Effect of anisotropy on the field induced quantum critical properties of the three dimensional s=1/2 Heisenberg model

The field induced quantum critical properties of the three dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg model has been studied. We have investigated the quantum phase transition between the spiral order and field induced ferromagnetic order by means of Bose-Einstein condensation of magnons in terms of a bosonic representation. The effect of in-plane anisotropy on the critical properties has been studied via the bosonic model by Green's function approach. We have found an analytic expression for the gap exponent in addition to numerical results for the critical magnetic field in terms of anisotropy parameter. The in-plane anisotropy breaks the U(1) symmetry explicitly which changes the universal behavior by a drastic change on the gap exponent. Moreover, the critical magnetic field depends strongly on the in-plane anisotropies. The divergence of the transverse structure factor at the antiferromagnetic wave vector confirms the onset of the magnetic order which scales with the negative value of gap exponent as the magnetic field approaches the critical one. The transverse staggered magnetization as an order parameter vanishes with exponent $\beta=0.5$ when the magnetic field reaches its critical value in low field region.Comment: 9 pages and 2 figure

A continuous model for microtubule dynamics with catastrophe, rescue and nucleation processes

Microtubules are a major component of the cytoskeleton distinguished by highly dynamic behavior both in vitro and in vivo. We propose a general mathematical model that accounts for the growth, catastrophe, rescue and nucleation processes in the polymerization of microtubules from tubulin dimers. Our model is an extension of various mathematical models developed earlier formulated in order to capture and unify the various aspects of tubulin polymerization including the dynamic instability, growth of microtubules to saturation, time-localized periods of nucleation and depolymerization as well as synchronized oscillations exhibited by microtubules under various experimental conditions. Our model, while attempting to use a minimal number of adjustable parameters, covers a broad range of behaviors and has predictive features discussed in the paper. We have analyzed the resultant behaviors of the microtubules changing each of the parameter values at a time and observing the emergence of various dynamical regimes.Comment: 25 pages, 12 figure

A first principle (3+1) dimensional model for microtubule polymerization

In this paper we propose a microscopic model to study the polymerization of microtubules (MTs). Starting from fundamental reactions during MT's assembly and disassembly processes, we systematically derive a nonlinear system of equations that determines the dynamics of microtubules in 3D. %coexistence with tubulin dimers in a solution. We found that the dynamics of a MT is mathematically expressed via a cubic-quintic nonlinear Schrodinger (NLS) equation. Interestingly, the generic 3D solution of the NLS equation exhibits linear growing and shortening in time as well as temporal fluctuations about a mean value which are qualitatively similar to the dynamic instability of MTs observed experimentally. By solving equations numerically, we have found spatio-temporal patterns consistent with experimental observations.Comment: 12 pages, 2 figures. Accepted in Physics Letters

An experimental investigation of the independent effect of suction and degree of saturation on very small-strain stiffness of unsaturated sand

The paper presents an experimental investigation of very small strain stiffness of unsaturated sand. A triaxial test apparatus was equipped with bender elements and compression discs in order to assess the stiffness at very small strains by measuring the velocity of propagation of shear and compression waves through an unsaturated sample. The negative water column method was adopted to apply suction at the base of the sample. The experiments were designed to investigate the independent effect of suction and degree of saturation on the wave propagation velocities. This was achieved by testing the sand sample on both the drying and wetting path

Model of ionic currents through microtubule nanopores and the lumen

It has been suggested that microtubules and other cytoskeletal filaments may act as electrical transmission lines. An electrical circuit model of the microtubule is constructed incorporating features of its cylindrical structure with nanopores in its walls. This model is used to study how ionic conductance along the lumen is affected by flux through the nanopores when an external potential is applied across its two ends. Based on the results of Brownian dynamics simulations, the nanopores were found to have asymmetric inner and outer conductances, manifested as nonlinear IV curves. Our simulations indicate that a combination of this asymmetry and an internal voltage source arising from the motion of the C-terminal tails causes a net current to be pumped across the microtubule wall and propagate down the microtubule through the lumen. This effect is demonstrated to enhance and add directly to the longitudinal current through the lumen resulting from an external voltage source, and could be significant in amplifying low-intensity endogenous currents within the cellular environment or as a nano-bioelectronic device.Comment: 43 pages, 6 figures, revised versio

Analytical thermal and cost optimization of micro-structured plate-fin heat sink

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.Microchannel heat sinks have been widely used in the field of thermo-fluids due to the rapid growth in technological applications which require high rates of heat transfer in relatively small spaces and volumes. In this work, a micro plate-fin heat sink is optimized parametrically, to minimize the thermal resistance and to maximize the cost performance of the heat sink. The width and the height of the microchannels, and the fin thickness are analytically optimized at a wide range of pumping power. Using an effective numeric test, the generated equations also discuss the optimum parameters at three sizes of the substrate plat of the heat sink. Results show that, at any pumping power there are specific values of the channel width and fin thickness which produce minimum thermal resistance in the heat sink. The results also illustrate that, a larger channel width and a smaller fin thickness lead to a better cost performance, and the optimum channel height decreases when the pumping power increases.cf201