Lattice Boltzmann Magnetohydrodynamics

Lattice gas and lattice Boltzmann methods are recently developed numerical schemes for simulating a variety of physical systems. In this paper a new lattice Boltzmann model for modeling two-dimensional incompressible magnetohydrodynamics (MHD) is presented. The current model fully utilizes the flexibility of the lattice Boltzmann method in comparison with previous lattice gas and lattice Boltzmann MHD models, reducing the number of moving directions from $36$ in other models to $12$ only. To increase computational efficiency, a simple single time relaxation rule is used for collisions, which directly controls the transport coefficients. The bi-directional streaming process of the particle distribution function in this paper is similar to the original model [ H. Chen and W. H. Matthaeus, Phys. Rev. Lett., {\bf 58}, 1845(1987), S.Chen, H.Chen, D.Mart\'{\i}nez and W.H.Matthaeus, Phys. Rev. Lett. {\bf 67},3776 (1991)], but has been greatly simplified, affording simpler implementation of boundary conditions and increasing the feasibility of extension into a workable three-dimensional model. Analytical expressions for the transport coefficients are presented. Also, as example cases, numerical calculation for the Hartmann flow is performed, showing a good agreement between the theoreticalComment: 45 pages, to appear in Physics of Plasma

Topological phase transition in a RNA model in the de Gennes regime

We study a simplified model of the RNA molecule proposed by G. Vernizzi, H. Orland and A. Zee in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain, while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (of the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures, the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytic expression for T_c. The regime studied for this model exhibits analogies with that for the dense polymer systems studied by de GennesComment: 15 pages, 4 figure

Optimal model reduction for sparse linear systems

A novel $H^2$ optimal model reduction problem is formulated for large-scale sparse linear systems as a nonconvex optimization problem. The analysis on the gradient of the objective function shows that the nonconvex optimization problem can be simplified to solve a linear equation in multi-input single-output (MISO) or single-input multi-input (SIMO) cases. Thus, a simple and efficient model reduction algorithm based on the simplified problem is proposed for huge-scale systems. Moreover, an additional algorithm with guaranteed global convergence is developed for multi-input multi-output (MIMO) cases by focusing on the convexity of the objective function in terms of each variable based on the proximal alternating projection method. Both the algorithms guarantee that all the eigenvalues of the state matrix of a generated reduced system with the state dimension $r$ completely coincide with the $r$ largest eigenvalues of the original state matrix. The numerical experiments demonstrate that the algorithm proposed for MISO or SIMO cases and the algorithm developed for MIMO cases can reduce sparse systems having original dimensions larger than $10^7$ and $10^6$ to a practical time period, respectively. Furthermore, it is shown that the proposed algorithms of this study deliver superior performance to an existing method for large-scale systems in terms of the objective function, eigenvalues of the reduced state matrix, and computational time

Exact solution for linear and nonlinear systems of PDEs by homotopy-perturbation method

In this paper, the homotopy-perturbation method (HPM)proposed by J.-H. He is adopted for solving linear and nonlinear systems of partial differential equations (PDEs). In this method, a homotopy parameter p, which takes the values from 0 to 1, is introduced. When p = 0, the system of equations usually reduces to a sufficiently simplified form, which normally admits a rather simple solution. As p gradually increases to 1, the system goes through a sequence of ‘deformations’, the solution of each of which is ‘close’ to that at the previous stage of ‘deformation’. Eventually at p = 1,the system takes the original form of the equation and the final stage of ‘deformation’ gives the desired solution. Some examples are presented to demonstrate the efficiency and simplicity of the method

Quantitative full-colour transmitted light microscopy and dyes for concentration mapping and measurement of diffusion coefficients in microfluidic architectures

International audienceA simple and versatile methodology has been developed for the simultaneous measurement of multiple concentration profiles of colourants in transparent microfluidic systems, using a conventional transmitted light microscope, a digital colour (RGB) camera and numerical image processing combined with multicomponent analysis. Rigorous application of the Beer-Lambert law would require monochromatic probe conditions, but in spite of the broad spectral bandwidths of the three colour channels of the camera, a linear relation between the measured optical density and dye concentration is established under certain conditions. An optimised collection of dye solutions for the quantitative optical microscopic characterisation of microfluidic devices is proposed. Using the methodology for optical concentration measurement we then implement and validate a simplified and robust method for the microfluidic measurement of diffusion coefficients using an H-filter architecture. It consists of measuring the ratio of the concentrations of the two output channels of the H-filter. It enables facile determination of the diffusion coefficient, even for non-fluorescent molecules and nanoparticles, and is compatible with non-optical detection of the analyte

Optimal Hamiltonian Simulation by Quantum Signal Processing

The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly simulation of physical systems. Surprisingly, this has been challenging, with current Hamiltonian simulation algorithms remaining abstract and often the result of sophisticated but unintuitive constructions. We contend that physical intuition can lead to optimal simulation methods by showing that a focus on simple single-qubit rotations elegantly furnishes an optimal algorithm for Hamiltonian simulation, a universal problem that encapsulates all the power of quantum computation. Specifically, we show that the query complexity of implementing time evolution by a $d$-sparse Hamiltonian $\hat{H}$ for time-interval $t$ with error $\epsilon$ is $\mathcal{O}(td\|\hat{H}\|_{\text{max}}+\frac{\log{(1/\epsilon)}}{\log{\log{(1/\epsilon)}}})$, which matches lower bounds in all parameters. This connection is made through general three-step "quantum signal processing" methodology, comprised of (1) transducing eigenvalues of $\hat{H}$ into a single ancilla qubit, (2) transforming these eigenvalues through an optimal-length sequence of single-qubit rotations, and (3) projecting this ancilla with near unity success probability.Comment: 6 pages, 1 figure. v2: notation simplified & updated for general audienc

Macromolecular confinement of therapeutic protein in polymeric particles for controlled release: insulin as a case study

Sustained release systems for therapeutic proteins have been widely studied targeting to improve the action of these drugs. Molecular entrapping of proteins is particularly challenging due to their conformational instability. We have developed a micro-structured poly-epsilon-caprolactone (PCL) particle system loaded with human insulin using a simple double-emulsion w/o/w method followed by solvent evaporation method. This formulation is comprised by spheric-shaped microparticles with average size of 10 micrometers. In vitro release showed a biphasic behavior such as a rapid release with about 50% of drug delivered within 2 hours and a sustained phase for up to 48 h. The subcutaneous administration of microencapsulated insulin showed a biphasic effect on glycemia in streptozotocin-induced diabetic mice, compatible with short and intermediate-acting behaviors, with first transition peak at about 2 h and the second phase exerting effect for up to 48h after s.c. administration. This study reveals that a simplified double-emulsion system results in biocompatible human-insulin-loaded PCL microparticles that might be used for further development of optimized sustained release formulations of insulin to be used in the restoration of hormonal levels