Universal distributions for growth processes in 1+1 dimensions and random matrices

We develop a scaling theory for Kardar-Parisi-Zhang growth in one dimension by a detailed study of the polynuclear growth model. In particular, we identify three universal distributions for shape fluctuations and their dependence on the macroscopic shape. These distribution functions are computed using the partition function of Gaussian random matrices in a cosine potential.     

The universal macroscopic statistics and phase transitions of rank distributions

We establish a “Central Limit Theorem” for rank distributions, which provides a detailed characterization and classification of their universal macroscopic statistics and phase transitions. The limit theorem is based on the statistical notion of Lorenz curves, and is termed the “Lorenzian Limit Law” (LLL). Applications of the LLL further establish: (i) a statistical explanation for the universal emergence of Pareto’s law in the context of rank distributions; (ii) a statistical classification of universal macroscopic network topologies; (iii) a statistical classification of universal macroscopic socioeconomic states; (iv) a statistical classification of Zipf’s law, and a characterization of the “self-organized criticality” it manifests.     

Hyperscaling for polymer rings

The statistics of a long closed self-avoiding walk (SAW) or polymer ring on a d-dimensional lattice obeys hyperscaling. The combination p_NR²_N^d/2μ^−N (where p_N is the number of configurations of an oriented and rooted N-step ring, R²_N a typical average size squared, and μ the SAW effective connectivity constant of the lattice) is equal for N å ∞ to a lattice-dependent constant times a universal amplitude A(d). The latter amplitude is calculated directly from the minimal continous Edwards model to second order in 4 − d. The case of rings at the upper critical dimension d = 4 is also studied. The results are checked against field-theoretical calculations, and former simulations. As a consequence, we show that the universal constant λ appearing to second order in in all critical phenomena amplitude ratios is equal to .     

Off-critical Casimir effect in Ising slabs with symmetric boundary conditions in d=3

Extended de Gennes-Fisher (EdGF) local-functional method has been applied to the thermodynamic Casimir effect away from the critical point for systems in the Ising universality class confined between parallel plane plates with symmetric boundary conditions [denoted (ab)=(++)]. Results on the universal scaling functions of the Casimir force W++(y) (y is a temperature-dependent scaling variable) and Gibbs adsorption G[over ](y) are presented in spatial dimension d=3. Also, the mean-field form of the universal scaling function of the Gibbs adsorption G[over ](y) is derived within the local functional theory. Asymptotic behavior of W++(y) for large values of the scaling variable y is analyzed in general dimension d.     

Universal scaling behavior at the upper critical dimension of nonequilibrium continuous phase transitions

In this work we analyze the universal scaling functions and the critical exponents at the upper critical dimension of a continuous phase transition. The consideration of the universal scaling behavior yields a decisive check of the value of the upper critical dimension. We apply our method to a nonequilibrium continuous phase transition. By focusing on the equation of state of the phase transition it is easy to extend our analysis to all equilibrium and nonequilibrium phase transitions observed numerically or experimentally.     

Universality in some classical Coulomb systems of restricted dimension

Coulomb systems in which the particles interact through thed-dimensional Coulomb potential but are confined in a flat manifold of dimensiond–1 are considered. The actual Coulomb potential acting is defined by particular boundary conditions involving a characteristic macroscopic distanceW in the direction perpendicular to the manifold: either it is periodic of periodW in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distanceW from it, or it vanishes on two parallel walls at a distanceW from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences onW (universal means independent of the microscopic detail). The casesd=2 are discussed in detail, and the generic results are checked on an exactly solvable model. The cased=3 of a plane parallel to an ideal conductor is also explicitly worked out.Laboratoire associé au Centre National de la Recherche Scientifique-URA D0063.     

固体破坏的损伤演化诱致突变现象

固体破坏问题在理论上及实际上均极为重要，是涉及力学，物理学及非线性科学等学科的一个十分复杂基本问题，文章介绍了基于细观非线性动力学模型的研究所取得的进展，发现系统显示一种共性特征，称为演化诱致突变，即演化模式从整体稳定向灾变性模式转变，宏观破坏的样本个性行为，以及宏观性质对细观无序性的敏感性。     

Gravitational dressing of D-instantons

The non-perturbative corrections to the universal hypermultiplet moduli space metric in the type-IIA superstring compactification on a Calabi–Yau threefold are investigated in the presence of 4d, N=2 supergravity. These corrections come from multiple wrapping of the BPS (Euclidean) D2-branes around certain (BPS) Calabi–Yau 3-cycles, and they are known as the D-instantons. The exact universal hypermultiplet metric is governed by a quaternionic potential that satisfies the SU(∞) Toda equation. When the supergravity decouples, the metric is hyper-Kähler. We propose the mechanism that gravitationally dress any (D-instanton) hyper-Kähler metric to the (universal hypermultiplet) quaternionic metric of the same dimension.     

Higgs production via gluon fusion in a six-dimensional universal extra dimension model on S 2/Z 2

We investigate Higgs boson production process via gluon fusion at LHC in our six-dimensional universal extra dimension model compactified on a spherical orbifold S ²/Z ₂. We find a striking result that the Higgs production cross section in our model is predicted to have 30(10)% enhancement compared to the predictions of the Standard Model (the minimal universal extra dimension model) for the compactification scale of order 1 TeV.     

Sample-Specific Behavior in Failure Models of Disordered Media

The concept "sample-specific" is suggested to describe the behavior of disordered media close to macroscopic failure. It is pointed out that the transition from universal scaling to samplespecific behavior may be a common phenomenon in failure models of disordered media. The dynamical evolution plays an important role in the transition.     

Numerical and analytic results for the macroscopic magneto-transport of three-dimensional periodic composites

The strong-field magneto-transport in a generic three-dimensional composite with a periodic microstructure where all the constituents are normal metals is considered. The macroscopic response in such systems turns out to be considerably simpler than it is in the absence of a magnetic field. Closed form asymptotic expressions are found for the microscopic current distributions and macroscopic effective magneto-resistivity tensor components. Numerical calculations of the current distributions and effective magneto-resistivity tensor components are also performed and compared with the closed form asymptotic expressions. A new critical point is identified.     

Validity of the law of mass action in three-dimensional coagulation processes

Diffusion-limited reactions are studied in detail on the classical coalescing process. We demonstrate how, with the aid of a recent renormalization group approach, fluctuations can be integrated systematically. We thereby obtain an exact relation between the microscopic physics (lattice structure and particle shape and size) and the macroscopic decay rate in the law of mass action. Moreover, we find a strong violation of the law of mass action. The corresponding term in the kinetic equations originates in long-wavelength fluctuations and is a universal function of the macroscopic decay rate.     

Local weak ferromagnetism in single-crystalline ferroelectric BiFeO3

Polarized small-angle neutron scattering studies of single-crystalline multiferroic BiFeO(3) reveal a long-wavelength spin density wave generated by ～1° spin canting of the spins out of the rotation plane of the antiferromagnetic cycloidal order. This signifies weak ferromagnetism within mesoscopic regions of dimension 0.03 microns along [110], to several microns along [111], confirming a long-standing theoretical prediction. The average local magnetization is 0.06 μ(B)/Fe. Our results provide an indication of the intrinsic macroscopic magnetization to be expected in ferroelectric BiFeO(3) thin films under strain, where the magnetic cycloid is suppressed.     

Note on the Kaplan–Yorke Dimension and Linear Transport Coefficients

A number of new relations between the Kaplan–Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small but non-zero external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the linear transport coefficients in terms of the Kaplan–Yorke dimension is derived. Alternatively, the Kaplan–Yorke dimension for a dissipative macroscopic system can be expressed in terms of the linear transport coefficients of the system. The agreement with computer simulations for an atomic fluid at small shear rates is very good.     

Universality behind Basquin's Law of Fatigue

Basquin's law of fatigue states that the lifetime of the system has a power-law dependence on the external load amplitude, tf approximately sigma 0- alpha, where the exponent alpha has a strong material dependence. We show that in spite of the broad scatter of the exponent alpha, the fatigue fracture of heterogeneous materials exhibits universal features. We propose a generic scaling form for the macroscopic deformation and show that at the fatigue limit the system undergoes a continuous phase transition. On the microlevel, the fatigue fracture proceeds in bursts characterized by universal power-law distributions. We demonstrate that the system dependent details are contained in Basquin's exponent for time to failure, and once this is taken into account, remaining features of failure are universal.     

Universal decoherence in solids

Symmetry implications for the decoherence of quantum oscillations of a two-state system in a solid are studied. When the oscillation frequency is small compared to the Debye frequency, the universal lower bound on the decoherence due to the atomic environment is derived in terms of the macroscopic parameters of the solid, with no unknown interaction constants.