Non-static Models Research Articles

Distance is a barrier to recycling – or is it? Surprises from a clean test

The distance of recycling bins from households is often considered important by practitioners, but published evidence for this uses only indirect and self-reported data. This study aims to provide such evidence by obtaining a clean test using measured distances in a walled community with 1200 households with the same building types, local governance, recycling and waste arrangements. The number of deposits each month of food waste for recycling at a designated site are logged via smart-cards allocated per household. The number of days per month that each household deposits showed a highly significant - but small - negative correlation with distance of the bin: fewer householders participate if further away, accounting for 3% of the variation. Surprisingly, there is no variation with distance among those who do participate: their recycling frequency does not vary. This second result is not consistent with the first in terms of cost/benefit concepts assumed by government planners, nor with the static theories of behaviour currently used in waste management research. We recommend that recycling practitioners note the smallness of the contribution of distance to recycling performance, and not overrate it. And we recommend that researchers make better use of non-static models (which model different stages towards behaviour change), which our second result appears to call for.

Cylindrical symmetric, non-rotating and non-static or static black hole solutions and the naked singularities

In this work, a four-dimensional cylindrical symmetric and non-static or static space-times in the backgrounds of anti-de Sitter (AdS) spaces with perfect stiff fluid, anisotropic fluid and electromagnetic field as the stress–energy tensor, is presented. For suitable parameter conditions in the metric function, the solution represents non-static or static non-rotating black hole solution. In addition, we show for various parameter conditions, the solution represents static and/or non-static models with a naked singularity without an event horizon.

Comparing Linear and Non-Linear Benchmarks of Exchange Rate Forecasting

Throughout the past 3 decades, the random walk model served as exchange rate forecasting benchmark to verify that a model is able to outperform a random process. However, its application as forecasting benchmark is contradictory. Rather than serving as a benchmark that explains exchange rate behaviour, it serves as a benchmark of what we do not understand in exchange rate forecasting - the random component. In order to accommodate for the observed mean reverting and non-linear patterns in exchange rate information, this study considers various univariate models to serve as linear or nonlinear benchmarks of exchange rate forecasting. The results of forecasting performance indicate that the random walk model is an insufficient benchmark to explain exchange rate movements for nonstatic models. As linear alternative, an autoregressive model performed best to explain the mean reverting patterns in exchange rate information for quarterly, monthly and weekly forecasts of the exchange rate. As non-linear alternative, a Kernel regression was best able to explain volatile exchange rate movements associated with daily forecasts of the exchange rate.

The (2+1)-dimensional axial universes—solutions to the Einstein equations, dimensional reduction points and Klein–Fock–Gordon waves

The paper presents a generalization and further development of our recent publications, where solutions of the Klein–Fock–Gordon equation defined on a few particular D = (2 + 1)-dimensional static spacetime manifolds were considered. The latter involve toy models of two-dimensional spaces with axial symmetry, including dimensional reduction to the one-dimensional space as a singular limiting case. Here, the non-static models of space geometry with axial symmetry are under consideration. To make these models closer to physical reality, we define a set of ‘admissible’ shape functions ρ(t, z) as the (2 + 1)-dimensional Einstein equation solutions in the vacuum spacetime, in the presence of the Λ-term and for the spacetime filled with the standard ‘dust’. It is curious that in the last case the Einstein equations reduce to the well-known Monge–Ampère equation, thus enabling one to obtain the general solution of the Cauchy problem, as well as a set of other specific solutions involving one arbitrary function. A few explicit solutions of the Klein–Fock–Gordon equation in this set are given. An interesting qualitative feature of these solutions relates to the dimensional reduction points, their classification and time behavior. In particular, these new entities could provide us with novel insight into the nature of P- and T-violations and of the Big Bang. A short comparison with other attempts to utilize the dimensional reduction of the spacetime is given.

Cylindrically symmetric inhomogeneous cosmological models with viscous fluid and varying Λ

Cylindrically symmetric non-static cosmological models representing a bulk viscous fluid distribution have been obtained which are inhomogeneous and anisotropic. Without assuming anyadhoc law, we obtain a cosmological constant as a decreasing function of time. Various physical and geometrical features of the models are also discussed.

Static data association with a terrain-based prior density

We consider the problem of estimating the states of a static set of targets, given a collection of densities, each representing the state of a single target. We assume there is no a priori knowledge of which of the given densities represent common targets, but that a prior density for the target locations is available. For a two-dimensional (2-D) location estimation problem, we construct a prior density model based on known features of the terrain. We then give a simple Gaussian association-estimation algorithm using the prior density and present some simulation results. We briefly discuss extensions to nonstatic models.

Some FRW models with variable G and

Einstein's field equations with G and both varying with time are considered in the context of general homogeneous, isotropic universes in a way which conserves the energy momentum tensor of the matter content. It is found that the solutions of the field equations, which are based on the variation of as but with different constants of proportionality, describe significantly different cosmological scenarios. It is also found that the non-static models with constant density having a vacuum-like equation of state are endowed with inflation for a wide class of functions G(t) and and a static universe with constant density without the vacuum-like equation of state, can exist only for k = 1 with constant G and .

A class of shear-free, non-static models for anisotropic magnetofluid systems

A class of spherically symmetric non-static models compatible with relativistic anisotropic magnetofluid systems is obtained under the special feature that flow lines are shear-free but expanding and non-geodesic. In addition, some conformally flat solutions leading to generalized versions of Robertson–Walker models are derived. Moreover, it is proved that if the space–time admits conformal motion then the associated solution does not admit proper conformal symmetry vectors. The models found are of Petrov type I, D, or O.

Nonstatic models of the effective dielectric constants of natural media that allow for scattering by inclusion particles

The possibility of allowance for scattering in the description of the dielectric constant of a natural medium using the dynamic polarizability of the spherical particles of which the medium is composed is analyzed. It is shown that the proposed approach is also suitable for multicomponent mixtures. A model of the dielectric properties of wet snow is considered as an example. It is shown that when the effects of scattering and the spatial distrubution of the moisture in the snow are taken into account, there is agreement between the experimental and theoretical dependences of the dielectric constant of wet snow.

Implications of the Compton effect interpretation of the red shift

The Compton effect interpretation of astrophysical red shifts not only provides the mechanism for intrinsic red shifts of quasi-stellar sources, the solar limb, and other objects, but also results in a new cosmological model. This static model of the Universe is consistent with the Einstein static universe, since there are no unbalanced processes introduced into the model that would cause it to either expand or contract. The amount of radiation being transformed into matter is equal to the amount of radiation being released by the destruction of matter. The observed red shift is explained without the presumption that objects are moving away from each other. Thus, all the reasons for changing to nonstatic models of the Universe are answered by this model.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonstationary carrier dynamics in quarter-micron Si MOSFETs

An application of Monte Carlo particle and relaxation time approximation modeling to quarter-micron Si MOSFETs is presented. Through a comparison between these two nonstatic models and a conventional model, nonstationary carrier transport is shown to dominate in 0.4 mu m or less channel devices, with peak velocities exceeding 1.0*10/sup 7/ cm/s. It is shown that the relaxation time approximation model tends to overestimate nonstationary carrier dynamics, especially the energy distribution.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the Behavior of Non-Static Models of the Universe When the Cosmological Term is Omitted

If the cosmological term in the equations of relativistic mechanics is set equal to zero, it has been shown by Einstein that a non-static model of the universe filled with a homogeneous distribution of incoherent matter would expand to a maximum volume and then start contracting. This, however, is a very special model of the universe filled with a highly simplified fluid, and subjected to changes which can be shown to be thermodynamically reversible; and it has recently been pointed out by one of the present authors that we can also expect a similar expansion to a maximum volume with much more general models of the universe allowing irreversible as well as reversible changes in the fluid filling the model. The present article gives a somewhat detailed analysis of the behavior of a wide class of non-static models of the universe when the cosmological term is set equal to zero, and shows that we may expect a continued succession of expansions and contractions without reference to the reversible or irreversible nature of the processes taking place in the fluid filling the model. The bearings of this finding on the problems of relativistic thermodynamics, which have already been treated by one of the present authors, are again noted.

Possibilities in Relativistic Thermodynamics for Irreversible Processes Without Exhaustion of Free Energy

Previous applications of relativistic thermodynamics have been either to systems in static thermodynamic equilibrium or to non-static systems in which reversible processes are taking place. The present article deals with non-static systems in which irreversible processes take place. It is shown that the failure of the principle of energy conservation to hold in relativistic mechanics in its older simple form removes a classical limitation on the irreversible increases in entropy which can take place in an isolated system. The removal of this limitation provides possibilities in relativistic thermodynamics for irreversible processes to take place in an isolated system without ever reaching an unsurpassable state of maximum entropy and minimum free energy where further change would be impossible. Such possibilities are found to be illustrated by non-static models of the universe which could undergo a continued series of irreversible expansions and contractions without ever arriving at a state of rest. Special attention is given to a non-static model of the universe in which the irreversible annihilation of matter would take place in the later stages of expansion and the irreversible formation of matter out of radiation in the later stages of contraction. Finally, remarks are made concerning the bearing of the findings on the interpretation of phenomena in the actual universe.

On the Theoretical Requirements for a Periodic Behaviour of the Universe

This article investigates, on the basis of relativistic mechanics and relativistic thermodynamics, the theoretical requirements for nonstatic models of the universe to exhibit a behaviour which is periodic in time. The discussion is limited to models which can be regarded from a large-scale point of view as filled with a uniform distribution of fluid, and the time coordinate is purposely chosen so as to agree with the proper time that would be used by local observers at rest in this fluid. It is first shown that the analytical requirements which would correspond to the continuous expansion and contraction of such models between definite maximum and minimum limits, together with the thermodynamic requirement that the expansion and contraction must be reversible, could not both be simultaneously satisfied with any fluid for filling the model which has reasonable properties. Attention is then turned to models of the universe having line elements which would be quasi-periodic in the time. A wide range of possibilities is found for models which would expand from zero proper volume to a maximum and then return, the treatment failing however to provide the analytical conditions for a minimum at the lower limit. It is pointed out, nevertheless, that from a physical point of view contraction to zero proper volume could only be followed by renewed expansion, so that we might expect for such models a continued series of expansions and contractions. Furthermore, it is found possible to satisfy the analytical requirements for such quasi-periodic behaviour by models which would expand and contract at a finite rate reversibly without increase in entropy, so that we might then expect a continued series of identical expansions and contractions. It is pointed out that Einstein's recent model of a nonstatic universe filled with incoherent matter, exerting no pressure and unaccompanied by radiation, would satisfy the thermodynamic as well as the analytical requirements for such a series of identical repetitions, and models filled solely with black-body radiation and with an equilibrium mixture of radiation and perfect gas are discussed which also satisfy these requirements. In conclusion some remarks are made concerning the bearing of such findings on the behaviour of the actual universe.