Spin coupling and magnetic field effects on the finite-size free energy and its non-extensivity for 1-D Ising model with nearest and next-nearest neighbor interactions in nanosystem

The effects of second-neighbor spin coupling interactions and a magnetic field are investigated on the free energies of a finite-size 1-D Ising model. For both ferromagnetic of nearest neighbor (NN) and next-nearest neighbor (NNN) spin coupling interactions, the finite-size free energy first increases and then approaches a constant value for any size of the spin chain. In contrast, when NNN and NN spin coupling interactions are antiferromagnetic and ferromagnetic, respectively, the finite-size free energy gradually decreases by increasing the competition factor and eventually vanishes for large values of it. When a magnetic field is applied, the finite-size free energy decreases with respect to the case of zero magnetic fields for both ferromagnetic and antiferromagnetic spin coupling interactions. Deviation of free energy per size for finite-size systems relative to the infinite system increases when the spin coupling interactions as well as the f parameter (the ratio of the magnetic field to NN spin coupling interaction) increase.     

Detecting community structure using label propagation with weighted coherent neighborhood propinquity

Community detection has become an important methodology to understand the organization and function of various real-world networks. The label propagation algorithm (LPA) is an almost linear time algorithm proved to be effective in finding a good community structure. However, LPA has a limitation caused by its one-hop horizon. Specifically, each node in LPA adopts the label shared by most of its one-hop neighbors; much network topology information is lost in this process, which we believe is one of the main reasons for its instability and poor performance. Therefore in this paper we introduce a measure named weighted coherent neighborhood propinquity (weighted-CNP) to represent the probability that a pair of vertices are involved in the same community. In label update, a node adopts the label that has the maximum weighted-CNP instead of the one that is shared by most of its neighbors. We propose a dynamic and adaptive weighted-CNP called entropic-CNP by using the principal of entropy to modulate the weights. Furthermore, we propose a framework to integrate the weighted-CNP in other algorithms in detecting community structure. We test our algorithm on both computer-generated networks and real-world networks. The experimental results show that our algorithm is more robust and effective than LPA in large-scale networks.     

Sous ellipticite dans le cadre du calcul S(m,g)

Abstract

We study the regularity of the free boundary in the two membranes problem. We prove that around any point the free boundary is either a C ^{1, α} surface or a cusp, as in the obstacle problem. We also prove C ^{1, 1} regularity for the pair of functions solving the problem.     

On a nonlocal elliptic problem arising in the confinement of a plasma in a current carrying stellarator

This paper deals with a nonlocal free boundary problem arising in the study of the dynamics of the confinement of a plasma in a Stellarator device. The free boundary represents the separation between the plasma and vacuum regions, and the nonlocal term involves the notions of relative rearrangement and monotone rearrangement. We establish some new properties on the decreasing rearrangement that can be used to prove the convergence of the approximate problem, and then prove the existence of solutions by Galerkin method. Copyright © 2013 John Wiley & Sons, Ltd.     

Computational chemistry in drug lead discovery and design

The main contributions of our group during the last 15 years developing and using biomolecular simulation tools in drug lead discovery and design, in close collaboration with experimental researchers, are presented. Special emphasis has been given to methodological improvements in the following areas: (1) target homology modeling incorporating knowledge about known ligands to accurately characterize the binding site; (2) designing alternative strategies to account for protein flexibility in high-throughput docking; (3) development of stochastic- and normal-mode-based methods to de novo design structurally diverse protein conformers; (4) development and validation of quantum mechanical semi-empirical linear-scaling calculations to correctly estimate ligand binding free energy. Several successful cases of computer-aided drug discovery are also presented, especially our recent work on viral targets.     

Piperazine‐functionalized nickel ferrite nanoparticles as efficient and reusable catalysts for the solvent‐free synthesis of 2‐amino‐4H‐chromenes

Piperazine‐functionalized nickel ferrite (NiFe₂O₄) nanoparticles were synthesized as recoverable heterogeneous base catalysts using a routine method. The synthesized materials were characterized using various spectroscopic techniques such as infrared, X‐ray diffraction, scanning electron microscopy, energy‐dispersive X‐ray, thermogravimetry analysis, and vibrating sample magnetometry. Catalytic efficiency was investigated in the synthesis of 2‐amino‐4H‐chromene derivatives via a one‐pot three component reaction of aldehyde and malononitrile with β or α‐naphthol/5‐methyle resorcinol under solvent‐free conditions with good to high yields. This method is operationally simple and has several advantages such as good to high yield, short reaction times, solvent‐free conditions, and easy synthesis. Moreover, the catalyst was recovered easily using an external magnet and reused three times without distinctive loss in catalytic activity.     

Catalyst- and organic solvent-free synthesis of thioacids in water

Thioacids and thioamino acids were synthesized in excellent yields from readily available acyl benzotriazoles and sodium hydrosulfide in water at room temperature. The new methodology features mild reaction conditions, high yields, short reaction times, and does not involve the use of organic solvents or bases. The reaction is eco-friendly, and the workup procedure is simple and does not require chromatographic separation.     

Finite-Temperature Dimer Method for Finding Saddle Points on Free Energy Surfaces

The dimer method and its variants have been shown to be efficient in finding saddle points on potential surfaces. In the dimer method, the most unstable direction is approximately obtained by minimizing the total potential energy of the dimer. Then, the force in this direction is reversed to move the dimer toward saddle points. When the finite-temperature effect is important for a high-dimensional system, one usually needs to describe the dynamics in a low-dimensional space of reaction coordinates. In this case, transition states are collected as saddle points on the free energy surface. The traditional dimer method cannot be directly employed to find saddle points on a free energy surface since the surface is not known a priori. Here, we develop a finite-temperature dimer method for searching saddle points on the free energy surface. In this method, a constrained rotation dynamics of the dimer system is used to sample dimer directions and an efficient average method is used to obtain a good approximation of the most unstable direction. This approximated direction is then used in reversing the force component and evolving the dimer toward saddle points. Our numerical results suggest that the new method is efficient in finding saddle points on free energy surfaces. © 2019 Wiley Periodicals, Inc.