The missing stress-geometry equation in granular media

The simplest solvable problem of stress transmission through a static granular material is when the grains are perfectly rigid and have an average coordination number of $\bar{z}=d+1$. Under these conditions there exists an analysis of stress which is independent of the analysis of strain and the $d$ equations of force balance $\nabla_{j} \sigma_{ij}({\vec r}) = g_{i}({\vec r})$ have to be supported by $\frac{d(d-1)}{2}$ equations. These equations are of purely geometric origin. A method of deriving them has been proposed in an earlier paper. In this paper alternative derivations are discussed and the problem of the "missing equations" is posed as a geometrical puzzle which has yet to find a systematic solution as against sensible but fundamentally arbitrary approaches.Comment: 10 pages, 4 figures, accepted by Physica

The Stress Transmission Universality Classes of Periodic Granular Arrays

The transmission of stress is analysed for static periodic arrays of rigid grains, with perfect and zero friction. For minimal coordination number (which is sensitive to friction, sphericity and dimensionality), the stress distribution is soluble without reference to the corresponding displacement fields. In non-degenerate cases, the constitutive equations are found to be simple linear in the stress components. The corresponding coefficients depend crucially upon geometrical disorder of the grain contacts.Comment: 7 pages, 1 figur

Mass Dependent αS\alpha_S Evolution and the Light Gluino Existence

There is an intriguing discrepancy between \alpha_s(M_Z) values measured directly at the CERN $Z_0$-factory and low-energy (at few GeV) measurements transformed to $Q=M_{Z_0}$ by a massless QCD \alpha_s(Q) evolution relation. There exists an attempt to reconcile this discrepancy by introducing a light gluino \gl in the MSSM. We study in detail the influence of heavy thresholds on \alpha_s(Q) evolution. First, we consruct the "exact" explicit solution to the mass-dependent two-loop RG equation for the running \alpha_s(Q). This solution describes heavy thresholds smoothly. Second, we use this solution to recalculate anew \alpha_s(M_Z) values corresponding to "low-energy" input data. Our analysis demonstrates that using {\it mass-dependent RG procedure} generally produces corrections of two types: Asymptotic correction due to effective shift of threshold position; Local threshold correction only for the case when input experiment lies in the close vicinity of heavy particle threshold: $Q_{expt} \simeq M_h$. Both effects result in the effective shift of the \asmz values of the order of $10^{-3}$. However, the second one could be enhanced when the gluino mass is close to a heavy quark mass. For such a case the sum effect could be important for the discussion of the light gluino existence as it further changes the \gl mass.Comment: 13, Late

Correlated N-boson systems for arbitrary scattering length

We investigate systems of identical bosons with the focus on two-body correlations and attractive finite-range potentials. We use a hyperspherical adiabatic method and apply a Faddeev type of decomposition of the wave function. We discuss the structure of a condensate as function of particle number and scattering length. We establish universal scaling relations for the critical effective radial potentials for distances where the average distance between particle pairs is larger than the interaction range. The correlations in the wave function restore the large distance mean-field behaviour with the correct two-body interaction. We discuss various processes limiting the stability of condensates. With correlations we confirm that macroscopic tunneling dominates when the trap length is about half of the particle number times the scattering length.Comment: 15 pages (RevTeX4), 11 figures (LaTeX), submitted to Phys. Rev. A. Second version includes an explicit comparison to N=3, a restructured manuscript, and updated figure

Time Delay Correlations in Chaotic Scattering: Random Matrix Approach

We study the correlations of time delays in a model of chaotic resonance scattering based on the random matrix approach. Analytical formulae which are valid for arbitrary number of open channels and arbitrary coupling strength between resonances and channels are obtained by the supersymmetry method. We demonstrate that the time delay correlation function, though being not a Lorentzian, is characterized, similar to that of the scattering matrix, by the gap between the cloud of complex poles of the $S$-matrix and the real energy axis.Comment: 15 pages, LaTeX, 4 figures availible upon reques

A numerical reinvestigation of the Aoki phase with N_f=2 Wilson fermions at zero temperature

We report on a numerical reinvestigation of the Aoki phase in lattice QCD with two flavors of Wilson fermions where the parity-flavor symmetry is spontaneously broken. For this purpose an explicitly symmetry-breaking source term $h\bar{\psi} i \gamma_{5} \tau^{3}\psi$ was added to the fermion action. The order parameter $$ was computed with the Hybrid Monte Carlo algorithm at several values of $(\beta,\kappa,h)$ on lattices of sizes $4^4$ to $12^4$ and extrapolated to $h=0$. The existence of a parity-flavor breaking phase can be confirmed at $\beta=4.0$ and 4.3, while we do not find parity-flavor breaking at $\beta=4.6$ and 5.0.Comment: 8 pages, 5 figures, Revised version as to be published in Phys.Rev.

Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems

We extend quantum kinetic theory to deal with a strongly Bose-condensed atomic vapor in a trap. The method assumes that the majority of the vapor is not condensed, and acts as a bath of heat and atoms for the condensate. The condensate is described by the particle number conserving Bogoliubov method developed by one of the authors. We derive equations which describe the fluctuations of particle number and phase, and the growth of the Bose-Einstein condensate. The equilibrium state of the condensate is a mixture of states with different numbers of particles and quasiparticles. It is not a quantum superposition of states with different numbers of particles---nevertheless, the stationary state exhibits the property of off-diagonal long range order, to the extent that this concept makes sense in a tightly trapped condensate.Comment: 3 figures submitted to Physical Review

Efficient arithmetic on elliptic curves in characteristic 2

International audienceWe present normal forms for elliptic curves over a field of characteristic 2 analogous to Edwards normal form, and determine bases of addition laws, which provide strikingly simple expressions for the group law. We deduce efficient algorithms for point addition and scalar multiplication on these forms. The resulting algorithms apply to any elliptic curve over a field of characteristic 2 with a 4-torsion point, via an isomorphism with one of the normal forms. We deduce algorithms for duplication in time $2M + 5S + 2m_c$ and for addition of points in time $7M + 2S$, where $M$ is the cost of multiplication, $S$ the cost of squaring , and $m_c$ the cost of multiplication by a constant. By a study of the Kummer curves $\mathcal{K} = E/\{\pm1]\}$, we develop an algorithm for scalar multiplication with point recovery which computes the multiple of a point P with $4M + 4S + 2m_c + m_t$ per bit where $m_t$ is multiplication by a constant that depends on $P$

Curvature effects on the surface thickness and tension at the free interface of 4^4He systems

The thickness $W$ and the surface energy $\sigma_A$ at the free interface of superfluid $^4$He are studied. Results of calculations carried out by using density functionals for cylindrical and spherical systems are presented in a unified way, including a comparison with the behavior of planar slabs. It is found that for large species $W$ is independent of the geometry. The obtained values of $W$ are compared with prior theoretical results and experimental data. Experimental data favor results evaluated by adopting finite range approaches. The behavior of $\sigma_A$ and $W \sigma_A$ exhibit overshoots similar to that found previously for the central density, the trend of these observables towards their asymptotic values is examined.Comment: 35 pages, TeX, 5 figures, definitive versio

Elliptic Curve Scalar Multiplication Combining Yao’s Algorithm and Double Bases

Abstract. In this paper we propose to take one step back in the use of double base number systems for elliptic curve point scalar multiplication. Using a mod-ified version of Yao’s algorithm, we go back from the popular double base chain representation to a more general double base system. Instead of representing an integer k as Pn i=1 2 bi3ti where (bi) and (ti) are two decreasing sequences, we only set a maximum value for both of them. Then, we analyze the efficiency of our new method using different bases and optimal parameters. In particular, we pro-pose for the first time a binary/Zeckendorf representation for integers, providing interesting results. Finally, we provide a comprehensive comparison to state-of-the-art methods, including a large variety of curve shapes and latest point addition formulae speed-ups