On the scaling factors α(z) and δ(z)

We introduce a new method to determine the scaling factors α(z) and δ(z) for the period-doubling route to chaos in dissipative systems, exemplified by the one-dimensional mapping x_n+1=1−λ∣x_n∣^z. With the help of the Feigenbaum universal functions g(x) and h(x) we derive the inequality α^z−α<δ(z)<α^z, implying in particular that δ(z) remains finite (≲30) in the limit z → ∞.     

Measurement of the spin parameters A and Ann in pp elastic scattering in the 1–3 GeV/c region

We have measured the asymmetry parameter A and the spin correlation parameter A_nn in pp elastic scattering, using the Argonne ZGS polarized proton beam and a polarized proton target. Angular distributions of A and A_nn for |t| ? 0.2 (GeV/c)²wereobtainedateightmomentabetween 1.10 and 2if2.75 GeV/c. We find significant structure in both the energy and t-dependence of A_nn at these energies. At p_lab ≈ 1.34 GeV/cA_nn reaches a very large value of about 0.8–0.9 near θ_cm = 90°.     

A multi-channel scattering theory for some time dependent Hamiltonians,charge transfer problem

Scattering theory for time dependent HamiltonianH(t)=?(1/2) Δ+ΣV _j (x?q _j (t)) is discussed. The existence, asymptotic orthogonality and the asymptotic completeness of the multi-channel wave operators are obtained under the conditions that the potentials are short range: |V _j (x)|≦C _j (1+|x|)^?2?ε, roughly spoken; and the trajectoriesq _j (t) are straight lines at remote past and far future, and |q _j (t)?q _k (t)| → ∞ ast → ± ∞ (j≠k).     

Pseudoscalar quarkonium exclusive decays to vector meson pair

The pseudoscalar quarkonia exclusive decays to light mesons still poses a challenge to the theoretical understanding of quarkonium properties in decay. In this work, we evaluate the processes of pseudoscalar heavy quarkonium decays into vector meson pairs, especially the helicity suppressed processes of ηb→J/ψJ/ψ and ηc→VV. In the framework of NRQCD, the branching fraction of Br[ηb→J/ψJ/ψ] are evaluated at the next-to-leading order of perturbative QCD; and within the light-cone distribution formalism, we calculate also the higher twist effects in these processes. Numerical results show that the higher twist terms contribute more than what from the NLO QCD corrections in the process of ηb→J/ψJ/ψ. It is found that the experimental results on ηc→VV are hard to be understood by merely the quark model and perturbative QCD calculation.     

New features of a smectic-A-crystal-B phase transition in a homologous series of liquid crystals

The components L _j of the Lorentz tensor and the polarizability density of molecules G in the smectic-A and crystalline-B phases have been determined for homologues of the series of alkyl-p-(4-alkoxybenzylideneamino-)cinnamates. The quantity L _j (G) in both phases is a linear (quadratic) function of the orientational order parameter of molecules S, which is invariant (noninvariant) with respect to the A-B transition, which is manifested in the form of jumps δL _j and δG and enhancement of the G(S) dependence. An increase in the length of terminal molecular chains and weakening of interlayer correlation of molecules are accompanied by strengthening of the A-B transition of the first order and G(S) dependences in both phases together with an increase in δL _j and δG. Change δG and dependence G(S) in the B phase are related to change in the conformation (flattening) of aromatic molecular cores.     

Exact solutions for a diffusion equation with a nonlinear external force

This work is devoted to investigate the solutions of the one-dimensional diffusion equation by taking the nonlinear external force F(x,t;ρ)=−k(t)x+K/x+κx|x|^α−1η[ρ(x,t)] into account. Our investigation is first performed by considering the case α=0 and η=1, which results in a Burgers like equation with a spatial and time dependent external force. After, we consider the case α≠0 and η=α+1 and show that the solution found may be expressed in terms of the q-exponential functions present in the Tsallis formalism. In addition, we also discuss the stationary solution for α and η arbitraries.     

Magnetic properties of transition metal substituted MnP

The magnetic properties of polycrystalline samples of Mn_1?tT_tP (T = V, Cr, Fe and Co for 0.00 ≦ t ≦ 0.50) are studied by magnetic susceptibility, magnetization and neutron diffraction measurements. The magnetic phase diagrams of the Mn_1?tT_tP phases exhibit paramagnetic, ferromagnetic, helimagnetic and spin glass regions depending on temperature and substitution (T, t). The concentrated spin glass regions observed in Mn_1?tV_tP and Mn_1?tCo_tP (0.30 ≦ t ≦ 0.50) are believed to result from the disorder in the metal sublattice. The variation of the magnetic moment of the ordered Mn_1?tT_tP phases with the substitution (T, t) is discussed.     

Analysis of the lattice,strong coupling series for g0φ4 field theory in d dimensions

We analyze the renormalized strong coupling series for lattice g₀φ⁴ field theory which is a double series in x = M⁴a⁴/g₀a_4?dandy = 1/M²a², where M is the renormalized mass, a the lattice spacing, g₀ the bare coupling constant and d the dimension of space-time. We extrapolate to large y for fixed x by using a Padé-like extrapolation technique. We study the dimensionless renormalized coupling constant G/M^4?d and find that as we approach the continuum(x → 0, y → ∞) the entire spectrum of g₀ from zero to infinity can be studied. Our results for d = 1,2,3,4 based on a series in y up to y⁵ and in x up to x³ show that for fixed lattice spacing a, G/M^4?d is a monotonic function of g₀ ranging from zero at g₀ = 0 to a maximum at g₀ = ∞. Using the high temperature expansion results, we have also derived 9 terms in y on 8 lattices of dimension 1,2,3 and 4 for the linear term in x, and studied this series to see if one can see a breakdown in this monotonic behavior of G for large y. The analysis of this latter series is inconclusive.     

Anomaly in the lattice partition function

The lattice partition function Z(T)=σ_(Si) exp(−H/k_BT), where H, k_B and T are the Hamiltonian of the system, the Boltzmann constant and the absolute temperature, respectively, leads to a vanishing spontaneous magnetisation for all temperatures, independently of the lattice considered. This feature is related to the symmetry breaking in these systems. In comparing this relation to the well-known partition function Z(T)=σ_n exp(−E_n/k_BT) where E_n is energy, we observe an incompatibility which could be the reason that this partition function leads to a vanishing spontaneous magnetisation.     

The muon spectra from decays ofW- andZ-bosons produced ine + e −-collisions

The muon spectra from the decays ofW-andZ-bosons, produced ine ⁺ e ^?→W ⁺ W ^?,e ⁺ e ^?→Zγ,e ⁺ e ^?→ZZ ande ⁺ e ^?→ZH reactions have been obtained (H is the Higgs boson). It has been shown (in terms of Glashow-Weinberg-Salam theory) that the main source of muons are thee ⁺ e ^?→Zγ ande ⁺ e ^?→W ⁺ W ^? processes (over theW-boson production threshold). The contribution of thee ⁺ e ^?→ZZ ande ⁺ e ^?→ZH reactions to the inclusive muon spectra is small. It has been also shown, that it is possible to distinguish contributions of thee ⁺ e ^?→Zγ ande ⁺ e ^?→W ⁺ W ^? reactions if the decay muons move at a small angle to the initial electron momentum.     

Extremal Theory for Spectrum of Random Discrete Schrödinger Operator. III. Localization Properties

In this paper, we study the asymptotic localization properties with high probability of the Kth eigenfunction (associated with the Kth largest eigenvalue, K?1 fixed) of the multidimensional Anderson Hamiltonian in torus V increasing to the whole of lattice. Denote by z _K,V ∈V the site at which the Kth largest value of potential is attained. It is well-known that if the tails of potential distribution are heavier than the double exponential function and satisfies additional regularity and continuity conditions at infinity, then the Kth eigenfunction is asymptotically delta-function at the site z _τ(K),V (localization centre) for some random τ(K)=τ _V (K)?1. We study the asymptotic behavior of the index τ _V (K) by distinguishing between three cases of the tails of potential distribution: (i) for the “heavy tails” (including Gaussian), τ _V (K) is asymptotically bounded; (ii) for the light tails, but heavier than the double exponential, the index τ _V (K) unboundedly increases like |V|^o(1); (iii) finally, for the double exponential tails with high disorder, the index τ _V (K) behaves like a power of |V|. For Weibull’s and fractional-double exponential types distributions associated with the case (ii), we obtain the first order expansion formulas for logτ _V (K).     

Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(S_α(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)^2H+σX(τ)dB_H(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.     

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.     

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).     

Coevolutionary extremal dynamics on gasket fractal

We considered a Bak-Sneppen model on a Sierpinski gasket fractal. We calculated the avalanche size distribution and the distribution of distances between subsequent minimal sites. To observe the temporal correlations of the avalanche, we estimated the return time distribution, the first-return time, and the all-return time distribution. The avalanche size distribution follows the power law, P(s)∼s−τ, with the exponent τ=1.004(7). The distribution of jumping sites also follows the power law, P(r)∼r−π, with the critical exponent π=4.12(4). We observe the periodic oscillation of the distribution of the jumping distances which originated from the jumps of the level when the minimal site crosses the stage of the fractal. The first-return time distribution shows the power law, Pf(t)∼t−τf, with the critical exponent τf=1.418(7). The all-return time distribution is also characterized by the power law, Pa(t)∼t−τa, with the exponent τa=0.522(4). The exponents of the return time satisfy the scaling relation τf+τa=2 for τf?2.     

Light-Front Zero-Mode Issue for the Transition Form Factors Between Pseudoscalar and Vector Mesons

We study the light-front zero-mode contribution to the transition form factors (g, f, a _±, T _i ) (i = 1, 2, 3) for the exclusive semileptonic P → V ?ν _? and rare P → V ? ⁺?^? decays using a covariant fermion field theory model in (3+1) dimensions. While the zero-mode contribution in principle depends on the form of the vector meson vertex Γ ^μ  = γ ^μ ? (2k ? P _V ) ^μ /D, the six form factors (g, f, a ₊, T ₁, T ₂, T ₃) are found to be free from the zero mode if the denominator D contains the term proportional to the light-front longitudinal momentum fraction factor (1/x) ⁿ of the struck quark with the power n > 0. Although the form factor a _? is not free from the zero mode, the zero-mode contribution comes only either from the simple vertex Γ ^μ  = γ ^μ term or from the other term just with a constant D (i.e. n = 0). We identify the zero-mode operator that is convoluted with the initial- and final-state valence wave functions to generate the zero-mode contribution to a _?.     

Current-voltage dependencies of heterogeneous semiconductor systems

Computed current-voltage (J–V) dependencies of heterogeneous (powder) semiconductor systems reveal an anomalous dependence between the constant-voltage current J and the uncompensated donor (acceptor) concentration N. Over a range of N(N₁ < n < N₂) of approximately one decade, J decreases by as much as four decades with increasing N. For N > N₂, the grain Schottky barrier thickness d is less than the grain half-width l/2, the grain surface potential V_s is almost independent of N and the J–V dependence is superlinear. For N₁ < N < N₂, d > l/2, V_s decreases linearly with N, J increases strongly with decreasing N and the J–V dependence is superlinear. For N < N₁, d > l/2. V_s ? V_th ( = kT/q) and J ∝ NV. The phenomenon is used to account for some observed J–V dependencies with column II-chalcogenide and ZnO powder semiconductor systems (electro-optic displays, electrophotographic receptors and heterogeneous catalysts).     

The derivative nonlinear Schrödinger equation on the half-line

We analyze the derivative nonlinear Schrödinger equation on the half-line using the Fokas method. Assuming that the solution q(x,t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x,t dependence and is given in terms of the spectral functions a(ζ), b(ζ) (obtained from the initial data q₀(x)=q(x,0)) as well as A(ζ), B(ζ) (obtained from the boundary values g₀(t)=q(0,t) and g₁(t)=q_x(0,t)). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. Given initial and boundary values {q₀(x),g₀(t),g₁(t)} such that there exist spectral functions satisfying the global relation, we show that the function q(x,t) defined by the above Riemann-Hilbert problem exists globally and solves the derivative nonlinear Schrödinger equation with the prescribed initial and boundary values.     

Is every approximate trajectory of some process near an exact trajectory of a nearby process?

This paper deals with the problem “Can a noisy orbit be tracked by a real orbit?” In particular, we will study the one-parameter family of tent maps and the one-parameter family of quadratic maps. We writeg _μ for eitherf _μ orF _μ withf _μ (x)=μx forx≦1/2 andf _μ (x)=μ(1?x) forx≧1/2, andF _μ (x)=μx(1?x). For a given μ we will say:g _μ permits increased parameter shadowing if for each δ _x >0 there exists someδ _μ >0 and some δ _f >0 such that every δ _f -pseudog _μ -orbit starting in some invariant interval can be δ _x -shadowed by a realg _α -orbit with α=μ+δ _μ . We show thatg _μ typically permits increased parameter shadowing.