussin, T.A. Majid, S.A.M. Sanusi, First and second order Markov chain models for synthetic gen- eration of wind speed time series, Energy 30 (2005) 693-708. [2] H. Nfaoui, H. Essiarab, A.A.M. Sayigh, A stochastic Markov chain model for simulating wind speed time series at Tangiers, Morocco, Re- newable Energy 29 (2004) 1407-1418. [3] F. Youcef Ettoumi, H. Sauvageot, A.-E.-H. Adane, Statistical bivariate modeling of wind using first-order Markov chain and Weibull distribu- tion, Renewable Energy 28 (2003) 1787-1802. [4]F. Petroni, G. D'Amico, F. Prattico, Indexed semi-Markov process for wind speed modeling. To be submitted.
The one-dimensional hydrogen atom revisited
NASA Astrophysics Data System (ADS)
Palma, G.; Raff, U.
2006-09-01
The one-dimensional Schrodinger hydrogen atom is an interesting mathematical and physical problem for the study of bound states, eigenfunctions, and quantum-degeneracy issues. This one-dimensional physical system has given rise to some intriguing controversy for more than four decades. Presently, still no definite consensus seems to have been reached. We reanalyzed this apparently controversial problem, approaching it from a Fourier-transform representation method combined with some fundamental (basic) ideas found in self-adjoint extensions of symmetric operators. In disagreement with some previous claims, we found that the complete Balmer energy spectrum is obtained together with an odd-parity set of eigenfunctions. Closed-form solutions in both coordinate and momentum spaces were obtained. No twofold degeneracy was observed as predicted by the degeneracy theorem in one dimension, though it does not necessarily have to hold for potentials with singularities. No ground state with infinite energy exists since the corresponding eigenfunction does not satisfy the Schrodinger equation at the origin.
Analysis of nonstationary signals and fields with the use of enclosed semi-Markov processes
NASA Astrophysics Data System (ADS)
Kravchenko, V. F.; Lutsenko, V. I.; Masalov, S. A.; Pustovoit, V. I.
2013-11-01
In this study, the possibility to describe the signals scattered by various physical objects such as underlying surfaces of land and sea, the segments of "clear sky," and processes of various physical natures, such as fluctuations of the refractive index of the troposphere and electromagnetic and acoustic radiation of a lithospheric nature, by enclosed semi-Markov processes is investigated. This approach makes it possible to construct statistic models for a broad class of signals and processes. In some cases, statistics based on atomic functions and WA systems of the Kravchenko-Rvachev functions show the best results.
Three one-dimensional structural heating programs
NASA Technical Reports Server (NTRS)
Wing, L. D.
1978-01-01
Two computer programs for calculating profiles in a ten-element structure consisting of up to ten materials are presented, along with a third program for calculating the mean temperature for a payload container placed in an orbiting vehicle cargo bay. The three programs are related by the sharing of a common analytical technique; the energy balance is based upon one-dimensional heat transfer. The first program, NQLDW112, assumes a non-ablating surface. NQLDW117 is very similar but allows the outermost element to ablate. NQLDW040 calculates an average temperature profile through an idealized model of the real payload cannister and contents in the cargo bay of an orbiting vehicle.
Aperiodicity in one-dimensional cellular automata
Jen, E.
1990-01-01
Cellular automata are a class of mathematical systems characterized by discreteness (in space, time, and state values), determinism, and local interaction. A certain class of one-dimensional, binary site-valued, nearest-neighbor automata is shown to generate infinitely many aperiodic temporal sequences from arbitrary finite initial conditions on an infinite lattice. The class of automaton rules that generate aperiodic temporal sequences are characterized by a particular form of injectivity in their interaction rules. Included are the nontrivial linear'' automaton rules (that is, rules for which the superposition principle holds); certain nonlinear automata that retain injectivity properties similar to those of linear automata; and a wider subset of nonlinear automata whose interaction rules satisfy a weaker form of injectivity together with certain symmetry conditions. A technique is outlined here that maps this last set of automata onto a linear automaton, and thereby establishes the aperiodicity of their temporal sequences. 12 refs., 3 figs.
Superfluid helium-4 in one dimensional channel
NASA Astrophysics Data System (ADS)
Kim, Duk Y.; Banavar, Samhita; Chan, Moses H. W.; Hayes, John; Sazio, Pier
2013-03-01
Superfluidity, as superconductivity, cannot exist in a strict one-dimensional system. However, the experiments employing porous media showed that superfluid helium can flow through the pores of nanometer size. Here we report a study of the flow of liquid helium through a single hollow glass fiber of 4 cm in length with an open id of 150 nm between 1.6 and 2.3 K. We found the superfluid transition temperature was suppressed in the hollow cylinder and that there is no flow above the transition. Critical velocity at temperature below the transition temperature was determined. Our results bear some similarity to that found by Savard et. al. studying the flow of helium through a nanohole in a silicon nitrite membrane. Experimental study at Penn State is supported by NSF Grants No. DMR 1103159.
Unitary equivalent classes of one-dimensional quantum walks
NASA Astrophysics Data System (ADS)
Ohno, Hiromichi
2016-06-01
This study investigates unitary equivalent classes of one-dimensional quantum walks. We prove that one-dimensional quantum walks are unitary equivalent to quantum walks of Ambainis type and that translation-invariant one-dimensional quantum walks are Szegedy walks. We also present a necessary and sufficient condition for a one-dimensional quantum walk to be a Szegedy walk.
Assessing the inherent uncertainty of one-dimensional diffusions
NASA Astrophysics Data System (ADS)
Eliazar, Iddo; Cohen, Morrel H.
2013-01-01
In this paper we assess the inherent uncertainty of one-dimensional diffusion processes via a stochasticity classification which provides an à la Mandelbrot categorization into five states of uncertainty: infra-mild, mild, borderline, wild, and ultra-wild. Two settings are considered. (i) Stopped diffusions: the diffusion initiates from a high level and is stopped once it first reaches a low level; in this setting we analyze the inherent uncertainty of the diffusion's maximal exceedance above its initial high level. (ii) Stationary diffusions: the diffusion is in dynamical statistical equilibrium; in this setting we analyze the inherent uncertainty of the diffusion's equilibrium level. In both settings general closed-form analytic results are established, and their application is exemplified by stock prices in the stopped-diffusions setting, and by interest rates in the stationary-diffusions setting. These results provide a highly implementable decision-making tool for the classification of uncertainty in the context of one-dimensional diffusions.
Cryptography using multiple one-dimensional chaotic maps
NASA Astrophysics Data System (ADS)
Pareek, N. K.; Patidar, Vinod; Sud, K. K.
2005-10-01
Recently, Pareek et al. [Phys. Lett. A 309 (2003) 75] have developed a symmetric key block cipher algorithm using a one-dimensional chaotic map. In this paper, we propose a symmetric key block cipher algorithm in which multiple one-dimensional chaotic maps are used instead of a one-dimensional chaotic map. However, we also use an external secret key of variable length (maximum 128-bits) as used by Pareek et al. In the present cryptosystem, plaintext is divided into groups of variable length (i.e. number of blocks in each group is different) and these are encrypted sequentially by using randomly chosen chaotic map from a set of chaotic maps. For block-by-block encryption of variable length group, number of iterations and initial condition for the chaotic maps depend on the randomly chosen session key and encryption of previous block of plaintext, respectively. The whole process of encryption/decryption is governed by two dynamic tables, which are updated time to time during the encryption/decryption process. Simulation results show that the proposed cryptosystem requires less time to encrypt the plaintext as compared to the existing chaotic cryptosystems and further produces the ciphertext having flat distribution of same size as the plaintext.
A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes
NASA Technical Reports Server (NTRS)
Carpenter, Russell; Lee, Taesul
2008-01-01
Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.
Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks
NASA Astrophysics Data System (ADS)
Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue
2014-11-01
Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011), 10.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011), 10.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.
One-dimensional immiscible displacement experiments
NASA Astrophysics Data System (ADS)
Thomson, N. R.; Graham, D. N.; Farquhar, G. J.
1992-08-01
In recent years, a great deal of attention has focused on the development of various methods to predict the fate of immiscible contaminants (NAPL's) in soils. In an attempt to satisfy this requirement, a host of numerical models has been developed. Unfortunately, there exist little experimental data to verify the assumptions used in the derivation of these immiscible flow models. One objective of this paper is to report on a non-destructive measurement technique which was used to capture the relative organic-phase saturation variations in a number of two-phase flow displacement experiments. The data obtained from these experiments were compared to results obtained from a one-dimensional, finite-element based, two-phase flow model. The experiments consisted of five separate trials using three different immiscible liquids (hydraulic oil, kerosene and hexane) in a water-saturated column. Irregular immiscible liquid infiltration fronts were observed in four of the five experiments, indicating that very small-scale heterogeneities control the infiltration of immiscible liquids into soil. Independent of the column experiments, saturation-capillary pressure curves were determined for the various liquids. In general, the simulated NAPL saturation vs. time profiles agreed very well with the observations for all five of the trials.
Transport in a one-dimensional hyperconductor
NASA Astrophysics Data System (ADS)
Plamadeala, Eugeniu; Mulligan, Michael; Nayak, Chetan
2016-03-01
We define a "hyperconductor" to be a material whose electrical and thermal dc conductivities are infinite at zero temperature and finite at any nonzero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially gap-generating interactions and potentially localizing disorder. In this paper, we compute the low-temperature dc and ac electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, which allows us to exhibit examples of violations of the Wiedemann-Franz law. The temperature dependence of the electrical conductivity, which is characterized by the parameter ΔX, is a power law, σ ∝1 /T1 -2 (2 -ΔX) when ΔX≥2 , down to zero temperature when the Fermi surface is commensurate with the lattice. There is a surface in parameter space along which ΔX=2 and ΔX≈2 for small deviations from this surface. In the generic (incommensurate) case with weak disorder, such scaling is seen at high temperatures, followed by an exponential increase of the conductivity lnσ ˜1 /T at intermediate temperatures and, finally, σ ∝1 /T2 -2 (2 -ΔX) at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.
Transport in a One-Dimensional Hyperconductor
NASA Astrophysics Data System (ADS)
Plamadeala, Eugeniu; Mulligan, Michael; Nayak, Chetan
We define a `hyperconductor' to be a material whose electrical and thermal DC conductivities are infinite at zero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially-gap-generating interactions and arbitrary potentially-localizing disorder. We compute the low-temperature DC and AC electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, and exhibit examples of violations of the Wiedemann-Franz law. We show that the temperature dependence of the electrical conductivity is a power law, σ ~ 1 /T 1 - 2 (2 -ΔX) for ΔX >= 2 , down to zero temperature when the Fermi surface is commensurate with the lattice. In the incommensurate case with weak disorder, such scaling is seen at high-temperatures, followed by an exponential increase of the conductivity lnσ ~ 1 / T at intermediate temperatures and, finally, σ ~ 1 /T 2 - 2 (2 -ΔX) at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.
NASA Astrophysics Data System (ADS)
Maity, R.; Prasad, D.
2011-01-01
In this paper, Split Markov Process (SMP) is developed to assess one-step-ahead variation of daily rainfall at a rain gauge station. SMP is an advancement of general Markov Process (MP) and specially developed for probabilistic assessment of change in daily rainfall magnitude. The approach is based on a first-order Markov chain to simulate daily rainfall variation at a point through state/sub-state Transitional Probability Matrix (TPM). The state/sub-state TPM is based on the historical transitions from a particular state to a particular sub-state, which is the basic difference between SMP and general MP. In MP, the transition from a particular state to another state is investigated. However, in SMP, the daily rainfall magnitude is categorized into different states and change in magnitude from one temporal step to another is categorized into different sub-states for the probabilistic assessment of rainfall variation. The cumulative state/sub-state TPM is represented in a contour plot at different probability levels. The developed cumulative state/sub-state TPM is used to assess the possible range of rainfall in next time step, in a probabilistic sense. Application of SMP is investigated for daily rainfall at Khandwa station in the Nimar district of Madhya Pradesh, India. Eighty years of daily monsoon rainfall is used to develop the state/sub-state TPM and twenty years data is used to investigate its performance. It is observed that the predicted range of daily rainfall captures the actual observed rainfall with few exceptions. Overall, the assessed range, particularly the upper limit, provides a quantification possible extreme value in the next time step, which is very useful information to tackle the extreme events, such flooding, water logging etc.
Costa, O. L. V.; Dufour, F.
2011-06-15
This paper deals with the expected discounted continuous control of piecewise deterministic Markov processes (PDMP's) using a singular perturbation approach for dealing with rapidly oscillating parameters. The state space of the PDMP is written as the product of a finite set and a subset of the Euclidean space Double-Struck-Capital-R {sup n}. The discrete part of the state, called the regime, characterizes the mode of operation of the physical system under consideration, and is supposed to have a fast (associated to a small parameter {epsilon}>0) and a slow behavior. By using a similar approach as developed in Yin and Zhang (Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach, Applications of Mathematics, vol. 37, Springer, New York, 1998, Chaps. 1 and 3) the idea in this paper is to reduce the number of regimes by considering an averaged model in which the regimes within the same class are aggregated through the quasi-stationary distribution so that the different states in this class are replaced by a single one. The main goal is to show that the value function of the control problem for the system driven by the perturbed Markov chain converges to the value function of this limit control problem as {epsilon} goes to zero. This convergence is obtained by, roughly speaking, showing that the infimum and supremum limits of the value functions satisfy two optimality inequalities as {epsilon} goes to zero. This enables us to show the result by invoking a uniqueness argument, without needing any kind of Lipschitz continuity condition.
Fisher informations and local asymptotic normality for continuous-time quantum Markov processes
NASA Astrophysics Data System (ADS)
Catana, Catalin; Bouten, Luc; Guţă, Mădălin
2015-09-01
We consider the problem of estimating an arbitrary dynamical parameter of an open quantum system in the input-output formalism. For irreducible Markov processes, we show that in the limit of large times the system-output state can be approximated by a quantum Gaussian state whose mean is proportional to the unknown parameter. This approximation holds locally in a neighbourhood of size {t}-1/2 in the parameter space, and provides an explicit expression of the asymptotic quantum Fisher information in terms of the Markov generator. Furthermore we show that additive statistics of the counting and homodyne measurements also satisfy local asymptotic normality and we compute the corresponding classical Fisher informations. The general theory is illustrated with the examples of a two-level system and the atom maser. Our results contribute towards a better understanding of the statistical and probabilistic properties of the output process, with relevance for quantum control engineering, and the theory of non-equilibrium quantum open systems.
Switched Fault Diagnosis Approach for Industrial Processes based on Hidden Markov Model
NASA Astrophysics Data System (ADS)
Wang, Lin; Yang, Chunjie; Sun, Youxian; Pan, Yijun; An, Ruqiao
2015-11-01
Traditional fault diagnosis methods based on hidden Markov model (HMM) use a unified method for feature extraction, such as principal component analysis (PCA), kernel principal component analysis (KPCA) and independent component analysis (ICA). However, every method has its own limitations. For example, PCA cannot extract nonlinear relationships among process variables. So it is inappropriate to extract all features of variables by only one method, especially when data characteristics are very complex. This article proposes a switched feature extraction procedure using PCA and KPCA based on nonlinearity measure. By the proposed method, we are able to choose the most suitable feature extraction method, which could improve the accuracy of fault diagnosis. A simulation from the Tennessee Eastman (TE) process demonstrates that the proposed approach is superior to the traditional one based on HMM and could achieve more accurate classification of various process faults.
A one-dimensional basic oscillator model of the vircator
NASA Astrophysics Data System (ADS)
Biswas, Debabrata
2009-06-01
A one-dimensional model of the virtual cathode oscillator (vircator) is proposed keeping only the essential physical processes. The basic model consists of a radiating charge in an oscillating electric field. Using parameters from (realistic) particle-in-cell simulations such as the charge Q and amplitude E1 of the oscillating electric field, the model correctly predicts the amplitude of virtual cathode oscillation and the power radiated. The basic model is then extended to incorporate beam-cavity interaction and the resonance effect.
First Passage Moments of Finite-State Semi-Markov Processes
Warr, Richard; Cordeiro, James
2014-03-31
In this paper, we discuss the computation of first-passage moments of a regular time-homogeneous semi-Markov process (SMP) with a finite state space to certain of its states that possess the property of universal accessibility (UA). A UA state is one which is accessible from any other state of the SMP, but which may or may not connect back to one or more other states. An important characteristic of UA is that it is the state-level version of the oft-invoked process-level property of irreducibility. We adapt existing results for irreducible SMPs to the derivation of an analytical matrix expression for the first passage moments to a single UA state of the SMP. In addition, consistent point estimators for these first passage moments, together with relevant R code, are provided.
Quasi-one-dimensional foam drainage
NASA Astrophysics Data System (ADS)
Grassia, P.; Cilliers, J. J.; Neethling, S. J.; Ventura-Medina, E.
Foam drainage is considered in a froth flotation cell. Air flow through the foam is described by a simple two-dimensional deceleration flow, modelling the foam spilling over a weir. Foam microstructure is given in terms of the number of channels (Plateau borders) per unit area, which scales as the inverse square of bubble size. The Plateau border number density decreases with height in the foam, and also decreases horizontally as the weir is approached. Foam drainage equations, applicable in the dry foam limit, are described. These can be used to determine the average cross-sectional area of a Plateau border, denoted A, as a function of position in the foam. Quasi-one-dimensional solutions are available in which A only varies vertically, in spite of the two-dimensional nature of the air flow and Plateau border number density fields. For such situations the liquid drainage relative to the air flow is purely vertical. The parametric behaviour of the system is investigated with respect to a number of dimensionless parameters: K (the strength of capillary suction relative to gravity), α (the deceleration of the air flow), and n and h (respectively, the horizontal and vertical variations of the Plateau border number density). The parameter K is small, implying the existence of boundary layer solutions: capillary suction is negligible except in thin layers near the bottom boundary. The boundary layer thickness (when converted back to dimensional variables) is independent of the height of the foam. The deceleration parameter α affects the Plateau border area on the top boundary: weaker decelerations give larger Plateau border areas at the surface. For weak decelerations, there is rapid convergence of the boundary layer solutions at the bottom onto ones with negligible capillary suction higher up. For strong decelerations, two branches of solutions for A are possible in the K=0 limit: one is smooth, and the other has a distinct kink. The full system, with small but non
"Markov at the bat": a model of cognitive processing in baseball batters.
Gray, Rob
2002-11-01
Anecdotal evidence from players and coaches indicates that cognitive processing (e.g., expectations about the upcoming pitch) plays an important role in successful baseball batting, yet this aspect of hitting has not been investigated in detail. The present study provides experimental evidence that prior expectations significantly influence the timing of a baseball swing. A two-state Markov model was used to predict the effects of pitch sequence and pitch count on batting performance. The model is a hitting strategy of switching between expectancy states using a simple set of transition rules. In a simulated batting experiment, the model provided a good fit to the hitting performance of 6 experienced college baseball players, and the estimated model parameters were highly correlated with playing level. PMID:12430839
Sieve estimation in a Markov illness-death process under dual censoring.
Boruvka, Audrey; Cook, Richard J
2016-04-01
Semiparametric methods are well established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However, often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings, unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem, we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials. PMID:26598559
Costa, O. L. V.; Dufour, F.
2010-10-15
The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP's) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.
Partially ordered mixed hidden Markov model for the disablement process of older adults
Ip, Edward H.; Zhang, Qiang; Rejeski, W. Jack; Harris, Tamara B.; Kritchevsky, Stephen
2013-01-01
At both the individual and societal levels, the health and economic burden of disability in older adults is enormous in developed countries, including the U.S. Recent studies have revealed that the disablement process in older adults often comprises episodic periods of impaired functioning and periods that are relatively free of disability, amid a secular and natural trend of decline in functioning. Rather than an irreversible, progressive event that is analogous to a chronic disease, disability is better conceptualized and mathematically modeled as states that do not necessarily follow a strict linear order of good-to-bad. Statistical tools, including Markov models, which allow bidirectional transition between states, and random effects models, which allow individual-specific rate of secular decline, are pertinent. In this paper, we propose a mixed effects, multivariate, hidden Markov model to handle partially ordered disability states. The model generalizes the continuation ratio model for ordinal data in the generalized linear model literature and provides a formal framework for testing the effects of risk factors and/or an intervention on the transitions between different disability states. Under a generalization of the proportional odds ratio assumption, the proposed model circumvents the problem of a potentially large number of parameters when the number of states and the number of covariates are substantial. We describe a maximum likelihood method for estimating the partially ordered, mixed effects model and show how the model can be applied to a longitudinal data set that consists of N = 2,903 older adults followed for 10 years in the Health Aging and Body Composition Study. We further statistically test the effects of various risk factors upon the probabilities of transition into various severe disability states. The result can be used to inform geriatric and public health science researchers who study the disablement process. PMID:24058222
Mo, Yongpeng; Shi, Zongqian; Jia, Shenli; Wang, Lijun
2015-02-15
The inter-contact region of vacuum circuit breakers is filled with residual plasma at the moment when the current is zero after the burning of metal vapor arc. The residual plasma forms an ion sheath in front of the post-arc cathode. The sheath then expands towards the post-arc anode under the influence of a transient recovery voltage. In this study, a one-dimensional particle-in-cell model is developed to investigate the post-arc sheath expansion. The influence of ion and electron temperatures on the decrease in local plasma density at the post-arc cathode side and post-arc anode side is discussed. When the decay in the local plasma density develops from the cathode and anode sides into the high-density region and merges, the overall plasma density in the inter-contact region begins to decrease. Meanwhile, the ion sheath begins to expand faster. Furthermore, the theory of ion rarefaction wave only explains quantitatively the decrease in the overall plasma density at relatively low ion temperatures. With the increase of ion temperature to certain extent, another possible reason for the decrease in the overall plasma density is proposed and results from the more active thermal diffusion of plasma.
Strongly-Refractive One-Dimensional Photonic Crystal Prisms
NASA Technical Reports Server (NTRS)
Ting, David Z. (Inventor)
2004-01-01
One-dimensional (1D) photonic crystal prisms can separate a beam of polychromatic electromagnetic waves into constituent wavelength components and can utilize unconventional refraction properties for wavelength dispersion over significant portions of an entire photonic band rather than just near the band edges outside the photonic band gaps. Using a ID photonic crystal simplifies the design and fabrication process and allows the use of larger feature sizes. The prism geometry broadens the useful wavelength range, enables better optical transmission, and exhibits angular dependence on wavelength with reduced non-linearity. The properties of the 1 D photonic crystal prism can be tuned by varying design parameters such as incidence angle, exit surface angle, and layer widths. The ID photonic crystal prism can be fabricated in a planar process, and can be used as optical integrated circuit elements.
Coherent and passive one dimensional quantum memory
NASA Astrophysics Data System (ADS)
Ping, Yuting; Jefferson, John H.; Lovett, Brendon W.
2014-10-01
We show that the state of a flying qubit may be transferred to a chain of identical, (near) ferromagnetically polarized, but non-interacting, static spin-\\frac{1}{2} particles in a passive way. During this process the flying qubit is coherently polarized, emerging in the direction of the majority static spins. We conjecture that this process is reversible for any number of flying qubits injected sequentially in an arbitrary superposition state, proving this explicitly for an arbitrary state of one and two flying qubits. We also find a special case in which we are able to prove the conjecture for an arbitrary number of qubits. Our architecture thus has the potential to be exploited as a passive quantum memory to encode the flying qubits without the necessity of resetting between successive encoding operations. We also illustrate that the quantum information may be spread over many static spins in the memory chain, making the mechanism resistant to spin decoherence and other imperfections. We discuss implementing the memory system with trapped bosonic atoms, controlled by a spatial light modulator.
An information theoretic approach for generating an aircraft avoidance Markov Decision Process
NASA Astrophysics Data System (ADS)
Weinert, Andrew J.
Developing a collision avoidance system that can meet safety standards required of commercial aviation is challenging. A dynamic programming approach to collision avoidance has been developed to optimize and generate logics that are robust to the complex dynamics of the national airspace. The current approach represents the aircraft avoidance problem as Markov Decision Processes and independently optimizes a horizontal and vertical maneuver avoidance logics. This is a result of the current memory requirements for each logic, simply combining the logics will result in a significantly larger representation. The "curse of dimensionality" makes it computationally inefficient and unfeasible to optimize this larger representation. However, existing and future collision avoidance systems have mostly defined the decision process by hand. In response, a simulation-based framework was built to better understand how each potential state quantifies the aircraft avoidance problem with regards to safety and operational components. The framework leverages recent advances in signals processing and database, while enabling the highest fidelity analysis of Monte Carlo aircraft encounter simulations to date. This framework enabled the calculation of how well each state of the decision process quantifies the collision risk and the associated memory requirements. Using this analysis, a collision avoidance logic that leverages both horizontal and vertical actions was built and optimized using this simulation based approach.
Mapping absorption processes onto a Markov chain, conserving the mean first passage time
NASA Astrophysics Data System (ADS)
Biswas, Katja
2013-04-01
The dynamics of a multidimensional system is projected onto a discrete state master equation using the transition rates W(k → k‧ t, t + dt) between a set of states {k} represented by the regions {ζk} in phase or discrete state space. Depending on the dynamics Γi(t) of the original process and the choice of ζk, the discretized process can be Markovian or non-Markovian. For absorption processes, it is shown that irrespective of these properties of the projection, a master equation with time-independent transition rates \\bar{W}(k\\rightarrow k^{\\prime }) can be obtained, which conserves the total occupation time of the partitions of the phase or discrete state space of the original process. An expression for the transition probabilities \\bar{p}(k^{\\prime }|k) is derived based on either time-discrete measurements {ti} with variable time stepping Δ(i + 1)i = ti + 1 - ti or the theoretical knowledge at continuous times t. This allows computational methods of absorbing Markov chains to be used to obtain the mean first passage time (MFPT) of the system. To illustrate this approach, the procedure is applied to obtain the MFPT for the overdamped Brownian motion of particles subject to a system with dichotomous noise and the escape from an entropic barrier. The high accuracy of the simulation results confirms with the theory.
Glas, Julia; Dümcke, Sebastian; Zacher, Benedikt; Poron, Don; Gagneur, Julien; Tresch, Achim
2016-03-18
Hidden Markov models (HMMs) have been extensively used to dissect the genome into functionally distinct regions using data such as RNA expression or DNA binding measurements. It is a challenge to disentangle processes occurring on complementary strands of the same genomic region. We present the double-stranded HMM (dsHMM), a model for the strand-specific analysis of genomic processes. We applied dsHMM to yeast using strand specific transcription data, nucleosome data, and protein binding data for a set of 11 factors associated with the regulation of transcription.The resulting annotation recovers the mRNA transcription cycle (initiation, elongation, termination) while correctly predicting strand-specificity and directionality of the transcription process. We find that pre-initiation complex formation is an essentially undirected process, giving rise to a large number of bidirectional promoters and to pervasive antisense transcription. Notably, 12% of all transcriptionally active positions showed simultaneous activity on both strands. Furthermore, dsHMM reveals that antisense transcription is specifically suppressed by Nrd1, a yeast termination factor. PMID:26578558
Interpreting functions of one-dimensional kinematics
NASA Astrophysics Data System (ADS)
Canty, Reality S.
The present work examined several factors related to interpreting graphical representations of motion concepts. Since the seminal work of Larkin and Simon (1987), cognitive research has investigated informational equivalence and computational efficiency by contrasting performance across different representations systems such as line versus bar graph (Ali & Peebles, 2012; Shah & Freedman, 2009; Zacks & Tversky, 1999), table versus graph (Speier, 2006; Vessey, 1991) or table versus map (Smelcer & Carmel, 1997). Physics education research has focused on difficulties related to interpreting motion concepts in graphs, accounting for them in terms of misconceptions. Kinematics, the branch of physics concerned with the motion of objects, makes an interesting study of informational equivalence and computational efficiency because its three primary representations -- position-time, velocity-time, and acceleration-time graphs -- can reflect the same information in the same representational system which provides a different type of contrast than has usually been used in this area of cognitive research. In the present work, four experiments were used to test several hypotheses concerned with whether information about the motion of objects can be directly read-off the graph or whether it needed additional processing beyond what was directly visible; Palmer (1987) referred to this as the derivational structure of representations. The main findings across the four experiments were that (a) graph type was not a reliable factor of graph interpretation difficulty, (b) derivational structure was useful for analyzing tasks but there was no evidence supporting it as a process account, (c) graph-based judgment is susceptible to visual features in the graph that trigger powerful spatial-conceptual correspondences particularly height (e.g., higher means more, lower means less), direction of slope (e.g., zero, positive, negative), and curvature (e.g., increasing rate of change, decreasing
Plug-in Estimator of the Entropy Rate of a Pure-Jump Two-State Markov Process
NASA Astrophysics Data System (ADS)
Regnault, Philippe
2009-12-01
The entropy of a distribution with finite support is widely used in all applications involving random variables. A natural equivalent for random processes is the entropy rate. For ergodic pure-jump finite-state Markov processes, this rate is an explicit function of the stationary distribution and the infinitesimal generator. The case of two-state Markov processes is of particular interest. We estimate the entropy rate of such processes by plug-in, from estimators of the stationary distribution and the infinitesimal generator. Three situations of observation are discussed, several independant trajectories are observed, one long trajectory is observed, or the process is observed at discrete times. The asymptotic behavior of the plug-in estimators is established.
Inferring Transition Rates of Networks from Populations in Continuous-Time Markov Processes.
Dixit, Purushottam D; Jain, Abhinav; Stock, Gerhard; Dill, Ken A
2015-11-10
We are interested inferring rate processes on networks. In particular, given a network's topology, the stationary populations on its nodes, and a few global dynamical observables, can we infer all the transition rates between nodes? We draw inferences using the principle of maximum caliber (maximum path entropy). We have previously derived results for discrete-time Markov processes. Here, we treat continuous-time processes, such as dynamics among metastable states of proteins. The present work leads to a particularly important analytical result: namely, that when the network is constrained only by a mean jump rate, the rate matrix is given by a square-root dependence of the rate, kab ∝ (πb/πa)(1/2), on πa and πb, the stationary-state populations at nodes a and b. This leads to a fast way to estimate all of the microscopic rates in the system. As an illustration, we show that the method accurately predicts the nonequilibrium transition rates in an in silico gene expression network and transition probabilities among the metastable states of a small peptide at equilibrium. We note also that the method makes sensible predictions for so-called extra-thermodynamic relationships, such as those of Bronsted, Hammond, and others. PMID:26574334
Griffin, William A.; Li, Xun
2016-01-01
Sequential affect dynamics generated during the interaction of intimate dyads, such as married couples, are associated with a cascade of effects—some good and some bad—on each partner, close family members, and other social contacts. Although the effects are well documented, the probabilistic structures associated with micro-social processes connected to the varied outcomes remain enigmatic. Using extant data we developed a method of classifying and subsequently generating couple dynamics using a Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM). Our findings indicate that several key aspects of existing models of marital interaction are inadequate: affect state emissions and their durations, along with the expected variability differences between distressed and nondistressed couples are present but highly nuanced; and most surprisingly, heterogeneity among highly satisfied couples necessitate that they be divided into subgroups. We review how this unsupervised learning technique generates plausible dyadic sequences that are sensitive to relationship quality and provide a natural mechanism for computational models of behavioral and affective micro-social processes. PMID:27187319
Griffin, William A; Li, Xun
2016-01-01
Sequential affect dynamics generated during the interaction of intimate dyads, such as married couples, are associated with a cascade of effects-some good and some bad-on each partner, close family members, and other social contacts. Although the effects are well documented, the probabilistic structures associated with micro-social processes connected to the varied outcomes remain enigmatic. Using extant data we developed a method of classifying and subsequently generating couple dynamics using a Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM). Our findings indicate that several key aspects of existing models of marital interaction are inadequate: affect state emissions and their durations, along with the expected variability differences between distressed and nondistressed couples are present but highly nuanced; and most surprisingly, heterogeneity among highly satisfied couples necessitate that they be divided into subgroups. We review how this unsupervised learning technique generates plausible dyadic sequences that are sensitive to relationship quality and provide a natural mechanism for computational models of behavioral and affective micro-social processes. PMID:27187319
One-Dimensional Analysis Techniques for Pulsed Blowing Distribution
NASA Astrophysics Data System (ADS)
Chambers, Frank
2005-11-01
Pulsed blowing offers reductions in bleed air requirements for aircraft flow control. Efficient pulsed blowing systems require careful design to minimize bleed air use while distributing blowing to multiple locations. Pulsed blowing systems start with a steady flow supply and process it to generate a pulsatile flow. The fluid-acoustic dynamics of the system play an important role in overall effectiveness. One-dimensional analysis techniques that in the past have been applied to ventilation systems and internal combustion engines have been adapted to pulsed blowing. Pressure wave superposition and reflection are used with the governing equations of continuity, momentum and energy to determine particle velocities and pressures through the flow field. Simulations have been performed to find changes in the amplitude and wave shape as pulses are transmitted through a simple pulsed blowing system. A general-purpose code is being developed to simulate wave transmission and allow the determination of blowing system dynamic parameters.
Users manual for a one-dimensional Lagrangian transport model
Schoellhamer, D.H.; Jobson, H.E.
1986-01-01
A Users Manual for the Lagrangian Transport Model (LTM) is presented. The LTM uses Lagrangian calculations that are based on a reference frame moving with the river flow. The Lagrangian reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used Eulerian reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)
Growth of One-Dimensional MnO2 Nanostructure
NASA Astrophysics Data System (ADS)
Lu, Pai; Xue, Dongfeng
Large scale MnO2 nanorods were controllably synthesized from the inexpensive precursors (e.g., manganese acetate, ammonium persulfate) via a facile one-step low temperature hydrothermal strategy. The crystal phase and microscopic morphology of the as-prepared MnO2 nanorods were characterized by X-ray powder diffraction (XRD) and scanning electron microscope (SEM). Through investigating the morphology evolution of MnO2 products in the whole synthesis process, a novel growth mechanism of these MnO2 nanorods was proposed, which may be efficiently extended to other material systems as a general approach towards one-dimensional nanostructures. The obtained MnO2 nanorods may have potential applications in Li-ion batteries and supercapacitors.
Towards a Theory of Sampled-Data Piecewise-Deterministic Markov Processes
NASA Technical Reports Server (NTRS)
Herencia-Zapana, Heber; Gonzalez, Oscar R.; Gray, W. Steven
2006-01-01
The analysis and design of practical control systems requires that stochastic models be employed. Analysis and design tools have been developed, for example, for Markovian jump linear continuous and discrete-time systems, piecewise-deterministic processes (PDP's), and general stochastic hybrid systems (GSHS's). These model classes have been used in many applications, including fault tolerant control and networked control systems. This paper presents initial results on the analysis of a sampled-data PDP representation of a nonlinear sampled-data system with a jump linear controller. In particular, it is shown that the state of the sampled-data PDP satisfies the strong Markov property. In addition, a relation between the invariant measures of a sampled-data system driven by a stochastic process and its associated discrete-time representation are presented. As an application, when the plant is linear with no external input, a sufficient testable condition for the convergence in distribution to the invariant delta Dirac measure is given.
Topological states in one dimensional solids and photonic crystals
NASA Astrophysics Data System (ADS)
Atherton, Timothy; Mathur, Harsh
2011-03-01
We show that the band structure of a one-dimensional solid with particle-hole symmetry may be characterized by a topological index that owes its existence to the non-trivial homotopy of the space of non-degenerate real symmetric matrices. Moreover we explicitly demonstrate a theorem linking the topological index to the existence of bound states on the surface of a semi-infinite one dimensional solid. Our analysis is a one-dimensional analogue of the analysis of topological insulators in two and three dimensions by Balents and Moore; our results may be relevant to long molecules that are the one dimensional analogue of topological insulators. We propose the realization of this physics in a one-dimensional photonic crystal. In this case the topology of the bandstructure reveals itself not as a bound surface state but as a Lorentzian feature in the time delay of light that is otherwise perfectly reflected by the photonic crystal.
Feng, Yan; Qiu, Yu; Zhou, Xuezhong; Wang, Yixin; Xu, Hao; Liu, Baoyan
2013-01-01
Objective. Initial optimized prescription of Chinese herb medicine for unstable angina (UA). Methods. Based on partially observable Markov decision process model (POMDP), we choose hospitalized patients of 3 syndrome elements, such as qi deficiency, blood stasis, and turbid phlegm for the data mining, analysis, and objective evaluation of the diagnosis and treatment of UA at a deep level in order to optimize the prescription of Chinese herb medicine for UA. Results. The recommended treatment options of UA for qi deficiency, blood stasis, and phlegm syndrome patients were as follows: Milkvetch Root + Tangshen + Indian Bread + Largehead Atractylodes Rhizome (ADR = 0.96630); Danshen Root + Chinese Angelica + Safflower + Red Peony Root + Szechwan Lovage Rhizome Orange Fruit (ADR = 0.76); Snakegourd Fruit + Longstamen Onion Bulb + Pinellia Tuber + Dried Tangerine peel + Largehead Atractylodes Rhizome + Platycodon Root (ADR = 0.658568). Conclusion. This study initially optimized prescriptions for UA based on POMDP, which can be used as a reference for further development of UA prescription in Chinese herb medicine. PMID:24078826
A test of multiple correlation temporal window characteristic of non-Markov processes
NASA Astrophysics Data System (ADS)
Arecchi, F. T.; Farini, A.; Megna, N.
2016-03-01
We introduce a sensitive test of memory effects in successive events. The test consists of a combination K of binary correlations at successive times. K decays monotonically from K = 1 for uncorrelated events as a Markov process. For a monotonic memory fading, K<1 always. Here we report evidence of a K>1 temporal window in cognitive tasks consisting of the visual identification of the front face of the Necker cube after a previous presentation of the same. We speculate that memory effects provide a temporal window with K>1 and this experiment could be a possible first step towards a better comprehension of this phenomenon. The K>1 behaviour is maximal at an inter-measurement time τ around 2s with inter-subject differences. The K>1 persists over a time window of 1s around τ; outside this window the K<1 behaviour is recovered. The universal occurrence of a K>1 window in pairs of successive perceptions suggests that, at variance with single visual stimuli eliciting a suitable response, a pair of stimuli shortly separated in time displays mutual correlations.
Markov-CA model using analytical hierarchy process and multiregression technique
NASA Astrophysics Data System (ADS)
Omar, N. Q.; Sanusi, S. A. M.; Hussin, W. M. W.; Samat, N.; Mohammed, K. S.
2014-06-01
The unprecedented increase in population and rapid rate of urbanisation has led to extensive land use changes. Cellular automata (CA) are increasingly used to simulate a variety of urban dynamics. This paper introduces a new CA based on an integration model built-in multi regression and multi-criteria evaluation to improve the representation of CA transition rule. This multi-criteria evaluation is implemented by utilising data relating to the environmental and socioeconomic factors in the study area in order to produce suitability maps (SMs) using an analytical hierarchical process, which is a well-known method. Before being integrated to generate suitability maps for the periods from 1984 to 2010 based on the different decision makings, which have become conditioned for the next step of CA generation. The suitability maps are compared in order to find the best maps based on the values of the root equation (R2). This comparison can help the stakeholders make better decisions. Thus, the resultant suitability map derives a predefined transition rule for the last step for CA model. The approach used in this study highlights a mechanism for monitoring and evaluating land-use and land-cover changes in Kirkuk city, Iraq owing changes in the structures of governments, wars, and an economic blockade over the past decades. The present study asserts the high applicability and flexibility of Markov-CA model. The results have shown that the model and its interrelated concepts are performing rather well.
A markov decision process model for the optimal dispatch of military medical evacuation assets.
Keneally, Sean K; Robbins, Matthew J; Lunday, Brian J
2016-06-01
We develop a Markov decision process (MDP) model to examine aerial military medical evacuation (MEDEVAC) dispatch policies in a combat environment. The problem of deciding which aeromedical asset to dispatch to each service request is complicated by the threat conditions at the service locations and the priority class of each casualty event. We assume requests for MEDEVAC support arrive sequentially, with the location and the priority of each casualty known upon initiation of the request. The United States military uses a 9-line MEDEVAC request system to classify casualties as being one of three priority levels: urgent, priority, and routine. Multiple casualties can be present at a single casualty event, with the highest priority casualty determining the priority level for the casualty event. Moreover, an armed escort may be required depending on the threat level indicated by the 9-line MEDEVAC request. The proposed MDP model indicates how to optimally dispatch MEDEVAC helicopters to casualty events in order to maximize steady-state system utility. The utility gained from servicing a specific request depends on the number of casualties, the priority class for each of the casualties, and the locations of both the servicing ambulatory helicopter and casualty event. Instances of the dispatching problem are solved using a relative value iteration dynamic programming algorithm. Computational examples are used to investigate optimal dispatch policies under different threat situations and armed escort delays; the examples are based on combat scenarios in which United States Army MEDEVAC units support ground operations in Afghanistan. PMID:25223847
Analysis of the non-Markov parameter in continuous-time signal processing
NASA Astrophysics Data System (ADS)
Varghese, J. J.; Bellette, P. A.; Weegink, K. J.; Bradley, A. P.; Meehan, P. A.
2014-02-01
The use of statistical complexity metrics has yielded a number of successful methodologies to differentiate and identify signals from complex systems where the underlying dynamics cannot be calculated. The Mori-Zwanzig framework from statistical mechanics forms the basis for the generalized non-Markov parameter (NMP). The NMP has been used to successfully analyze signals in a diverse set of complex systems. In this paper we show that the Mori-Zwanzig framework masks an elegantly simple closed form of the first NMP, which, for C1 smooth autocorrelation functions, is solely a function of the second moment (spread) and amplitude envelope of the measured power spectrum. We then show that the higher-order NMPs can be constructed in closed form in a modular fashion from the lower-order NMPs. These results provide an alternative, signal processing-based perspective to analyze the NMP, which does not require an understanding of the Mori-Zwanzig generating equations. We analyze the parametric sensitivity of the zero-frequency value of the first NMP, which has been used as a metric to discriminate between states in complex systems. Specifically, we develop closed-form expressions for three instructive systems: band-limited white noise, the output of white noise input to an idealized all-pole filter,f and a simple harmonic oscillator driven by white noise. Analysis of these systems shows a primary sensitivity to the decay rate of the tail of the power spectrum.
NASA Astrophysics Data System (ADS)
Kim, M.; Ghate, A.; Phillips, M. H.
2009-07-01
The current state of the art in cancer treatment by radiation optimizes beam intensity spatially such that tumors receive high dose radiation whereas damage to nearby healthy tissues is minimized. It is common practice to deliver the radiation over several weeks, where the daily dose is a small constant fraction of the total planned. Such a 'fractionation schedule' is based on traditional models of radiobiological response where normal tissue cells possess the ability to repair sublethal damage done by radiation. This capability is significantly less prominent in tumors. Recent advances in quantitative functional imaging and biological markers are providing new opportunities to measure patient response to radiation over the treatment course. This opens the door for designing fractionation schedules that take into account the patient's cumulative response to radiation up to a particular treatment day in determining the fraction on that day. We propose a novel approach that, for the first time, mathematically explores the benefits of such fractionation schemes. This is achieved by building a stylistic Markov decision process (MDP) model, which incorporates some key features of the problem through intuitive choices of state and action spaces, as well as transition probability and reward functions. The structure of optimal policies for this MDP model is explored through several simple numerical examples.
Composition of Web Services Using Markov Decision Processes and Dynamic Programming
Uc-Cetina, Víctor; Moo-Mena, Francisco; Hernandez-Ucan, Rafael
2015-01-01
We propose a Markov decision process model for solving the Web service composition (WSC) problem. Iterative policy evaluation, value iteration, and policy iteration algorithms are used to experimentally validate our approach, with artificial and real data. The experimental results show the reliability of the model and the methods employed, with policy iteration being the best one in terms of the minimum number of iterations needed to estimate an optimal policy, with the highest Quality of Service attributes. Our experimental work shows how the solution of a WSC problem involving a set of 100,000 individual Web services and where a valid composition requiring the selection of 1,000 services from the available set can be computed in the worst case in less than 200 seconds, using an Intel Core i5 computer with 6 GB RAM. Moreover, a real WSC problem involving only 7 individual Web services requires less than 0.08 seconds, using the same computational power. Finally, a comparison with two popular reinforcement learning algorithms, sarsa and Q-learning, shows that these algorithms require one or two orders of magnitude and more time than policy iteration, iterative policy evaluation, and value iteration to handle WSC problems of the same complexity. PMID:25874247
One-dimensional Bose-Einstein condensation of photons in a microtube
NASA Astrophysics Data System (ADS)
Kruchkov, Alex J.
2016-04-01
This paper introduces a quasiequilibrium one-dimensional Bose-Einstein condensation of photons trapped in a microtube. Light modes with a cutoff frequency (a photon's "mass") interact through different processes of absorption, emission, and scattering on molecules and atoms. In this paper we study the conditions for the one-dimensional condensation of light and the role of photon-photon interactions in the system. The technique in use is the Matsubara Green's functions formalism modified for the quasiequilibrium system under study.
NASA Astrophysics Data System (ADS)
Esquível, Manuel L.; Fernandes, José Moniz; Guerreiro, Gracinda R.
2016-06-01
We introduce a schematic formalism for the time evolution of a random population entering some set of classes and such that each member of the population evolves among these classes according to a scheme based on a Markov chain model. We consider that the flow of incoming members is modeled by a time series and we detail the time series structure of the elements in each of the classes. We present a practical application to data from a credit portfolio of a Cape Verdian bank; after modeling the entering population in two different ways - namely as an ARIMA process and as a deterministic sigmoid type trend plus a SARMA process for the residues - we simulate the behavior of the population and compare the results. We get that the second method is more accurate in describing the behavior of the populations when compared to the observed values in a direct simulation of the Markov chain.
Projected metastable Markov processes and their estimation with observable operator models
NASA Astrophysics Data System (ADS)
Wu, Hao; Prinz, Jan-Hendrik; Noé, Frank
2015-10-01
The determination of kinetics of high-dimensional dynamical systems, such as macromolecules, polymers, or spin systems, is a difficult and generally unsolved problem — both in simulation, where the optimal reaction coordinate(s) are generally unknown and are difficult to compute, and in experimental measurements, where only specific coordinates are observable. Markov models, or Markov state models, are widely used but suffer from the fact that the dynamics on a coarsely discretized state spaced are no longer Markovian, even if the dynamics in the full phase space are. The recently proposed projected Markov models (PMMs) are a formulation that provides a description of the kinetics on a low-dimensional projection without making the Markovianity assumption. However, as yet no general way of estimating PMMs from data has been available. Here, we show that the observed dynamics of a PMM can be exactly described by an observable operator model (OOM) and derive a PMM estimator based on the OOM learning.
Projected metastable Markov processes and their estimation with observable operator models
Wu, Hao Prinz, Jan-Hendrik Noé, Frank
2015-10-14
The determination of kinetics of high-dimensional dynamical systems, such as macromolecules, polymers, or spin systems, is a difficult and generally unsolved problem — both in simulation, where the optimal reaction coordinate(s) are generally unknown and are difficult to compute, and in experimental measurements, where only specific coordinates are observable. Markov models, or Markov state models, are widely used but suffer from the fact that the dynamics on a coarsely discretized state spaced are no longer Markovian, even if the dynamics in the full phase space are. The recently proposed projected Markov models (PMMs) are a formulation that provides a description of the kinetics on a low-dimensional projection without making the Markovianity assumption. However, as yet no general way of estimating PMMs from data has been available. Here, we show that the observed dynamics of a PMM can be exactly described by an observable operator model (OOM) and derive a PMM estimator based on the OOM learning.
Electrical transport in doped one-dimensional nanostructures.
Li, Tan; Wang, Jianning; Zhang, Yumin
2005-09-01
Mobility and noise are two important issues for electronic devices, and they have many new features in one-dimensional (1D) doped nanostructures. For the convenience of readers the background of solid state physics is reviewed first, and then the transport process in 3D crystal material is introduced. Velocity saturation is an important phenomenon in modern electronic devices, and it is analyzed in an intuitive approach. It is predicted FinFET will be the next generation MOSFET, and its structure and characteristics are introduced. With the reduction of device dimensions the mesoscopic phenomena begin to show up. A simple way to treat transport problem in this domain is the Landauer-Büttiker formula, and the basic equation is derived. Finally the 1D quantum wire structure grown from a bottom-up approach is reviewed. Owing to the good material quality the scattering is very weak, and the wave properties of the coherent transport are discussed. Engineering applications of nanostructures in electronic information processing that manipulates time varying signals often involve device characterizations in the time domain. Since carrier transport in nanostructures is inherently a random process and it causes random fluctuations in quantities like current and voltage, so background knowledge in the microscopic origins of noise and other related practical issues is important to identify enough noise margins for reliable system design. This subject is the focus of the second part of the review article. PMID:16193956
Extending the Analysis of One-Dimensional Motion.
ERIC Educational Resources Information Center
Canderle, Luis H.
1999-01-01
Proposes that introductory physics courses extend the analysis of one-dimensional motion to a more sophisticated level. Gives four experimental setups and graphical analysis of the distance, velocity, and acceleration in the vertical and horizontal directions. (WRM)
Asymptotic formula for eigenvalues of one dimensional Dirac system
NASA Astrophysics Data System (ADS)
Ulusoy, Ismail; Penahlı, Etibar
2016-06-01
In this paper, we study the spectral problem for one dimensional Dirac system with Dirichlet boundary conditions. By using Counting lemma, we give an asymptotic formulas of eigenvalues of Dirac system.
Nucleation and growth of nanoscaled one-dimensional materials
NASA Astrophysics Data System (ADS)
Cui, Hongtao
Nanoscaled one-dimensional materials have attracted great interest due to their novel physical and chemical properties. The purpose of this dissertation is to study the nucleation and growth mechanisms of carbon nanotubes and silicon nitride nanowires with their field emission applications in mind. As a result of this research, a novel methodology has been developed to deposit aligned bamboo-like carbon nanotubes on substrates using a methane and ammonia mixture in microwave plasma enhanced chemical deposition. Study of growth kinetics suggests that the carbon diffusion through bulk catalyst particles controls growth in the initial deposition process. Microstructures of carbon nanotubes are affected by the growth temperature and carbon concentration in the gas phase. High-resolution transmission electron microscope confirms the existence of the bamboo-like structure. Electron diffraction reveals that the iron-based catalyst nucleates and sustains the growth of carbon nanotubes. A nucleation and growth model has been constructed based upon experimental data and observations. In the study of silicon nitride nanoneedles, a vapor-liquid-solid model is employed to explain the nucleation and growth processes. Ammonia plasma etching is proposed to reduce the size of the catalyst and subsequently produce the novel needle-like nanostructure. High-resolution transmission electron microscope shows the structure is well crystallized and composed of alpha-silicon nitride. Other observations in the structure are also explained.
Automated quantification of one-dimensional nanostructure alignment on surfaces
NASA Astrophysics Data System (ADS)
Dong, Jianjin; Goldthorpe, Irene A.; Mohieddin Abukhdeir, Nasser
2016-06-01
A method for automated quantification of the alignment of one-dimensional (1D) nanostructures from microscopy imaging is presented. Nanostructure alignment metrics are formulated and shown to be able to rigorously quantify the orientational order of nanostructures within a two-dimensional domain (surface). A complementary image processing method is also presented which enables robust processing of microscopy images where overlapping nanostructures might be present. Scanning electron microscopy (SEM) images of nanowire-covered surfaces are analyzed using the presented methods and it is shown that past single parameter alignment metrics are insufficient for highly aligned domains. Through the use of multiple parameter alignment metrics, automated quantitative analysis of SEM images is shown to be possible and the alignment characteristics of different samples are able to be quantitatively compared using a similarity metric. The results of this work provide researchers in nanoscience and nanotechnology with a rigorous method for the determination of structure/property relationships, where alignment of 1D nanostructures is significant.
Automated quantification of one-dimensional nanostructure alignment on surfaces.
Dong, Jianjin; Goldthorpe, Irene A; Abukhdeir, Nasser Mohieddin
2016-06-10
A method for automated quantification of the alignment of one-dimensional (1D) nanostructures from microscopy imaging is presented. Nanostructure alignment metrics are formulated and shown to be able to rigorously quantify the orientational order of nanostructures within a two-dimensional domain (surface). A complementary image processing method is also presented which enables robust processing of microscopy images where overlapping nanostructures might be present. Scanning electron microscopy (SEM) images of nanowire-covered surfaces are analyzed using the presented methods and it is shown that past single parameter alignment metrics are insufficient for highly aligned domains. Through the use of multiple parameter alignment metrics, automated quantitative analysis of SEM images is shown to be possible and the alignment characteristics of different samples are able to be quantitatively compared using a similarity metric. The results of this work provide researchers in nanoscience and nanotechnology with a rigorous method for the determination of structure/property relationships, where alignment of 1D nanostructures is significant. PMID:27119552
Characterization of Thermal Transport in One-dimensional Solid Materials
Liu, Guoqing; Lin, Huan; Tang, Xiaoduan; Bergler, Kevin; Wang, Xinwei
2014-01-01
The TET (transient electro-thermal) technique is an effective approach developed to measure the thermal diffusivity of solid materials, including conductive, semi-conductive or nonconductive one-dimensional structures. This technique broadens the measurement scope of materials (conductive and nonconductive) and improves the accuracy and stability. If the sample (especially biomaterials, such as human head hair, spider silk, and silkworm silk) is not conductive, it will be coated with a gold layer to make it electronically conductive. The effect of parasitic conduction and radiative losses on the thermal diffusivity can be subtracted during data processing. Then the real thermal conductivity can be calculated with the given value of volume-based specific heat (ρcp), which can be obtained from calibration, noncontact photo-thermal technique or measuring the density and specific heat separately. In this work, human head hair samples are used to show how to set up the experiment, process the experimental data, and subtract the effect of parasitic conduction and radiative losses. PMID:24514072
NASA Astrophysics Data System (ADS)
Akselrod, D.; Sinha, A.; Kirubarajan, T.
2007-09-01
In this paper, we consider the problem of collaborative sensor management with particular application to using unmanned aerial vehicles (UAVs) for multitarget tracking. The problem of decentralized cooperative control considered in this paper is an optimization of the information obtained by a number of unmanned aerial vehicles (UAVs) equipped with Ground Moving Target Indicator (GMTI) radars, carrying out surveillance over a region which includes a number of confirmed and suspected moving targets. The goal is to track confirmed targets and detect new targets in the area. Each UAV has to decide on the most optimal path with the objective to track as many targets as possible maximizing the information obtained during its operation with the maximum possible accuracy at the lowest possible cost. Limited communication between UAVs and uncertainty in the information obtained by each UAV regarding the location of the ground targets are addressed in the problem formulation. In order to handle these issues, the problem is presented as a decentralized operation of a group of decision-makers lacking full observability of the global state of the system. Markov Decision Processes (MDPs) are incorporated into the solution. Given the MDP model, a local policy of actions for a single agent (UAV) is given by a mapping from a current partial view of a global state observed by an agent to actions. The available probability model regarding possible and confirmed locations of the targets is considered in the computations of the UAVs' policies. The authors present multi-level hierarchy of MDPs controlling each of the UAVs. Each level in the hierarchy solves a problem at a different level of abstraction. Simulation results are presented on a representative multisensor-multitarget tracking problem.
Learning to maximize reward rate: a model based on semi-Markov decision processes
Khodadadi, Arash; Fakhari, Pegah; Busemeyer, Jerome R.
2014-01-01
When animals have to make a number of decisions during a limited time interval, they face a fundamental problem: how much time they should spend on each decision in order to achieve the maximum possible total outcome. Deliberating more on one decision usually leads to more outcome but less time will remain for other decisions. In the framework of sequential sampling models, the question is how animals learn to set their decision threshold such that the total expected outcome achieved during a limited time is maximized. The aim of this paper is to provide a theoretical framework for answering this question. To this end, we consider an experimental design in which each trial can come from one of the several possible “conditions.” A condition specifies the difficulty of the trial, the reward, the penalty and so on. We show that to maximize the expected reward during a limited time, the subject should set a separate value of decision threshold for each condition. We propose a model of learning the optimal value of decision thresholds based on the theory of semi-Markov decision processes (SMDP). In our model, the experimental environment is modeled as an SMDP with each “condition” being a “state” and the value of decision thresholds being the “actions” taken in those states. The problem of finding the optimal decision thresholds then is cast as the stochastic optimal control problem of taking actions in each state in the corresponding SMDP such that the average reward rate is maximized. Our model utilizes a biologically plausible learning algorithm to solve this problem. The simulation results show that at the beginning of learning the model choses high values of decision threshold which lead to sub-optimal performance. With experience, however, the model learns to lower the value of decision thresholds till finally it finds the optimal values. PMID:24904252
Dynamics of a tracer granular particle as a nonequilibrium Markov process.
Puglisi, Andrea; Visco, Paolo; Trizac, Emmanuel; van Wijland, Frédéric
2006-02-01
The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation, describing the dynamics of the tracer into a master equation for a continuous Markov process. The transition rates depend on the stationary velocity distribution of the gas. When the gas has a Gaussian velocity probability distribution function (PDF), the stationary velocity PDF of the tracer is Gaussian with a lower temperature and satisfies detailed balance for any value of the restitution coefficient alpha. As soon as the velocity PDF of the gas departs from the Gaussian form, detailed balance is violated. This nonequilibrium state can be characterized in terms of a Lebowitz-Spohn action functional W(tau) defined over trajectories of time duration tau. We discuss the properties of this functional and of a similar functional W(tau), which differs from the first for a term that is nonextensive in time. On the one hand, we show that in numerical experiments (i.e., at finite times tau), the two functionals have different fluctuations and W always satisfies an Evans-Searles-like symmetry. On the other hand, we cannot observe the verification of the Lebowitz-Spohn-Gallavotti-Cohen (LS-GC) relation, which is expected for W(tau) at very large times tau. We give an argument for the possible failure of the LS-GC relation in this situation. We also suggest practical recipes for measuring W(tau) and W(tau) in experiments. PMID:16605329
ERIC Educational Resources Information Center
Wollmer, Richard D.
The true state of the system described here is characterized by a probability vector. At each stage of the system an action must be chosen from a finite set of actions. Each possible action yields an expected reward, transforms the system to a new state in accordance with a Markov transition matrix, and yields an observable outcome. The problem of…
An adaptive grid algorithm for one-dimensional nonlinear equations
NASA Technical Reports Server (NTRS)
Gutierrez, William E.; Hills, Richard G.
1990-01-01
Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and
A Smart Colorful Supercapacitor with One Dimensional Photonic Crystals
Liu, Cihui; Liu, Xing; Xuan, Hongyun; Ren, Jiaoyu; Ge, Liqin
2015-01-01
To meet the pressing demands for portable and flexible equipment in contemporary society, developing flexible, lightweight, and sustainable supercapacitor systems with large power densities, long cycle life, and ease of strongly required. However, estimating the state-of-charge of existing supercapacitors is difficult, and thus their service life is limited. In this study, we fabricate a flexible color indicative supercapacitor device with mesoporous polyaniline (mPANI)/Poly(N-Isopropyl acrylamide-Graphene Oxide-Acrylic Acid) (P(NiPPAm-GO-AA)) one dimensional photonic crystals (1DPCs) as the electrode material through a low-cost, eco-friendly, and scalable fabrication process. We found that the state-of-charge could be monitored by the structural color oscillation due to the change in the photonic band gap position of the 1DPCs. The flexible 1DPCs supercapacitor is thin at 3 mm and exhibits good specific capacitance of 22.6 F g−1 with retention of 91.1% after 3,000 cycles. This study shows the application of the 1DPCs supercapacitor as a visual ultrathin power source. The technology may find many applications in future wearable electronics. PMID:26689375
One-dimensional flows of an imperfect diatomic gas
NASA Technical Reports Server (NTRS)
1959-01-01
With the assumptions that Berthelot's equation of state accounts for molecular size and intermolecular force effects, and that changes in the vibrational heat capacities are given by a Planck term, expressions are developed for analyzing one-dimensional flows of a diatomic gas. The special cases of flow through normal and oblique shocks in free air at sea level are investigated. It is found that up to a Mach number 10 pressure ratio across a normal shock differs by less than 6 percent from its ideal gas value; whereas at Mach numbers above 4 the temperature rise is considerable below and hence the density rise is well above that predicted assuming ideal gas behavior. It is further shown that only the caloric imperfection in air has an appreciable effect on the pressures developed in the shock process considered. The effects of gaseous imperfections on oblique shock-flows are studied from the standpoint of their influence on the life and pressure drag of a flat plate operating at Mach numbers of 10 and 20. The influence is found to be small. (author)
Carbyne with finite length: The one-dimensional sp carbon
Pan, Bitao; Xiao, Jun; Li, Jiling; Liu, Pu; Wang, Chengxin; Yang, Guowei
2015-01-01
Carbyne is the one-dimensional allotrope of carbon composed of sp-hybridized carbon atoms. Definitive evidence for carbyne has remained elusive despite its synthesis and preparation in the laboratory. Given the remarkable technological breakthroughs offered by other allotropes of carbon, including diamond, graphite, fullerenes, carbon nanotubes, and graphene, interest in carbyne and its unusual potential properties remains intense. We report the first synthesis of carbyne with finite length, which is clearly composed of alternating single bonds and triple bonds, using a novel process involving laser ablation in liquid. Spectroscopic analyses confirm that the product is the structure of sp hybridization with alternating carbon-carbon single bonds and triple bonds and capped by hydrogen. We observe purple-blue fluorescence emissions from the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital of carbyne. Condensed-phase carbyne crystals have a hexagonal lattice and resemble the white crystalline powder produced by drying a carbyne solution. We also establish that the combination of gold and alcohol is crucial to carbyne formation because carbon-hydrogen bonds can be cleaved with the help of gold catalysts under the favorable thermodynamic environment provided by laser ablation in liquid and because the unique configuration of two carbon atoms in an alcohol molecule matches the elementary entity of carbyne. This laboratory synthesis of carbyne will enable the exploration of its properties and applications. PMID:26601318
Carbyne with finite length: The one-dimensional sp carbon.
Pan, Bitao; Xiao, Jun; Li, Jiling; Liu, Pu; Wang, Chengxin; Yang, Guowei
2015-10-01
Carbyne is the one-dimensional allotrope of carbon composed of sp-hybridized carbon atoms. Definitive evidence for carbyne has remained elusive despite its synthesis and preparation in the laboratory. Given the remarkable technological breakthroughs offered by other allotropes of carbon, including diamond, graphite, fullerenes, carbon nanotubes, and graphene, interest in carbyne and its unusual potential properties remains intense. We report the first synthesis of carbyne with finite length, which is clearly composed of alternating single bonds and triple bonds, using a novel process involving laser ablation in liquid. Spectroscopic analyses confirm that the product is the structure of sp hybridization with alternating carbon-carbon single bonds and triple bonds and capped by hydrogen. We observe purple-blue fluorescence emissions from the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital of carbyne. Condensed-phase carbyne crystals have a hexagonal lattice and resemble the white crystalline powder produced by drying a carbyne solution. We also establish that the combination of gold and alcohol is crucial to carbyne formation because carbon-hydrogen bonds can be cleaved with the help of gold catalysts under the favorable thermodynamic environment provided by laser ablation in liquid and because the unique configuration of two carbon atoms in an alcohol molecule matches the elementary entity of carbyne. This laboratory synthesis of carbyne will enable the exploration of its properties and applications. PMID:26601318
Berry phase oscillations in a one-dimensional Dirac comb
NASA Astrophysics Data System (ADS)
Hodge, William; Cassera, Nicholas; Rave, Matthew
In quantum mechanics, the Berry phase is a geometric phase acquired by a wave function over the course of a cycle, when subjected to adiabatic processes. In general, this phase is due to the geometry of the underlying parameter space and thus depends only on the path taken. In any system described by a periodic potential, the torus topology of the Brillouin zone itself can lead to such a phase. In this work, we numerically calculate the Berry phase for a one-dimensional Dirac comb described by N distinct wells per unit cell. As expected, the resulting Berry phase exhibits a rich band-dependence. In the case where N = 2 , we find that the Berry phase corresponding to the nth energy band oscillates such that γn (x) =An sin (πx) cos [ (2 n - 1) πx ] , where An is a band-dependent constant and 0 < x < 1 is the relative position of the two wells. This expression, obtained using perturbation theory, gives excellent agreement with exact numerical results, even at low energy levels. The Berry phase exhibits a similar behavior for cases where N > 2 .
Using the NASA GRC Sectored-One-Dimensional Combustor Simulation
NASA Technical Reports Server (NTRS)
Paxson, Daniel E.; Mehta, Vishal R.
2014-01-01
The document is a user manual for the NASA GRC Sectored-One-Dimensional (S-1-D) Combustor Simulation. It consists of three sections. The first is a very brief outline of the mathematical and numerical background of the code along with a description of the non-dimensional variables on which it operates. The second section describes how to run the code and includes an explanation of the input file. The input file contains the parameters necessary to establish an operating point as well as the associated boundary conditions (i.e. how it is fed and terminated) of a geometrically configured combustor. It also describes the code output. The third section describes the configuration process and utilizes a specific example combustor to do so. Configuration consists of geometrically describing the combustor (section lengths, axial locations, and cross sectional areas) and locating the fuel injection point and flame region. Configuration requires modifying the source code and recompiling. As such, an executable utility is included with the code which will guide the requisite modifications and insure that they are done correctly.
A Smart Colorful Supercapacitor with One Dimensional Photonic Crystals
NASA Astrophysics Data System (ADS)
Liu, Cihui; Liu, Xing; Xuan, Hongyun; Ren, Jiaoyu; Ge, Liqin
2015-12-01
To meet the pressing demands for portable and flexible equipment in contemporary society, developing flexible, lightweight, and sustainable supercapacitor systems with large power densities, long cycle life, and ease of strongly required. However, estimating the state-of-charge of existing supercapacitors is difficult, and thus their service life is limited. In this study, we fabricate a flexible color indicative supercapacitor device with mesoporous polyaniline (mPANI)/Poly(N-Isopropyl acrylamide-Graphene Oxide-Acrylic Acid) (P(NiPPAm-GO-AA)) one dimensional photonic crystals (1DPCs) as the electrode material through a low-cost, eco-friendly, and scalable fabrication process. We found that the state-of-charge could be monitored by the structural color oscillation due to the change in the photonic band gap position of the 1DPCs. The flexible 1DPCs supercapacitor is thin at 3 mm and exhibits good specific capacitance of 22.6 F g-1 with retention of 91.1% after 3,000 cycles. This study shows the application of the 1DPCs supercapacitor as a visual ultrathin power source. The technology may find many applications in future wearable electronics.
One-Way Markov Process Approach to Repeat Times of Large Earthquakes in Faults
NASA Astrophysics Data System (ADS)
Tejedor, Alejandro; Gomez, Javier B.; Pacheco, Amalio F.
2012-11-01
One of the uses of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. We propose a general one-way Markovian model in which the waiting time distribution, its first moments, coefficient of variation, and functions of error and alarm (related to the predictability of the model) can be obtained analytically. The fact that in any one-way Markov cycle the coefficient of variation of the corresponding distribution of cycle lengths is always lower than one concurs with observations of large earthquakes in seismic faults. The waiting time distribution of one of the limits of this model is the negative binomial distribution; as an application, we use it to fit the Parkfield earthquake series in the San Andreas fault, California.
Some topological states in one-dimensional cold atomic systems
Mei, Feng; Zhang, Dan-Wei; Zhu, Shi-Liang
2015-07-15
Ultracold atoms trapped in optical lattices nowadays have been widely used to mimic various models from condensed-matter physics. Recently, many great experimental progresses have been achieved for producing artificial magnetic field and spin–orbit coupling in cold atomic systems, which turn these systems into a new platform for simulating topological states. In this paper, we give a review focusing on quantum simulation of topologically protected soliton modes and topological insulators in one-dimensional cold atomic system. Firstly, the recent achievements towards quantum simulation of one-dimensional models with topological non-trivial states are reviewed, including the celebrated Jackiw–Rebbi model and Su–Schrieffer–Heeger model. Then, we will introduce a dimensional reduction method for systematically constructing high dimensional topological states in lower dimensional models and review its applications on simulating two-dimensional topological insulators in one-dimensional optical superlattices.
The nature of one-dimensional carbon: polyynic versus cumulenic.
Neiss, Christian; Trushin, Egor; Görling, Andreas
2014-08-25
A question of both fundamental as well as practical importance is the nature of one-dimensional carbon, in particular whether a one-dimensional carbon allotrope is polyynic or cumulenic, that is, whether bond-length alternation occurs or not. By combining the concept of aromaticity and antiaromaticity with the rule of Peierls distortion, the occurrence and magnitude of bond-length alternation in carbon chains with periodic boundary conditions and corresponding carbon rings as a function of the chain or ring length can be explained. The electronic properties of one-dimensional carbon depend crucially on the bond-length alternation. Whereas it is generally accepted that carbon chains in the limit of infinite length have a polyynic structure at the minimum of the potential energy surface with bond-length alternation, we show here that zero-point vibrations lead to an effective equalization of all carbon-carbon bond lengths and thus to a cumulenic structure. PMID:24962252
One-dimensional rainbow technique using Fourier domain filtering.
Wu, Yingchun; Promvongsa, Jantarat; Wu, Xuecheng; Cen, Kefa; Grehan, Gerard; Saengkaew, Sawitree
2015-11-16
Rainbow refractometry can measure the refractive index and the size of a droplet simultaneously. The refractive index measurement is extracted from the absolute rainbow scattering angle. Accordingly, the angular calibration is vital for accurate measurements. A new optical design of the one-dimensional rainbow technique is proposed by using a one-dimensional spatial filter in the Fourier domain. The relationship between the scattering angle and the CCD pixel of a recorded rainbow image can be accurately determined by a simple calibration. Moreover, only the light perpendicularly incident on the lens in the angle (φ) direction is selected, which exactly matches the classical inversion algorithm used in rainbow refractometry. Both standard and global one-dimensional rainbow techniques are implemented with the proposed optical design, and are successfully applied to measure the refractive index and the size of a line of n-heptane droplets. PMID:26698532
One-Dimensional Quasicrystals from Incommensurate Charge Order
NASA Astrophysics Data System (ADS)
Flicker, Felix; van Wezel, Jasper
2015-12-01
Artificial quasicrystals are nowadays routinely manufactured, yet only two naturally occurring examples are known. We present a class of systems with the potential to be realized both artificially and in nature, in which the lowest energy state is a one-dimensional quasicrystal. These systems are based on incommensurately charge-ordered materials, in which the quasicrystalline phase competes with the formation of a regular array of discommensurations as a way of interpolating between incommensurate charge order at high temperatures and commensurate order at low temperatures. The nonlocal correlations characteristic of the quasicrystalline state emerge from a free-energy contribution localized in reciprocal space. We present a theoretical phase diagram showing that the required material properties for the appearance of such a ground state allow for one-dimensional quasicrystals to form in real materials. The result is a potentially wide class of one-dimensional quasicrystals.
One dimensional speckle fields generated by three phase level diffusers
NASA Astrophysics Data System (ADS)
Cabezas, L.; Amaya, D.; Bolognini, N.; Lencina, A.
2015-02-01
Speckle patterns have usually been obtained by using ground glass as random diffusers. Liquid-crystal spatial light modulators have opened the possibility of engineering tailored speckle fields obtained from designed diffusers. In this work, one-dimensional Gaussian speckle fields with fully controllable features are generated. By employing a low-cost liquid-crystal spatial light modulator, one-dimensional three phase level diffusers are implemented. These diffusers make it possible to control average intensity distribution and statistical independence among the generated patterns. The average speckle size is governed by an external slit pupil. A theoretical model to describe the generated speckle patterns is developed. Experimental and theoretical results confirming the generation of one-dimensional speckle fields are presented. Some possible applications of these speckles, such as atom trapping and super-resolution imaging, are briefly envisaged.
Quantum solution for the one-dimensional Coulomb problem
Nunez-Yepez, H. N.; Salas-Brito, A. L.; Solis, Didier A.
2011-06-15
The one-dimensional hydrogen atom has been a much studied system with a wide range of applications. Since the pioneering work of Loudon [R. Loudon, Am. J. Phys. 27, 649 (1959).], a number of different features related to the nature of the eigenfunctions have been found. However, many of the claims made throughout the years in this regard are not correct--such as the existence of only odd eigenstates or of an infinite binding-energy ground state. We explicitly show that the one-dimensional hydrogen atom does not admit a ground state of infinite binding energy and that the one-dimensional Coulomb potential is not its own supersymmetric partner. Furthermore, we argue that at the root of many such false claims lies the omission of a superselection rule that effectively separates the right side from the left side of the singularity of the Coulomb potential.
Pose estimation for one-dimensional object with general motion
NASA Astrophysics Data System (ADS)
Liu, Jinbo; Song, Ge; Zhang, Xiaohu
2014-11-01
Our primary interest is in real-time one-dimensional object's pose estimation. In this paper, a method to estimate general motion one-dimensional object's pose, that is, the position and attitude parameters, using a single camera is proposed. Centroid-movement is necessarily continuous and orderly in temporal space, which means it follows at least approximately certain motion law in a short period of time. Therefore, the centroid trajectory in camera frame can be described as a combination of temporal polynomials. Two endpoints on one-dimensional object, A and B, at each time are projected on the corresponding image plane. With the relationship between A, B and centroid C, we can obtain a linear equation system related to the temporal polynomials' coefficients, in which the camera has been calibrated and the image coordinates of A and B are known. Then in the cases that object moves continuous in natural temporal space within the view of a stationary camera, the position of endpoints on the one-dimensional object can be located and also the attitude can be estimated using two end points. Moreover the position of any other point aligned on one-dimensional object can also be solved. Scene information is not needed in the proposed method. If the distance between the endpoints is not known, a scale factor between the object's real positions and the estimated results will exist. In order to improve the algorithm's performance from accuracy and robustness, we derive a pain of linear and optimal algorithms. Simulations' and experiments' results show that the method is valid and robust with respect to various Gaussian noise levels. The paper's work contributes to making self-calibration algorithms using one-dimensional objects applicable to practice. Furthermore, the method can also be used to estimate the pose and shape parameters of parallelogram, prism or cylinder objects.
Lateral electronic screening in quasi-one-dimensional plasmons.
Lichtenstein, T; Tegenkamp, C; Pfnür, H
2016-09-01
The properties of one-dimensional (1D) plasmons are rather unexplored. We investigated the plasmonic collective excitations, measured as one-dimensional plasmon dispersions with electron energy loss spectroscopy, highly resolved both in energy and lateral momentum, for both phases of Au induced chains on stepped Si(553) substrates. We observe 1D dispersions that are strongly influenced by the lateral chain width and by the interchain coupling. Indications for the existence of two different plasmons originating from two surface bands of the systems are given for the low coverage phase. PMID:27384978
Explicit solutions of one-dimensional total variation problem
NASA Astrophysics Data System (ADS)
Makovetskii, Artyom; Voronin, Sergei; Kober, Vitaly
2015-09-01
This work deals with denosing of a one-dimensional signal corrupted by additive white Gaussian noise. A common way to solve the problem is to utilize the total variation (TV) method. Basically, the TV regularization minimizes a functional consisting of the sum of fidelity and regularization terms. We derive explicit solutions of the one-dimensional TV regularization problem that help us to restore noisy signals with a direct, non-iterative algorithm. Computer simulation results are provided to illustrate the performance of the proposed algorithm for restoration of noisy signals.
Lateral electronic screening in quasi-one-dimensional plasmons
NASA Astrophysics Data System (ADS)
Lichtenstein, T.; Tegenkamp, C.; Pfnür, H.
2016-09-01
The properties of one-dimensional (1D) plasmons are rather unexplored. We investigated the plasmonic collective excitations, measured as one-dimensional plasmon dispersions with electron energy loss spectroscopy, highly resolved both in energy and lateral momentum, for both phases of Au induced chains on stepped Si(553) substrates. We observe 1D dispersions that are strongly influenced by the lateral chain width and by the interchain coupling. Indications for the existence of two different plasmons originating from two surface bands of the systems are given for the low coverage phase.
Wuebbles, D.J.
1981-09-01
Since the LLNL one-dimensional coupled transport and chemical kinetics model of the troposphere and stratosphere was originally developed in 1972 (Chang et al., 1974), there have been many changes to the model's representation of atmospheric physical and chemical processes. A brief description is given of the current LLNL one-dimensional coupled transport and chemical kinetics model of the troposphere and stratosphere.
One dimensional blood flow in a planetocentric orbit
NASA Astrophysics Data System (ADS)
Haranas, Ioannis; Gkigkitzis, Ioannis
2012-05-01
All life on earth is accustomed to the presence of gravity. When gravity is altered, biological processes can go awry. It is of great importance to ensure safety during a spaceflight. Long term exposure to microgravity can trigger detrimental physiological responses in the human body. Fluid redistribution coupled with fluid loss is one of the effects. In particular, in microgravity blood volume is shifted towards the thorax and head. Sympathetic nervous system-induced vasoconstriction is needed to maintain arterial pressure, while venoconstriction limits venous pooling of blood prevents further reductions in venous return of blood to the heart. In this paper, we modify an existing one dimensional blood flow model with the inclusion of the hydrostatic pressure gradient that further depends on the gravitational field modified by the oblateness and rotation of the Earth. We find that the velocity of the blood flow VB is inversely proportional to the blood specific volume d, also proportional to the oblateness harmonic coefficient J2, the angular velocity of the Earth ωE, and finally proportional to an arbitrary constant c. For c = -0.39073 and ξH = -0.5 mmHg, all orbits result to less blood flow velocities than that calculated on the surface of the Earth. From all considered orbits, elliptical polar orbit of eccentricity e = 0.2 exhibit the largest flow velocity VB = 1.031 m/s, followed by the orbits of inclination i = 45°and 0°. The Earth's oblateness and its rotation contribute a 0.7% difference to the blood flow velocity.
Construction and optoelectronic properties of organic one-dimensional nanostructures.
Zhao, Yong Sheng; Fu, Hongbing; Peng, Aidong; Ma, Ying; Liao, Qing; Yao, Jiannian
2010-03-16
In the last 10 years, nanomaterials based on small organic molecules have attracted increasing attention. Such materials have unique optical and electronic properties, which could lead to new applications in nanoscale devices. Zero-dimensional (0D) organic nanoparticles with amorphous structures have been widely studied; however, the systematic investigation of crystalline one-dimensional (1D) organic nanostructures has only emerged in recent years. Researchers have used inorganic 1D nanomaterials, such as wires, tubes, and belts, as building blocks in optoelectronic nanodevices. We expect that their organic counterparts will also play an important role in this field. Because organic nanomaterials are composed of molecular units with weaker intermolecular interactions, they allow for higher structural tunability, reactivity, and processability. In addition, organic materials usually possess higher luminescence efficiency and can be grown on almost any solid substrate. In this Account, we describe recent progress in our group toward the construction of organic 1D nanomaterials and studies of their unique optical and electronic properties. First, we introduce the techniques for synthesizing 1D organic nanostructures. Because this strategy is both facile and reliable, liquid phase synthesis is most commonly used. More importantly, this method allows researchers to produce composite materials, including core/sheath and uniformly doped structures, which allow to investigate the interactions between different components in the nanomaterials, including fluorescent resonance energy transfer and photoinduced electron transfer. Physical vapor deposition allows for the synthesis of organic 1D nanomaterials with high crystallinity. Nanomaterials produced with this method offer improved charge transport properties and better optoelectronic performance in areas including multicolor emission, tunable emission, optical waveguide, and lasing. Although inorganic nanomaterials have
One dimensional time-to-explode (ODTX) in HMX spheres
Breshears, D.
1997-06-02
In a series of papers researchers at Lawrence Livermore National Laboratory (LLNL) have reported measurements of the time to explosion in spheres of various high explosives following a rapid, uniform increase in the surface temperature of the sphere. Due to the spherical symmetry, the time-dependent properties of the explosive (temperature, chemical composition, etc.) are functions of the radial spatial coordinate only; thus the name one-dimensional time-to-explosion (ODTX). The LLNL researchers also report an evolving series of computational modeling results for the ODTX experiments, culminating in those obtained using a sophisticated heat transfer code incorporating accurate descriptions of chemical reaction. Although the chemical reaction mechanism used to describe HMX decomposition is quite simple, the computational results agree very well with the experimental data. In addition to reproducing the magnitude and temperature dependence of the measured times to explosion, the computational results also agree with the results of post reaction visual inspection. The ODTX experiments offer a near-ideal example of a transport process (heat transfer in this case) tightly coupled with chemical reaction. The LLNL computational model clearly captures the important features of the ODTX experiments. An obvious question of interest is to what extent the model and/or its individual components (specifically the chemical reaction mechanism) are applicable to other experimental scenarios. Valid exploration of this question requires accurate understanding of (1) the experimental scenario addressed by the LLNL model and (2) details of the application of the model. The author reports here recent work addressing points (1) and (2).
A difference characteristic for one-dimensional deterministic systems
NASA Astrophysics Data System (ADS)
Shahverdian, A. Yu.; Apkarian, A. V.
2007-06-01
A numerical characteristic for one-dimensional deterministic systems reflecting its higher order difference structure is introduced. The comparison with Lyapunov exponent is given. A difference analogy for Eggleston theorem as well as an estimate for Hausdorff dimension of the difference attractor, formulated in terms of the new characteristic is proved.
Teaching Module for One-Dimensional, Transient Conduction.
ERIC Educational Resources Information Center
Ribando, Robert J.; O'Leary, Gerald W.
1998-01-01
Describes a PC-based teaching module designed to instruct engineering students in transient one-dimensional conduction heat transfer analysis. The discussion considers problem formulation, nondimensionalization, discretization, numerical stability and the time-step restriction, program operation, and program verification. (MES)
Synchronization of One-Dimensional Stochastically Coupled Cellular Automata
NASA Astrophysics Data System (ADS)
Mrowinski, Maciej J.; Kosinski, Robert A.
In this work the authors study synchronization resulting from the asymmetric stochastic coupling between two one-dimensional chaotic cellular automata and provide a simple analytical model to explain this phenomenon. The authors also study synchronization in a more general case, using sets of rules with a different number of states and different values of Langton's parameter λ.
The Long Decay Model of One-Dimensional Projectile Motion
ERIC Educational Resources Information Center
Lattery, Mark Joseph
2008-01-01
This article introduces a research study on student model formation and development in introductory mechanics. As a point of entry, I present a detailed analysis of the Long Decay Model of one-dimensional projectile motion. This model has been articulated by Galileo ("in De Motu") and by contemporary students. Implications for instruction are…
Minimum critical length for superconductivity in one-dimensional wires
Chi, C.C.; Santhanam, P.; Wind, S.J.; Brady, M.J.; Bucchignano, J.J. )
1994-08-01
We have experimentally studied the superconducting behavior of one-dimensional aluminum wires of various lengths. Each wire had much wider two-dimensional contact pads on both sides. At a temperature [ital T] below [ital T][sub [ital c
Underwater striling engine design with modified one-dimensional model
NASA Astrophysics Data System (ADS)
Li, Daijin; Qin, Kan; Luo, Kai
2015-09-01
Stirling engines are regarded as an efficient and promising power system for underwater devices. Currently, many researches on one-dimensional model is used to evaluate thermodynamic performance of Stirling engine, but in which there are still some aspects which cannot be modeled with proper mathematical models such as mechanical loss or auxiliary power. In this paper, a four-cylinder double-acting Stirling engine for Unmanned Underwater Vehicles (UUVs) is discussed. And a one-dimensional model incorporated with empirical equations of mechanical loss and auxiliary power obtained from experiments is derived while referring to the Stirling engine computer model of National Aeronautics and Space Administration (NASA). The P-40 Stirling engine with sufficient testing results from NASA is utilized to validate the accuracy of this one-dimensional model. It shows that the maximum error of output power of theoretical analysis results is less than 18% over testing results, and the maximum error of input power is no more than 9%. Finally, a Stirling engine for UUVs is designed with Schmidt analysis method and the modified one-dimensional model, and the results indicate this designed engine is capable of showing desired output power.
Underwater striling engine design with modified one-dimensional model
NASA Astrophysics Data System (ADS)
Li, Daijin; Qin, Kan; Luo, Kai
2015-05-01
Stirling engines are regarded as an efficient and promising power system for underwater devices. Currently, many researches on one-dimensional model is used to evaluate thermodynamic performance of Stirling engine, but in which there are still some aspects which cannot be modeled with proper mathematical models such as mechanical loss or auxiliary power. In this paper, a four-cylinder double-acting Stirling engine for Unmanned Underwater Vehicles (UUVs) is discussed. And a one-dimensional model incorporated with empirical equations of mechanical loss and auxiliary power obtained from experiments is derived while referring to the Stirling engine computer model of National Aeronautics and Space Administration (NASA). The P-40 Stirling engine with sufficient testing results from NASA is utilized to validate the accuracy of this one-dimensional model. It shows that the maximum error of output power of theoretical analysis results is less than 18% over testing results, and the maximum error of input power is no more than 9%. Finally, a Stirling engine for UUVs is designed with Schmidt analysis method and the modified one-dimensional model, and the results indicate this designed engine is capable of showing desired output power.
Approximate Approaches to the One-Dimensional Finite Potential Well
ERIC Educational Resources Information Center
Singh, Shilpi; Pathak, Praveen; Singh, Vijay A.
2011-01-01
The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (m[subscript i]) is taken to be distinct from mass outside (m[subscript o]). A relevant parameter is the mass…
PREMIXED ONE-DIMENSIONAL FLAME (PROF) CODE USER'S MANUAL
The report is a user's manual that describes the problems that can be treated by the Premixed One-dimensional Flame (PROF) code. It also describes the mathematical models and solution procedures applied to these problems. Complete input instructions and a description of output ar...
One-Dimensional Ising Model with "k"-Spin Interactions
ERIC Educational Resources Information Center
Fan, Yale
2011-01-01
We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…
Sandia One-Dimensional Direct and Inverse Thermal Code
Energy Science and Technology Software Center (ESTSC)
1995-02-27
SODDIT is a reliable tool for solving a wide variety of one-dimensional transient heat conduction problems. Originally developed in 1972 to predict the ablation of graphite/carbon bodies reentering the earth''s atmosphere, it has since been modified by the authors to extend its capabilities well beyond its original scope.
Zero-n gap in one dimensional photonic crystal
NASA Astrophysics Data System (ADS)
Chobey, Mahesh K.; Suthar, B.
2016-05-01
We study a one-dimensional (1-D) photonic crystal composed of Double Positive (DPS) and Double Negative (DNG) material. This structure shows omnidirectional photonic bandgap, which is insensitive with angle of incidence and polarization. To study the effect of structural parameters on the photonic band structure, we have calculated photonic band gap at various thicknesses of DPS and DNG.
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.
Reflection properties of one dimensional plasma photonic crystal
NASA Astrophysics Data System (ADS)
Kumar, Arun; Khundrakpam, Pinky; Sharma, Priyanka
2013-06-01
In this paper band structure and reflection properties of on one-dimensional plasma photonic crystal (PPC) containing alternate layers of dielectric and micro-plasma have been presented. For the purpose of computation, transfer matrix method has been used. It is found that width of the forbidden band gap(s) can be increased by increasing the thickness of plasma layers.
Toward precise solution of one-dimensional velocity inverse problems
Gray, S.; Hagin, F.
1980-01-01
A family of one-dimensional inverse problems are considered with the goal of reconstructing velocity profiles to reasonably high accuracy. The travel-time variable change is used together with an iteration scheme to produce an effective algorithm for computation. Under modest assumptions the scheme is shown to be convergent.
Luque-Vasquez, Fernando Minjarez-Sosa, J. Adolfo Rosas-Rosas, Luz del Carmen
2010-06-15
This paper deals with a class of semi-Markov control models with Borel state and control spaces, possibly unbounded costs, and unknown holding times distribution F. Assuming that F does not depend on state-action pairs, we combine suitable methods of statistical estimation of the mean holding time with control procedures to construct an average cost optimal Markovian policy {pi}-hat={l_brace}f{sub n}{r_brace}, and an optimal stationary policy {l_brace}f{sub {infinity}}{r_brace}, where f{sub n} converges to f{sub {infinity}} in the sense of Schael.
Ignition transient analysis of a solid rocket motor using a one dimensional two fluid model
NASA Astrophysics Data System (ADS)
Pardue, Byron A.; Han, Samuel S.
1992-07-01
A one dimensional two fluid numerical model has been used to study the ignition transient stage of a Space Shuttle solid rocket motor. During the ignition phase of a solid rocket motor a pressure transient is induced by complex transport processes involving the igniter gas heat transfer to the propellant, chemical reactions at the propellant surface, and the interaction of the fluid with the attached rocket nozzle. One dimensional models used in the past neglected the aluminum oxide particles which are present in the combustion gases. The current model uses the IPSA (Inter-Phase-Slip-Algorithm) to solve the transient compressible flow equations for the rocket chamber and attached nozzle. Numerical results for head end pressure changes and overall thrust are compared with both measurement data and predictions of a one dimensional one fluid model.
One-dimensional Bose-Einstein condensation of photons in a microtube
NASA Astrophysics Data System (ADS)
Kruchkov, Alex
This study introduces a quasiequilibrium one-dimensional Bose-Einstein condensation of photons trapped in a microscopical waveguide. Light modes with a cut-off frequency (''photon's mass'') interact through different processes of absorption, re-emition, and scattering on molecules of dye. In this work I consider conditions for the one-dimensional condensation of light and the role of photon-photon interactions in the system. The computational technique in use is the Matsubara's Green's functions formalism modified for the quasiequilibrium system under study.
One-dimensional crystal growth model on a square lattice substrate
NASA Astrophysics Data System (ADS)
Cheng, Yi; Lu, Chenxi; Yang, Bo; Tao, Xiangming; Wang, Jianfeng; Ye, Gaoxiang
2016-08-01
A one-dimensional crystal growth model along the preferential growth direction is established. The simulation model is performed on a square lattice substrate. First, particles are deposited homogeneously and, as a result, each of the lattice sites is occupied by one particle. In the subsequent stage, N nuclei are selected randomly on the substrate, then the growth process starts by adsorbing the surrounding particles along the preferential growth directions of the crystals. Finally, various one-dimensional crystals with different length and width form. The simulation results are in good agreement with the experimental findings.
Control policies for a water-treatment system using the Markov Decision Process.
NASA Astrophysics Data System (ADS)
Chiam, Tze; Mitchell, Cary; Yih, Yuehwern
the system's current state but not the "path" that it has taken. Due to this "memoryless" property and the stochastic properties of the system, the state transition can be modeled by the Markov process. A reward system was constructed to assign reward values to every state visited. A water system is considered to be in a "good" state when it has sufficient clean water to meet the demands of crewmembers. Such states will receive a much higher reward value than states in which crewmembers suffer from water deficiencies. Transition probabilities are obtained through simulation using the Markovian model. Nine policies based on different values of treatment efficiencies for both subsystems were defined. One policy is applied to the system at every hour. The choice of policy to apply affects the system behavior (and state). Hence, it is important to apply a policy that is "best" for the system every hour. The Policy Iteration algorithm is used for this purpose. This algorithm provides the best policy under steady-state conditions. The transition probabilities and reward values are formulated into appropriate mathematical representation and are solved by applying the Policy Iteration algorithm. A system that uses the best policy is compared against one that uses a fixed policy by the use of a paired-t test. Results show that a system applying best policies has statistically better performance than a system operating on a fixed policy. This methodology is also applicable to various other scenarios with different system design, magnitude of "stochastic-ness", including system modules such as the crop system. Research sponsored in part by NASA grant NAG5-12686.
Stifter, Cynthia A.; Rovine, Michael
2016-01-01
The focus of the present longitudinal study, to examine mother-infant interaction during the administration of immunizations at two and six months of age, used hidden Markov modeling, a time series approach that produces latent states to describe how mothers and infants work together to bring the infant to a soothed state. Results revealed a 4-state model for the dyadic responses to a two-month inoculation whereas a 6-state model best described the dyadic process at six months. Two of the states at two months and three of the states at six months suggested a progression from high intensity crying to no crying with parents using vestibular and auditory soothing methods. The use of feeding and/or pacifying to soothe the infant characterized one two-month state and two six-month states. These data indicate that with maturation and experience, the mother-infant dyad is becoming more organized around the soothing interaction. Using hidden Markov modeling to describe individual differences, as well as normative processes, is also presented and discussed.
On a Result for Finite Markov Chains
ERIC Educational Resources Information Center
Kulathinal, Sangita; Ghosh, Lagnojita
2006-01-01
In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…
Versatile hydrothermal synthesis of one-dimensional composite structures
NASA Astrophysics Data System (ADS)
Luo, Yonglan
2008-12-01
In this paper we report on a versatile hydrothermal approach developed to fabricate one-dimensional (1D) composite structures. Sulfur and selenium formed liquid and adsorbed onto microrods as droplets and subsequently reacted with metallic ion in solution to produce nanoparticles-decorated composite microrods. 1D composites including ZnO/CdS, ZnO/MnS, ZnO/CuS, ZnO/CdSe, and FeOOH/CdS were successfully made using this hydrothermal strategy and the growth mechanism was also discussed. This hydrothermal strategy is simple and green, and can be extended to the synthesis of various 1D composite structures. Moreover, the interaction between the shell nanoparticles and the one-dimensional nanomaterials were confirmed by photoluminescence investigation of ZnO/CdS.
Spatial coherence properties of one dimensional exciton-polariton condensates.
Fischer, J; Savenko, I G; Fraser, M D; Holzinger, S; Brodbeck, S; Kamp, M; Shelykh, I A; Schneider, C; Höfling, S
2014-11-14
In this work, we combine a systematic experimental investigation of the power- and temperature-dependent evolution of the spatial coherence function, g^{(1)}(r), in a one dimensional exciton-polariton channel with a modern microscopic numerical theory based on a stochastic master equation approach. The spatial coherence function g^{(1)}(r) is extracted via high-precision Michelson interferometry, which allows us to demonstrate that in the regime of nonresonant excitation, the dependence g^{(1)}(r) reaches a saturation value with a plateau, which is determined by the intensity of the pump and effective temperature of the crystal lattice. The theory, which was extended to allow for treating incoherent excitation in a stochastic frame, matches the experimental data with good qualitative and quantitative agreement. This allows us to verify the prediction that the decay of the off-diagonal long-range order can be almost fully suppressed in one dimensional condensate systems. PMID:25432043
Excitonic condensation in spatially separated one-dimensional systems
Abergel, D. S. L.
2015-05-25
We show theoretically that excitons can form from spatially separated one-dimensional ground state populations of electrons and holes, and that the resulting excitons can form a quasicondensate. We describe a mean-field Bardeen-Cooper-Schrieffer theory in the low carrier density regime and then focus on the core-shell nanowire giving estimates of the size of the excitonic gap for InAs/GaSb wires and as a function of all the experimentally relevant parameters. We find that optimal conditions for pairing include small overlap of the electron and hole bands, large effective mass of the carriers, and low dielectric constant of the surrounding media. Therefore, one-dimensional systems provide an attractive platform for the experimental detection of excitonic quasicondensation in zero magnetic field.
Pairing correlations in a trapped one-dimensional Fermi gas
NASA Astrophysics Data System (ADS)
Kudla, Stephen; Gautreau, Dominique M.; Sheehy, Daniel E.
2015-04-01
We use a BCS-type variational wave function to study attractively interacting quasi-one-dimensional fermionic atomic gases, motivated by cold-atom experiments that access the one-dimensional regime using an anisotropic harmonic trapping potential (with trapping frequencies ωx=ωy≫ωz ) that confines the gas to a cigar-shaped geometry. To handle the presence of the trap along the z direction, we construct our variational wave function from the harmonic oscillator Hermite functions, which are the eigenstates of the single-particle problem. Using an analytic determination of the effective interaction among harmonic oscillator states along with a numerical solution of the resulting variational equations, we make specific experimental predictions for how pairing correlations would be revealed in experimental probes, such as the local density and the momentum correlation function.
Scaling properties of one-dimensional driven-dissipative condensates
NASA Astrophysics Data System (ADS)
He, Liang; Sieberer, Lukas M.; Altman, Ehud; Diehl, Sebastian
2015-10-01
We numerically investigate the scaling properties of a one-dimensional driven-dissipative condensate described by a stochastic complex Ginzburg-Landau equation (SCGLE). We directly extract the static and dynamical scaling exponents from the dynamics of the condensate's phase field, and find that both coincide with the ones of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation. We furthermore calculate the spatial and the temporal two-point correlation functions of the condensate field itself. The decay of the temporal two-point correlator assumes a stretched-exponential form, providing further quantitative evidence for an effective KPZ description. Moreover, we confirm the observability of this nonequilibrium scaling for typical current experimental setups with exciton-polariton systems, if cavities with a reduced Q factor are used.
Dynamics of one-dimensional Kerr cavity solitons.
Leo, François; Gelens, Lendert; Emplit, Philippe; Haelterman, Marc; Coen, Stéphane
2013-04-01
We present an experimental observation of an oscillating Kerr cavity soliton, i.e., a time-periodic oscillating one-dimensional temporally localized structure excited in a driven nonlinear fiber cavity with a Kerr-type nonlinearity. More generally, these oscillations result from a Hopf bifurcation of a (spatially or temporally) localized state in the generic class of driven dissipative systems close to the 1 : 1 resonance tongue. Furthermore, we theoretically analyze dynamical instabilities of the one-dimensional cavity soliton, revealing oscillations and different chaotic states in previously unexplored regions of parameter space. As cavity solitons are closely related to Kerr frequency combs, we expect these dynamical regimes to be highly relevant for the field of microresonator-based frequency combs. PMID:23572006
Fate of classical solitons in one-dimensional quantum systems.
Pustilnik, M.; Matveev, K. A.
2015-11-23
We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.
One-dimensional XY model: Ergodic properties and hydrodynamic limit
NASA Astrophysics Data System (ADS)
Shuhov, A. G.; Suhov, Yu. M.
1986-11-01
We prove theorems on convergence to a stationary state in the course of time for the one-dimensional XY model and its generalizations. The key point is the well-known Jordan-Wigner transformation, which maps the XY dynamics onto a group of Bogoliubov transformations on the CAR C *-algebra over Z 1. The role of stationary states for Bogoliubov transformations is played by quasifree states and for the XY model by their inverse images with respect to the Jordan-Wigner transformation. The hydrodynamic limit for the one-dimensional XY model is also considered. By using the Jordan-Wigner transformation one reduces the problem to that of constructing the hydrodynamic limit for the group of Bogoliubov transformations. As a result, we obtain an independent motion of "normal modes," which is described by a hyperbolic linear differential equation of second order. For the XX model this equation reduces to a first-order transfer equation.
Improving the One Dimensional Schr"odinger Equation
NASA Astrophysics Data System (ADS)
Schorer, Bradley; Bricher, Stephen; Murray, Joelle
2009-05-01
The simple harmonic oscillator (SHO) model is a useful approach for approximating energies close to the ground state in a one dimensional hydrogen atom. According to empirical evidence, the actual potential results in an asymmetric equilibrium point and exhibits and exhibits asymptotic behavior at large distances from the nucleus. This creates a problem in the SHO model, as it does not possess such characteristics, and as a result, has energy values that do not match do not agree with the known energy levels very well. We propose a new one dimensional potential that more accurately fits the empirical data than the SHO model. We test our model by comparing the Schr"odinger equation's energy states to accepted energy levels of the hydrogen atom. Possible other uses for this model include the description of energy levels of atoms other than the hydrogen atom.
One-dimensional Hubbard-Luttinger model for carbon nanotubes
NASA Astrophysics Data System (ADS)
Ishkhanyan, H. A.; Krainov, V. P.
2015-06-01
A Hubbard-Luttinger model is developed for qualitative description of one-dimensional motion of interacting Pi-conductivity-electrons in carbon single-wall nanotubes at low temperatures. The low-lying excitations in one-dimensional electron gas are described in terms of interacting bosons. The Bogolyubov transformation allows one to describe the system as an ensemble of non-interacting quasi-bosons. Operators of Fermi excitations and Green functions of fermions are introduced. The electric current is derived as a function of potential difference on the contact between a nanotube and a normal metal. Deviations from Ohm law produced by electron-electron short-range repulsion as well as by the transverse quantization in single-wall nanotubes are discussed. The results are compared with experimental data.
Entanglement vs. gap for one-dimensional spin systems
Hastings, Matthew; Aharonov, Dorit; Gottesman, Daniel
2008-01-01
We study the relationship between entanglement and spectral gap for local Hamiltonians in one dimension. The area law for a one-dimensional system states that for the ground state, the entanglement of any interval is upper-bounded by a constant independent of the size of the interval. However, the possible dependence of the upper bound on the spectral gap {Delta} is not known, as the best known general upper bound is asymptotically much larger than the largest possible entropy of any model system previously constructed for small {Delta}. To help resolve this asymptotic behavior, we construct a family of one-dimensional local systems for which some intervals have entanglement entropy which is polynomial in 1/{Delta}, whereas previously studied systems had the entropy of all intervals bounded by a constant times log(1/{Delta}).
Quasi-Dirac points in one-dimensional graphene superlattices
NASA Astrophysics Data System (ADS)
Chen, C. H.; Tseng, P.; Hsueh, W. J.
2016-08-01
Quasi-Dirac points (QDPs) with energy different from the traditional Dirac points (TDPs) have been found for the first time in one-dimensional graphene superlattices. The angular-averaged conductance reaches a minimum value at the QDPs, at which the Fano factor approaches 1/3. Surprisingly, the minimum conductance at these QDPs may be lower than that at the TDPs under certain conditions. This is remarkable as the minimum conductance attainable in graphene superlattices was believed to appear at TDPs.
Superlensing properties of one-dimensional dielectric photonic crystals
NASA Astrophysics Data System (ADS)
Savo, Salvatore; di Gennaro, Emiliano; Andreone, Antonello
2009-10-01
We present the experimental observation of the superlensing effect in a slab of a one-dimensional photonic crystal made of tilted dielectric elements. We show that this flat lens can achieve subwavelength resolution in different frequency bands. We also demonstrate that the introduction of a proper corrugation on the lens surface can dramatically improve both the transmission and the resolution of the imaged signal.
Many-body Anderson localization in one-dimensional systems
NASA Astrophysics Data System (ADS)
Delande, Dominique; Sacha, Krzysztof; Płodzień, Marcin; Avazbaev, Sanat K.; Zakrzewski, Jakub
2013-04-01
We show, using quasi-exact numerical simulations, that Anderson localization in a disordered one-dimensional potential survives in the presence of attractive interaction between particles. The localization length of the particles' center of mass—computed analytically for weak disorder—is in good agreement with the quasi-exact numerical observations using the time evolving block decimation algorithm. Our approach allows for simulation of the entire experiment including the final measurement of all atom positions.
Topological modes in one-dimensional solids and photonic crystals
NASA Astrophysics Data System (ADS)
Atherton, Timothy J.; Butler, Celia A. M.; Taylor, Melita C.; Hooper, Ian R.; Hibbins, Alastair P.; Sambles, J. Roy; Mathur, Harsh
2016-03-01
It is shown theoretically that a one-dimensional crystal with time-reversal and particle-hole symmetries is characterized by a topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the construction and simulation of a photonic crystal analog in the microwave regime. It is shown that the edge mode couples to modes external to the photonic crystal via a Fano resonance.
Thermalization in a one-dimensional integrable system
Grisins, Pjotrs; Mazets, Igor E.
2011-11-15
We present numerical results demonstrating the possibility of thermalization of single-particle observables in a one-dimensional system, which is integrable in both the quantum and classical (mean-field) descriptions (a quasicondensate of ultracold, weakly interacting bosonic atoms are studied as a definite example). We find that certain initial conditions admit the relaxation of single-particle observables to the equilibrium state reasonably close to that corresponding to the Bose-Einstein thermal distribution of Bogoliubov quasiparticles.
Defects in a nonlinear pseudo one-dimensional solid
NASA Astrophysics Data System (ADS)
Blanchet, Graciela B.; Fincher, C. R., Jr.
1985-03-01
These infrared studies of acetanilide together with the existence of two equivalent structures for the hydrogen-bonded chain suggest the possibility of a topological defect state rather than a Davydov soliton as suggested previously. Acetanilide is an example of a class of one-dimensional materials where solitons are a consequence of a twofold degenerate structure and the nonlinear dynamics of the hydrogen-bonded network.
Cooling of a One-Dimensional Bose Gas
NASA Astrophysics Data System (ADS)
Rauer, B.; Grišins, P.; Mazets, I. E.; Schweigler, T.; Rohringer, W.; Geiger, R.; Langen, T.; Schmiedmayer, J.
2016-01-01
We experimentally study the dynamics of a degenerate one-dimensional Bose gas that is subject to a continuous outcoupling of atoms. Although standard evaporative cooling is rendered ineffective by the absence of thermalizing collisions in this system, we observe substantial cooling. This cooling proceeds through homogeneous particle dissipation and many-body dephasing, enabling the preparation of otherwise unexpectedly low temperatures. Our observations establish a scaling relation between temperature and particle number, and provide insights into equilibration in the quantum world.
Nonequilibrium statistical mechanics in one-dimensional bose gases
NASA Astrophysics Data System (ADS)
Baldovin, F.; Cappellaro, A.; Orlandini, E.; Salasnich, L.
2016-06-01
We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann–Vlasov equation with contact interaction, we derive an effective 1D Landau–Vlasov equation under the condition of a strong transverse harmonic confinement. We investigate the existence of out-of-equilibrium states, obtaining stability criteria similar to those of classical plasmas.
Cloud pumping in a one-dimensional photochemical model
NASA Technical Reports Server (NTRS)
Costen, Robert C.; Tennille, Geoffrey M.; Levine, Joel S.
1988-01-01
Cloud pumping data based on tropical maritime updraft statistics are incorporated in a one-dimensional steady-state eddy diffusive photochemical model of the troposphere. It is suggested that regions with weaker convection, such as the midlatitudes, may also experience substantial effects from cloud pumping. The direct effects of cloud pumping on CO were found to be more significant than implied by sensitivity studies. The (CH3)2S profile computed with cloud pumping agrees well with previous data.
On numerical modeling of one-dimensional geothermal histories
Haugerud, R.A.
1989-01-01
Numerical models of one-dimensional geothermal histories are one way of understanding the relations between tectonics and transient thermal structure in the crust. Such models can be powerful tools for interpreting geochronologic and thermobarometric data. A flexible program to calculate these models on a microcomputer is available and examples of its use are presented. Potential problems with this approach include the simplifying assumptions that are made, limitations of the numerical techniques, and the neglect of convective heat transfer. ?? 1989.
Growth of one-dimensional single-crystalline hydroxyapatite nanorods
NASA Astrophysics Data System (ADS)
Ren, Fuzeng; Ding, Yonghui; Ge, Xiang; Lu, Xiong; Wang, Kefeng; Leng, Yang
2012-06-01
A facile, effective and template/surfactant-free hydrothermal route in the presence of sodium bicarbonate was developed to synthesize highly uniform single-crystalline hydroxyapatite (HA) nanorods with the lengths of several hundred nanometers and aspect ratio up to ˜20. One dimensional (1-D) growth and aspect ratio could be controlled by hydrothermal reaction time and temperature. The longitudinal axis, also the growth direction of the nanorods, is parallel to the [001] direction of HA hexagonal crystal structure.
Quasi-One-Dimensional Modeling of Pulse Detonation Rocket Engines
NASA Technical Reports Server (NTRS)
Morris, Christopher I.
2002-01-01
. While such a nozzle is a considerable idealization, it is clear that nozzle design and optimization will play a critical role in whether the performance potential of PDREs can be effectively realized in practice. In order to study PDRE nozzle issues with greater accuracy, a quasi-one-dimensional, finite-rate chemistry CFD code has been developed by the author. Comparisons of the code with both the previous MOC model and experimental data from Stanford University are reported. The effect of constant-gamma and finite-rate chemistry assumptions on the flowfield and performance is examined. Parametric studies of the effect of nozzle throat size and expansion ratio, at various blowdown pressure ratios, are reported.
One-dimensional optical wave turbulence: Experiment and theory
NASA Astrophysics Data System (ADS)
Laurie, Jason; Bortolozzo, Umberto; Nazarenko, Sergey; Residori, Stefania
2012-05-01
We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave
Species segregation in one-dimensional granular-system simulations.
Pantellini, F; Landi, S
2008-02-01
We present one-dimensional molecular dynamics simulations of a two-species, initially uniform, freely evolving granular system. Colliding particles swap their relative position with a 50% probability allowing for the initial spatial ordering of the particles to evolve in time and frictional forces to operate. Unlike one-dimensional systems of identical particles, two-species one-dimensional systems of quasi-elastic particles are ergodic and the particles' velocity distributions tend to evolve towards Maxwell-Boltzmann distributions. Under such conditions, standard fluid equations with merely an additional sink term in the energy equation, reflecting the non-elasticity of the interparticle collisions, provide an excellent means to investigate the system's evolution. According to the predictions of fluid theory we find that the clustering instability is dominated by a non-propagating mode at a wavelength of the order 10 pi L/N epsilon , where N is the total number of particles, L the spatial extent of the system and epsilon the inelasticity coefficient. The typical fluid velocities at the time of inelastic collapse are seen to be supersonic, unless N epsilon
Pooley, C M; Bishop, S C; Marion, G
2015-06-01
Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob-Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed 'model-based proposal' (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2-8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large. PMID:25994297
Pooley, C. M.; Bishop, S. C.; Marion, G.
2015-01-01
Bayesian statistics provides a framework for the integration of dynamic models with incomplete data to enable inference of model parameters and unobserved aspects of the system under study. An important class of dynamic models is discrete state space, continuous-time Markov processes (DCTMPs). Simulated via the Doob–Gillespie algorithm, these have been used to model systems ranging from chemistry to ecology to epidemiology. A new type of proposal, termed ‘model-based proposal’ (MBP), is developed for the efficient implementation of Bayesian inference in DCTMPs using Markov chain Monte Carlo (MCMC). This new method, which in principle can be applied to any DCTMP, is compared (using simple epidemiological SIS and SIR models as easy to follow exemplars) to a standard MCMC approach and a recently proposed particle MCMC (PMCMC) technique. When measurements are made on a single-state variable (e.g. the number of infected individuals in a population during an epidemic), model-based proposal MCMC (MBP-MCMC) is marginally faster than PMCMC (by a factor of 2–8 for the tests performed), and significantly faster than the standard MCMC scheme (by a factor of 400 at least). However, when model complexity increases and measurements are made on more than one state variable (e.g. simultaneously on the number of infected individuals in spatially separated subpopulations), MBP-MCMC is significantly faster than PMCMC (more than 100-fold for just four subpopulations) and this difference becomes increasingly large. PMID:25994297
Bojesen, Troels Arnfred
2013-04-01
We present a multihistogram reweighting technique for nonequilibrium Markov chains with discrete energies. The method generalizes the single-histogram method of Yin et al. [Phys. Rev. E 72, 036122 (2005)], making it possible to calculate the time evolution of observables at a posteriori chosen couplings based on a set of simulations performed at other couplings. In the same way as multihistogram reweighting in an equilibrium setting improves the practical reweighting range as well as use of available data compared to single-histogram reweighting, the method generalizes the multihistogram advantages to nonequilibrium simulations. We demonstrate the procedure for the Ising model with Metropolis dynamics, but stress that the method is generally applicable to a range of models and Monte Carlo update schemes. PMID:23679555
NASA Astrophysics Data System (ADS)
Haruna, Taichi; Nakajima, Kohei
2013-05-01
Transfer entropy is a measure of the magnitude and the direction of information flow between jointly distributed stochastic processes. In recent years, its permutation analogues are considered in the literature to estimate the transfer entropy by counting the number of occurrences of orderings of values, not the values themselves. It has been suggested that the method of permutation is easy to implement, computationally low cost and robust to noise when applying to real world time series data. In this paper, we initiate a theoretical treatment of the corresponding rates. In particular, we consider the transfer entropy rate and its permutation analogue, the symbolic transfer entropy rate, and show that they are equal for any bivariate finite-alphabet stationary ergodic Markov process. This result is an illustration of the duality method introduced in [T. Haruna, K. Nakajima, Physica D 240, 1370 (2011)]. We also discuss the relationship among the transfer entropy rate, the time-delayed mutual information rate and their permutation analogues.
El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar
2014-11-01
Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data. PMID:26353069
Applications of One-Dimensional Nanomaterials for Stretchable Electronics
NASA Astrophysics Data System (ADS)
Xu, Feng
Electronics that can be stretched and/or conformal to curvilinear surfaces has recently attracted broad attention. Success of stretchable electronics depends on the availability of electronic materials and structures that can be highly stretched, compressed, bent, and twisted. One-dimensional (1D) nanomaterials are expected to aid the development of the stretchable electronic systems by improving performance, expanding integration possibilities, and potentially lowering cost, due to their superior mechanical/electronic/optical properties, high aspect ratios, and compatibility with bulk synthesis. This dissertation is primarily focused on the application of 1D nanomaterials, including silicon nanowires (SiNWs), carbon nanotubes (CNTs) and silver nanowires (AgNWs) for stretchable electronics. The mechanical properties of SiNWs, grown by the vapor-liquid-solid process, were first studied with in situ tensile tests inside a scanning electron microscope (SEM). It was found that the fracture strain increased from 2.7% to about 12% when the NW diameter decreased from 60 to 15 nm. The Young's modulus decreased while the fracture strength increased up to 12.2 GPa, as the nanowire diameter decreased. The fracture strength also increased with the decrease of the side surface area. Repeated loading and unloading during tensile tests demonstrated that the nanowires are linear elastic until fracture without appreciable plasticity. Then, SiNW coils were fabricated on elastomeric substrates by a controlled buckling process. SiNWs were first transferred onto prestrained and ultraviolet/ozone (UVO)-treated poly(dimethylsiloxane) (PDMS) substrates and buckled upon release of the prestrain. Two buckling modes (the in-plane wavy mode and the three-dimensional coiled mode) were found; a transition between them was achieved by controlling the UVO treatment of PDMS. Structural characterization revealed that the NW coils were oval-shaped. The oval-shaped NW coils exhibited very large
One-Dimensional Scanning Approach to Shock Sensing
NASA Technical Reports Server (NTRS)
Tokars, Roger; Adamovsky, Girgory; Floyd, Bertram
2009-01-01
Measurement tools for high speed air flow are sought both in industry and academia. Particular interest is shown in air flows that exhibit aerodynamic shocks. Shocks are accompanied by sudden changes in density, pressure, and temperature. Optical detection and characterization of such shocks can be difficult because the medium is normally transparent air. A variety of techniques to analyze these flows are available, but they often require large windows and optical components as in the case of Schlieren measurements and/or large operating powers which precludes their use for in-flight monitoring and applications. The one-dimensional scanning approach in this work is a compact low power technique that can be used to non-intrusively detect shocks. The shock is detected by analyzing the optical pattern generated by a small diameter laser beam as it passes through the shock. The optical properties of a shock result in diffraction and spreading of the beam as well as interference fringes. To investigate the feasibility of this technique a shock is simulated by a 426 m diameter optical fiber. Analysis of results revealed a direct correlation between the optical fiber or shock location and the beam s diffraction pattern. A plot of the width of the diffraction pattern vs. optical fiber location reveals that the width of the diffraction pattern was maximized when the laser beam is directed at the center of the optical fiber. This work indicates that the one-dimensional scanning approach may be able to determine the location of an actual shock. Near and far field effects associated with a small diameter laser beam striking an optical fiber used as a simulated shock are investigated allowing a proper one-dimensional scanning beam technique.
One-dimensional hydrodynamic model generating a turbulent cascade
NASA Astrophysics Data System (ADS)
Matsumoto, Takeshi; Sakajo, Takashi
2016-05-01
As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analog (enstrophy) in the inviscid case. With a large-scale random forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency, and self-similarity in the dynamical system structure.
Correlations in light propagation in one-dimensional waveguides
NASA Astrophysics Data System (ADS)
Javanainen, Juha; Ruostekoski, Janne
2016-05-01
We study light propagation between atoms in a one-dimensional waveguide both analytically and using numerical simulations. We employ classical electrodynamics, but in the limit of low light intensity the results are essentially exact also for quantum mechanics. We characterize the cooperative interactions between the atoms mediated by the electromagnetic field. The focus is on resonance shifts for various statistics of the positions of the atoms, such as statistically independent positions or atoms in a regular lattice. These shifts, potentially important if 1D waveguides are to be used in metrology, are different from the usual resonance shifts found in three spatial dimensions.
Cooling of a One-Dimensional Bose Gas.
Rauer, B; Grišins, P; Mazets, I E; Schweigler, T; Rohringer, W; Geiger, R; Langen, T; Schmiedmayer, J
2016-01-22
We experimentally study the dynamics of a degenerate one-dimensional Bose gas that is subject to a continuous outcoupling of atoms. Although standard evaporative cooling is rendered ineffective by the absence of thermalizing collisions in this system, we observe substantial cooling. This cooling proceeds through homogeneous particle dissipation and many-body dephasing, enabling the preparation of otherwise unexpectedly low temperatures. Our observations establish a scaling relation between temperature and particle number, and provide insights into equilibration in the quantum world. PMID:26849577
An improved lambda-scheme for one-dimensional flows
NASA Technical Reports Server (NTRS)
Moretti, G.; Dipiano, M. T.
1983-01-01
A code for the calculation of one-dimensional flows is presented, which combines a simple and efficient version of the lambda-scheme with tracking of discontinuities. The latter is needed to identify points where minor departures from the basic integration scheme are applied to prevent infiltration of numerical errors. Such a tracking is obtained via a systematic application of Boolean algebra. It is, therefore, very efficient. Fifteen examples are presented and discussed in detail. The results are exceptionally good. All discontinuites are captured within one mesh interval.
Quantum mechanics of graphene with a one-dimensional potential
Miserev, D. S.; Entin, M. V.
2012-10-15
Electron states in graphene with a one-dimensional potential have been studied. An approximate solution has been obtained for a small angle between vectors of the incident electron momentum and potential gradient. Exactly solvable problems with a potential of the smoothened step type U(x) Utanh(x/a) and a potential with a singularity U(x) = -U/(|x| + d) are considered. The transmission/reflection coefficients and phases for various potential barriers are determined. A quasi-classical solution is obtained.
Solution methods for one-dimensional viscoelastic problems
NASA Technical Reports Server (NTRS)
Stubstad, John M.; Simitses, George J.
1987-01-01
A recently developed differential methodology for solution of one-dimensional nonlinear viscoelastic problems is presented. Using the example of an eccentrically loaded cantilever beam-column, the results from the differential formulation are compared to results generated using a previously published integral solution technique. It is shown that the results obtained from these distinct methodologies exhibit a surprisingly high degree of correlation with one another. A discussion of the various factors affecting the numerical accuracy and rate of convergence of these two procedures is also included. Finally, the influences of some 'higher order' effects, such as straining along the centroidal axis are discussed.
One-dimensional physics in the 21st century
NASA Astrophysics Data System (ADS)
Giamarchi, Thierry
2016-03-01
This paper presents a brief introduction to some of the systems and questions concerning one-dimensional interacting quantum systems. Historically, organic conductors and superconductors - a field extremely active in the "Laboratoire de physique des solides" in Orsay, in a good part thanks to the influence of Jacques Friedel, played a crucial role in this field. I will describe some of the aspects of this physics and also review some of the very exciting theoretical and experimental developments that took place in the 1D world in the last 15 years or so. xml:lang="fr"
Decay of fermionic quasiparticles in one-dimensional quantum liquids.
Matveev, K A; Furusaki, A
2013-12-20
The low-energy properties of one-dimensional quantum liquids are commonly described in terms of the Tomonaga-Luttinger liquid theory, in which the elementary excitations are free bosons. To this approximation, the theory can be alternatively recast in terms of free fermions. In both approaches, small perturbations give rise to finite lifetimes of excitations. We evaluate the decay rate of fermionic excitations and show that it scales as the eighth power of energy, in contrast to the much faster decay of bosonic excitations. Our results can be tested experimentally by measuring the broadening of power-law features in the density structure factor or spectral functions. PMID:24483750
One-dimensional intense laser pulse solitons in a plasma
Sudan, R.N.; Dimant, Y.S.; Shiryaev, O.B.
1997-05-01
A general analytical framework is developed for the nonlinear dispersion relations of a class of large amplitude one-dimensional isolated envelope solitons for modulated light pulse coupled to electron plasma waves, previously investigated numerically [Kozlov {ital et al.}, Zh. Eksp. Teor. Fiz. {bold 76}, 148 (1979); Kaw {ital et al.}, Phys. Rev. Lett. {bold 68}, 3172 (1992)]. The analytical treatment of weakly nonlinear solitons [Kuehl and Zhang, Phys. Rev. E {bold 48}, 1316 (1993)] is extended to the strongly nonlinear limit. {copyright} {ital 1997 American Institute of Physics.}