Showing papers on "Constant (mathematics) published in 1980"

New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance

Abstract: Measurements of the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field-effect transistor, show that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device. Preliminary data are reported.

Molecular dynamics simulations at constant pressure and/or temperature

Abstract: In the molecular dynamics simulation method for fluids, the equations of motion for a collection of particles in a fixed volume are solved numerically. The energy, volume, and number of particles are constant for a particular simulation, and it is assumed that time averages of properties of the simulated fluid are equal to microcanonical ensemble averages of the same properties. In some situations, it is desirable to perform simulations of a fluid for particular values of temperature and/or pressure or under conditions in which the energy and volume of the fluid can fluctuate. This paper proposes and discusses three methods for performing molecular dynamics simulations under conditions of constant temperature and/or pressure, rather than constant energy and volume. For these three methods, it is shown that time averages of properties of the simulated fluid are equal to averages over the isoenthalpic–isobaric, canonical, and isothermal–isobaric ensembles. Each method is a way of describing the dynamics of a certain number of particles in a volume element of a fluid while taking into account the influence of surrounding particles in changing the energy and/or density of the simulated volume element. The influence of the surroundings is taken into account without introducing unwanted surface effects. Examples of situations where these methods may be useful are discussed.

Interaction Effects in Disordered Fermi Systems in Two Dimensions

Abstract: Interaction effects in disordered Fermi systems are considered in the metallic regime. In two dimensions, logarithmic corrections are obtained for conductivity, density of states, specific heat, and Hall constant. These results are compared with a recent theory of localization as well as some experiments.

Solvability of the initial-boundary-value problem for the equations of motion of a viscous compressible fluid

Abstract: It is proved that the initial-boundary-value problem for the system of equations describing the motion of a compressible fluid with a constant viscosity is locally solvable with respect to time. The heat conductivity is not taken into account. The solution is found in the class Wq2.1, q>3.

Two Species Competition in a Periodic Environment

Abstract: The classical Lotka-Volterra equations for two competing species have constant coefficients. In this paper these equations are studied under the assumption that the coefficients are periodic functions of a common period. As a generalization of the existence theory for equilibria in the constant coefficient case, it is shown that there exists a branch of positive periodic solutions which connects (i.e. bifurcates from) the two nontrivial periodic solutions lying on the coordinate axes. This branch exists for a finite interval or “spectrum” of bifurcation parameter values (the bifurcation parameter being the average of the net inherent growth rate of one species). The stability of these periodic solutions is studied and is related to the theory of competitive exclusion. A specific example of independent ecological interest is examined by means of which it is shown under what circumstances two species, which could not coexist in a constant environment, can coexist in a limit cycle fashion when subjected to suitable periodic harvesting or removal rates.

Determination of generic dimensions of controllable subspaces and its application

Abstract: The controllable subspace and its dimension of a structured linear system vary as a function of the free parameters. However, the dimension is stable in the sense that it takes, for almost any system parameters, some maximal constant which is the generic rank of the controllability matrix. In this paper, this maximal constant is called the generic dimension of the controllable subspace. Two simple methods for determining generic dimensions of controllable subspaces are derived. As an application, the results are applied to the determination of system types of linear multivariable unity feedback systems.

Are Competition Coefficients Constant? Inductive Versus Deductive Approaches

Abstract: One measure of the strength of a competitive interaction between two species is the competition coefficient (usually denoted by aij). This is defined as the ratio of the effect of an individual of speciesj on the per capita rate of increase of species i relative to the effect of an individual of species i on the per capita rate of increase of its own species (Schoener 1974). In the Lotka-Volterra model of competing species, the competition coefficient is a constant, and therefore independent of the density of species ij, or that of any other species in the community. Studies on Drosophila species (Ayala et al. 1973), microcrustaceans (Neill 1974), and an amphibian (Rana, Ambystoma) community (Wilbur 1972) have shown that competition coefficients are not independent of population densities in these communities. Smith-Gill and Gill (1978) have recently provided another example in which the assumption of a constant ratio of interto intraspecific ompetition appears to be inadequate. From their study and the others listed above, they draw the conclusion that \"linear approximations of competition coefficients are probably insufficient and misleading,\" (p. 568). This is clearly an inductive conclusion, based on a very limited number of studies on a small number of species. If one had to predict whether a model with constant competition coefficients was likely to be adequate for describing a given competitive community on the basis of results from other communities, it would be desirable to have a much larger data base than the studies mentioned in the previous paragraph. Any given competitive community is likely to differ from the ones studied thus far in some significant respect. For example, one might argue that birds are more likely to display constant competition coefficients because they lack the size of age-specific effects that appear to be present in the studies reviewed above. Smith-Gill and Gill apparently were aware of this problem and stated that \". . . we considered the deductive approach more powerful than inductive experimentation,\" (p. 558). Nevertheless, their approach is clearly inductive. I will suggest in this note that it is possible to apply a deductive approach to the question of whether the ratio of interto intraspecific ompetition between two given species is likely to be independent of population densities. The conclusion reached here is, however, similar to that of Smith-Gill and Gill; i.e., competition coefficients are likely to be functions of population densities. Whether or not a model with constant competition coefficients is adequate to describe a given interspecific interaction depends on the mechanism of the interaction. There are presently two published models of which I am aware that result in constant competition coefficients. One is based on an exploitative mechanism of competition (MacArthur 1968, 1972), and the other is based on interference competition (Schoener 1973). These models are reviewed here. I suggest that (1) they are based on several assumptions which are seldom satisfied, and (2) more reasonable assumptions lead to nonconstant competition coefficients.

Friction and velocity in Kramers’ theory of chemical kinetics

Abstract: The Fokker–Planck equation for the phase space distribution function is studied as a means of calculating rate constants for chemical reactions. For the case of a symmetric double minimum potential and moderate friction, the eigenfunction of interest is found via a similarity transformation coupled with singular perturbation methods, and the corresponding eigenvalue is obtained by using a variational formula. The resulting expression for the rate constant is seen to be a generalization of the well known Kramers formula. Its range of validity is determined by solving the Fokker–Planck equation numerically, and it is found that the new formula is quite accurate if the barrier height and the friction constant are at least moderately large. For the case of low friction, exact numerical values of the rate constant are obtained and these are used to develop a semitheoretical formula which is valid over the entire range of friction constants. This then permits an evaluation of the range of applicability of the rate constant predicted by the transition state method.

Population models in a periodically fluctuating environment

Abstract: We investigate the behavior of population models in the presence of a periodically fluctuating environment. We consider in particular single-species models and models of interspecific competition. It is shown that the fluctuations cause constant equilibrium states to be replaced by periodic equilibrium states, with a shift in the mean value relative to the constant-environment state. It is shown also that the locations of points of exchange of stability may be changed as a result of the fluctuations.

The choice of an effective time constant for diffusive processes in finite systems (Thermal conduction and sputtering examples)

Abstract: The problem is discussed of assigning a single effective time constant for thermal, diffusion and other relaxation processes in which the time dependence departs markedly from a simple exponential form. The practical advantages of a 'first-moment' definition are pointed out and illustrated by examples from thermal conduction and the preferential sputtering of binary alloys.

Efficient access of compressed data

Abstract: In this paper a compression technique is presented which allows a high degree of compression but requires only logarithmic access time. The technique is a constant suppression scheme, and is most applicable to stable databases whose distribution of constants is fairly clustered. Furthermore, the repeated use of the technique permits the supression of a multiple number of different constants. Of particular interest is the applicaticn of the constant suppression technique to databases whose composite key is made up of an incomplete cross product of several attribute domains. The scheme for compressing the full cross product composite key is well known. In this paper, harever, the general, incomplete case is also handled by applying the constant suppression technique in conjunction with a composite key suppression scheme.

The propulsion by large amplitude waves of uniflagellar micro-organisms of finite length

Abstract: The fluid mechanics of self-propelling, slender uniflagellar micro-organisms is examined theoretically. The mathematical analysis of these motions is based upon the Stokes equations, and the body is represented by a continuous distribution of stokeslets and doublets of undetermined strength. Since the body is self-propelling, additional constraints on the total force and moment upon it are applied. A system of singular integral and auxiliary equations, in which the propulsive velocity and viscous force per unit length are the unknowns, is derived. The vector integral equation is decomposed into near- and far-field contributions, and the solution is determined by a straightforward iterative procedure. The flagella considered are of constant radius and are restricted to planar undulations. The analysis is applied to a small amplitude wave form of infinite length, and a third-order analytic solution is obtained. By means of numerical computation, the method is extended to large amplitude wave forms of both infinite and finite length. The validity and accuracy of the solution method, the effect of local curvature, and an approximate model for an attached cell body-proper are evaluated in light of alternative theories. The solution method is systematically applied to a variety of wave-form shapes representative of actual flagella. For a sinusoidal wave form, the variations in propulsive velocity, power output and propulsive efficiency are examined as functions of the number of wavelengths on the flagellum, the amplitude and the flagellar radius. Wave forms of variable amplitude and variable wavelength are also considered. Among the significant results are the effect of the cell body on pitching, the significant differences between constant frequency and constant phase-speed undulations for variable wavelength wave forms, and comparisons with other pertinent theories.

Oscillating properties of the solutions of a class of neutral type functional differential equations

Abstract: The present paper deals with some oscillating and asymptotic properties of the functional differential equations of the formwhere λ is an arbitrary positive constant and τ > 0 is a constant delay.

Some New Algorithms for High-Precision Computation of Euler’s Constant

Abstract: We describe several new algorithms for the high-precision computation of Euler’s constant γ = 0.577 .... Using one of the algorithms, which is based on an identity involving Bessel functions, γ has been computed to 30,100 decimal places. By computing their regular continued fractions we show that, if γ or exp(γ) is of the form P/Q for integers P and Q,then |Q| > 1015000

Some remarks on the development of a standardized time constant.

Abstract: A method is provided to estimate the original event-related potential waveshapes from data obtained by filtering with different time constants. As is shown, even averaged data can be transformed easily. It is suggested that investigators recording with time constants present transformed DC data as further information.

8-9 – special functions

Abstract: Publisher Summary This chapter discusses the special functions. A single-valued function f(z) of a complex variable, which is not a constant, is said to be elliptic if it has two periods 2ω1 and 2ω2. The ratio of the periods of an analytic function cannot be a real number. For an elliptic function f(z), the z-plane can be partitioned into parallelograms. A nonconstant elliptic function has a finite number of poles in a period parallelogram; it can have no more than two simple and one second-order pole in such a parallelogram. The sum of the residues of an elliptic function, with respect to all the poles belonging to a period parallelogram, is equal to zero. The difference between the sum of all the zeros and the sum of all the poles of an elliptic function that are located in a period parallelogram is equal to one of its periods.

Angular momentum and separation constant in the Kerr metric

Abstract: The Kerr metric admits a Killing tensor which yields a second-order constant of motion for classical trajectories. We find an explicit expression for this constant using a particular coordinate system, the oblate spheroidal. Owing to the separability of the Hamilton-Jacobi equation in this system, it is easy to show that the second-order constant is, in fact, the square of the total angular momentum of the particle at infinity, corrected with terms which arise from the non-inertial character of the coordinate system.

The dielectric constant of an interacting electron gas

Abstract: A simple method is proposed for finding the local-field correction to the dielectric constant of a system of interacting electrons. In this method, the local distortion of the mean induced density near an individual electron owing to exchange-correlation effects is automatically taken into account by determining the self-consistent potential at the given space-time point under the extra condition that one of the electrons of the system lies at that point. The stated method for accounting for exchange-correlation effects is initially developed within the framework of the single-particle approximation, and then is generalized to the case of analyzing the complete many-electron problem. By using it one can easily reproduce most of the currently known results on the dielectric constant, including those derived by the powerful methods of many-body theory. This study analyzes the contemporary state of the theory of the dielectric constant of an interacting electron gas and briefly presents an application of this theory for describing the physical properties of simple metals.

21 The Ubiquitous Role of Preparation

Abstract: A preparation-theory hypothesis of the psychological refractory period was supported by a step function relating RT (reaction time) to ISI (intersignal interval) for constant ISIs with adequate controls. The contribution of probability effects was demonstrated with varied ISIs. Preparation theory proposes that RT is an inverse function of available preparation capacity, which is apportionable but which may be shared. Equations derived from preparation models for the effect of number of alternatives, both equally and unequally probable, fit existing data reasonably well. Experiments on the aged support the distinction between preparatory ability and its control.

Microwave properties of solid CO2

Abstract: Measurements over the range of 2.2 to 12.0 GHz show that CO2 snow is a slightly lossy dielectric whose constant varies with density following the Rayleigh formula to 1.27 g/cu cm. It is independent of frequency and does not vary with temperature in the 113 to 183 K range; frequency independence and agreement with the Rayleigh fit are obtained from measurements on dry block ice. The dielectric constant of solid CO2 in block form is lower than that of solid water ice or solid rock; in powder form, the constant for CO2 is also lower than that of H2O (snow) or soils. These measurements may be useful in limiting the interpretations of the Viking radio reflection experiment; a radio value of 3.0 for the dielectric constant near the North Pole would be strong evidence against the presence of cm thicknesses of CO2 in that region.

Constant spacing document feeder

Abstract: A constant spacing document feeder employs a motor control circuit which drives a feed wheel at an average speed which is dependent upon the length of a document. Since the spacing between successive documents is a function of the length of each following document, by varying the speed of the feed wheel in accordance with the length of each document, the spacing between each document can be maintained substantially constant.

Solution of the discrete coagulation equation

Abstract: An approximate analytical solution of the discrete coagulation equation is obtained for an arbitrary initial distribution and a general form of the coagulation coefficient, β ij = c 0 + ∑ q=1 Q C q f iq g jq that encompasses most of the forms used in practice. The classic Smoluchowski solution for monodisperse initial distribution and constant βij is thus extended. The approximate nature of the solution arises from the solution for the total number concentration N∞(t ), in which certain moments of the distribution must be assumed constant. In implementing the solution these moments can be updated as a function of time, so that the present solution can be viewed as an alternative to direct numerical solution of the coagulation equation.

Vertical Structure of Time-Dependent Flow Dominated by Friction in a Well-Mixed Fluid

Abstract: Solutions of a linear hydrodynamic equation of motion with linear boundary conditions are obtained to describe the horizontal current, as a function of depth and time, determined by a given history of the wind force and pressure gradient up to that time, at a fixed point in the horizontal plane, in well-mixed water of finite depth. The bottom friction is assumed to be proportional to the bottom current, with zero bottom current and zero bottom friction considered as limiting cases. The general solution is established as an eigenfunction expansion when the eddy viscosity is given as a positive function of depth. Explicit formulas are worked out for viscosity functions that are constant, exponential, or varying as a power of the height from somewhere below the bottom or above the top of the water. For the latter the limit as the viscosity goes to zero at the bottom or top is considered. Numerical results are presented for viscosities that are constant, exponential, linear, or varying as the 3/4 power.