Phase separation in polydisperse rod–coil block copolymers

The stability limits of the homogeneous state of melts of rod–coil RC$RC$, R_C2$R{C}_2$, and CRC$CRC$ polydisperse block copolymers have been investigated in the framework of the weak segregation theory. It was assumed that the number of units in either the rod-like R$R$ or the flexible C$C$ block is a random variable distributed by the Schulz–Zimm distribution. Inspection of the spinodal curves shows that the copolymer melts with polydisperse rigid blocks are less stable with respect to formation of the nematic state than melts with the monodisperse ones. If flexible C$C$ blocks are polydisperse the homogeneous state of a rod–coil melt is less stable against microphase separation than the homogeneous state of monodisperse melt of the same architecture.     

Research on the evolution model of an energy supply–demand network

A universal bipartite model is proposed based on an energy supply–demand network. The analytical expression of SPL distribution of the node weight, the “shifting coefficient” α$\alpha$ and the scaling exponent γ$\gamma$ are presented without edge weight growth by using the mean-field theory approach. The numerical results of SPL distribution of the node weight, the “shifting coefficient” α$\alpha$ and the scaling exponent γ$\gamma$ with edge weight growth are also presented. The production’s SPL distribution of the US coal enterprizes from 1991 to 2009 is obtained from the empirical analysis. The numerical results obtained from the model are in good agreement with the empirical results.     

Supertwistors and massive particles

In the (super)twistor formulation of massless (super)particle mechanics, the mass-shell constraint is replaced by a “spin-shell” constraint from which the spin content can be read off. We extend this formalism to massive (super)particles (with N$N$-extended space–time supersymmetry) in three and four space–time dimensions, explaining how the spin-shell constraints are related to spin, and we use it to prove equivalence of the massive N=1$N=1$ and BPS-saturated N=2$N=2$ superparticle actions. We also find the supertwistor form of the action for “spinning particles” with N$N$-extended worldline supersymmetry, massless in four dimensions and massive in three dimensions, and we show how this simplifies special features of the N=2$N=2$ case.     

Stochastic resonance in bistable systems with nonlinear dissipation and multiplicative noise: A microscopic approach

We have studied the stochastic resonance (SR) of bistable systems coupled to a bath with a nonlinear system–bath interaction, by using the microscopic, generalized Caldeira–Leggett (CL) model. The adopted CL model yields the non-Markovian Langevin equation with nonlinear dissipation and state-dependent (multiplicative) diffusion which preserve the fluctuation–dissipation relation (FDR). Results of our simulations are given as follows: (1) the spectral power amplification (SPA) exhibits SR not only for a$a$ and b$b$ but also for τ$\tau$ while the stationary probability distribution function is independent of them where a$a$ and b$b$ denote magnitudes of multiplicative and additive noises, respectively, and τ$\tau$ expresses the relaxation time of Ornstein–Uhlenbeck (OU) colored noise; (2) the SPA for coexisting additive and multiplicative noises has a single-peak but two-peak structure as functions of a$a$, b$b$ and/or τ$\tau$. Results (1) and (2) are qualitatively different from previous ones obtained by phenomenological Langevin models where the FDR is not held or indefinite. These show an importance of the FDR in a study on SR of open bistable systems.     

On the geometry of prequantization spaces

Given a Poisson (or more generally Dirac) manifold P$P$, there are two approaches to its geometric quantization: one involves a circle bundle Q$Q$ over P$P$ endowed with a Jacobi (or Jacobi–Dirac) structure; the other one involves a circle bundle with a (pre)contact groupoid structure over the (pre)symplectic groupoid of P$P$. We study the relation between these two prequantization spaces. We show that the circle bundle over the (pre)symplectic groupoid of P$P$ is obtained from the Lie groupoid of Q$Q$ via an S¹$S^1$ reduction that preserves both the Lie groupoid and the geometric structures.     

Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis

Investigating long-range correlation by the Hurst exponent, H$H$, is crucial in the study of time series. Recently, empirical-mode-decomposition-based arbitrary-order Hilbert spectral analysis (EMD-HSA) has been proposed to numerically obtain without proof a scaling relationship, generated from the amplitude–frequency distribution, related to H$H$. We propose a formalism to empirically study EMD-HSA, to deduce its scaling exponent ξ(q)$\xi \left(q\right)$ from the perspective of EMD-based arbitrary-order Hilbert marginal spectrum (EMD-HMS), and to numerically compare the results with the expected H$H$. EMD-HSA and EMD-HMS experiments show that, by incompletely removing (quasi-)periodic trends, the sunspot series should have an H$H$ value around 0.12.     

MAP,MAC, and vortex-rings configurations in the Weinberg–Salam model

We report on the presence of new axially symmetric monopoles, antimonopoles and vortex-rings solutions of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. When the ?$?$-winding number n=1$n=1$, and 2, the configurations are monopole–antimonopole pair (MAP) and monopole–antimonopole chain (MAC) with poles of alternating sign magnetic charge arranged along the z$z$-axis. Vortex-rings start to appear from the MAP and MAC configurations when the winding number n=3$n=3$. The MAP configurations possess zero net magnetic charge whereas the MAC configurations possess net magnetic charge of 4πn/e$4\pi n/e$.     

Implication of Tsallis entropy in the Thomas–Fermi model for self-gravitating fermions

The Thomas–Fermi approach for self-gravitating fermions is revisited within the theoretical framework of the q$q$-statistics  . Starting from the q$q$-deformation of the Fermi–Dirac distribution function, a generalized Thomas–Fermi equation is derived. It is shown that the Tsallis entropy   preserves a scaling property of this equation. The q$q$-statistical   approach to Jeans’ instability in a system of self-gravitating fermions is also addressed. The dependence of the Jeans’ wavenumber (or the Jeans length) on the parameter q$q$ is traced. It is found that the q$q$-statistics makes the Fermionic system unstable at scales shorter than the standard Jeans length.     

Non-convergent perturbation theory and misleading inferences about parameter relationships: The case of superexchange

We discuss the well-known three-centre cation–anion–cation model for superexchange in insulating transition-metal compounds using limiting expansions for the Anderson–Hubbard model. We find that due to the interfering energy scales in the model, a limiting expression for the superexchange J$J$ for the idealized Mott–Hubbard (M–H) case t?U?Δ$t?U?\Delta$ cannot be formally defined. We further show that the decomposition of the superexchange into range-dependent components is formally invalid. The well-known t⁴$t^4$ superexchange expression, obtained from path-dependent series expansions, is not unique to these systems as it can also be obtained with many other different expansions, in which either the d$d$–p$p$ energy difference Δ$\Delta$ or the d$d$-electron correlation U$U$ can actually be small. Particularly for milder relationships between the parameters, i.e.  t?U?Δ$t?U?\Delta$, the reverse from the usual form of the series expansions can yield better agreement with the exact results. This implies that the fitting of experimental data to the simple expressions derived from path-dependent series expansions can lead to qualitatively incorrect relationships between the parameters, fictitiously within the M–H regime.     

Cyclic groups and quantum logic gates

We present a formula for an infinite number of universal quantum logic gates, which are 4$4$ by 4$4$ unitary solutions to the Yang–Baxter (Y–B) equation. We obtain this family from a certain representation of the cyclic group of order n$n$. We then show that this discrete   family, parametrized by integers n$n$, is in fact, a small sub-class of a larger continuous   family, parametrized by real numbers θ$\theta$, of universal quantum gates. We discuss the corresponding Yang-Baxterization and related symmetries in the concomitant Hamiltonian.     

Theoretical study of solvent-mediated Ising-like systems: One-dimensional version

We theoretically study physical properties of solutes placed in a straight line and at regular intervals. The solute is a rigid-body and has an arrow-like shape, which changes its direction up (↑$\uparrow$) or down (↓$\downarrow$). If the rigid solutes are immersed in a continuum solvent, nothing happens in the system (it is an obvious fact). However, the property of the directions differs in a granular solvent (e.g., hard-sphere solvent). Depending on the distance between the nearest-neighbor solutes, the directional correlation between them is periodically changed as follows: “parallel-tendency (↑↑$\uparrow \uparrow$)” ↔$\leftrightarrow$ “random” ↔$\leftrightarrow$ “antiparallel-tendency (↑↓$\uparrow \downarrow$)”. Studying a newly created nanosystem, it is able to discover interesting properties hiding in the nanosystem. We believe that such an approach contributes to the development of nanotechnology.     

Hermitian–Einstein connections on polystable orthogonal and symplectic parabolic Higgs bundles

Let X$X$ be a smooth complex projective curve and S⊂X$S\subset X$ a finite subset. We show that an orthogonal or symplectic parabolic Higgs bundle on X$X$ with parabolic structure over S$S$ admits a Hermitian–Einstein connection if and only if it is polystable.     

On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty principle to Rényi entropies. We recall that in both Shannon and Rényi cases, and for a given dimension n$n$, the only case of equality occurs for Gaussian random vectors. We show that as n$n$ grows, however, the bound is also asymptotically attained in the cases of n$n$-dimensional Student-t$t$ and Student-r$r$ distributions. A complete analytical study is performed in a special case of a Student-t$t$ distribution. We also show numerically that this effect exists for the particular case of a n$n$-dimensional Cauchy variable, whatever the Rényi entropy considered, extending the results of Abe and illustrating the analytical asymptotic study of the Student-t$t$ case. In the Student-r$r$ case, we show numerically that the same behavior occurs for uniformly distributed vectors. These particular cases and other ones investigated in this paper are interesting since they show that this asymptotic behavior cannot be considered as a “Gaussianization” of the vector when the dimension increases.     

Spin-1 Blume–Capel model with random crystal field effects

The random-crystal field spin-1 Blume–Capel model is investigated by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The crystal field is either turned on randomly with probability p$p$ or turned off with q=1−p$q=1-p$ in a bimodal distribution. Then the phase diagrams are constructed on the crystal field (Δ$\Delta$)–temperature (kT/J)$(kT/J)$ planes for given values of p$p$ and on the (kT/J,p$kT/J,p$) planes for given Δ$\Delta$ by studying the thermal variations of the order parameters. In the latter, we only present the second-order phase transition lines, because of the existence of irregular wiggly phase transitions which are not good enough to construct lines. In addition to these phase transitions, the model also yields tricritical points for all values of p$p$ and the reentrant behavior at lower p$p$ values.     

The spatial distribution of clusters and the formation of mixed languages in bilingual competition

We use cellular automata simulation methods to study the competition between two languages (language A$A$ and B$B$). We assume each of the two languages consists of F$F$ independent features and define an individual as two F$F$-length “identity level” integer strings. The value of each integer of the strings indicates whether the individual is willing or unwilling to express a certain feature and how his willingness or unwillingness is. In our model, individuals who speak either language A$A$ or B$B$ are randomly placed on a square lattice initially and programmed to evolve under the communication and interaction methods. First, we consider the situation that the competition occurs between two languages with only one feature. We find the differences between short-time coexistence processes and long-time coexistence processes and discuss how the spatial distribution of languages evolves. We observe that periodic line-shaped boundaries take shape in some simulations and lead to long-time coexistence between the two languages. Then we study the multi-feature cases when F=10$F=10$ and find the correlation among the evolution of different features decreases with time. We also observe the extinction of two primitive languages and formation of mixed languages.     

On interrelations of recurrences and connectivity trends between stock indices

Financial data has been extensively studied for correlations using Pearson’s cross-correlation coefficient ρ$\rho$ as the point of departure. We employ an estimator based on recurrence plots — the correlation of probability of recurrence (CPR$CPR$) — to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR$CPR$ approach in order to get more robust results. We examine trends in CPR$CPR$ for an approximately 19-month window moved along the time series and compare them to trends in ρ$\rho$. Binning CPR$CPR$ into three levels of connectedness (strong, moderate, and weak), we extract the trends in number of connections in each bin over time. We also look at the behavior of CPR$CPR$ during the dot-com bubble by shifting the time series to align their peaks. CPR$CPR$ mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonically towards increasing global connectivity. This is in contrast to ρ$\rho$, which gives a picture of ever-increasing correlation. CPR$CPR$ also exhibits that time-shifted markets have high connectivity around the dot-com bubble of 2000. We use significance tests using twin surrogates to interpret all the measures estimated in the study.