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At least 19 recordsLinked to original sources

arXiv2007

Estimation of experimental data redundancy and related statistics

Redundancy of experimental data is the basic statistic from which the complexity of a natural phenomenon and the proper number of experiments needed for its exploration can be estimated. The redundancy is expressed by the entropy of information pertaining to the probability density function of experimental variables. Since the calculation of entropy is inconvenient due to integration over a range of variables, an approximate expression for redundancy is derived that includes only a sum over the set of experimental data about these variables. The approximation makes feasible an efficient estimation of the redundancy of data along with the related experimental information and information cost function. From the experimental information the complexity of the phenomenon can be simply estimated, while the proper number of experiments needed for its exploration can be determined from the minimum of the cost function. The performance of the approximate estimation of these statistics is demonstrated on two-dimensional normally distributed random data.

physics.data-an↗

arXiv2007

Use of Triangular Elements for Nearly Exact BEM Solutions

A library of C functions yielding exact solutions of potential and flux influences due to uniform surface distribution of singularities on flat triangular and rectangular elements has been developed. This library, ISLES, has been used to develop the neBEM solver that is both precise and fast in solving a wide range of problems of scientific and technological interest. Here we present the exact expressions proposed for computing the influence of uniform singularity distributions on triangular elements and illustrate their accuracy. We also present a study concerning the time taken to evaluate these long and complicated expressions \textit{vis a vis} that spent in carrying out simple quadratures. Finally, we solve a classic benchmark problem in electrostatics, namely, estimation of the capacitance of a unit square plate raised to unit volt. For this problem, we present the estimated values of capacitance and compare them successfully with some of the most accurate results available in the literature. In addition, we present the variation of the charge density close to the corner of the plate for various degrees of discretization. The variations are found to be smooth and converging. This is in clear contrast to the criticism commonly leveled against usual BEM solvers.

math.NA↗

arXiv2008

On monotonicity, stability, and construction of central schemes for hyperbolic conservation laws with source terms (Revised Version)

The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms of its corresponding scheme in variations. Such an approach leads to application of the stability theory for linear equation systems to establish stability of the corresponding non-linear scheme. The main methodological innovation is the theorems establishing the notion that a non-linear scheme is stable (and monotone) if the corresponding scheme in variations is stable (and, respectively, monotone). Criteria are developed for monotonicity and stability of difference schemes associated with the numerical analysis of systems of partial differential equations. The theorem of Friedrichs (1954) is generalized to be applicable to variational schemes with non-symmetric matrices. A new modification of the central Lax-Friedrichs (LxF) scheme is developed to be of the second order accuracy. A monotone piecewise cubic interpolation is used in the central schemes to give an accurate approximation for the model in question. The stability and monotonicity of the modified scheme are investigated. Some versions of the modified scheme are tested on several conservation laws, and the scheme is found to be accurate and robust. As applied to hyperbolic conservation laws with, in general, stiff source terms, it is constructed a second order scheme based on operator-splitting techniques.

physics.comp-ph↗

arXiv2008

Descriptor approach for eliminating spurious eigenvalues in hydrodynamic equations

We describe a general framework for avoiding spurious eigenvalues -- unphysical unstable eigenvalues that often occur in hydrodynamic stability problems. In two example problems, we show that when system stability is analyzed numerically using {\em descriptor} notation, spurious eigenvalues are eliminated. Descriptor notation is a generalized eigenvalue formulation for differential-algebraic equations that explicitly retains algebraic constraints. We propose that spurious eigenvalues are likely to occur when algebraic constraints are used to analytically reduce the number of independent variables in a differential-algebraic system of equations before the system is approximated numerically. In contrast, the simple and easily generalizable descriptor framework simultaneously solves the differential equations and algebraic constraints and is well-suited to stability analysis in these systems.

physics.comp-ph↗

arXiv2007

Combined Extended Rejoinder to "Extended Comment on "One-Range Addition Theorems for Coulomb Interaction Potential and Its Derivatives" by I. I. Guseinov (Chem. Phys., Vol. 309 (2005), pp. 209-213)"

This article is a thorough critique to the Weniger's comments made to our papers published in prestigious journals in the recent years. A detailed and critical examination of the arguments that led to the suggested comment by Weniger reveals some serious flaws. In our published papers we have shown that the unsymmetrical and symmetrical one-range addition theorems for Slater type orbitals, Coulomb-Yukawa like correlated interaction potentials (CIPs) and their derivatives are derived from the expansions in terms of -ETOs that are complete and orthonormal sets of exponential type orbitals in corresponding Hilbert spaces, where The concrete criticism raised in Weniger's comment against our papers actually touches a very minor aspect of the works that are not relevant at all for the conclusions, which are made. As can be seen from our papers, all of the formulas for different kinds of multicenter integrals over Slater type orbitals with integer and noninteger principal quantum numbers obtained by the use of unsymmetrical and symmetrical one-range addition theorems were tested by computer calculations. We reject the Weniger's personal views about papers published by Guseinov and his coworkers from 1978 to 2006 and respectable referees on one-range addition theorems and multicenter integrals. All claims of inconsistencies and flaws in the theoretical framework are rejected as unfounded. This rejoinder paper contains all of the answers to Weniger's comments.

physics.chem-ph↗

arXiv2007

Theoretical spectroscopic studies of the atomic transitions and lifetimes of low-lying states in Ti IV

The astrophysically important electric quadrupole (E2) and magnetic dipole (M1) transitions for the low-lying states of triply ionized titanium (Ti IV) are calculated very accurately using a state-of-art all-order many-body theory called Coupled Cluster (CC) theory in the relativistic frame-work. Different many-body correlations of the CC theory has been estimated by studying the core and valence electron excitations to the unoccupied states. The calculated excitation energies of different states are in very good agreement with the measurements. Also we compare our calculated electric dipole (E1) transition amplitudes of few transitions with recent many-body calculations by different groups. We have also carried out the calculations for the lifetimes of the low-lying states of Ti IV. A long lifetime is found for the first excited 3d$^{2}D_{5/2}$ state, which suggested that Ti IV may be one of the useful candidates for many important studies. Most of the results reported here are not available in the literature, to the best of our knowledge.

physics.atom-ph↗

arXiv2007

Polarizability of molecular chains: does one need exact exchange?

Standard density functional approximations greatly over-estimate the static polarizability of longchain polymers, but Hartree-Fock or exact exchange calculations do not. Simple self-interaction corrected (SIC) approximations can be even better than exact exchange, while their computational cost can scale only linearly with the number of occupied orbitals.

physics.atm-clus↗

arXiv2007

Prisoner's Dilemma in One-Dimensional Cellular Automata: Visualization of Evolutionary Patterns

The spatial Prisoner's Dilemma is a prototype model to show the emergence of cooperation in very competitive environments. It considers players, at site of lattices, that can either cooperate or defect when playing the Prisoner's Dilemma with other z players. This model presents a rich phase diagram. Here we consider players in cells of one-dimensional cellular automata. Each player interacts with other z players. This geometry allows us to vary, in a simple manner, the number of neighbors ranging from one up to the lattice size, including self-interaction. This approach has multiple advantages. It is simple to implement numerically and we are able to retrieve all the previous results found in the previously considered lattices, with a faster convergence to stationary values. More remarkable, it permits us to keep track of the spatio-temporal evolution of each player of the automaton. Giving rise to interesting patterns. These patterns allow the interpretation of cooperation/defection clusters as particles, which can be absorbed and collided among themselves. The presented approach represents a new paradigm to study the emergence and maintenance of cooperation in the spatial Prisoner's Dilemma.

physics.comp-ph↗

arXiv2007

Lattice Boltzmann simulation of electrowetting-on-dielectric in a rough-wall channel

A lattice Boltzmann model was proposed to simulate electrowetting-on-dielectric (EWOD). The insulative vapor and the electrolyte liquid droplet were simulated by the lattice Boltzmann method respectively, and the linear property between cosine of contact angle and the electric field force confirms the reliability of this model. In the simulation of electrolyte flowing in a rough-wall channel under an external electric field, we found that a narrow channel is more sensitive than a broad channel and the flux decreases monotonously as the electric field increase, but may suddenly increase if the electric field is strong enough.

physics.comp-ph↗

arXiv2008

An exhaustive exploration of the parameter space of the Prisoners' Dilemma in one-dimensional cellular automata

The Prisoner's Dilemma (PD) is one of the most popular games of the Game Theory due to the emergence of cooperation among competitive rational players. In this paper, we present the PD played in cells of one-dimension cellular automata, where the number of possible neighbors that each cell interacts, z, can vary. This makes possible to retrieve results obtained previously in regular lattices. Exhaustive exploration of the parameters space is presented. We show that the final state of the system is governed mainly by the number of neighbors z and there is a drastic difference if it is even or odd.

physics.soc-ph↗

arXiv2007

Noise limits in the assembly of diffraction data

We obtain an information theoretic criterion for the feasibility of assembling diffraction signals from noisy tomographs when the positions of the tomographs within the signal are unknown. For shot-noise limited data, the minimum number of detected photons per tomograph for successful assembly is much smaller than previously believed necessary, growing only logarithmically with the number of resolution elements of the diffracting object. We also demonstrate assembly up to the information theoretic limit with a constraint-based algorithm.

physics.comp-ph↗

arXiv2010

Are biological neurons that vicious ? Or only their models ?

This paper has been withdrawn. Its main conclusions have been published in "On dynamics of integrate-and-fi re neural networks with conductance based synapses", arXiv:0709.4370 and http://www.frontiersin.org/computational_neuroscience/10.3389/neuro.10/002.2008/abstract

physics.bio-ph↗

arXiv2007

Discovering Important Nodes Through Graph Entropy Encoded in Urban Space Syntax

Potentially influential spaces in the spatial networks of cities can be detected by means of the entropy participation ratios. Local (connectivity) and global (centrality) entropies are considered. While the connectivity entropy has a tendency to increase with the city size, the centrality entropy is decreasing that reflects the global connectedness of cities. In urban networks, the local and global properties of nodes are positively correlated that indicates the intelligibility of cities. Correlations between entropy participation ratios can be used in purpose of intelligibility measurements and city networks comparisons.

physics.soc-ph↗

arXiv2007

A General Strategy for Physics-Based Model Validation Illustrated with Earthquake Phenomenology, Atmospheric Radiative Transfer, and Computational Fluid Dynamics

Validation is often defined as the process of determining the degree to which a model is an accurate representation of the real world from the perspective of its intended uses. Validation is crucial as industries and governments depend increasingly on predictions by computer models to justify their decisions. In this article, we survey the model validation literature and propose to formulate validation as an iterative construction process that mimics the process occurring implicitly in the minds of scientists. We thus offer a formal representation of the progressive build-up of trust in the model, and thereby replace incapacitating claims on the impossibility of validating a given model by an adaptive process of constructive approximation. This approach is better adapted to the fuzzy, coarse-grained nature of validation. Our procedure factors in the degree of redundancy versus novelty of the experiments used for validation as well as the degree to which the model predicts the observations. We illustrate the new methodology first with the maturation of Quantum Mechanics as the arguably best established physics theory and then with several concrete examples drawn from some of our primary scientific interests: a cellular automaton model for earthquakes, an anomalous diffusion model for solar radiation transport in the cloudy atmosphere, and a computational fluid dynamics code for the Richtmyer-Meshkov instability. This article is an augmented version of Sornette et al. [2007] that appeared in Proceedings of the National Academy of Sciences in 2007 (doi: 10.1073/pnas.0611677104), with an electronic supplement at URL http://www.pnas.org/cgi/content/full/0611677104/DC1. Sornette et al. [2007] is also available in preprint form at physics/0511219.

physics.comp-ph↗

arXiv2007

Statistical properties of agent-based market area model

One dimensional stylized model taking into account spatial activity of firms with uniformly distributed customers is proposed. The spatial selling area of each firm is defined by a short interval cut out from selling space (large interval). In this representation, the firm size is directly associated with the size of its selling interval. The recursive synchronous dynamics of economic evolution is discussed where the growth rate is proportional to the firm size incremented by the term including the overlap of the selling area with areas of competing firms. Other words, the overlap of selling areas inherently generate a negative feedback originated from the pattern of demand. Numerical simulations focused on the obtaining of the firm size distributions uncovered that the range of free parameters where the Pareto's law holds corresponds to the range for which the pair correlation between the nearest neighbor firms attains its minimum.

q-fin.GN↗

arXiv2007

Wealth distribution in a System with Wealth-limited Interactions

We model a closed economic system with interactions that generates the features of empirical wealth distribution across all wealth brackets, namely a Gibbsian trend in the lower and middle wealth range and a Pareto trend in the higher range, by simply limiting the an agents' interaction to only agents with nearly the same wealth. To do this, we introduce a parameter BETA that limits the range on the wealth of a partner with which an agent is allowed to interact. We show that this wealth-limited interaction is enough to distribute wealth in a purely power law trend. If the interaction is not wealth limited, the wealth distribution is expectedly Gibbsian. The value of BETA where the transition from a purely Gibbsian law to a purely power law distribution happens depends on whether the choice of interaction partner is mutual nor not. For a non-mutual choice, where the richer agent gets to decide, the transition happens at BETA=1.0. For a mutual choice, the transition is at BETA= 0.60. In order to generate a mixed Gibbs-Pareto distribution, we apply another wealth-based rule that depends on the parameter w_limit. An agent whose wealth is below w_limit can choose any partner to interact with, while an agent whose wealth is above w_limit is subject to the wealth-limited range in his choice of partner. A Gibbs-Pareto distribution appears if both these wealth-based rules are applied.

q-fin.GN↗

arXiv2008

Absolute FKBP binding affinities obtained via non-equilibrium unbinding simulations

We compute absolute binding affinities for two ligands bound to the FKBP protein using non-equilibrium unbinding simulations. The methodology is straight-forward, requiring little or no modification to many modern molecular simulation packages. The approach makes use of a physical pathway, eliminating the need for complicated alchemical decoupling schemes. Results of this study are promising. For the ligands studied here the binding affinities are typically estimated within less than 4.0 kJ/mol of the target values; and the target values are within less than 1.0 kJ/mol of experiment. These results suggest that non-equilibrium simulation could provide a simple and robust means to estimate protein-ligand binding affinities.

physics.bio-ph↗

arXiv2007

Parallel multiscale modeling of biopolymer dynamics with hydrodynamic correlations

We employ a multiscale approach to model the translocation of biopolymers through nanometer size pores. Our computational scheme combines microscopic Molecular Dynamics (MD) with a mesoscopic Lattice Boltzmann (LB) method for the solvent dynamics, explicitly taking into account the interactions of the molecule with the surrounding fluid. We describe an efficient parallel implementation of the method which exhibits excellent scalability on the Blue Gene platform. We investigate both dynamical and statistical aspects of the translocation process by simulating polymers of various initial configurations and lengths. For a representative molecule size, we explore the effects of important parameters that enter in the simulation, paying particular attention to the strength of the molecule-solvent coupling and of the external electric field which drives the translocation process. Finally, we explore the connection between the generic polymers modeled in the simulation and DNA, for which interesting recent experimental results are available.

physics.comp-ph↗