Time in a simple model of a physical system

We build a model of time starting from the primitive concept of base-setB≡{α _i |i∈I} of all physical systems, whose elements are called pre-particles α _i . We assume thatB is a denumerably infinite set. Particles or bodies are represented by the subsets of the power setP (B) of the base-setB. A physical system is represented by a set of particles. We introduce the distinction between evolving and non-evolving particles, and assume that the former are represented by those subsets ofP (B) which are chains. Making use of the above concepts we define the state of a particle and the indicator of the state of a particle with respect to a given state of the same or another particle. Then we define in terms of indicators the concepts of instant, time-set, degenerate time-set, event, and clock. For the time related to a given clock one has a set in which the order relation is is in general not connected. Some theorems are proved.     

A unified view of particles and fields in a simple model of a physical system

We start from the primitive concepts of preparticle and membership relation of set theory to obtain the derivative concepts of particle (already introduced in a previous work), field, and the interaction between systems of particles. We have explicitly stated, in addition, what the relationship between a system of particles and the field it produces is in the present model of physical systems. In order to discuss the motion of particles we have analyzed one of the possible definitions of a reference frame.On leave of absence from Instituto Venezolane de Investigaciones Científicas (I.V.I.C.).     

Flux vortex pinning in a simple model system

Results of numerical calculations of flux vortex pinning by random one and two dimensional arrays of identical pinning centres are reported. Three different methods for determining the critical state flux gradient are described and the critical state concept is shown to break down for samples smaller than a certain size.     

Optical conductivity in a simple model of a pseudogap state of a two-dimensional system

Calculations of the optical conductivity are performed in a simple model of the electronic spectrum of a two-dimensional system with “hot regions” on the Fermi surface. The model leads to a strong restructuring of the spectral density (pseudogap) in these regions. It is shown that this model makes it possible to reproduce qualitatively the basic features of the optical measurements in the pseudogap state of high-temperature superconducting cuprates. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 6, 447–452 (25 March 1999)     

Complex dynamics of a simple distributed self-oscillatory model system with delay

A simple model for a distributed self-oscillatory system with cubic nonlinearity and delay is presented. Conditions for oscillation self-excitation and stationary oscillation conditions, as well as the stability of the oscillations, are analyzed. Nonstationary self-modulation regimes (including conditions of complex dynamics and chaos) are simulated numerically over a wide range of control parameters. As the factor of nonequilibrium grows, regular and chaotic regimes alternate in a complex manner. The transitions to chaos may follow all scenarios known for finite-dimensional systems. The model suggested is somewhat akin to a number of earlier finite-dimensional models aimed at studying mode competition in resonance electron masers.     

Nerve impulse propagation in a branching nerve system: A simple model

Local spatial changes of nerve axon geometry such as diameter increase and branching, may cause that action potential waves approaching a region of geometric change fail to propagate beyond it.In this paper, this effect will be examined for a special kind of nonuniformity, within the framework of a simple model: an initial value problem for a single nonlinear diffusion equation on an unbounded domain.     

Coupled normal heat and matter transport in a simple model system.

We introduce the first simple mechanical system that shows fully realistic transport behavior while still being exactly solvable at the level of equilibrium statistical mechanics. The system is a Lorentz gas with fixed freely rotating circular scatterers which scatter point particles via perfectly rough collisions. Upon imposing either a temperature gradient and/or a chemical potential gradient, a stationary state is attained for which local thermal equilibrium holds. Transport in this system is normal in the sense that the transport coefficients which characterize the flow of heat and matter are finite in the thermodynamic limit. Moreover, the two flows are nontrivially coupled, satisfying Onsager's reciprocity relations.     

Quantum system in contact with a thermal environment: Rigorous treatment of a simple model

We study the quantum dynamics of a particle of massM in an external potentialV(Q), interacting with a simple model environment—a harmonic chain of 2N particles with massm and spring constantk. The classical version of this model was studied by Rubin and is equivalent to standard models of a particle interacting with a phonon bath. Settingm=m*/L andk=k*L, we prove that for a suitable class of potentialsV and initial states ₀, the time evolution of the massM particle converges, whenN andL , to the time evolution governed by the Quantum Langevin Equation (QLE) which has been found by Ford, Kac and Mazur. Furthermore we show that, for this class of potentials, the QLE has a unique solution for all positive times, such solution can be expressed as a convergent expansion in the deviation ofV(Q) from a harmonic potential. The equilibrium properties of the particle with massM can be expressed in terms of an integral, over path space, with a Gaussian measure which has mean zero and covariance proportional to ; where is the friction constant, andh is the Plancks' constant (divided by 2).Supported in part by AFOSR Grant No. 86-0010     

Velocity autocorrelations in a simple model

A one-dimensional Lorentz-type model is studied where a point particle is reflected with some given probability p off randomly located fixed scatterers. The diffusion constant is calculated exactly, and the velocity autocorrelation is shown to decay like $\text{t}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$, for 0<p<1. For finite times, there are oscillations superimposed on this power decay. For p → 1, these oscillations dominate the behaviour for all times.     

Period-doubling bifurcations in a simple model

Periodic solutions in a simple model, whose solution shows successive period-doubling bifurcations leading to chaotic motion, are calculated by using the harmonic balance method. The result is in good agreement with that of computer simulation.     

Self-interaction correction in a simple model

We discuss various ways to handle self-interaction corrections (SIC) to Density Functional Theory (DFT) calculations. To that end, we use a simple model of few particles in a finite number of states together with a simple zero-range interaction for which full Hartree-Fock can easily be computed as a benchmark. The model allows to shed some light on the balance between orthonormality of the involved states and energy variance.     

Complex mixed-mode periodic and chaotic oscillations in a simple three-variable model of nonlinear system

A detailed study of a generic model exhibiting new type of mixed-mode oscillations is presented. Period doubling and various period adding sequences of bifurcations are observed. New type of a family of 1D (one-dimensional) return maps is found. The maps are discontinuous at three points and consist of four branches. They are not invertible. The model describes in a qualitative way mixed-mode oscillations with two types of small amplitude oscillations at local maxima and local minima of large amplitude oscillations, which have been observed recently in the Belousov-Zhabotinsky system. (c) 2000 American Institute of Physics.     

Quantum statistics in a simple model of space-time

A classification of particles in two classes is proposed in the framework of a model of space-time previously introduced. One of them is constituted by particles being represented by sets of sets of preparticles. The other kind is constituted by particles represented by cuts or discontinuities in a space-time. We prove here that particles of the first and second kind follow the Bose-Einstein and Fermi-Dirac statistics, respectively.A short communication was presented at the Sanibel Symposium (Part III): On Fundamentals of Quantum Statistics and Quantum Theory, Palm Coast, Florida, March 17–20, 1980     

Criticality in a simple model for brain functioning

We introduce a simple model for a set of interacting idealized neurons. The model presents a self-organized state in which avalanches of all sizes are observed and activity is detected in the whole extension of the simulated system without a typical length scale. The basic elements of the model are endowed with the main features of a neuron function. On this basis it is speculated that the collective system that they form, i.e., the brain, could display self-organized criticality in some situations.     

Meson spectrum in a simple planar bootstrap model

A simple planar cluster-multiperipheral model with a finite-energy sum rule constraint is set up, and self-consistency is imposed. This dynamically generates a zero-parameter infinitely-rising vector-tensor Regge trajectory which is in good agreement with experiment.     

Long-range spatial correlations in a simple diffusion model

A simple anisotropic diffusion model, according to semiphenomenological arguments, exhibits long-ranged spatial correlations in uniform stationary states.