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

Phase transitions in the steady state behavior of mechanically perturbed spin glasses and ferromagnets

We analyze the steady state regime of systems interpolating between spin glasses and ferromagnets under a tapping dynamics recently introduced by analogy with the dynamics of mechanically perturbed granular media. A crossover from a second order to first order ferromagnetic transition as a function of the spin coupling distribution is found. The flat measure over blocked states introduced by Edwards for granular media is used to explain this scenario. Annealed calculations of the Edwards entropy are shown to qualitatively explain the nature of the phase transitions. A Monte-Carlo construction of the Edwards measure confirms that this explanation is also quantitatively accurate

Geometry of Frictionless and Frictional Sphere Packings

We study static packings of frictionless and frictional spheres in three dimensions, obtained via molecular dynamics simulations, in which we vary particle hardness, friction coefficient, and coefficient of restitution. Although frictionless packings of hard-spheres are always isostatic (with six contacts) regardless of construction history and restitution coefficient, frictional packings achieve a multitude of hyperstatic packings that depend on system parameters and construction history. Instead of immediately dropping to four, the coordination number reduces smoothly from $z=6$ as the friction coefficient $\mu$ between two particles is increased.Comment: 6 pages, 9 figures, submitted to Phys. Rev.

Linear response of vibrated granular systems to sudden changes in the vibration intensity

The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the evolution of the system. The existence of a critical time separating regimes of ``anomalous'' and ``normal'' responses is predicted. A simple model fitting into the general framework is analyzed in the detail. The relationship between this work and previous studies is discussed.Comment: 10 pages, 6 figures; fixed errata, updtated reference

Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order

We calculate the partition function of partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order using the supersymmetry method in the formulation without a singlet particle. We include a nonzero imaginary chemical potential and show that the finite-volume corrections to the low-energy constants $\Sigma$ and $F$ for the partially quenched partition function, and hence for spectral correlation functions of the Dirac operator, are the same as for the unquenched partition function. We briefly comment on how to minimize these corrections in lattice simulations of QCD. As a side result, we show that the zero-momentum integral in the formulation without a singlet particle agrees with previous results from random matrix theory.Comment: 19 pages, 4 figures; minor changes, to appear in JHE

Prospects for detecting an ηc′\eta_c' in two photon processes

We argue that an experimental search for an $\eta_c'$, the first radial excitation of the $\eta_c(2980)$, may be carried out using the two photon process e^+e^- \to e^+e^- \gamma \gamma \ra e^+e^-\eta_c'. We estimate the partial width $\Gamma_{\gamma \gamma}(\eta_c')$ and the branching fraction $B(\eta_c' \to h)$, where $h$ is an exclusive hadronic channel, and find that for $h = K^o_s K^\pm \pi^\mp$ it may be possible to observe this state in two photon collisions at CLEO-II.Comment: 9 pages, LATEX forma

Dilatancy transition in a granular model

We introduce a model of granular matter and use a stress ensemble to analyze shearing. Monte Carlo simulation shows the model to exhibit a second order phase transition, associated with the onset of dilatancy.Comment: Future versions can be obtained from: http://www.ma.utexas.edu/users/radin/papers/shear2.pd

Time-resolved spectroscopy of the excited electronic state of reaction centers of Rhodopseudomonas viridis

The spectral properties of the excited electronic state of the reaction centers of Rhodopseudomonas (Rps.) viridis are studied by dichroic transient absorption spectroscopy with sub-picosecond time resolution. The theoretical analysis of the experimental results allows the assignment of the transient absorption from two dimer bands of the special pair and show its excitonic coupling to other pigments

Dynamics of a passive sliding particle on a randomly fluctuating surface

We study the motion of a particle sliding under the action of an external field on a stochastically fluctuating one-dimensional Edwards-Wilkinson surface. Numerical simulations using the single-step model shows that the mean-square displacement of the sliding particle shows distinct dynamic scaling behavior, depending on whether the surface fluctuates faster or slower than the motion of the particle. When the surface fluctuations occur on a time scale much smaller than the particle motion, we find that the characteristic length scale shows anomalous diffusion with $\xi(t)\sim t^{2\phi}$, where $\phi\approx 0.67$ from numerical data. On the other hand, when the particle moves faster than the surface, its dynamics is controlled by the surface fluctuations and $\xi(t)\sim t^{{1/2}}$. A self-consistent approximation predicts that the anomalous diffusion exponent is $\phi={2/3}$, in good agreement with simulation results. We also discuss the possibility of a slow cross-over towards asymptotic diffusive behavior. The probability distribution of the displacement has a Gaussian form in both the cases.Comment: 6 pages, 4 figures, error in reference corrected and new reference added, submitted to Phys. Rev.

The Role of Friction in Compaction and Segregation of Granular Materials

We investigate the role of friction in compaction and segregation of granular materials by combining Edwards' thermodynamic hypothesis with a simple mechanical model and mean-field based geometrical calculations. Systems of single species with large friction coefficients are found to compact less. Binary mixtures of grains differing in frictional properties are found to segregate at high compactivities, in contrary to granular mixtures differing in size, which segregate at low compactivities. A phase diagram for segregation vs. friction coefficients of the two species is generated. Finally, the characteristics of segregation are related directly to the volume fraction without the explicit use of the yet unclear notion of compactivity.Comment: 9 pages, 6 figures, submitted to Phys. Rev.