Super-exponential inflation from a dynamical foliation of a 5D vacuum state

We introduce super-exponential inflation (ω<−1) from a 5D Riemann-flat canonical metric on which we make a dynamical foliation. The resulting metric describes a super accelerated expansion for the early universe well known as super-exponential inflation that, for very large times, tends to an asymptotic de Sitter (vacuum dominated) expansion. The scalar field fluctuations are analyzed. The important result here obtained is that the spectral index for energy density fluctuations is not scale invariant, and for cosmological scales becomes ns(k<k_?)?1. However, for astrophysical scales this spectrum changes to negative values ns(k>k_?)<0.     

Quantum Hall effect in higher dimensions

Following recent work on the quantum Hall effect on S⁴, we solve the Landau problem on the complex projective spaces $\text{C}\text{P}{}^{\mathrm{k}}$ and discuss quantum Hall states for such spaces. Unlike the case of S⁴, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of $\text{C}\text{P}{}^2$ in some detail considering both Abelian and nonAbelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of $\text{C}\text{P}{}^3$ is related to the case of S⁴.     

Analytic properties of moments matrices

Associated with each matrix element of the Generalized Moments Expansion, GMX(n,m) there is a unique expansion for the ground state energy in terms of the “connected moments” Ik of the Hamiltonian. That is, for any set {n,m} a polynomial in the Ik's may be generated to any desired order L, which is dependent upon the highest moment calculated. Here we wish to study the eigenvectors and eigenvalues of the GMX matrix itself. Furthermore we investigate the interplay between the set {n,m} and the order L of the matrix in determining which combination {n,m,L} yields the “best” (i.e. most convergent) result for the ground state energy.     

Random pseudofractal networks with competition

In this paper, we present a simple rule which assigns fitness to each edge to generate random pseudofractal networks (RPNs). This RPN model is both scale-free and small-world. We obtain the theoretical results that the power-law exponent is γ=2+1/(1+α) for the tunable parameter α>-1, and that the degree distribution is of an exponential form for others. Analytical results also show that an RPN has a large clustering coefficient and can process hierarchical structure as C(k)∼k^-1 that is in accordance with many real networks. And we prove that the mean distance L(N) scales slower logarithmically with network size N. In particular, we explain the effect of nodes with degree 2 on the clustering coefficient. These results agree with numerical simulations very well.     

Testing CIELAB-based color-difference formulae using large color differences

Three advanced CIELAB-based color-difference formulae, CMC, CIE94, and CIEDE2000, together with the basic CIELAB equation, were tested using large color-difference visual data (maximum average size was 12 CIELAB ΔE units) produced in this study. The color-difference comparison experiment was carried out at CIE Gray and Blue centers by a panel of 6 normal color-vision observers using CRT-generated stimuli based on the psychophysical method of constant stimuli. The experimental data, processed via probit analysis, were well fitted to chromaticity ellipses with a high reliance according to the observer accuracy in terms ofPF/3 measure. A detailed comparison was performed to analyze the agreement between predicted color differences from all formulae and their corresponding visual scales in all measurement planes of CIELAB space. The results show that the CIEDE2000 marginally outperformed the others at all color centers while CIE94 was the worst in original formulae or with optimizedk _L value, but the CIELAB performed worst when the parametric factors ofk _L,k_c, andk _H were all optimized, with the CMC always lying between these extremes.     

GPU-based single-cluster algorithm for the simulation of the Ising model

We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L = 4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L = 256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.     

Time Scale Separation and Dynamic Heterogeneity in the Low Temperature East Model

We consider the non-equilibrium dynamics of the East model, a linear chain of 0–1 spins evolving under a simple Glauber dynamics in the presence of a kinetic constraint which forbids flips of those spins whose left neighbor is 1. We focus on the glassy effects caused by the kinetic constraint as ${q\downarrow 0}$ , where q is the equilibrium density of the 0s. In the physical literature this limit is equivalent to the zero temperature limit. We first prove that, for any given L = O(1/q), the divergence as ${q\downarrow 0}$ of three basic characteristic time scales of the East process of length L is the same. Then we examine the problem of dynamic heterogeneity, i.e., non-trivial spatio-temporal fluctuations of the local relaxation to equilibrium, one of the central aspects of glassy dynamics. For any mesoscopic length scale L = O(q ^?γ ), γ < 1, we show that the characteristic time scale of two East processes of length L and λ L respectively are indeed separated by a factor q ^?α , α = α(γ) > 0, provided that λ ≥ 2 is large enough (independent of q, λ = 2 for γ < 1/2). In particular, the evolution of mesoscopic domains, i.e., maximal blocks of the form 111..10, occurs on a time scale which depends sharply on the size of the domain, a clear signature of dynamic heterogeneity. A key result for this part is a very precise computation of the relaxation time of the chain as a function of (q, L), well beyond the current knowledge, which uses induction on length scales on one hand and a novel algorithmic lower bound on the other. Finally we show that no form of time scale separation occurs for γ = 1, i.e., at the equilibrium scale L = 1/q, contrary to what was assumed in the physical literature based on numerical simulations.     

Can relic superhorizon inhomogeneities be responsible for large-scale CMB anomalies?

We investigate the effects of the presence of relic classical superhorizon inhomogeneities during inflation. This superhorizon inhomogeneity appears as a gradient locally and picks out a preferred direction. Quantum fluctuations on this slightly inhomogeneous background are generally statistical anisotropic. We find a quadrupole modification to the ordinary isotropic spectrum. Moreover, this deviation from statistical isotropy is scale-dependent, with a ∼−1/k² factor. This result implies that the statistical anisotropy mainly appears on large scales, while the spectrum on small scales remains highly isotropic. Moreover, due to this −1/k² factor, the power on large scales is suppressed. Thus, our model can simultaneously explain the observed anisotropic alignments of the low-? multipoles and their low power.     

Kolmogorov’s Theory of Turbulence and Inviscid Limit of the Navier-Stokes Equations in $${\mathbb {R}^3}$$

We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in \mathbb R³{\mathbb {R}^3} . We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the α ^th -order fractional derivatives of the velocity for some α > 0 in the space variables in L ², which is independent of the viscosity μ > 0. Then it is shown that this key observation yields the L ²-equicontinuity in the time variable and the uniform bound in L ^q , for some q > 2, of the velocity independent of μ > 0. These results lead to the strong convergence of solutions of the Navier-Stokes equations to a solution of the Euler equations in \mathbb R³{\mathbb {R}^3} . We also consider passive scalars coupled to the incompressible Navier-Stokes equations and, in this case, find the weak-star convergence for the passive scalars with a limit in the form of a Young measure (pdf depending on space and time). Not only do we offer a framework for mathematical existence theories, but also we offer a framework for the interpretation of numerical solutions through the identification of a function space in which convergence should take place, with the bounds that are independent of μ > 0, that is in the high Reynolds number limit.     

Extensive numerical study of the anomalous dynamic scaling of the Wolf-Villain model

In order to study the microscopic physical mechanisms of roughness surfaces exhibiting the anomalous scaling behavior, the Wolf-Villain model in 1+1 and 2+1 dimensions is investigated by the kinetic Monte-Carlo simulation on long time and large length scale (the growth time and the system size are respectively extended to t=2²⁹, for 1+1 dimensions, and t=2²¹, L×L=512×512 for 2+1 dimensions). In the 2+1-dimensional simulations, the noise reduction technique is employed so as to eliminate the crossover effects in the growth process. Our calculations show that the Wolf-Villain model in 1+1 dimensions very probably exhibits intrinsic anomalous scaling behavior in the time and length simulation range of this paper, and the 2+1-dimensional Wolf-Villain model leads to a pyramidal mounded morphology. Some properties of the mounded pattern in the 2+1-dimensional Wolf-Villain model are discussed in the final part of this presentation.     

Mimicking Complexity of Structured Data Matrix’s Information Content: Categorical Exploratory Data Analysis

We develop Categorical Exploratory Data Analysis (CEDA) with mimicking to explore and exhibit the complexity of information content that is contained within any data matrix: categorical, discrete, or continuous. Such complexity is shown through visible and explainable serial multiscale structural dependency with heterogeneity. CEDA is developed upon all features’ categorical nature via histogram and it is guided by all features’ associative patterns (order-2 dependence) in a mutual conditional entropy matrix. Higher-order structural dependency of k(≥3) features is exhibited through block patterns within heatmaps that are constructed by permuting contingency-kD-lattices of counts. By growing k, the resultant heatmap series contains global and large scales of structural dependency that constitute the data matrix’s information content. When involving continuous features, the principal component analysis (PCA) extracts fine-scale information content from each block in the final heatmap. Our mimicking protocol coherently simulates this heatmap series by preserving global-to-fine scales structural dependency. Upon every step of mimicking process, each accepted simulated heatmap is subject to constraints with respect to all of the reliable observed categorical patterns. For reliability and robustness in sciences, CEDA with mimicking enhances data visualization by revealing deterministic and stochastic structures within each scale-specific structural dependency. For inferences in Machine Learning (ML) and Statistics, it clarifies, upon which scales, which covariate feature-groups have major-vs.-minor predictive powers on response features. For the social justice of Artificial Intelligence (AI) products, it checks whether a data matrix incompletely prescribes the targeted system.     

The spatial distribution of thermal and epithermal neutrons in a graphite moderated spallation neutron field

The Gamma-3 assembly is located at the Joint Institute for Nuclear Research, Dubna, Russia. It consists of a cylindrical lead target (ø = 8 cm, L = 58.8 cm) surrounded by reactor grade graphite (110 × 110 × 60 cm). The target was irradiated with a beam of 1.6 GeV deuterons from the Nuclotron accelerator and CR-39 track detectors coupled to LR-115 2B film were used to measure the slow neutron distribution on the surface of the graphite. The detection efficiency of the CR-39 in the CR-39/LR-115 2B system was measured using a custom made calibration setup and found to be (1.12 ± 0.05) × 10⁻³ and (6.1 ± 1.2) × 10⁻⁴ tracks per neutron, for thermal and epithermal neutrons respectively, under the etching and counting procedures described in this work. The irradiation of the Gamma-3 was also simulated using MCNPX 2.7 Monte Carlo code and good agreement between the experimental and calculated track densities was found. This serves as a good validation for the computational models used to simulate spallation neutron production, transport and moderation.     

Convergence Radii for Eigenvalues of Tri-Diagonal Matrices

Consider a family of infinite tri-diagonal matrices of the form L + zB, where the matrix L is diagonal with entries L _kk  = k ², and the matrix B is off-diagonal, with nonzero entries B _k,k+1 = B _k+1,k  = k ^α , 0 ≤ α < 2. The spectrum of L + zB is discrete. For small |z| the nth eigenvalue E _n (z), E _n (0) = n ², is a well-defined analytic function. Let R _n be the convergence radius of its Taylor’s series about z = 0. It is proved that

2D-to-3D percolation crossover of metal-insulator composites

Percolation properties and d.c. conductivity were determined for an L²×h-random resistor network model of metal-insulator composite films. The effects of the thickness h on the percolation threshold and conductivity were studied numerically in the limit of an infinite size of the L²-plane parallel to the film. For thicknesses ranging from h/L=0.01 to h/L=0.24, a crossover between a finite-size regime and a saturation regime was observed at h/L≈0.1. In the finite-size regime (h/L?0.01), the percolation threshold scales as pc(h)−pc3∝h−1/x, the exponent x being compatible with that of the critical exponent of the 3D correlation length, ν₃. The conductivity exponent t appeared to depend linearly on the ratio h/L with a slope νD compatible with 2+ν₂, where ν₂ is the 2D correlation length exponent. In the saturation regime, a scaling correction for the percolation threshold was found with an exponent 1+1/ν₃. In this regime we also observed a logarithmic dependence of the conductivity exponent on h/L.     

The small x gluon and $b\bar{b}$ production at the LHC

We study open b[`(b)]b\bar{b} production at large rapidity at the LHC in an attempt to pin down the gluon distribution at very low x. For the LHC energy of 7 TeV, at next-to-leading order (NLO), there is a large factorization scale uncertainty. We show that the uncertainty can be greatly reduced if events are selected in which the transverse momenta of the two B-mesons balance each other to some accuracy, that is |p _1T +p _2T |<k ₀. This will fix the scale μ _F ≃k ₀, and will allow the LHCb experiment, in particular, to study the x-behaviour of gluon distribution down to x∼10⁻⁵, at rather low scales, μ∼2 GeV. We evaluate the expected cross sections using, for illustrative purposes, various recent sets of Parton Distribution Functions.     

Breakdown of renormalizability in the Kondo problem in the high-temperature expansion of the free energy

It is shown that there are two energy scales in the Kondo problem: T _k and T ₀, one of which (T _k) is exponentially small in the coupling constant g. The second scale T ₀is proportional to the squared coupling constant. Perturbation theory is valid only in the region T? T ₀. The point T ₀ is apparently the crossover from weak to strong coupling. The first indications of the breakdown of the hypothesis of only one energy scale in the Kondo problem appear in fourth order of perturbation theory.     

A quantitative study on the effect of nitrogen concentration on two-dimensional electron gas (2DEG) mobility in a dilute nitride GaAsN/AlGaAs heterostructure

Detailed theoretical analysis of the temperature dependence of two-dimensional electron gas mobility data in GaAs_1−xN_x/Al_0.38Ga_0.62As samples (x=0, 0.1% and 0.4%) shows that, as x increases, the dislocation density and the number of ionized impurities in the potential well increase by a factor of ∼ ×300 and ∼ ×500, respectively.     

Partition function zeros and the three-dimensional Ising spin glass

We have computed the exact partition function of the 3D Ising spin glass on lattices of effective size 3×3×L_z, 4×4×L_z, and 5×5×L_z forL _z up to 9, and several random bond configurations. Studying the distribution of zeros of the associated partition functions, we find further evidence that these systems have a singularity in the thermodynamic limit.     

Microstructures and microwave dielectric properties of La1-xBx(Mg0.5Sn0.5)O3 ceramics

The microwave dielectric properties of La_1-xB_x(Mg_0.5Sn_0.5)O₃ ceramics were examined with a view to their exploitation for mobile communication. The La_1-xB_x(Mg_0.5Sn_0.5)O₃ ceramics were prepared by the conventional solid-state method with various sintering temperatures. The X-ray diffraction patterns of the La_0.995B_0.005(Mg_0.5Sn_0.5)O₃ ceramics revealed no significant variation of phase with sintering temperatures. A maximum apparent density of 6.58 g/cm³, a dielectric constant (ε_r) of 19.8, a quality factor (Q × f) of 41,800 GHz, and a temperature coefficient of resonant frequency (τ_f) of −86 ppm/°C were obtained for La_0.995B_0.005(Mg_0.5Sn_0.5)O₃ ceramics that were sintered at 1500 °C for 4 h.