Showing papers on "Constant (mathematics) published in 2002"
TL;DR: In this article, the linear theory of the time or frequency-dependent Poisson's ratio is developed and a series of experiments are conducted to determine the Poisson ratio of a homogeneous isotropic body.
Abstract: Poisson's ratio is an elastic constant defined as the ratio of thelateral contraction to the elongation in the infinitesimal uniaxialextension of a homogeneous isotropic body. In a viscoelastic materialPoisson's ratio is a function of time (or frequency) that depends on thetime regime chosen to elicit it. It is important as one of the materialfunctions that characterize bulk behavior. This paper develops the linear theory of the time- orfrequency-dependent Poisson's ratio, and it reviews work on itsexperimental determination. The latter poses severe difficulties in viewof the high accuracy required. Thus, reliable information on theviscoelastic Poisson's ratio is as yet rather scanty. The paper also reports on attempts to measure the Poisson's ratioof a viscoelastic material as a function of temperature. Lateralcontraction in creep and at constant rate of extension receivesattention as well.
401 citations
TL;DR: This work considers the implementation of abstract data types for the static objects: binary tree, rooted ordered tree, and a balanced sequence of parentheses to produce a succinct representation of planar graphs in which one can test adjacency in constant time.
Abstract: We consider the implementation of abstract data types for the static objects: binary tree, rooted ordered tree, and a balanced sequence of parentheses. Our representations use an amount of space within a lower order term of the information theoretic minimum and support, in constant time, a richer set of navigational operations than has previously been considered in similar work. In the case of binary trees, for instance, we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned. The approach is applied to produce a succinct representation of planar graphs in which one can test adjacency in constant time.
376 citations
TL;DR: A chi-squared distance analysis is used to compute a flexible metric for producing neighborhoods that are highly adaptive to query locations and the class conditional probabilities are smoother in the modified neighborhoods, whereby better classification performance can be achieved.
Abstract: Nearest-neighbor classification assumes locally constant class conditional probabilities. This assumption becomes invalid in high dimensions with finite samples due to the curse of dimensionality. Severe bias can be introduced under these conditions when using the nearest-neighbor rule. We propose a locally adaptive nearest-neighbor classification method to try to minimize bias. We use a chi-squared distance analysis to compute a flexible metric for producing neighborhoods that are highly adaptive to query locations. Neighborhoods are elongated along less relevant feature dimensions and constricted along most influential ones. As a result, the class conditional probabilities are smoother in the modified neighborhoods, whereby better classification performance can be achieved. The efficacy of our method is validated and compared against other techniques using both simulated and real-world data.
332 citations
TL;DR: In this article, the potential impact of improved future supernovae data on our understanding of the dark energy problem is discussed. But the focus is on the proposed satellite, which is planned to observe around 2000 supernova.
Abstract: We study the potential impact of improved future supernovae data on our understanding of the dark energy problem. We carefully examine the relative utility of different fitting functions that can be used to parametrize the dark energy models, and provide concrete reasons why a particular choice (based on a parametrization of the equation of state) is better in almost all cases. We discuss the details of a representative sample of dark energy models and show how future supernova observations could distinguish among these. As a specific example, we consider the proposed ``SNAP'' satellite which is planned to observe around 2000 supernovae. We show how a SNAP-class data set taken alone would be a powerful discriminator among a family of models that would be approximated by a constant equation of state for the most recent epoch of cosmic expansion. We show how this family includes most of the dark energy models proposed so far. We then show how an independent measurement of ${\ensuremath{\Omega}}_{\mathrm{m}}$ can allow SNAP to probe the evolution of the equation of state as well, allowing further discrimination among a larger class of proposed dark energy models. We study the impact of the satellite design parameters on this method to distinguish the models and compare SNAP to alternative measurements. We establish that if we exploit the full precision of SNAP it provides a very powerful probe.
309 citations
TL;DR: In this article, a stable, efficient approach to inverse Q filtering based on the theory of wavefield downward continuation is presented. But it is implemented in a layered manner, assuming a depth-dependent, layered-earth Q model.
Abstract: Stability and efficiency are two issues of general concern in inverse Q filtering. This paper presents a stable, efficient approach to inverse Q filtering, based on the theory of wavefield downward continuation. It is implemented in a layered manner, assuming a depth-dependent, layered-earth Q model. For each individual constant Q layer, the seismic wavefield recorded at the surface is first extrapolated down to the top of the current layer and a constant Q inverse filter is then applied to the current layer. When extrapolating within the overburden, instead of applying wavefield downward continuation directly, a reversed, upward continuation system is solved to obtain a stabilized solution. Within the current constant Q layer, the amplitude compensation operator, which is a 2-D function of traveltime and frequency, is approximated optimally as the product of two 1-D functions depending, respectively, on time and frequency. The constant Q inverse filter that compensates simultaneously for phase and amplitude effects is then implemented efficiently in the Fourier domain.
303 citations
TL;DR: In this paper, a molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure ensemble was proposed, which is tested for an atomic fluid (Ar) and works well.
Abstract: A molecular dynamics simulation method which can generate configurations belonging to the canonical (T, V, N) ensemble or the constant temperature constant pressure (T, P, N) ensemble, is proposed The physical system of interest consists of N particles (f degrees of freedom), to which an external, macroscopic variable and its conjugate momentum are added This device allows the total energy of the physical system to fluctuate The equilibrium distribution of the energy coincides with the canonical distribution both in momentum and in coordinate space The method is tested for an atomic fluid (Ar) and works well
300 citations
TL;DR: In this article, the particle contributions to the running of the cosmological and gravitational constants in the framework of the Standard Model in curved space-time are derived, in two different frameworks, whether the scaling dependences of these constants spoil primordial nucleosynthesis.
Abstract: In quantum field theory the parameters of the vacuum action are subject to renormalization group running. In particular, the ``cosmological constant'' is not a constant in a quantum field theory context, still less should be zero. In this paper we continue with previous work, and derive the particle contributions to the running of the cosmological and gravitational constants in the framework of the Standard Model in curved space-time. At higher energies the calculation is performed in a sharp cut off approximation. We assess, in two different frameworks, whether the scaling dependences of the cosmological and gravitational constants spoil primordial nucleosynthesis. Finally, the cosmological implications of the running of the cosmological constant are discussed.
274 citations
TL;DR: In this article, the authors considered the case of 3-dimensional spacetimes of constant 3D spatial curvature in the presence of a bulk cosmological constant and found the general solution of such a configuration under a Gauss-Bonnet term.
Abstract: We consider 5-dimensional spacetimes of constant 3-dimensional spatial curvature in the presence of a bulk cosmological constant. We find the general solution of such a configuration in the presence of a Gauss-Bonnet term. Two classes of non-trivial bulk solutions are found. The first class is valid only under a fine tuning relation between the Gauss-Bonnet coupling constant and the cosmological constant of the bulk spacetime. The second class of solutions are static and are the extensions of the AdS-Schwarzchild black holes. Hence in the absence of a cosmological constant or if the fine tuning relation is not true, the generalised Birkhoff's staticity theorem holds even in the presence of Gauss-Bonnet curvature terms. We examine the consequences in brane world cosmology obtaining the generalised Friedmann equations for a perfect fluid 3-brane and discuss how this modifies the usual scenario.
265 citations
TL;DR: In this article, the homotopy analysis method is applied to give an analytic approximation of temperature distributions for a laminar viscous flow over a semi-infinite plate.
Abstract: We apply a new analytic technique, namely the homotopy analysis method, to give an analytic approximation of temperature distributions for a laminar viscous flow over a semi-infinite plate. An explicit analytic solution of the temperature distributions is obtained in general cases and recurrence formulae of the corresponding constant coefficients are given. In the cases of constant plate temperature distribution and constant plate heat flux, the first-order derivative of the temperature on the plate at the 30th order of approximation is given. The convergence regions of these two formulae are greatly enlarged by the Pade technique. They agree well with numerical results in a very large region of Prandtl number 1[les ]Pr[les ]50 and therefore can be applied without interpolations.
265 citations
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TL;DR: In this paper, a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances is proposed.
Abstract: We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small at large length scales, so that sources with immense wavelengths and periods -- such as the vacuum energy-- produce minuscule curvature. Conventional astrophysics, cosmology and standard inflationary scenaria are unaffected, as they involve shorter length scales. A new possibility emerges that inflation may ``self-terminate'' naturally by its own action of stretching wavelengths to enormous sizes. In a simple limit our proposal leads to a modification of Einstein's equation by a single additional term proportional to the average space-time curvature of the Universe. It may also have a qualitative connection with the dS/CFT conjecture.
258 citations
TL;DR: For constant linear systems, integral reconstructors and generalized proportional-integral controllers are introduced, which permit to bypass the derivative term in the classic PID controllers and more generally the usual asymptotic observers.
Abstract: For constant linear systems we are introducing integral reconstructors and generalized proportional-integral controllers , which permit to bypass the derivative term in the classic PID controllers and more generally the usual asymptotic observers. Our approach, which is mainly of algebraic flavour, is based on the module-theoretic framework for linear systems and on operational calculus in Mikusinski's setting. Several examples are discussed.
TL;DR: In this article, a constant number Monte Carlo (CMC) simulation of the mean-field population balance equation is proposed, where a sample of the population whose size (number of particles in the sample) is kept constant throughout the simulation is tracked.
TL;DR: A sliding mode controller is designed for systems with multiple state delays and submitted to additive pertubations by using Liapunov-Krasovskii functionals and solving a convex minimisation problem expressed in terms of LMIs.
TL;DR: In this article, a criterion for a function to belong to or to is given, and various integral conditions under which a measurable function is constant are discussed, and the criterion for determining whether a function belongs to a certain class of functions is discussed.
Abstract: A criterion for a function to belong to or to is given. Various integral conditions under which a measurable function is constant are discussed.
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TL;DR: It is proved that if one can simulate these circuits classically efficiently then BQP ⊆ AM is possible.
Abstract: We present evidence that there exist quantum computations that can be carried out in constant depth, using 2-qubit gates, that cannot be simulated classically with high accuracy. We prove that if one can simulate these circuits classically efficiently then the complexity class BQP is contained in AM.
TL;DR: This paper proves quadratic lower bounds for depth-3 arithmetic circuits over fields of characteristic zero for the elementary symmetric functions, the (trace of) iterated matrix multiplication, and the determinant, and gives new shorter formulae of constant depth for the Elementary symmetrical functions.
Abstract: In this paper we prove quadratic lower bounds for depth-3 arithmetic circuits over fields of characteristic zero. Such bounds are obtained for the elementary symmetric functions, the (trace of) iterated matrix multiplication, and the determinant. As corollaries we get the first nontrivial lower bounds for computing polynomials of constant degree, and a gap between the power of depth-3 arithmetic circuits and depth-4 arithmetic circuits. We also give new shorter formulae of constant depth for the elementary symmetric functions.¶The main technical contribution relates the complexity of computing a polynomial in this model to the wealth of partial derivatives it has on every affine subspace of small co-dimension. Lower bounds for related models utilize an algebraic analog of the Neciporuk lower bound on Boolean formulae.
TL;DR: Kemeny's constant is revisited, generalized, derived upper and lower bounds on it, and given a novel interpretation in terms of the number of links a random surfer will follow to reach his final destination.
Abstract: We revisit Kemeny's constant in the context of Web navigation, also known as "surfing." We generalize the constant, derive upper and lower bounds on it, and give it a novel interpretation in terms of the number of links a random surfer will follow to reach his final destination.
01 Aug 2002
TL;DR: This work shows that the Consensus Patterns problem is NP-hard and gives a polynomial time approximation scheme (PTAS) for it, and presents an efficient approximation algorithm for the consensus pattern problem under the original relative entropy measure.
Abstract: Algorithms for finding similar, or highly conserved, regions in a group of sequences are at the core of many molecular biology problems Assume that we are given n DNA sequences s1, , sn The Consensus Patterns problem, which has been widely studied in bioinformatics research, in its simplest form, asks for a region of length L in each si, and a median string s of length L so that the total Hamming distance from s to these regions is minimized We show that the problem is NP-hard and give a polynomial time approximation scheme (PTAS) for it We then present an efficient approximation algorithm for the consensus pattern problem under the original relative entropy measure As an interesting application of our analysis, we further obtain a PTAS for a restricted (but still NP-hard) version of the important consensus alignment problem allowing at most constant number of gaps, each of arbitrary length, in each sequence
TL;DR: An analytic solution for a race model of n stochastic accumulators for multiple choice reaction time shows that to maintain a constant level of accuracy, the response criterion needs to be increased approximately logarithmically with n to compensate for the increase with n in the likelihood of an incorrect alternative.
01 Jan 2002
TL;DR: In this paper, the authors investigated the constant-wall-temperature convective heat transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions.
Abstract: We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions. Our investigation covers both the slip-flow regime 0≤Kn≤0.1, and most of the transition regime 0.1
TL;DR: In this article, the dynamic behavior of multi-span non-uniform beams transversed by a moving load at a constant and variable velocity is investigated using Bernoulli-Euler beam theory.
TL;DR: In this paper, the hyperbolic angle θ between the future-pointing unit normal vector field and the universal time axis is considered, and a uniqueness result for spacelike hypersurfaces of constant mean curvature under this assumption on θ, and also assuming certain matter energy conditions hold just at this point, is proved.
Abstract: On any spacelike hypersurface of constant mean curvature of a Generalized Robertson–Walker spacetime, the hyperbolic angle θ between the future-pointing unit normal vector field and the universal time axis is considered. It is assumed that θ has a local maximum. A physical consequence of this fact is that relative speeds between normal and comoving observers do not approach the speed of light near the maximum point. By using a development inspired from Bochner's well-known technique, a uniqueness result for spacelike hypersurfaces of constant mean curvature under this assumption on θ, and also assuming certain matter energy conditions hold just at this point, is proved.
TL;DR: In this paper, the Beverton-Holt equation is modified for population dynamics, where the constant carrying capacity of a population is replaced by a periodic sequence of positive carrying capacities.
Abstract: has a unique positive equilibrium K and all solutions with x0 . 0 approach K as t !1: This equation (known as the Beverton–Holt equation) arises in applications to population dynamics, and in that context K is the “carrying capacity” and r is the “inherent growth rate”. A modification of this equation that arises in the study of populations living in a periodically (seasonally) fluctuating environment replaces the constant carrying capacity K by a periodic sequence Kt of positive carrying capacities.
TL;DR: The constant K has the same meaning as above, and one notices that the error bound for the midpoint rule is one half that of the trapezoidal rule.
Abstract: The constant K has the same meaning as above. 1CAS = Computer Algebra System. 2The interval [0, 2π] is for convenience only. Everything we say can easily be extended to an arbitrary interval [a, b]. 3One notices that the error bound for the midpoint rule is one half that of the trapezoidal rule; compare (2) with (3). For a pretty geometrical explanation of why one can expect the midpoint rule to be better by about a factor of two, the reader is referred to Stewart [13, p. 460].
07 Nov 2002
TL;DR: In this paper, a comprehensive power analysis, keeping integrated circuits in mind, is presented while highlighting all conduction, switching, and dynamic power losses in a DC-DC converter, and it is concluded that a mode-hopping converter employing an asynchronous, constant on-time, variable frequency operation for low output currents and a synchronous, constant frequency CCM operation for high load currents yields the best efficiency performance.
Abstract: A comprehensive power analysis, keeping integrated circuits in mind, is presented while highlighting all conduction, switching, and dynamic power losses in a DC-DC converter. Synchronous rectification, zero-voltage switching, mode-hopping, and variable frequency operation are evaluated. The efficiency for constant frequency CCM, constant frequency DCM, and constant on-time, variable frequency DCM techniques is analyzed and the optimum technique is derived. It is concluded that a mode-hopping converter employing an asynchronous, constant on-time, variable frequency DCM operation for low output currents and a synchronous, constant frequency CCM operation for high load currents yields the best efficiency performance.
TL;DR: In this paper, a study of adsorption of copper(II) ions onto calcium alginate beads has been carried out and several empirical and semi-empirical models are proposed to describe and to fit all the experimental data, including pH as independent variable.
TL;DR: In this article, the authors examine the relation between liquid behavior at constant pressure and constant volume and compare the inherent structures excitation profiles for the two cases, and find a parallel between the range of volumes, relative to the total excess volume, that are explored in the first few orders of magnitude of relaxation time increase, and the ranges of amorphous state inherent structure energies, relative with the total range, that were explored in ergodic computer simulations.
Abstract: In pursuit of understanding of the paradoxical success of the Adam–Gibbs equation in both experiment and computer simulation studies, we examine the relation between liquid behavior at constant pressure and constant volume and compare the inherent structures excitation profiles for the two cases. This allows us to extend qualitatively the recent correlation of kinetic and thermodynamic measures of fragility to constant volume systems. The decreased fragility at constant volume is understood in terms of the relation Cp > CcðcpÞ > CcðcvÞ > Cv. In the process, we find a parallel between the range of volumes, relative to the total excess volume, that are explored in the first few orders of magnitude of relaxation time increase, and the range of amorphous state inherent structure energies, relative to the total range, that are explored in ergodic computer simulations, which also cover only this limited range of relaxation time change. The interesting question of whether or not fragile behavior is determined in the configurational or vibrational manifold of states is left unanswered in this work. However, the approximate proportionality of the configurational and total excess entropies that is needed to interpret the success of the Adam–Gibbs equation (which has been questioned by other authors) is confirmed within the needed limits, using data from three different types of investigation: experiments (on Se), simulation (of water in the SPC-E model), and analytical models of both defect crystals and configurationally excited liquids. Some consequences of the abrupt increases in vibrational heat capacity at Tg implied by this proportionality, are discussed. 2002 Elsevier Science B.V. All rights reserved.
TL;DR: In this article, a qualitative theory for the origin of the near constant loss is presented, which gives physical meanings of the two crossover frequencies and explains the role of the independent hopping frequency in determining them.
Abstract: Experimental frequency-dependent conductivity relaxation spectra of a number of molten, glassy, and crystalline ionic conductors that show both the presence of the near constant loss (NCL) and the cooperative ion hopping contribution are analyzed. On decreasing frequency, the NCL appears first but terminates at some frequency v_(x1). At still a lower frequency v_(x2) the cooperative ion hopping dispersion takes over. The independent ion hopping frequency v_(0) of the coupling model is calculated from the parameters characterizing the cooperative ion hopping dispersion. It is found for all ionic conductors that v_(x1)>>v_(0), and v_(0) always fall inside the frequency region v_(x1) > v > v_(x2). The empirical results leads to a qualitative theory for the origin of the NCL, which gives physical meanings of the two crossover frequencies v_(x1) and v_(x2), as well as explaining the role of the independent hopping frequency v_(0), in determining them. The weak temperature dependence of the NCL has been recaptured by the qualitative theory. An improved understanding is gained of the evolution of the ion dynamics from early times when the cages decay very slowly with time, giving rise to the near constant loss, to long times when ions move cooperatively, leading finally to dc conductivity.
TL;DR: A method based on augmenting an exact relation between a frequency-dependent diffusion constant and the imaginary time velocity autocorrelation function, combined with the maximum entropy numerical analytic continuation approach to study transport properties in quantum liquids is presented.
Abstract: We present a method based on augmenting an exact relation between a frequency-dependent diffusion constant and the imaginary time velocity autocorrelation function, combined with the maximum entropy numerical analytic continuation approach to study transport properties in quantum liquids. The method is applied to the case of liquid para-hydrogen at two thermodynamic state points: a liquid near the triple point and a high-temperature liquid. Good agreement for the self-diffusion constant and for the real-time velocity autocorrelation function is obtained in comparison to experimental measurements and other theoretical predictions. Improvement of the methodology and future applications are discussed.
TL;DR: In this paper, the authors investigated the ruin probability in the classical risk model under a positive constant interest force, and they restricted themselves to the case where the claim size is heavy-tailed, i.e. the equilibrium distribution function (e.d.f.) belongs to a wide subclass of the subexponential distributions.
Abstract: In this paper we investigate the ruin probability in the classical risk model under a positive constant interest force. We restrict ourselves to the case where the claim size is heavy-tailed, i.e. the equilibrium distribution function (e.d.f.) of the claim size belongs to a wide subclass of the subexponential distributions. Two-sided estimates for the ruin probability are developed by reduction from the classical model without interest force.