The rate matching effect: A hidden property of aperiodic stochastic resonance

We study a system S generating Poisson events, and a corresponding dichotomous signal as well, perturbed by a system P, also generating Poisson events and a corresponding dichotomous signal. The rates of events productions for system and perturbation are gS and gP, respectively. We call S events the events produced by the system S and P events those produced by the perturbation P. We show that this simple model reproduces the essence of recent experimental and theoretical results on aperiodic stochastic resonance. More remarkably, this simplified version of aperiodic stochastic resonance allows us to discover a property that has been overlooked by the earlier research work. The rate matching condition gS=gP is the border between two distinctly different conditions: For gS<gP, the P events are attractors of the S events and for gS>gP they become repellers of the S events. The transition from the former to the latter condition is very marked and takes place in a short region of either gS or gP, depending on which is the parameter changed, thereby resulting in a discontinuous transition.     

Bulk and surface localized modes on a magnetic nonlinear impurity

We study localized modes on a single magnetic impurity positioned in the bulk or at the surface of a one-dimensional chain, in the presence of a magnetic field B acting at the impurity site. The strong on-site nonlinear interaction U between two electrons of opposite spin at the impurity site, modelled here as a nonlinear local term, and the presence of the external field induce a strong correlation between parallel and antiparallel spin bound states. We find that, for an impurity in the bulk, a localized vector mode (with up and down spin components) is always possible for any given value of U and B, while for a surface impurity, a minimum value of both, U and B is needed to create a vector mode. In this case, up to two localized modes are possible, but only one of them is stable. The presence of the surface seems to destabilize the bulk mode in the parameter region U∼B, creating a “forbidden strip” region in parameter space, bounded by U=B+V and U=B−V, approximately.     

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.     

Classical bouncing Universes from vector fields

For the anisotropic Universe filled with massless vector field in the General Relativity frame we obtain bouncing solution for one of scale factors. We obtain the Universe with finite maximal energy density, finite value of R,RμνRμν,RμναβRμναβ and non-zero value of a scale factor for directions transverse to a vector field. Such a bounce can be also obtained for a massive vector field with kinetic initial conditions, which gives isotropic low energy limit. We discuss the existence of a bounce for a massless vector field with additional matter fields, such as cosmological constant or dust. We also discuss bouncing solution for massless vector field domination in n+2-dimensional space-time.     

Spin freezing properties in LaNi5-xFex

We report magnetic and transport measurements in the metallic pseudobinary compound LaNi_5-xFe_x, which show a Fe spin freezing. The magnetic phase diagram in the x-T plane is derived in the range 0 ⩽ x 1.2, 20 K ⩽ T ⩽ 300 K. Above a critical Fe concentration x_c ≈ 0.3, the system undergoes a superparamagnetic to long range ferromagnetic ordering at a finite temperature T. At lower concentrations, no long range spin ordering is observed, which suggests that x is the percolation threshold. Instead, a transition to a phase characterized by strong irreversibilities is observed at temperature T_f(x). Very strong ferromagnetic coupling interactions between Fe atoms are observed at low concentrations (x < x_c), which contrast with small values of T observed for x ∼ x_c. The results, together with the nature of the spin freezing are discussed in relation to the 2d character of the magnetic lattice.     

Ecological interaction and phylogeny, studying functionality on composed networks

We study a class of composed networks that are formed by two tree networks, T_P and T_A, whose end points touch each other through a bipartite network B_PA. We explore this network using a functional approach. We are interested in how much the topology, or the structure, of T_X (X=A or P) determines the links of B_PA. This composed structure is a useful model in evolutionary biology, where T_P and T_A are the phylogenetic trees of plants and animals that interact in an ecological community. We make use of ecological networks of dispersion of fruits, which are formed by frugivorous animals and plants with fruits; the animals, usually birds, eat fruits and disperse their seeds. We analyse how the phylogeny of T_X determines or is correlated with B_PA using a Monte Carlo approach. We use the phylogenetic distance among elements that interact with a given species to construct an index κ that quantifies the influence of T_X over B_PA. The algorithm is based on the assumption that interaction matrices that follows a phylogeny of T_X have a total phylogenetic distance smaller than the average distance of an ensemble of Monte Carlo realisations. We find that the effect of phylogeny of animal species is more pronounced in the ecological matrix than plant phylogeny.     

Functional properties of quantum logics

A quantum logic is defined as a setL of functions from the set of all statesS into [0, 1] satisfying the orthogonality postulate: for any sequencea ₁,a ₂, ... of members ofL satisfyinga _i+a _j≤1 fori≠j there isb∈L such thatb+a ₁+a ₂+...=1. Every logicL is in a natural way an orthomodular σ-orthocomplemented partially ordered set (L, ≤, ′) with members ofS inducing a full set of measures onL. It is shown that a logicL is quite full if and only if (L,≤,′) is isomorphic to an orthocomplemented set lattice of subsets ofS. Sufficient conditions are given in order that a quite full logic be representable in the set of projection quadratic formsf(u)=(Pu, u) on a complex Hilbert space, or in the set of trace functionsf(A)=Trace (AP) generated by projectionsP, where the domain off is the set of non-negative self-adjoint trace operators of trace 1 in a complex Hilbert space.     

Bryan's effect and isotropic nonlinear damping

Bryan's effect is the phenomenon of the rotation of the vibration pattern within the body of a rotating, vibrating body. In this paper we generalise Rayleigh's dissipation function whereby we include isotropic, nonlinear damping in the Euler–Lagrange equations. We then derive the equations of motion of a slowly rotating, vibrating, symmetric body. In so doing we analyse the effect that such damping has on Bryan's effect. Using a combination of linear and nonlinear damping in the equations of motion of a slowly rotating symmetric body, a numerical experiment indicates that underdamping, critical damping and overdamping scenarios appear to exist. For the underdamped case we compare the effect on amplitude of vibration made by linear, quadratic and a combination of these types of damping. Our final result for light, isotropic, nonlinear damping, mimicks a known result for light, isotropic, linear damping, namely for a slowly rotating symmetric body, Bryan's effect is invariant and the rate of rotation of the damped pattern is the same as it would be for the pattern of an ideal slowly rotating symmetric body.     

Orthomodular Lattices of Subspaces Obtained from Quadratic Forms

Being given a field K of characteristic different from 2 and 3, a 3-dimensional vector space E over K, and a nonsingular symmetric bilinear form φ over E, we define a structure of orthomodular lattice T(E,φ) on the set of all nonisotropic subspaces of E. We give a structure Theorem about the irreducible and 3-homogeneous subalgebras of T(E,φ). In particular, these subalgebras are all of the form T(E',φ ') where E' is a 3-dimensional subspace of E, if E is regarded as a vector space over a subfield K' of K, and φ ' is induced by φ. This structure Theorem allows us to achieve an old project, concerning minimal orthomodular lattices (an orthomodular lattice L is called minimal if it is nonmodular and if all its proper subalgebras are either modular, or isomorphic to L).     

Stability for the Korteweg-de Vries equation by inverse scattering theory

The stability problems for the Korteweg-de Vries equation, where linear stability fails, are investigated by the inverse scattering method. A rather general solution u(t, x) of the K-dV equation is shown to depend, for fixed time t, continuously on the initial condition u(0, x). For a continuum solution u_c(t, x), this continuity holds uniformly in t (stability), but for a soliton solution this is not true. A soliton solution can be uniquely decomposed into a continuum and discrete (soliton) part: u(t, x) = u_e(t, x) + u_d(t, x). Then the perturbed solution u is close to u after a suitable t-dependent “shift” of the soliton part (form stability).     

Normal forms generalizing action-angle coordinates for Hamiltonian actions of Lie groups

Let (M, Ω) be a symplectic manifold on which a Lie group G acts by a Hamiltonian action. Under some restrictive assumptions, we show that there exists a symplectic diffeomorphism ψ of a G-invariant open neighbourhood U of a given G-orbit in M, onto an open subset ψ(U) of a vector bundle F ^*, with base space G. Explicit expressions are given for the symplectic 2-form, for the momentum map and for a Hamiltonian vector field whose Hamiltonian function is G-invariant, on the model symplectic manifold ψ(U).     

Invariant states and conditional expectations of the anticommutation relations

The groupG of unitary elements of a maximal abelian von Neumann algebra on a separable, complex Hilbert spaceH acts as a group of automorphisms on the CAR algebraA(H) overH. It is shown that the set ofG-invariant states is a simplex, isomorphic to the set of regular probability measures on aw*-compact setS ofG-invariant generalized free states. The GNS Hilbert space induced by an arbitraryG-invariant state onA(H) supports a *-representation ofC(S); the canonical map ofA(H) intoC(S) can then be locally implemented by a normal,G-invariant conditional expectation.     

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.     

Overlapping branes in M-theory

We construct new supersymmetric solutions of D = 11 supergravity describing n orthogonally “overlapping” membranes and fivebranes for n = 2,…,8. Overlapping branes arise after separating intersecting branes in a direction transverse to all of the branes. The solutions, which generalize known intersecting brane solutions, preserve at least 2⁻ⁿ of the supersymmetry. Each pairwise overlap involves a membrane overlapping a membrane in a 0-brane, a fivebrane overlapping a fivebrane in a 3-brane or a membrane overlapping a fivebrane in a string. After reducing n overlapping membranes to obtain n overlapping D-2-branes in D = 10, T-duality generates new overlapping D-brane solutions in type IIA and type IIB string theory. Uplifting certain type IIA solutions leads to the D = 11 solutions. Some of the new solutions reduce to dilaton black holes in D = 4. Additionally, we present a D = 10 solution that describes two D-5-branes overlapping in a string. T-duality then generates further D = 10 solutions and uplifting one of the type IIA solutions gives a new D = 11 solution describing two fivebranes overlapping in a string.     

A variance formula related to a quantum conductance problem

Let t be a block of an Haar-invariant orthogonal (β=1), unitary (β=2) or symplectic (β=4) matrix from the classical compact groups O(n), U(n) or Sp(n), respectively. We obtain a close form for Var(tr(t^∗t)). The case for β=2 is related to a quantum conductance problem, and our formula recovers a result obtained by several authors. Moreover, our result shows that the variance has a limit ⁻¹(8β) for β=1,2 and 4 as the sizes of t go to infinity in a special way. Although t in our formulation comes from a block of an Haar-invariant matrix from the classical compact groups, the above limit is consistent with a formula by Beenakker, where t is a block of a circular ensemble.     

Mechanism of pion production in αp scattering at 1 GeV/nucleon

An analysis of the experimental data on one-pion and two-pion production in the p(??, ????)X reaction studied in a semi-exclusive experiment at an energy of E _?? = 4.2 GeV has been performed. The obtained results demonstrate that the inelastic ??-particle scattering on the proton at the energy of the experiment proceeds either through excitation and decay of the ?? resonance in the projectile ?? particle, or through excitation in the target proton of the Roper resonance, which decays into a nucleon and a pion, or a nucleon and a ?? meson??a system of two pions in the isospin I = 0, S-wave state.     

q-Deformation of symplectic dynamical symmetries in algebraic models of nuclear structure

With a view toward further nuclear structure applications of approaches based on quantum-deformed (or q-deformed) algebras, introduced to the authors by Yu.F. Smirnov, we construct a q analog of a boson realization of the symplectic noncompact sp(4, R) algebra together with a q analog of a fermion realization of the symplectic compact sp(4) algebra. The first study, on the q-deformed Sp(4,R) symmetry, is applied to the development of a q analog of the two-dimensional Interacting Boson Model with q-deformed SU(3) the underpinning dynamical symmetry group. An explicit realization in terms of q-tensor operators with respect to the standard su _q (2) algebra is given. The group-subgroup structure of this framework yields the physical interpretation of the generators of the groups under consideration. The second symplectic algebra, the q-deformed sp(4), is applied to studying isovector pairing correlations in atomic nuclei. A specific q deformation of the sp(4) algebra is realized in terms of q deformed fermion creation and annihilation operators of the shell model. The generators of the algebra close on four distinct realizations of the u _q (2) subalgebra. These reductions, which correspond to different types of pairing interactions, yield a complete classification of the basis states. An analysis of the role of the q deformation is based on a comparison of the results for energies of the lowest isovector-paired 0⁺ states in the deformed and nondeformed cases.     

The magnetic properties of a finite superlattice with two disordered interfaces

Within the framework of the effective field theory, based on a probability distribution technique, we examine the critical and compensation behaviors of a ferrimagnetic alternating superlattice on a simple cubic structure. The superlattice consists of k unit cells each of which consists of L layers of spin-1/2 A atoms, L layers of spin-1 B atoms and a disordered interface with two layers in between that is characterized by a random arrangement of A and B atoms A_pB_1−pA_1−pB_p with a negative coupling A − B. Considering a finite and infinite superlattices, the effect of the thickness of the film and the surface exchange coupling on the magnetic properties are studied. The obtained results show a number of characteristic phenomena.     

Weighted Graph Colorings

We study two weighted graph coloring problems, in which one assigns q colors to the vertices of a graph such that adjacent vertices have different colors, with a vertex weighting w that either disfavors or favors a given color. We exhibit a weighted chromatic polynomial Ph(G,q,w) associated with this problem that generalizes the chromatic polynomial P(G,q). General properties of this polynomial are proved, and illustrative calculations for various families of graphs are presented. We show that the weighted chromatic polynomial is able to distinguish between certain graphs that yield the same chromatic polynomial. We give a general structural formula for Ph(G,q,w) for lattice strip graphs G with periodic longitudinal boundary conditions. The zeros of Ph(G,q,w) in the q and w planes and their accumulation sets in the limit of infinitely many vertices of G are analyzed. Finally, some related weighted graph coloring problems are mentioned.     

Effect of random doping on the electronic spectrum in trans-polyacetylene

Random dopants in trans (CH)_x introduce a broad band of gap states which merges with the conduction and valence band edges at a doping concentration n_c of a few percent. This overlap of band and gap states leads to an onset of Pauli susceptibility, since the density of states at the Fermi energy E_F is nonzero for n>n_c. However, E_F lies in a region of localized states until n is considerably greater than n_c and the system remains a semiconductor.