Spontaneous bending of 2D molecular bottle-brush

Using a scaling approach we consider a 2D comb copolymer brush under bending deformations. We show that the rectilinear brush is locally stable and can be characterized by a persistence length λ increasing with the molecular weight of grafting side chains as λ ∼ M³. A bending instability due to redistribution of the side chains appears in the non-linear regime where bending is strong. Arguments are presented that the brush conformations consist of alternating rectilinear and bent sections corresponding to the different free-energy minima.     

Quantum Brownian Motion in a Simple Model System

We consider a quantum particle coupled (with strength λ) to a spatial array of independent non-interacting reservoirs in thermal states (heat baths). Under the assumption that the reservoir correlations decay exponentially in time, we prove that the motion of the particle is diffusive at large times for small, but finite λ. Our proof relies on an expansion around the kinetic scaling limit ( l\searrow 0{\lambda \searrow 0}, while time and space scale as λ⁻²) in which the particle satisfies a Boltzmann equation. We also show an equipartition theorem: the distribution of the kinetic energy of the particle tends to a Maxwell-Boltzmann distribution, up to a correction of O(λ²).     

Kinematical Reduction of Spatial Degrees of Freedom and Holographic Relation in Yang’s Quantized Space-Time Algebra

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞. S. Tanaka is an Em. Professor of Kyoto University.     

One-dimensional Anderson model with dichotomic correlation in the presence of external electric field

A one-dimensional diagonal tight binding electronic system with dichotomic correlated disorder in the presence of external d.c field is investigated. It is found numerically that the conductance distribution obeys fairly well to log-normal distribution in weak disorder strength in localized regime, which indicates validity of single parameter scaling theory in this limit. Contrary to the universal cumulant relation C ₁ = 2C ₂ in the absence of d.c. field, we demonstrated numerically that C ₁ ≫ 2C ₂ in the presence of the field in localized regime. We interpret this result as suppression of the fluctuation effects by the external field. In addition, it is obtained that the quantity NF _c , here N is the system size and F _c is the crossover field, decreases as the as the system energy E increases. Moreover, we find numerically a simple linear relation between the average logarithm of the conductance 〈ln(g)〉 and the field strength as 〈ln(g)〉 = C(N, λ)F, here C(N, λ) is a constant for particular values of N and λ, which is the Poisson parameter of the dichotomic process.     

New dynamic scaling in increasing systems

We report a new dynamic scaling ansatz for systems whose system size is increasing with time. We apply this new hypothesis in the Eden model in two geometries. In strip geometry, we impose the system to increase with a power law, L ∼ h ^a . In increasing linear clusters, if a < 1/z, where z is the dynamic exponent, the correlation length reaches the whole system, and we find two regimes: the first, where the interface fluctuations initially grow with an exponent β = 0.3, and the second, where a crossover comes out and fluctuations evolve as h ^aα . If a = 1/z, there is not a crossover and fluctuations keep on growing in a unique regimen with the same exponent β. In particular, in circular geometry, a = 1, we find this kind of regime and in consequence, a unique regime holds.      

The Scaling Limit Geometry of Near-Critical 2D Percolation

We analyze the geometry of scaling limits of near-critical 2D percolation, i.e., for p = p _c+λδ^1/ν, with ν = 4/3, as the lattice spacing δ → 0. Our proposed framework extends previous analyses for p = p _c, based on SLE ₆. It combines the continuum nonsimple loop process describing the full scaling limit at criticality with a Poissonian process for marking double (touching) points of that (critical) loop process. The double points are exactly the continuum limits of “macroscopically pivotal” lattice sites and the marked ones are those that actually change state as λ varies. This structure is rich enough to yield a one-parameter family of near-critical loop processes and their associated connectivity probabilities as well as related processes describing, e.g., the scaling limit of 2D minimal spanning trees.     

Contracted Representation of Yang's Spacetime Algebra and Buniy-Hsu-Zee's Discrete Spacetime

Motivated by the recent proposition by Buniy, Hsu, and Zee with respect to discrete spacetime and finite spatial degrees of freedom of our physical world with short- and long-distance scales, l _P and L, we reconsider the Lorentz-covariant Yang's quantized spacetime algebra (YSTA), which is intrinsically equipped with two such kinds of scale parameters, λ and R. In accordance with their proposition, we find the so-called contracted representation of YSTA with finite spatial degrees of freedom associated with the ratio R/λ, which gives a possibility of the divergence-free noncommutative field theory on YSTA. The canonical commutation relations familiar in the ordinary quantum mechanics appear as the cooperative Inonu-Wigner's contraction limit of YSTA, λ → 0 and R → ∓.     

The Effects of Time Delay on Stochastic Resonance in a Bistable System with Correlated Noises

The effects of time delay on stochastic resonance (SR) in a bistable system with time delay, correlated noises and periodic signal are studied by using the theory of signal-to-noise ratio (SNR). The expression of the SNR is derived under the adiabatic limit and the small delay time approximation. It is found that: (i) For the case of no correlations between multiplicative and additive noise, the delay time τ can enhance the SNR as a function of the multiplicative noise intensity α and it can restrain the SNR as a function of the additive noise intensity D; (ii) For the case of correlations between multiplicative and additive noise, τ can induce a minimum and maximum in curve of the SNR as a function of α, and can intensively restrain the SNR as a function of the D and there is a critical value of delay tim τ _c =0.1 in the height of the SNR peak with change of τ, i.e., when τ takes value blow τ _c , the τ boosts up the SNR as a function of the strength λ of correlations between multiplicative and additive noise, however, when τ takes value above τ _c , the τ restrains that.     

Mixing and sorting of bidisperse two-dimensional bubbles

We have examined a number of candidates for the minimum-surface-energy arrangement of two-dimensional clusters composed of N bubbles of area 1 and N bubbles of area λ ( λ≤1). These include hexagonal bubbles sorted into two monodisperse honeycomb tilings, and various mixed periodic tilings with at most four bubbles per unit cell. We identify, as a function of λ, the minimal configuration for N → ∞. For finite N, the energy of the external (i.e., cluster-gas) boundary and that of the interface between honeycombs in “phase-separated” clusters have to be taken into account. We estimate these contributions and find the lowest total energy configuration for each pair (N,λ). As λ is varied, this alternates between a circular cluster of one of the mixed tilings, and “partial wetting” of the monodisperse honeycomb of bubble area 1 by the monodisperse honeycomb of bubble area λ. Received 1 August 2002 RID="a" ID="a"e-mail: paulo@ist.utl.pt     

An Exact Inflationary Solution to Non-Minimally Coupling

We find a new exact inflationary solution to non-minimally coupled scalar field from a specific H(φ). The inflation is driven by the evolution of the scalar field with a new inflation potential. The spectral index of the scalar density fluctuations n _s is consistent with the result of WMAP3 for the power-law flat ΛCDM model. Our solution relaxes the constraint to the quartic coupling constant, e.g. when ξ=10³, λ≤8.9×10⁻¹¹.     

Modular conformal scaling group evidenced in lepton-quark mass

Lepton-quark mass may reflect a correspondence in spacetime structure described by a modular conformal scaling group. Stemming in part from a spacetime line element correspondenceds → (expλ _n)ds in which the eight quantitiesλ ₀,λ ₁, ...,λ ₇ constitute a closed set under a modular addition, the associated formula for lepton-quark mass (yielding values at the 1 GeV scale for the leptons and lighter quarks and at the physical pole for the top) is conjectured to bem=m _fQ²(exp −λ _n), wherem _f=10.245 TeV is the progenitor fermion mass,Q is the charge number of the lepton or quark, and the modular group parameterλ _n is indexed by a fermion principal quantum numbern that depends on three mutually independent projection operators.     

Absence of Magnetism in Continuous-Spin Systems with Long-Range Antialigning Forces

We consider continuous-spin models on the d-dimensional hypercubic lattice with the spins σ _x a priori uniformly distributed over the unit sphere in ℝ ⁿ (with n≥2) and the interaction energy having two parts: a short-range part, represented by a potential Φ, and a long-range antiferromagnetic part λ|x−y|^−s σ _x ⋅σ _y for some exponent s>d and λ≥0. We assume that Φ is twice continuously differentiable, finite range and invariant under rigid rotations of all spins. For d≥1, s∈(d,d+2] and any λ>0, we then show that the expectation of each σ _x vanishes in all translation-invariant Gibbs states. In particular, the spontaneous magnetization is zero and block-spin averages vanish in all (translation invariant or not) Gibbs states. This contrasts the situation of λ=0 where the ferromagnetic nearest-neighbor systems in d≥3 exhibit strong magnetic order at sufficiently low temperatures. Our theorem extends an earlier result of A. van Enter ruling out magnetized states with uniformly positive two-point correlation functions.     

Jeans-Buneman instability in a dusty plasma

A self consistent formulation of the Jeans instability of a dusty plasma with proper inclusion of charge dynamics is described. It is shown that charge fluctuations significantly affect the Jeans as well as the Buneman mode. For plasma particles (electrons and ions) in local thermal equilibrium, the Jeans lengthλ _J is given byλ _J≈λ _g F(R, ε, β/η), whereλ _g is the Debye length of the charged grains,R is the square of the ratio of the Jeans to the plasma frequency of the grains,ε is the square of the ratio of the Debye length of the grains and the plasma particles andβ/η is the ratio of the attachment to the decay frequency of the electronic charges to the grain surface. The functional form ofF is given in the text. Numerical investigation of the Jeans-Buneman mode for a two and three component plasma shows that the Jeans mode dominates atkλ _D≪1 (wherek is the wave number andλ _D is the Debye length of plasma particles), whereas atkλ _D≫1 only the Buneman mode operates. Charge fluctuations reduce the area of overlap of the two modes. Furthermore, in the absence of gravity, there exists a new, charge fluctuation induced unstable mode in a streaming dusty plasma. Astrophysical applications of the results are discussed.     

Fluctuations of Power Injection in Randomly Driven Granular Gases

We investigate the large deviation function π_∞(w) for the fluctuations of the power W(t) = wt, integrated over a time t, injected by a homogeneous random driving into a granular gas, in the infinite time limit. Our analytical study starts from a generalized Liouville equation and exploits a Molecular Chaos-like assumption. We obtain an equation for the generating function of the cumulants μ(λ) which appears as a generalization of the inelastic Boltzmann equation and has a clear physical interpretation. Reasonable assumptions are used to obtain μ(λ) in a closed analytical form. A Legendre transform is sufficient to get the large deviation function π_∞(w). Our main result, apart from an estimate of all the cumulants of W(t) at large times t, is that π_∞ has no negative branch. This immediately results in the inapplicability of the Gallavotti-Cohen Fluctuation Relation (GCFR), that in previous studies had been suggested to be valid for injected power in driven granular gases. We also present numerical results, in order to discuss the finite time behavior of the fluctuations of W (t) . We discover that their probability density function converges extremely slowly to its asymptotic scaling form: the third cumulant saturates after a characteristic time τ larger than ∼50 mean free times and the higher order cumulants evolve even slower. The asymptotic value is in good agreement with our theory. Remarkably, a numerical check of the GCFR is feasible only at small times (at most τ/10), since negative events disappear at larger times. At such small times this check leads to the misleading conclusion that GCFR is satisfied for π_∞(w). We offer an explanation for this remarkable apparent verification. In the inelastic Maxwell model, where a better statistics can be achieved, we are able to numerically observe the “failure” of GCFR.     

An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

Let λ _d (p) be the p monomer-dimer entropy on the d-dimensional integer lattice ℤ ^d , where p∈[0,1] is the dimer density. We give upper and lower bounds for λ _d (p) in terms of expressions involving λ _d−1(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of ℤ ^d is bounded above by λ _d (p). We compute the first three terms in the formal asymptotic expansion of λ _d (p) in powers of  \frac1d\frac{1}{d}. We prove that the lower asymptotic matching conjecture is satisfied for λ _d (p). Converted to a power series in p, our “formal” expansion shows remarkable validity in low dimensions, d=1,2,3, in which dimensions we give some numerical studies.     

Endogenous and exogenous dynamics in the fluctuations of capital fluxes

A phenomenological investigation of the endogenous and exogenous dynamics in the fluctuations of capital fluxes is carried out on the Chinese stock market using mean-variance analysis, fluctuation analysis, and their generalizations to higher orders. Non-universal dynamics have been found not only in the scaling exponent α, which is different from the universal values 1/2 and 1, but also in the distributions of the ratio η= σ^exo / σ^endo of individual stocks. Both the scaling exponent α of fluctuations and the Hurst exponent H_i increase in logarithmic form with the time scale Δt and the mean traded value per minute 〈f_i 〉, respectively. We find that the scaling exponent α^endo of the endogenous fluctuations is independent of the time scale. Multiscaling and multifractal features are observed in the data as well. However, the inhomogeneous impact model is not verified.     

Phase Diagram of Ising Systems with Additional Long Range Forces

We consider ferromagnetic Ising systems where the interaction is given by the sum of a fixed reference potential and a Kac potential of intensity λ≥0 and scaling parameter γ>0$. In the Lebowitz Penrose limit γ→0⁺$ the phase diagram in the (T,λ) positive quadrant is described by a critical curve λ^mf(T), which separates the regions with one and two phases, respectively below and above the curve. We prove that if $λ>^mf(T), i.e. above the curve, there are at least two Gibbs states for small values of γ. If instead λ<λ^mf(T) and if the reference Gibbs state (i.e. without the Kac potential) satisfies a mixing condition at the temperature T, then, at the same temperature the full interaction (i.e. with also the Kac potential) satisfies the Dobrushin Shlosman uniqueness condition for small values of γ so that there is a unique Gibbs state. Received: 9 April 1996 / Accepted: 26 November 1996     

The Discrete Spectrum in the Gaps of the Continuous One for Non-Signdefinite Perturbations with a Large Coupling Constant

Given two selfadjoint operators A and V=V ₊ -V _-, we study the motion of the eigenvalues of the operator A(t)=A-tV as t increases. Let α>0 and let λ be a regular point for A. We consider the quantities N ₊(λ,α), N _-(λ,α), N ₀(λ,α) defined as the number of the eigenvalues of the operator A(t) that pass point λ from the right to the left, from the left to the right or change the direction of their motion exactly at point λ, respectively, as t increases from 0 to α>0. An abstract theorem on the asymptotics for these quantities is presented. Applications to Schr?dinger operators and its generalizations are given. Received: 9 April 1997 / Accepted: 26 August 1997     

Directional cellular growth of Al-2?wt% Li bulk samples

Al-2 wt% Li alloy was prepared using metals of 99.99% high purity in the vacuum atmosphere. The bulk samples were directionally solidified upward with a constant growth rate, V, (∼8.30 μm/s) and different temperature gradients, G, (3.11–6.06 K/mm) and also with a constant G (6.06 K/mm) and different V (8.3–164.70 μm/s) in the directional solidification apparatus. The cellular spacings, λ, were measured from both transverse and longitudinal section of the specimens and expressed as functions of solidification processing parameters, G and V, by using a linear regression analysis. The effects of the G and V on λ, were investigated. The experimental results were compared with the current theoretical and numerical models, and similar previous experimental results.