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Microfluidic devices offer unique opportunities to directly observe multiphase flow in porous media. However, as a direct representation of flow in geological pore networks, conventional microfluidics face several challenges. One is that simultaneous two-phase flow is not possible in a 2D network without fluctuation occupancy of pores. Nonetheless, such flow is possible in a microfluidic network if wetting phase can form a bridge across the gap between solid surfaces at a pore constriction while non-wetting phase flows through the constriction. We call this phenomenon "bridging". Here we consider the conditions under which this is possible as a function of capillary pressure and geometry of the constriction. Using the Surface Evolver program, we determine conditions for stable interfaces in a constriction, the range of capillary pressures at which bridging can occur, and those where the wetting phase would invade and block the constriction to the flow of the non-wetting phase ("snap-off"). We assume that the channels have uniform depth, vertical walls, and flat bottom and top surfaces, and that one phase perfectly wets the solid surfaces. If the constriction is long and straight, snap-off occurs at the same capillary pressure as bridging. For long, curved channels, snap-off happens as liquid imbibes before bridging can occur. For constrictions between cylindrical pillars, however, there is a range of capillary pressures at which bridging is stable; the range is greater the narrower the diameter of the cylinders relative to the width of the constriction. For smaller-diameter pillars, snap-off as non-wetting phase invades a downstream pore body is not possible. We relate these results to the shape of pore networks commonly used in microfluidic studies of two-phase flow to consider whether two-phase flow is possible in these networks without fluctuating pore occupancy., Comment: 20 pages, 10 figures

We simulate the quasi-static motion of a spherical particle through a stable, horizontal soap film. The soap film subtends a fixed contact angle, in the range $10-135^\circ$, where it meets the particle. The tension and pressure forces acting on the particle are calculated in two cases: when the film is held within a vertical cylinder, trapping a bubble but otherwise free to move vertically, and when the outer rim of the film is held in a fixed circular wire frame. Film deformation is greater in the second case, and the duration of the interaction therefore increases, increasing the contact time between particle and film. As the soap film returns towards its equilibrium shape following the passage of the particle a small bubble is trapped for contact angles below a threshold value of $90^\circ$. We show that this bubble is larger when the particle is larger and when the contact angle is smaller., Comment: 12 pages

Recently a novel type of epithelial cell has been discovered and dubbed the "scutoid". It is induced by curvature of the bounding surfaces. We show by simulations and experiments that such cells are to be found in a dry foam subjected to this boundary condition.

We describe a numerical model to predict the rheology of two-dimensional dry foams. The model accurately describes soap film curvature, viscous friction with the walls, and includes the transport of surfactant within the films and across the vertices where films meet. It accommodates the changes in foam topology that occur when a foam flows and, in particular, accurately represents the relaxation of the foam following a topological change. The model is validated against experimental data, allowing the prediction of elastic and viscous parameters associated with different surfactant solutions.

We present simulations that show that an ideal two-dimensional foam with a finite contact angle develops an inhomogeneity for high liquid fraction $\phi$. In liquid-liquid emulsions this inhomogeneity is known as flocculation. In the case of an ordered foam this requires a perturbation, but in a disordered foam inhomogeneity grows steadily and spontaneously with $\phi$, as demonstrated in our simulations performed with the Surface Evolver.

Elastically-driven motion has been used as a strategy to achieve high speeds in small organisms and engineered micro-robotic devices. We examine the size-scaling relations determining the limit of elastic energy release from elastomer bands with mechanical properties similar to the biological protein resilin. The maximum center-of-mass velocity of the elastomer bands was found to be size-scale independent, while smaller bands demonstrated larger accelerations and shorter durations of elastic energy release. Scaling relationships determined from these measurements are consistent with the performance of small organisms which utilize elastic elements to power motion. Engineered devices found in the literature do not follow the same size-scaling relationships, which suggests an opportunity for improved design of engineered devices., Comment: 9 pages, 4 figures

We investigate the equilibrium properties of a single area-minimising bubble trapped between two narrowly-separated parallel curved plates. We begin with the simple case of a a bubble trapped between concentric spherical plates. We develop a model that shows that the surface tension energy of the bubble is lower when confined between spherical plates as compared to a bubble trapped between flat plates. We confirm our findings by comparing against Surface Evolver simulations. Next, we derive a simple model for a bubble between arbitrarily curved parallel plates. The energy is found to be higher when the local Gaussian curvature of the plates is negative and lower when the curvature is positive. To check the validity of the the model we consider a bubble trapped between concentric tori. In the toroidal case we find that the sensitivity of the bubble's energy to the local curvature acts as a geometric potential capable of driving bubbles from regions with negative to positive curvature., Comment: 10 figures & 1 movie (https://youtu.be/sOw8WIO3x1o)

In the course of animal development, the shape of tissue emerges in part from mechanical and biochemical interactions between cells. Measuring stress in tissue is essential for studying morphogenesis and its physical constraints. Experimental measurements of stress reported thus far have been invasive, indirect, or local. One theoretical approach is force inference from cell shapes and connectivity, which is non-invasive, can provide a space-time map of stress and relies on prefactors. Here, to validate force- inference methods, we performed a comparative study of them. Three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces, were tested by using two artificial and two experimental data sets. Our results using different datasets consistently indicate that our Bayesian force inference, by which cell-junction tensions and cell pressures are simultaneously estimated, performs best in terms of accuracy and robustness. Moreover, by measuring the stress anisotropy and relaxation, we cross-validated the force inference and the global annular ablation of tissue, each of which relies on different prefactors. A practical choice of force-inference methods in distinct systems of interest is discussed., Comment: 12 pages, 8 figures, EPJ E: Topical issue on "Physical constraints on morphogenesis and evolution"

A computer study of clusters of up to 200,000 equal-area bubbles shows for the first time that rounding conjectured optimal hexagonal planar soap bubble clusters reduces perimeter., Comment: 10 pages, 9 figures

We consider a parametrically driven damped discrete nonlinear Schr\"odinger (PDDNLS) equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental discrete bright solitons. We show that there are two types of onsite discrete soliton, namely onsite type I and II. We also show that there are four types of intersite discrete soliton, called intersite type I, II, III, and IV, where the last two types are essentially the same, due to symmetry. Onsite and intersite type I solitons, which can be unstable in the case of no dissipation, are found to be stabilized by the damping, whereas the other types are always unstable. Our further analysis demonstrates that saddle-node and pitchfork (symmetry-breaking) bifurcations can occur. More interestingly, the onsite type I, intersite type I, and intersite type III-IV admit Hopf bifurcations from which emerge periodic solitons (limit cycles). The continuation of the limit cycles as well as the stability of the periodic solitons are computed through the numerical continuation software Matcont. We observe subcritical Hopf bifurcations along the existence curve of the onsite type I and intersite type III-IV. Along the existence curve of the intersite type I we observe both supercritical and subcritical Hopf bifurcations., Comment: to appear in "Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations in Nonlinear Systems", B.A. Malomed, ed. (Springer, Berlin, 2012)

We present the activities of the "New Physics" working group for the "Physics at TeV Colliders" workshop (Les Houches, France, 30 May-17 June, 2011). Our report includes new agreements on formats for interfaces between computational tools, new tool developments, important signatures for searches at the LHC, recommendations for presentation of LHC search results, as well as additional phenomenological studies., Comment: 243 pages, report of the Les Houches 2011 New Physics Group; fix three figures

In this article we prove pathwise Holder convergence with optimal rates of the implicit Euler scheme for semi-linear parabolic stochastic differential equations with multiplicative noise, set in a UMD Banach space X. We assume the non-linearities to satisfy appropriate (local) Lipschitz conditions. The convergence results are obtained by first proving corresponding results for the splitting scheme. The results are applied to a class of second order parabolic SPDEs driven by multiplicative space-time white noise., Comment: 67 pages

Travelling solitary waves in the one-dimensional discrete nonlinear Schr\"{o}dinger equation (DNLSE) with saturable onsite nonlinearity are studied. A variational approximation (VA) for the solitary waves is derived in an analytical form. The stability is also studied by means of the VA, demonstrating that the solitons are stable, which is consistent with previously published results. Then, the VA is applied to predict parameters of travelling solitons with non-oscillatory tails (\textit{embedded solitons}, ESs). Two-soliton bound states are considered too. The separation distance between the solitons forming the bound state is derived by means of the VA. A numerical scheme based on the discretization of the equation in the moving coordinate frame is derived and implemented using the Newton--Raphson method. In general, a good agreement between the analytical and numerical results is obtained. In particular, we demonstrate the relevance of the analytical prediction of characteristics of the embedded solitons., Comment: This paper is to appear in Journal of Physics A

We consider a parametrically driven Klein--Gordon system describing micro- and nano-devices, with integrated electrical and mechanical functionality. Using a multiscale expansion method we reduce the system to a discrete nonlinear Schrodinger equation. Analytical and numerical calculations are performed to determine the existence and stability of fundamental bright and dark discrete solitons admitted by the Klein--Gordon system through the discrete Schrodinger equation. We show that a parametric driving can not only destabilize onsite bright solitons, but also stabilize intersite bright discrete solitons and onsite and intersite dark solitons. Most importantly, we show that there is a range of values of the driving coefficient for which dark solitons are stable, for any value of the coupling constant, i.e. oscillatory instabilities are totally suppressed. Stability windows of all the fundamental solitons are presented and approximations to the onset of instability are derived using perturbation theory, with accompanying numerical results. Numerical integrations of the Klein--Gordon equation are performed, confirming the relevance of our analysis.

We report unexpected behaviour in a family of Cu spin- 1/2 systems, in which an apparent gap in the low energy magneto-optical absorption spectrum opens at low temperature. This previously unreported collective phenomenon arises at temperatures where the energy of the dominant exchange interaction exceeds the thermal energy. Simulations of the observed shifts in electron paramagnetic resonance spectral weight, which include spin anisotropy, reproduce this behavior yielding the magnitude of the spin anisotropy in these compounds., Comment: 4 pages (slightly run over) 4 figures

Although the isotope effect in superconducting materials is well-documented, changes in the magnetic properties of antiferromagnets due to isotopic substitution are seldom discussed and remain poorly understood. This is perhaps surprising given the possible link between the quasi-two-dimensional (Q2D) antiferromagnetic and superconducting phases of the layered cuprates. Here we report the experimental observation of shifts in the N\'{e}el temperature and critical magnetic fields ($\Delta T_{\rm N}/T_{\rm N}\approx 4%$; $\Delta B_{\rm c}/B_{\rm c}\approx 4%$) in a Q2D organic molecular antiferromagnets on substitution of hydrogen for deuterium. These compounds are characterized by strong hydrogen bonds through which the dominant superexchange is mediated. We evaluate how the in-plane and inter-plane exchange energies evolve as the hydrogens on different ligands are substituted, and suggest a possible mechanism for this effect in terms of the relative exchange efficiency of hydrogen and deuterium bonds.

Pulsed-field magnetization experiments (fields $B$ of up to 85 T and temperatures $T$ down to 0.4 K) are reported on nine organic Cu-based two-dimensional (2D) Heisenberg magnets. All compounds show a low-$T$ magnetization that is concave as a function of $B$, with a sharp ``elbow'' transition to a constant value at a field $B_{\rm c}$. Monte-Carlo simulations including a finite interlayer exchange energy $J_{\perp}$ quantitatively reproduce the data; the concavity indicates the effective dimensionality and $B_{\rm c}$ is an accurate measure of the in-plane exchange energy $J$. Using these values and Ne\'el temperatures measured by muon-spin rotation, it is also possible to obtain a quantitative estimate of $|J_{\perp}/J|$. In the light of these results, it is suggested that in magnets of the form [Cu(HF$_2$)(pyz)$_2$]X, where X is an anion, the sizes of $J$ and $J_{\perp}$ are controlled by the tilting of the pyrazine (pyz) molecule with respect to the 2D planes.