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We define a lattice model for rock, absorbers, and gas that makes it possible to examine the flow of gas to a complicated absorbing boundary over long periods of time. The motivation is to deduce the geometry of the boundary from the time history of gas absorption. We find a solution to this model using Green's function techniques, and apply the solution to three absorbing networks of increasing complexity., Comment: 4 pages, 4 figures

We present a theoretical study of the two-dimensional spiral antiferromagnet Ba2CuGe2O7 in the presence of an external magnetic field. We employ a suitable nonlinear sigma model to calculate the T=0 phase diagram and the associated low-energy spin dynamics for arbitrary canted fields, in general agreement with experiment. In particular, when the field is applied parallel to the c axis, a previously anticipated Dzyaloshinskii-type incommensurate-to-commensurate phase transition is actually mediated by an intermediate phase, in agreement with our earlier theoretical prediction confirmed by the recent observation of the so-called double-k structure. The sudden pi/2 rotations of the magnetic structures observed in experiment are accounted for by a weakly broken U(1) symmetry of our model. Finally, our analysis suggests a nonzero weak-ferromagnetic component in the underlying Dzyaloshinskii-Moriya anisotropy, which is important for quantitative agreement with experiment., Comment: 17 pages, 14 figures. Corrected typos in the abstract

Cracks are the major vehicle for material failure, and often exhibit rather complex dynamics. The laws that govern their motion have remained an object of constant study for nearly a century. The simplest kind of dynamic crack is a single crack that moves along a straight line. We first briefly review current understanding of this "simple" object. We then critically examine the assumptions of the classic, scale-free, theory of dynamic fracture, and note when it works and how it may fail if certain of these assumptions are relaxed. A number of examples is provided, where the introduction of physical scales into this scale-free theory profoundly affects both a crack's structure and the resulting dynamics., Comment: 36 pages, 8 figures, a review paper submitted to "Annual Review of Condensed Matter Physics"

Meyer et al (2007) found that free-standing graphene sheets, just one atom thick, display spontaneous ripples. The ripples are of order 2-20 {\AA} high and 20-200 {\AA} wide. The sheets in which they appear are only one atom thick, and extend for around 5000 {\AA} through vacuum between metal struts that support them. Other groups have since created free-standing graphene as well (Garcia-Sanchez 2008 ; Bolotin et al. 2008), and similar ripples have been found for graphene on a glass substrate (Geringer et al. 2008). Here we show that these ripples can be explained as a consequence of adsorbed molecules sitting on random sites. The adsorbates cause the bonds between carbon atoms to lengthen slightly. Static buckles then result from a mechanism like the one that leads to buckling of leaves; buckles caused by roughly 20% coverage of adsorbates are consistent with experimental observations. We explain why this mechanism is more likely to explain rippled than thermal fluctuations or the Mermin-Wagner theorem, which have previously been invoked., Comment: 5 pages and 5 figures

This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where the disease can expand to an epidemic, the probability distribution function is the sum of two parts; one which is static at long times, and another whose mean grows exponentially. The time development of the mean number of infected individuals is obtained analytically. When epidemics occur, the probability distributions are very broad, and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals., Comment: 4 pages and 3 figures

We develop a Continuous Hugoniot Method for the efficient simulation of shock wave fronts with molecular dynamics. This approach achieves a significantly improved efficiency in the generation of a dense sampling of steady-state shock front states, and allows for the study of shocks as a function of a continuous shock strength parameter, $v_p$. This is, to our knowledge, the first attempt to map out the Hugoniot in a continuous fashion. We first apply this method to shocks in single-crystal Lennard-Jonesium along the <100> direction. Excellent agreement is found with both the published Lennard-Jones Hugoniot and results of conventional simulation methods. We next present a continuous numerical Hugoniot for shocks in tin which agrees to within 6% with experimental data. We study the strong shock to elastic-plastic shock transition in tin and find that it is a continuous transition consistent with a transcritical bifurcation., Comment: 15 pages, 21 figures

The rupture of rubber differs from conventional fracture. It is supersonic, and the speed is determined by strain levels ahead of the tip rather than total strain energy as for ordinary cracks. Dissipation plays a very important role in allowing the propagation of ruptures, and the back edges of ruptures must toughen as they contract, or the rupture is unstable. This article presents several levels of theoretical description of this phenomenon: first, a numerical procedure capable of incorporating large extensions, dynamics, and bond rupture; second, a simple continuum model that can be solved analytically, and which reproduces several features of elementary shock physics; and third, an analytically solvable discrete model that accurately reproduces numerical and experimental results, and explains the scaling laws that underly this new failure mode. Predictions for rupture speed compare well with experiment., Comment: 47 pages, 13 Figures

We describe the statistical mechanics of a new method to produce very cold atoms or molecules. The method results from trapping a gas in a potential well, and sweeping through the well a semi-permeable barrier, one that allows particles to leave but not to return. If the sweep is sufficiently slow, all the particles trapped in the well compress into an arbitrarily cold gas. We derive analytical expressions for the velocity distribution of particles in the cold gas, and compare these results with numerical simulations., Comment: 7 pages, 3 figures

We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy state of long strips is a twisted helical state like a telephone cord. We then extend the techniques used in this solution to two--dimensional sheets with more general metrics. We find evolution equations and show that when they are not singular, a surface is determined by knowledge of its metric, and the shape of the surface along one line. Finally, we provide numerical evidence that once these evolution equations become singular, either the surface is not differentiable, or else the metric deviates from the target metric as a result of minimization of a suitable energy functional ., Comment: 12 pages and 9 figures, many of them in color

This article presents a theory for the rupture of rubber. Unlike conventional cracks, ruptures in rubber travel faster than the speed of sound, and consist in two oblique shocks that meet at a point. Physical features of rubber needed for this phenomenon include Kelvin dissipation and an increase of toughness as rubber retracts. There are three levels of theoretical description: an approximate continuum theory, an exact analytical solution of a slightly simplified discrete problem, and numerical solution of realistic and fully nonlinear equations of motion., Comment: 4 pages and 2 figures

The shear wave speed is an upper limit for the speed of cracks loaded in tension in linear elastic solids. We have discovered that in a non-linear material, cracks in tension (Mode I) exceed this sound speed, and travel in an intersonic range between shear and longitudinal wave speeds. The experiments are conducted in highly stretched sheets of rubber; intersonic cracks can be produced simply by popping a balloon., Comment: 4 pages, 5 eps figures

Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is to discuss a collection of analytical and numerical results for the shape of a sheet with a non--flat metric. First, a simple condition is found to determine when a stretched sheet folded into a cylinder loses axial symmetry, and buckles like a flower. General expressions are next found for the energy of stretched sheet, both in forms suitable for numerical investigation, and for analytical studies in the continuum. The bulk of the paper focuses upon long thin strips of material with a linear gradient in metric. In some special cases, the energy--minimizing shapes of such strips can be determined analytically. Euler--Lagrange equations are found which determine the shapes in general. The paper closes with numerical investigations of these equations., Comment: 15 pages and 6 figures

We have found an oscillating instability of fast-running cracks in thin rubber sheets. A well-defined transition from straight to oscillating cracks occurs as the amount of biaxial strain increases. Measurements of the amplitude and wavelength of the oscillation near the onset of this instability indicate that the instability is a Hopf bifurcation.

We have measured the velocity of a running crack in brittle single crystal silicon as a function of energy flow to the crack tip. The experiments are designed to permit direct comparison with molecular dynamics simulations; therefore the experiments provide an indirect but sensitive test of interatomic potentials. Performing molecular dynamics simulations of brittle crack motion at the atomic scale we find that experiments and simulations disagree showing that interatomic potentials are not yet well understood., Comment: 4 pages, 4 figures, 19 references