Compressible effect algebras

We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J(a) ≤ a for all a ε E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.     

Itinerant magnetism in metallic glasses

It is argued that when a ferromagnetic transition metal T (e.g. Fe) is mixed with a metalloid M to form a metallic glass (having a narrow band of conduction electrons) the competing effects of the 3-d intra-atomic Coulomb repulsion and of the interaction between conduction and d-electrons make the magnetic moment of T-atoms to vanish when the concentration x of T-atoms is smaller than a critical concentration x_c. Experimental data for the magnetic moment of iron atoms in Fe_xB_1-x is analyzed along this line and a satisfactory fit is obtained. Inclusion of structural as well as compositional disorder effects could result in a better agreement between theory and experiment.     

Searching for a near neighbor particle in DSMC cells using pseudo-subcells

LeBeau et al. (2003) [4] introduced the ‘virtual-subcell’ (VSC) method of finding a collision partner for a given DSMC particle in a cell; all potential collision partners in the cell are examined to find the nearest neighbor, which becomes the collision partner. Here I propose a modification of the VSC method, the ‘pseudo-subcell’ (PSC) method, whereby the search for a collision partner stops whenever a ‘near-enough’ particle is found, i.e. whenever another particle is found within the ‘pseudo-subcell’ of radius δ centered on the first particle. The radius of the pseudo-subcell is given by δ = Fd_n, where d_n is the expected distance to the nearest neighbor and F is a constant which can be adjusted to give a desired trade-off between CPU time and accuracy as measured by a small mean collision separation (MCS). For 3D orthogonal cells, of various aspect ratios, d_n/L ≈ 0.746/N^0.383 where N is the number of particles in the cell and L is the cube root of the cell volume. There is a good chance that a particle will be found in the pseudo-subcell and there is a good chance that such a particle is in fact the nearest neighbor. If no particle is found within the pseudo-subcell the closest particle becomes the collision partner.     

On the criterion of the crystal-liquid phase transition

A localization criterion is proposed for the crystal-liquid phase transition (PT). According to this criterion, the PT begins when the E _d/k _b T ratio reaches a boundary value E _d(s)/k _b T _m such that a solid phase is present above it and a liquid phase is present below it in a phase diagram. Here, E _d is the energy of atom delocalization, k _b is the Boltzmann constant, T is the temperature, and E _d(s) is the delocalization energy for a solid phase at melting point T _m. This criterion is shown to generalize the Lindemann criterion of melting to the case of crystallization and the Löven criterion of crystallization to the case of melting. This localization criterion is found to be applicable for both normally melting substances and substances that melt with a decrease in the specific volume upon the transition into a liquid phase. The relation of the localization criterion to the vacancy and diffusional criteria of the crystal-liquid PT has been studied. The inequality T _N < T _m, where T _N is the temperature of the onset of crystallization, is explained using the localization criterion. The calculated values of the T _N /T _m ratio coincide well with the experimental estimates. The maximum value of T _N /T _m is likely to be most probable in crystals with a bcc structure and a small value of the Grüneisen parameter. The T _N /T _m ratio is analyzed at the points in the PT where no change in the specific volume occurs and an entropy jump is nonzero.     

A triangle model of criminality

This paper is concerned with a quantitative model describing the interaction of three sociological species, termed as owners, criminals and security guards, and denoted by X, Y and Z respectively. In our model, Y is a predator of the species X, and so is Z with respect to Y. Moreover, Z can also be thought of as a predator of X, since this last population is required to bear the costs of maintaining Z.We propose a system of three ordinary differential equations to account for the time evolution of X(t), Y(t) and Z(t) according to our previous assumptions. Out of the various parameters that appear in that system, we select two of them, denoted by H, and h, which are related with the efficiency of the security forces as a control parameter in our discussion. To begin with, we consider the case of large and constant owners population, which allows us to reduce (3), (4) and (5) to a bidimensional system for Y(t) and Z(t). As a preliminary step, this situation is first discussed under the additional assumption that Y(t)+Z(t) is constant. A bifurcation study is then performed in terms of H and h, which shows the key role played by the rate of casualties in Y and Z, that results particularly in a possible onset of bistability. When the previous restriction is dropped, we observe the appearance of oscillatory behaviours in the full two-dimensional system. We finally provide a exploratory study of the complete model (3), (4) and (5), where a number of bifurcations appear as parameter H changes, and the corresponding solutions behaviours are described.     

Movement of gas-filled cavities in alkalihalide crystals produced by external force fields

The migration of gas-filled cavities in KBr, NaCl, LiF single-crystals is investigated experimentally in an electric field and a temperature gradient.It is shown, that migration in an electric field is strongly dependent on the surface purity, due to its influence on matter transport along cavity surface. It is found that the velocity of cavity (v), having a ‘dirty’ surface follows a V～1/R dependence. (R—cavity size). In case of a ‘pure’ cavity surface. V is independent of R. Different types of V-vs-R dependence result in intermediate regions.Migration in a temperature gradient is also sensitive to surface purity. When the state of surface purity is determined, an appropriate critical size (R^*) exists such that if R is smaller than R^*, V～R and if R is larger than R^*, V is independent of R.Some constants of investigated process are determined from obtained experimental data.     

Bounded perturbations of the P(ϕ)2 theory

As a perturbation to the P(?)₂ theory we consider interaction densities of the form V(?(x)), where ?(x) is a scalar hermitian boson field and V(α) is a bounded real continuous function. It is proved that the asymptotic fields exist and are equal to the asymptotic fields of the P(?)₂ theory. The connection with non-polynomial theories of rational type is indicated. Furthermore the consequences of a bounded perturbation for the S-matrix and the spectral properties are discussed.     

Abe homotopy classification of topological excitations under the topological influence of vortices

Topological excitations are usually classified by the nth homotopy group πn. However, for topological excitations that coexist with vortices, there are cases in which an element of πn cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of πn corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of π₁ on πn. In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group κn. The nth Abe homotopy group κn is defined as a semi-direct product of π₁ and πn. In this framework, the action of π₁ on πn is understood as originating from noncommutativity between π₁ and πn. We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is Sn/K, where Sn is an n-dimensional sphere and K is a discrete subgroup of SO(n+1). We show that the influence of vortices on a topological excitation exists only if n is even and K includes a nontrivial element of O(n)/SO(n).     

On the Uniqueness of the Branching Parameter for a Random Cascade Measure

An independent random cascade measure μ is specified by a random generator (w ₁,...,w _c ), E ∑ w _i =1 where c is the branching parameter. It is shown under certain restrictions that, if μ has two generators with a.s. positive components, and the ratio ln c ₁/ln c ₂ for their branching parameters is an irrational number, then μ is a Lebesgue measure. In other words, when c is a power of an integer number p and the p is minimal for c, then a cascade measure that has the property of intermittency specifies p uniquely.     

Higher order solutions of Lieb-Liniger integral equation

We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum.     

On the ground state of an impurity in a dilute fermi gas

The system under consideration is a large collection of identical fermions (B), forming a background, into which is inserted a relatively small number of distinct impurity (I) particles. The background is considered to be dilute in the sense that R ? a, where R is the average separation of the B particles, and a is the range of their interaction potential; and the I particles are so dilute with respect to the B particles that I-I interactions can be ignored. The I particles are then all essentially at rest in their ground state. The BB and BI interaction potentials are chosen to be hard cores of the same range a. A series expansion is developed for the ground-state energy of the I particles, and the first four terms are calculated explicitly using two distinct methods, employing Feynman and Goldstone diagrams respectively. It is shown that each method has distinct advantages over the other, and that a judicious combination of both can be used to considerable benefit.     

Stochastic dynamics and Parrondo’s paradox

The Spanish physicist Juan Parrondo has provided two stochastic losing games such that for certain stochastic combinations one may obtain a winning game. If a large number of players are involved and if they try to play such that their gain in the next round is maximized one arrives at the problem of investigating a random walk on a certain space of measures.The appropriate abstract setting is as follows. There is given a compact metric space (M,d), and M is written as the union of certain closed subsets A₁,…,A_r. For every ρ=1,…,r there is prescribed a strict contraction Γ_ρ:A_ρ→M. A random walk (X_m)_m∈N0 on M is then defined as follows. The starting position is X₀=x₀, where x₀∈M is fixed, and if the walk at the m’th step is at position X_m∈M, then one chooses a ρ among the ρ with X_m∈A_ρ (with equal probability, say) and defines X_m+1 as Γ_ρ(X_m). Associated with the walk is a gainφ(X_m) in every round, where φ:M→R is a continuous function.The aim of the present investigations is the study of the expectation G_m of φ(X_m) as a function of m. Our main result states that the sequence (G_m) is “eventually approximately periodic” provided that all A_ρ are not only closed but also open in M: for every ε there is an l₀∈N such that (G_m) is l₀-periodic up to an error of at most ε for sufficiently large m. In fact it turns out that the behaviour of our process can be described well with a finite Markov chain.In the general case, however, the process might behave rather chaotically. We give an example where M is the unit interval. M is written as the union of two closed subsets A₁,A₂, the contractions Γ₁,Γ₂ are rather simple, but the expectations of the gains are not even Cesáro convergent.     

Function groups associated with constraint submanifolds

Let M be a submanifold of a manifold Q which has a generalized symplectic form ω. The submanifold M of Q is locally Hamiltonian if its vector fields are locally generated as a C^∞_ω- module by Hamiltonian vector fields of Q. If M is a first class submanifold, i.e., M is defined by first class constraints, then it is shown that M is locally Hamiltonian. It follows that if M is first class then M is a leaf of the singular foliation associated with the function group of all first class functions.     

Generalised Kerr-Schild space-times

If V is a space-time with metric tensor g_μν admitting a null, geodesic shear free vector field l_μ, then one may determine a function H so that the spacetime $\text{V}\text{?}$ with metric g_μν = g_μν + 2Hl_μl_ν satisfies the Einstein field equations for various material sources, and for no sources. When V is Minkowski space, $\text{V}\text{?}$ is a Kerr-Schild space-time. In case V is a vacuum space-time, one may choose H so that the source is a null fluid with no pressure. In case V is a Robertson-Walker universe H may be chosen so that the source has a stress-energy tensor with one timelike proper vector and three spacelike ones. There are two equal proper values associated with the latter vectors and one which differs from these. The stress-energy tensor describing this source may be interpreted as representing a perfect fluid with anisotropic pressures or as one describing the sum of a perfect fluid with isotropic pressures and a presureless null fluid. Vaidya's Kerr metric in a cosmological background [Pramana8 (1977) 512–517] is discussed as is the metric representing an accelerating point mass in an expanding universe.     

Coalescence process in heavy-ion collisions based on schematic model

Two identical heavy-ions represented by Fermi gases of cubic shape collide and coalesce to form a rectangular shape. The energy release due to the coalescence is estimated by using simple model and the energy of the coalescent nucleus is calculated as a function of the shape parameters. We find that a rectangular shape, which is compressed in the direction of collision, is energetically more favoured. The structure of the coalescent nucleus is next investigated. It is expressed as a superposition ofn-particlen-hole states. We find that the probability distribution ofn-particlen-hole states has a Gaussian form and its peak value ofn is proportional to the excitation energy, while the width is proportional to the square root of the excitation energy. The average energy of then-particlen-hole states is found to be approximatelynε _F whereε _F is the Fermi energy. Finally discussions are given in connection with experimental data.     

On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model

We elaborate on the trigonometric version of intertwining vectors and factorized L-operators. The starting point is the corresponding elliptic construction with Belavin's R-matrix. The naive trigonometric limit is singular and a careful analysis is needed. It is shown that the construction admits several different trigonometric degenerations. As a by-product, a quantum Lax operator for the trigonometric Ruijsenaars model intertwined by a non-dynamical R-matrix is obtained. The latter differs from the standard trigonometric R-matrix of A_n type. A connection with the dynamical R-matrix approach is discussed.     

The mass of the muon

It is shown that a classical relativistic charged particle has an anomalous magnetic moment g=4α/3. If such a “dressed” particle with its mass m, charge e, and anomalous magnetic moment g is quantized by a generalized Dirac equation, then the wave equation predicts a second mass m_μ=m_e(3/2α+1). It is suggested that a magnetic portion of the self-energy is quantized.     

Magnetization reversal dependence on magnetic properties of a spin torque oscillator with in-plane anisotropy free layer and orthogonal polarizer

The effect of magnetic properties on magnetization dynamics is studied for a spin torque oscillator (STO) composed of a free layer with an in-plane magnetic anisotropy and a reference layer with a fixed out-of plane magnetization. A transition from damped to uniform oscillations is observed for a critical value of saturation magnetization M_S). In the uniform oscillations regime, the frequency is inversely proportional to M_S. Similarly, the critical current for achieving uniform oscillations is investigated as a function of free layer intrinsic properties. In a second part of the study, the magnetostatic field (H_m) from the reference layer is considered and it is revealed that the out-of plane component of magnetization has a strong dependence on H_m. For a particular configuration, H_m could reduce the out-of plane component maximizing thus the out-put signal of the STO.     

First-order transitions from singly peaked distributions

Suppose that, in the thermodynamic limit, a single-component particle system exhibits a standard first-order transition marked by a jump in the density, ρ, at a chemical potential μ_σ(T). In grand canonical simulations of model fluids that realize such a transition when L→∞ (where L is the linear dimension of the simulation volume) the presence of the transition is typically signaled by the appearance of a double-peaked structure in the distribution function, P_N(T,μ_σ;L), of the particle number, N. A simple, explicit counterexample is presented, however, that proves, contrary to popular beliefs, that the converse proposition is false: i.e., a single-peaked distribution, P_N(T,μ_σ;L), may, when L→∞, give rise to a first-order transition. Alternatively, the existence of a first-order transition does not imply a double-peaked distribution. Systems that may exhibit such single-peaked, first-order behavior are discussed and a possible route to constructing explicit models exhibiting the phenomenon is described. Strategies to use in simulating such systems are briefly considered in the light of related studies.     

Bifurcation to infinitely many sinks

This paper considers one parameter families of diffeomorphisms {F _t } in two dimensions which have a curve of dissipative saddle periodic pointsP _t , i.e.F _t ⁿ (P _t )=P _t and |detDF _t ⁿ (P _t )|<1. The family is also assumed to create new homoclinic intersections of the stable and unstable manifolds ofP _t as the parameter varies throught ₀. Gavirlov and Silnikov proved that if the new homoclinic intersections are created nondegenerately att ₀, then there is an infinite cascade of periodic sinks, i.e. there are parameter valuest _n accumulating att ₀ for which there is a sink of periodn [GS2, Sect. 4]. We show that this result is true for real analytic diffeomorphisms even if the homoclinic intersection is created degenerately. We give computer evidence to show that this latter result is probably applicable to the Hénon map forA near 1.392 andB equal ?0.3. Newhouse proved a related result which showed the existence of infinitely many periodic sinks for a single diffeomorphism which is a perturbation of a diffeomorphism with a nondegenerate homoclinic tangency. We give the main geometric ideas of the proof of this theorem. We also give a variation of a key lemma to show that the result is true for a fixed one parameter family which creates a nondegenerate tangency. Thus under the nondegeneracy assumption, not only is there a cascade of sinks proved by Gavrilov and Silnikov, but also a single parameter valuet* with infinitely many sinks.