Classical bouncing Universes from vector fields

For the anisotropic Universe filled with massless vector field in the General Relativity frame we obtain bouncing solution for one of scale factors. We obtain the Universe with finite maximal energy density, finite value of R,RμνRμν,RμναβRμναβ and non-zero value of a scale factor for directions transverse to a vector field. Such a bounce can be also obtained for a massive vector field with kinetic initial conditions, which gives isotropic low energy limit. We discuss the existence of a bounce for a massless vector field with additional matter fields, such as cosmological constant or dust. We also discuss bouncing solution for massless vector field domination in n+2-dimensional space-time.     

Spatial scaling in fracture propagation in dilute systems

The geometry of fracture patterns in a dilute elastic network is explored using molecular dynamics simulation. The network in two dimensions is subjected to a uniform strain which drives the fracture to develop by the growth and coalescence of the vacancy clusters in the network. For strong dilution, it has been shown earlier that there exists a characteristic time t_c at which a dynamical transition occurs with a power law divergence (with the exponent z) of the average cluster size. Close to t_c, the growth of the clusters is scale-invariant in time and satisfies a dynamical scaling law. This paper shows that the cluster growth near t_c also exhibits spatial scaling in addition to the temporal scaling. As fracture develops with time, the connectivity length xi of the clusters increases and diverges at t_c as xi ∼ (t_c − t)^−ν, with ν = 0.83 ± 0.06. As a result of the scale-invariant growth, the vacancy clusters attain a fractal structure at t_c with an effective dimensionality d_f ∼ 1.85 ± 0.05. These values are independent (within the limit of statistical error) of the concentration (provided it is sufficiently high) with which the network is diluted to begin with. Moreover, the values are very different from the corresponding values in qualitatively similar phenomena suggesting a different universality class of the problem. The values of ν and d_f supports the scaling relation z = νd_f with the value of z obtained before.     

Spin dynamics in general relativity

The energy-momentum tensor of a fluid composed of spinning particles is presented in a form that is structurally similar to that of a fluid with the energy flux q^a with respect to the fluid velocity u^a, isotropic pressure p and the trace-free anisotropic pressure π^ab. The effect of spin in the evolution of a shear free cosmological model with irrotational geodesic flow is considered.     

Large amplitude oscillations (switching) of bi-stable vortex structures in zero field

A ferromagnetic block (2a×2b×2c) with three unequal axes supports a vortex structure that intersects each of the two opposite surfaces of largest area. Swirls appear at points (xp, yp, c) and (?xp, yp, ?c) in state-A. In state-B the swirls are at points (?xp, ?yp, c) and (xp, ?yp, ?c). With micromagnetic simulations we demonstrate the possibility of a nucleation-free switching between those states, with possible applicability in devices. The oscillations are accompanied by large external fields from the magnetic charge at the core of the intersections of the vortices with the surface. These fields of the order of a quarter of the saturation inductance move over a distance 2xp～c in fractions of a ns.     

Solitary wave interactions in lattice systems with pure higher-order nonlinearity

In this paper, we investigate in detail the interactions of solitary waves in lattice systems with interaction potential V(q)=qⁿ/n, where n is 4,6,8…, through their all possible collision types, and establish a quantitative connection between the scattering property of solitary waves and the chaotic dynamics of the systems. Kink and antikink are excited in such lattice systems and the variation of their scattering effect with n is concerned. After a kink-antikink collision, the dominant interaction in the systems, if n is small, is that solitary waves pass through each other and the scattering effect increases with n; if n is large, solitary waves reflect back sometimes due to the influence of phase and this leads to a decrease of the scattering effect with n. The largest Lyapunov exponents of systems at fixed energy density first increase and then decrease with n, which is consistent with a variation of the scattering effect. The application of the special scattering behaviors between kink and antikink in information propagation is also discussed.     

Influence of the size distribution of granules and of their attractive interaction on the percolation threshold in granulated alloys

Numerical simulation was applied to study the influence of the size distribution of granules and the interaction between them on the percolation threshold in granulated metal-insulator alloys. An alloy model was considered in which metal granules have two characteristic sizes, l and L (with L>l), and the size distribution of granules of greater size L having an average value of approximately L ₀ is described by a normal distribution with a standard deviation d, by a step function with a halfwidth d, or by a delta function. A model with attraction between granules and mechanisms of trapping of an additional granule by an already developed cluster with a characteristic trapping range R was also considered. The percolation threshold significantly grows with the ratio L ₀/l and with R for both two-and three-dimensional cases and tends to flattening at large L/l or R. The calculated results make it possible to explain the high percolation threshold observed for the majority of granulated alloys.     

Structural and magnetic properties in the powder form of Sn1−xCrxO2 solid solution

Structural and magnetic properties were studied in powder form of Sn_1−xCr_xO₂ with x=0.01, 0.02, 0.03, 0.04 and 0.05 in nominal composition. The structural parameters were obtained at room temperature by the Rietveld refinement of the x-ray powder diffraction profiles. Samples of x=0 to 0.04 are tetragonal phase with a space group P4₂/mnm. The lattice parameters indicate three-step changes with increasing Cr content. The distortion of the metal-oxygen octahedral unit occurs. The substitution of Cr ions on the Sn sites shortens the lattice parameters and the octahedral unit becomes elongated with a displacement of an apical oxygen from x=0 to x=0.02. The incorporation of Cr over x=0.02 leads to the recovery of the length of lattice parameters together with a relaxation of the octahedral unit. This result indicates a possible interstitial occupation of Cr ions from x=0.03 to x=0.04. The Cr doping reaches a saturation limit at x=0.05 with a trace of the excess Cr oxides in the x-ray study. A room temperature ferromagnetism appears in the sample with x=0.01 and becomes remarkable in one with x=0.02. The magnetization decreases with increasing the Cr doping with the amount x>0.02. Thus, the appearance of ferromagnetism highly correlated with the oxygen displacements at the apical position of the octahedral in the Sn_1−xCr_xO₂ system at room temperature. The critical oxygen displacement in the elongated octahedral at around x=0.02 may encourage the vacancy of the apical oxygen and eventually leads to appearance of a ferromagnetism based on an F-center exchange with a micro- and/or nano-structural transition. The observed ferromagnetism is highly correlated with the averaged structural change appeared in the x-ray powder diffraction.     

Supermembranes and the signature of spacetime

We consider extended objects with s space and t time world-volume dimensions moving in a spacetime with S⩾ s space and T⩾t time dimensions. The requirements of spacetime supersymmetry and world-volume fermionic gauge invariance severely restrict the possible values of S and T. If we furthermore insist that the transverse group SO(S − s, T−t) be compact to avoid ghosts, then t=T. The results may be interpreted as a set of superconformal field theories with s+t⩽6 and N⩽8 whose superconformal groups are in one-to-one correspondence with those in Nahm's classification. Although the choice t = T = 1 is not uniquely singled out, it does seem to play a preferred role.     

Generalised Kerr-Schild space-times

If V is a space-time with metric tensor g_μν admitting a null, geodesic shear free vector field l_μ, then one may determine a function H so that the spacetime $\text{V}\text{?}$ with metric g_μν = g_μν + 2Hl_μl_ν satisfies the Einstein field equations for various material sources, and for no sources. When V is Minkowski space, $\text{V}\text{?}$ is a Kerr-Schild space-time. In case V is a vacuum space-time, one may choose H so that the source is a null fluid with no pressure. In case V is a Robertson-Walker universe H may be chosen so that the source has a stress-energy tensor with one timelike proper vector and three spacelike ones. There are two equal proper values associated with the latter vectors and one which differs from these. The stress-energy tensor describing this source may be interpreted as representing a perfect fluid with anisotropic pressures or as one describing the sum of a perfect fluid with isotropic pressures and a presureless null fluid. Vaidya's Kerr metric in a cosmological background [Pramana8 (1977) 512–517] is discussed as is the metric representing an accelerating point mass in an expanding universe.     

Occupancy Distributions Arising in Sampling from Gibbs-Poisson Abundance Models

Estimating the number n of unseen species from a k-sample displaying only p≤k distinct sampled species has received attention for long. It requires a model of species abundance together with a sampling model. We start with a discrete model of iid stochastic species abundances, each with Gibbs-Poisson distribution. A k-sample drawn from the n-species abundances vector is the one obtained while conditioning it on summing to k. We discuss the sampling formulae (species occupancy distributions, frequency of frequencies) in this context. We then develop some aspects of the estimation of n problem from the size k of the sample and the observed value of P _n,k , the number of distinct sampled species. It is shown that it always makes sense to study these occupancy problems from a Gibbs-Poisson abundance model in the context of a population with infinitely many species. From this extension, a parameter γ naturally appears, which is a measure of richness or diversity of species. We rederive the sampling formulae for a population with infinitely many species, together with the distribution of the number P _k of distinct sampled species. We investigate the estimation of γ problem from the sample size k and the observed value of P _k . We then exhibit a large special class of Gibbs-Poisson distributions having the property that sampling from a discrete abundance model may equivalently be viewed as a sampling problem from a random partition of unity, now in the continuum. When n is finite, this partition may be built upon normalizing n infinitely divisible iid positive random variables by its partial sum. It is shown that the sampling process in the continuum should generically be biased on the total length appearing in the latter normalization. A construction with size-biased sampling from the ranked normalized jumps of a subordinator is also supplied, would the problem under study present infinitely many species. We illustrate our point of view with many examples, some of which being new ones.     

Quantum mechanics of graphene with a one-dimensional potential

Electron states in graphene with a one-dimensional potential have been studied. An approximate solution has been obtained for a small angle between vectors of the incident electron momentum and potential gradient. Exactly solvable problems with a potential of the smoothened step type U(x) = Utanh(x/a) and a potential with a singularity U(x) = ?U/(|x| + d) are considered. The transmission/reflection coefficients and phases for various potential barriers are determined. A quasi-classical solution is obtained.     

Composite nucleon approach to the deuteron problem

A composite model is suggested for the nucleons by assuming a longrange strong gluon force between a diquark boson B and a quark A. In the proton, A is trapped inside B in an oscillator potential and, in the neutron, A is on the surface of B in a hydrogenlike state. Nucleon form factors are obtained in agreement with experiments. The model contains a mechanism for a large effective mass of the quark A. When B is identified with π and A with μ, one can fix the gluon charge value and obtain the magnetic moments of the proton and neutron. The (πμ) atomic model for the nucleon can be used to construct the deuteron on a hydrogen molecule model. It leads to values for the binding energy, electric quadrupole moment, and form factors of the deuteron that are in agreement with experiments.     

Heat Transfer and Pressure Drop of Nanofluid with Rod-like Particles in Turbulent Flows through a Curved Pipe

Pressure drop, heat transfer, and energy performance of ZnO/water nanofluid with rodlike particles flowing through a curved pipe are studied in the range of Reynolds number 5000 ≤ Re ≤ 30,000, particle volume concentration 0.1% ≤ Φ ≤ 5%, Schmidt number 10⁴ ≤ Sc ≤ 3 × 10⁵, particle aspect ratio 2 ≤ λ ≤ 14, and Dean number 5 × 10³ ≤ De ≤ 1.5 × 10⁴. The momentum and energy equations of nanofluid, together with the equation of particle number density for particles, are solved numerically. Some results are validated by comparing with the experimental results. The effect of Re, Φ, Sc, λ, and De on the friction factor f and Nusselt number Nu is analyzed. The results showed that the values of f are increased with increases in Φ, Sc, and De, and with decreases in Re and λ. The heat transfer performance is enhanced with increases in Re, Φ, λ, and De, and with decreases in Sc. The ratio of energy PEC for nanofluid to base fluid is increased with increases in Re, Φ, λ, and De, and with decreases in Sc. Finally, the formula of ratio of energy PEC for nanofluid to base fluid as a function of Re, Φ, Sc, λ, and De is derived based on the numerical data.     

Overdamped motion of interacting particles in general confining potentials: time-dependent and stationary-state analyses

By comparing numerical and analytical results, it is shown that a system of interacting particles under overdamped motion is very well described by a nonlinear Fokker-Planck equation, which can be associated with nonextensive statistical mechanics. The particle-particle interactions considered are repulsive, motivated by three different physical situations: (i) modified Bessel function, commonly used in vortex-vortex interactions, relevant for the flux-front penetration in disordered type-II superconductors; (ii) Yukawa-like forces, useful for charged particles in plasma, or colloidal suspensions; (iii) derived from a Gaussian potential, common in complex fluids, like polymer chains dispersed in a solvent. Moreover, the system is subjected to a general confining potential, ??(x)?=?(??|x| ^z )/z (???>?0, z?>?1), so that a stationary state is reached after a sufficiently long time. Recent numerical and analytical investigations, considering interactions of type (i) and a harmonic confining potential (z?=?2), have shown strong evidence that a q-Gaussian distribution, P(x,t), with q?=?0, describes appropriately the particle positions during their time evolution, as well as in their stationary state. Herein we reinforce further the connection with nonextensive statistical mechanics, by presenting numerical evidence showing that: (a) in the case z?=?2, different particle-particle interactions only modify the diffusion parameter D of the nonlinear Fokker-Planck equation; (b) for z????2, all cases investigated fit well the analytical stationary solution P _st(x), given in terms of a q-exponential (with the same index q?=?0) of the general external potential ??(x). In this later case, we propose an approximate time-dependent P(x,t) (not known analytically for z????2), which is in very good agreement with the simulations for a large range of times, including the approach to the stationary state. The present work suggests that a wide variety of physical phenomena, characterized by repulsive interacting particles under overdamped motion, present a universal behavior, in the sense that all of them are associated with the same entropic form and nonlinear Fokker-Planck equation.     

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.     

Martingales, detrending data, and the efficient market hypothesis

We discuss martingales, detrending data, and the efficient market hypothesis (EMH) for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that martingale stochastic processes generate uncorrelated, generally non-stationary increments. Generally, a test for a martingale is therefore a test for uncorrelated increments. A detrended process with an x-dependent drift coefficient is generally not a martingale, and so we extend our analysis to include the class of (x,t)-dependent drift coefficients of interest in finance. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. And while a Markovian market has no memory to exploit and presumably cannot be beaten systematically, it has never been shown that martingale memory cannot be exploited in 3-point or higher correlations to beat the market. We generalize our Markov scaling solutions presented earlier, and also generalize the martingale formulation of the EMH to include (x,t)-dependent drift in log returns. We also use the analysis of this paper to correct a misstatement of the ‘fair game’ condition in terms of serial correlations in Fama's paper on the EMH. We end with a discussion of Levy's characterization of Brownian motion and prove that an arbitrary martingale is topologically inequivalent to a Wiener process.     

Beyer’s non-linearity parameter (B/A) in benzylidene aniline Schiff base liquid crystalline systems

The non-linearity parameter B/A is estimated for a number of liquid crystal materials of the type N-(p-n-alkoxy benzylidene)-p-n-alkyl anilines, popularly known as nO.m, where n and m are the aliphatic chains on either side of the rigid core, which can be varied from 1 to 18 to realize a number of LC materials with a variety LC phase variants. The B/A values are computed from both density and sound velocity data following standard relations reported in literature. This systematic study in a homologous series provides an opportunity to study how this parameter behaves with (1) either the alkoxy and/or alkyl chain number, (2) with the total chain number (n+m), (3) with increase in molecular weight and (4) whether the linear relations reported in literature either with αT [thermal expansion coefficient (α) and temperature (T)] and sound velocity (u) will hold good or not and if so to what extent. The results are discussed with the body of data available in literature on liquids, liquid mixtures and other LC materials.     

Fracto-mechanoluminescence and mechanics of fracture of solids

The present paper explores the correlation between fracto-mechanoluminescence and fracture of solids and thereby provides a clear understanding of the physics of fracto-mechanoluminescence. When a fluorescent or non-photoluminescent crystal is fractured impulsively by dropping a load on it, then initially the mechanoluminescence (ML) intensity increases linearly with time, attains a maximum value I_m at a particular time t_m and later on it decreases exponentially with time. However, when a phosphorescent crystal is fractured impulsively by dropping a load on it, then initially the ML intensity increases linearly with time, attains a maximum value I_m at a particular time t_m and later on it decreases initially at a fast rate and then at a slow rate. For low impact velocity the value of t_m is constant, however, for higher impact velocity t_m decreases logarithmally with the increasing impact velocity. Whereas the peak ML intensity I_m increases linearly with the impact velocity, the total ML intensity I_T, initially increases linearly with the impact velocity and then it tends to attain a saturation value for higher values of the impact velocity. The value of t_m increases logarithmally with the thickness of crystals, I_m increases linearly with the area of cross-section of crystals and I_T increases linearly with the volume of crystals. Generally, the ML of non-irradiated crystals decreases with increasing temperature of crystals. Depending on the prevailing conditions the ML spectra consist of either gas discharge spectra or solid state luminescence spectra or combination of the both. On the basis of the rate of generation of cracks and the rate of creation of new surface area of crystals, expressions are derived for the ML intensity and they are found to explain satisfactorily the temporal, spectral, thermal, crystal-size, impact velocity, surface area, and other characteristics of ML. The present investigation may be useful in designing of damage sensors, fracture sensors, ML-based safety management monitoring system, fuse-system for army warheads, milling machine, etc. The present study may be helpful in understanding the processes involved in earthquakes, earthquake lights and mine-failure as they basically involve fracture of solids.     

Monte Carlo simulation of film growth in a phase separating binary alloy model

Using a kinetic Monte Carlo method, we simulate binary film (A_0.5B_0.5/A) growth on an L×L square lattice with the focus on the domain growth behaviour. We compute the average domain area, A(t), as a measure of domain size. For a sufficiently large system, we find that A(t) grows with a power law in time with A(t)∼t^2/3 after the initial transient time. This implies that the dynamic exponent for domain growth with non-conserved order parameter is z=3, a value which was theoretically predicted for the conserved order parameter case. Further analysis reveals that such a power-law behaviour emerges because the order parameter is approximately conserved after the early stage of growth.     

On the fractal dimension of the Henon attractor

We re-measured the fractal dimension of the Hénon attractor by direct box-counting. We paid special attention to (a) optimal speed and use of storage, and (b) systematic corrections due to the finiteness of the number of iterations. Covering with grids of up to 9600 × 9600 boxes, we observe that the number N(?, n) of boxes visited after n iterations obeys a scaling law N(?, ∞) - N(?, n) ≈ const × ?^-αn^-β (for n → ∞) with α = 2.42 ± 0.15, β = 0.89 ± 0.03. Using this extrapolate to n → ∞, we obtain D = 1.28 ± 0.01 in disagreement with previous box-counting estimates, but in agreement with a recent indirect evaluation.