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.     

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σ_r+iσ_i (where σ_r and σ_i are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σ_rσ_i-plane whose center is at the origin and ²(radius)=RM₁/P_r, where R is the Rayleigh number,M₁ is the magnetic number and P_r is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.     

Irreducible kernels and nonperturbative expansions in a theory with purem →m interaction

Recent results on the structure of theS matrix at them-particle threshold (m≧2) in a simplifiedm→m scattering theory with no subchannel interaction are extended to the Green functionF on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure ofF arounds=(mμ)² depending on the parity of (m?1)(ν?1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernelU which is the analogue of theK matrix in the two different parity cases (m?1)(ν?1) odd or even, and related local expansion ofF, for (m?1)(ν?1) even, in powers of σ_β ln σ(σ=(mμ)²?s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernelU. The links between the kernelU and Bethe-Salpeter type kernelsG of the theory are exhibited in both parity cases, as also the links between the above expansion ofF and local expansions, in the Bethe-Salpeter type framework, ofF _λ in terms of Feynman-type integrals in which each vertex is a kernelG and which include both dominant and subdominant contributions.     

Ab-initio interpretation of 〈r−3〉 electronic quantities in the hfs of Mg I 3s 3p 3 P and1 P

It has been known for a long time that, in a two-electron arc spectrum, the properties of the³ P and¹ P terms of the lowests p configuration cannot be interpreted correctly in a pure-configuration model. Following the experimental determination of the hyperfine constantA(3s 3p ¹ P ₁) in Mg I by Kluge and Otten, this paper presents the ab-initio interpretation of the 〈r ^?3〉_3p hyperfine electronic quantities in 3s 3p through the use of the multiconfigurational Hartree-Fock method. It appears that taking into account the effects of the monoelectronic excitations 3s→nd, 2p→np and 3p→np leads to ab-initio evaluations in very good agreement with experiment. The case of the 3p→np excitation, to which Brillouin's theorem should apply in principle, is discussed. Using the same method, a refined evaluation is proposed for the nuclear electric-quadrupole moment of Mg²⁵ (Q=0.200 ± 0.01 barn).     

Thermal relaxation of charm in hadronic matter

The thermal relaxation rate of open-charm (D) mesons in hot and dense hadronic matter is calculated using empirical elastic scattering amplitudes. D-meson interactions with thermal pions are approximated by D^? resonances, while scattering off other hadrons (K, η, ρ, ω, K^?, N, Δ) is evaluated using vacuum scattering amplitudes as available in the literature based on effective Lagrangians and constrained by realistic spectroscopy. The thermal relaxation time of D-mesons in a hot π gas is found to be around 25-50 fm/c for temperatures T=150-180 MeV, which reduces to 10-25 fm/c in a hadron-resonance gas. The latter values, argued to be conservative estimates, imply significant modifications of D-meson spectra in heavy-ion collisions. Close to the critical temperature (Tc), the spatial diffusion coefficient (Ds) is surprisingly similar to recent calculations for charm quarks in the Quark-Gluon Plasma using non-perturbative T-matrix interactions. This suggests a possibly continuous minimum structure of Ds around Tc.     

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.     

Duality Theorems in Ergodic Transport

We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose ?? is the shift acting on Bernoulli space X={1,2,??,d}^?, and, consider a fixed continuous cost function c:X×X???. Denote by ?? the set of all Borel probabilities ?? on X×X, such that, both its x and y marginals are ??-invariant probabilities. We are interested in the optimal plan ?? which minimizes ??c? d?? among the probabilities in ??. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan ?? by convex combinations of plans such that the support projects in periodic orbits.     

Self-similarity of low-p T cumulative pion production in proton-nucleus collisions at high energies

The experimental data on inclusive spectra of the π⁺ mesons produced in p + A collisions at the incident proton momentum of 400 GeV/c obtained by G. Leksin group at FNAL are analyzed in the framework of z-scaling. Self-similarity of the hadron production in the low-p _T cumulative region is verified. Scaling function ψ(z) for the Li, Be, C, Al, Cu, Ta nuclei is constructed. It is expressed via the invariant cross section and average multiplicity density of charged particles. Results of the analysis of the low-p _T data are compared with the high-p _T data sets obtained by J. Cronin, R. Sulyaev and D. Jaffe groups. A microscopic scenario of p + A interactions in terms of momentum fractions x ₁, x ₂ is discussed. Indication on self-similarity of the cumulative pion production in p + A collisions over a wide kinematical range has been found. Based on the universality of the shape of the scaling function the inclusive cross sections of the π⁺ mesons produced in p + A collisions on the Li, Be, C, Al, Cu, Ta targets in deep-cumulative region (x ₂ ? 1/A) are predicted.     

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.     

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.     

Universal fluctuations in the support of the random walk

A random walk starts from the origin of ad-dimensional lattice. The occupation numbern(x,t) equals unity if aftert steps site x has been visited by the walk, and zero otherwise. We study translationally invariant sumsM(t) of observables defined locally on the field of occupation numbers. Examples are the numberS(t) of visited sites, the areaE(t) of the (appropriately defined) surface of the set of visited sites, and, in dimension d=3, the Euler index of this surface. Ind≤ 3, theaverages - M(t) all increase linearly witht ast ® ∞. We show that in d=3, to leading order in an asymptotic expansion int, thedeviations from average ΔM(t) = M(t) -M(t) are, up to a normalization, allidentical to a single “universal” random variable. This result resembles an earlier one in dimensiond=2; we show that this universality breaks down ford>3.     

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.     

An approach to radially symmetrical solutions of the sine-Gordon equation

The solution φ(r, t) of the radially symmetric sine-Gordon equation is considered in three and two spatial dimensions for initial curves, analogous to a 2π-kink, in the expanding and in the shrinking phase, for R(t)j? R(0). It is shown that the parameterization φ(r, t) = 4 arcian exp[γ(r?R(0)] + x(r, t), where R(t) describes the exact propagation of the maximum of φ,(r, t), is suitable. Using an appoximate differential equation, recently given for the propagation of the solitary ring wave, a rough analytic approximation for the correction function x(r = R(t), t) is found and tested numerically. A relationship between the fluctuations in x(r = R(t), t) and those in $\text{R}\text{?}\text{(t), t)}\text{and}\text{R(t)}$ explains why the solitary wave is almost stable. From x(r = R(t), t) and the supposition x(1, t) ≈ x(∞, t) ≈ 0 an assymetry in φ_r(r, t) with respect to r = R(t) is predicted. It also exhibits fluctuations corresponding to those in x(r = R(t), t). The condition for validity of this approximation apparently is also a limit for the stability of the solitary ring wave.     

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.     

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.     

Comparative sperm ultrastructure of twelve leptodactylid frog species with insights into their phylogenetic relationships

The spermatozoa of representatives of three Neotropical frog subfamilies, Leiuperinae, Leptodactylinae and Paratelmatobiinae, were observed using Transmission Electron Microscopy, with the aim of identifying ultrastructural traits that provide insights into the phylogenetic relationships among these anurans, which are currently unclear. In the leiuperines, spermatozoa of Physalaemus albifrons, P. cicada, P. deimaticus and P. feioi were characterized by an acrosomal vesicle covering the subacrosomal cone that was not observed in the spermatozoa of Physalaemus centralis and P. cuvieri. The tail of the spermatozoa of P. albifrons, P. centralis, P. cicada, P. cuvieri, P. deimaticus, and P. feioi presented a long undulating membrane, whereas Engystomops petersi and E. freibergi, which form a sister clade to Physalaemus, had an axial fiber, which were absent in Physalaemus. Other leiuperine, E. puyango had an abaxonemal bulb-like swelling distally to the paraxonemal rod, which were also absent in Physalaemus. These differences support the revalidation of Engystomops as a true taxon, distinct from Physalaemus. The tail of the spermatozoa of E. petersi and E. freibergi was similar to that of Paratelmatobius poecilogaster (Paratelmatobiinae). The spermatozoa of Leptodactylus natalenis (Leptodactylinae) had undulating membrane and axial fiber, in contrast with Adenomera marmorata, which lacked these structures. Morphological differences between A. marmorata and L. natalensis sperm cells appeared to validate the allocation of A. marmorata into a genus distinct from Leptodactylus. Overall, dissimilarities in the spermatozoa of the leptodactylids provided an important phylogenetic signal for the understanding of their taxonomic relationships.     

Obliquely propagating magnetosonic waves in multicomponent quantum magnetoplasma

Linear properties of obliquely propagating magnetosonic waves (both fast and slow) in multicomponent (electron-positron-ion (e-p-i) and dust-electron-ion (d-e-i)) quantum magnetoplasma are studied. It is found that the quantum Bohm potential term significantly changes the propagation of fast and slow magnetosonic waves in both e-p-i and d-e-i quantum plasmas. The variation of the dispersion characteristics with the increase/decrease of positron concentration in e-p-i and dust concentration in d-e-i quantum magnetoplasma is explored. Finally, the effect of angle θ (that the ambient magnetic field makes with the x-axis) on the dispersion properties of magnetosonic waves in multicomponent quantum magnetoplasma is investigated. The relevance of the present investigation to the dense astrophysical environments and microelectronic devices is also pointed out.     

Modulated quasi-two-dimensional antiferromagnetic structures in La1 − y Nd y MnO3 + δ manganites

The structural, electronic, and magnetic phase transitions induced by the isovalent substitution of the rare-earth Nd³⁺ ion for the La³⁺ ion with a larger radius have been investigated in the system of self-doped manganites La_{1 ? y} Nd _y MnO_{3 + δ} (0 ≤ y ≤ 1; δ ～ 0.1). For the average radius of the ions in A-sites of the lattice 〈r _A 〉 〈 1.19 Å (y 〉 0.5), the phenomena revealed in the manganites are as follows: the ordering of Mn e _g orbitals, the transition from the pseudocubic O* phase to the orthorhombic O’ phase, the opening of the dielectric Jahn-Teller gap, the frustration of the collinear ferromagnetic (FM) state, and the transition from the lowtemperature canted FM to canted antiferromagnetic (AFM) state of Mn spins. It is assumed that, in samples with neodymium concentrations y = 0.9 and 1.0 (〈r _A 〉 ≈ 1.16 Å) at temperatures T < 12 K, there coexist A- and E-type modulated AFM states similar to the sinusoidal and helical structures of Mn spins, which were previously studied in RMnO₃ multiferroics. The magnetic T-H phase diagrams of these samples are characteristic of quasi-two-dimensional antiferromagnets with a very low (zero) magnetic anisotropy in the ab planes. Under these conditions, the phase transition from the A-type AFM phase to the spin-flop state occurs in a relatively weak magnetic field. The AFM ordering of the Nd magnetic moments with a critical phase transition temperature T _Nd ≌ 6 K is induced in magnetic fields with a strength H ≥ 3.5 kOe. For the NdMnO_{3 + δ} manganite in a magnetic field H = 10.7 kOe, the curves M(T) are characterized by additional very narrow peaks near temperatures T ₁ ≌ 4.5 K and T ₂ ≌ 5 K. The additional features revealed for the first time in the magnetization near T = 0 are assumed to be caused by the quantization of the spectrum of free holes in the ab planes by a strong magnetic field.     

On the Deser,Gilbert, Sudarshan representation for functions Wi(ν, q2)(i = 1, 2) describing the electroproduction process

The Deser, Gilbert, Sudarshan representation (D.G.S.R.) for the functions W_i(ν, q²) (i = 1,2) is considered as equations determining spectral functions h_i(a, α) via the values W_i(ν, q²) in the physical region of the electroproduction channel. It is shown that if W_i(ν, q²) obey the microcausality and spectrality conditions, then the equations for h_i(a, α) have solutions in the class of Schwartz temperated distributions and thereby the D.G.S.R. is proved. Formulae are obtained expressing spectral functions in the D.G.S.R. through the values of functions W_i(ν, q²) in the physical region of the electroproduction channel.     

Coagulation equations with gelation

Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernelK _ij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the pre- and postgelation stage in terms of the model parameters; we calculate bounds on the time of gelationt _c , and give an exact postgelation solution for the modelK _ij =(ij ^ω ) (ω>1/2) andK _ij =a ^i+j (a>1). For the modelK _ij =i ^ω +j ^ω (ω<1, without gelation) initial solutions are given. It is argued that the kernelK _ij ～ij ^ω with ω?1?1/d (d is dimensionality) effectively models the sol-gel transformation in polymerizing systems and approximately accounts for the effects of cross-linking and steric hindrance neglected in the classical theory of Flory and Stockmayer (Ω=1). For allΩ the exponents,t=Ω+3/2 andσ=Ω?1/2,γ=(3/2?Ω)/(Ω ? 1/2) andΒ=1, characterize the size distribution, at and slightly below the gel point, under the assumption that scaling is valid.