Dynamic phase transitions and dynamic phase diagrams in the kinetic spin-5/2 Blume-Capel model in an oscillating external magnetic field: Effective-field theory and the Glauber-type stochastic dynamics approach

Using an effective field theory with correlations, we study a kinetic spin-5/2 Blume-Capel model with bilinear exchange interaction and single-ion crystal field on a square lattice. The effective-field dynamic equation is derived by employing the Glauber transition rates. First, the phases in the kinetic system are obtained by solving this dynamic equation. Then, the thermal behavior of the dynamic magnetization, the hysteresis loop area and correlation are investigated in order to characterize the nature of the dynamic transitions and to obtain dynamic phase transition temperatures. Finally, we present the phase diagrams in two planes, namely (T/zJ, h₀/zJ) and (T/zJ, D/zJ), where T absolute temperature, h₀, the amplitude of the oscillating field, D, crystal field interaction or single-ion anisotropy constant and z denotes the nearest-neighbor sites of the central site. The phase diagrams exhibit four fundamental phases and ten mixed phases which are composed of binary, ternary and tetrad combination of fundamental phases, depending on the crystal field interaction parameter. Moreover, the phase diagrams contain a dynamic tricritical point (T), a double critical end point (B), a multicritical point (A) and zero-temperature critical point (Z).     

Compensation temperatures,magnetic susceptibilities and phase diagrams of a mixed ferrimagnetic ternary system on the Bethe lattice

Compensation behaviors, magnetic susceptibilities and the phase diagrams of the ternary system of the type ABC consisting of Ising spins σ = 1/2, S = 3/2 and m = 5/2 in the presence of a single-ion anisotropy are studied on the Bethe lattice within the framework of the exact recursion relations. Both ferromagnetic and antiferromagnetic exchange interactions are considered. The exact expressions for sublattice magnetizations and magnetic susceptibilities are obtained, and then thermal behaviors of the sublattice magnetizations, total magnetization, magnetic sublattice susceptibilities and total susceptibility are investigated. We find that the system only undergoes a second order phase transition for the different and same bilinear nearest-neighbor exchange interaction parameters, but displays compensation behaviors for only different bilinear interaction parameters. We also present the phase diagrams for the different and same bilinear nearest-neighbor exchange interaction parameters. A comparison is made with the other ternary system of the type ABC consisting of different spin values.     

Archimedes with Cabri: Visualization and Experimental Verification of Mathematical Ideas

This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain-teasers involving the use of computers or computational theory. Snapshots are subject to peer review. This snapshot explores a classic geometry theorem of Archimedes. The author shows how the use of a dynamic geometry environment can deepen and guide the process of proof. The Cabri environment enabled exploration in a new way that connected steps in the proof to geometric properties and intuitions that served as a foundation for deductive reasoning. Computer Math Snapshots Editor: Uri Wilensky , Center for Connected Learning and Computer-Based Modeling Northwestern University, USA E-mail: uri@northwestern.edu     

Site characteristics in metal organic frameworks for gas adsorption

Metal organic frameworks (MOFs) are a new class of nanoporous materials that have many potential advantages over traditional nanoporous materials for several chemical technologies including gas adsorption, catalysis, membrane-based gas separation, sensing, and biomedical devices. Knowledge on the interaction of guest molecules with the MOF surface is required to design and develop these MOF-based processes. In this review, we examine the importance of identification of gas adsorption sites in MOFs using the current state-of-the-art in experiments and computational modeling. This review provides guidelines to design new MOFs with useful surface properties that exhibit desired performances, such as high gas storage capacity, and high gas selectivity.     

Dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h₀/J), (D/J, T/J) and (K/J, T/J) planes, where T, h₀, D, K and z are the temperature, magnetic field amplitude, crystal–field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.     

One-Step Synthesis of Triblock Copolymers via Simultaneous Reversible-Addition Fragmentation Chain Transfer (RAFT) and Ring-Opening Polymerization Using a Novel Difunctional Macro-RAFT Agent Based on Polyethylene Glycol

One-step synthesis of the triblock copolymers was carried out by reversible addition–fragmentation chain transfer (RAFT) polymerization of methyl methacrylate (MMA) and ring-opening polymerization (ROP) of β-butyrolactone (BL) or ?-caprolactone (CL) using a novel difunctional macro-RAFT agent. For this purpose, primarily PEG-Br (polyethylene glycol bromine) was obtained by using 3-bromopropanoyl chloride and PEGs (polyethylene glycols) with different molecular weights. Then, macro-RAFT agent was synthesized by the reaction of potassium ethyl xanthogenate and PEG-Br. By using macro-RAFT agent, poly(MMA-b-EG-b-BL), and poly(MMA-b-EG-b-CL) triblock copolymers were synthesized by changing some polymerization conditions such as monomer/initiator concentration, polymerization time. The effect of the reaction conditions on the polydispersity and molecular weights were also investigated. The block lengths of the triblock copolymers were calculated by using ¹H-nuclear magnetic resonance (¹H-NMR) spectra. It was observed that the block length could be altered by varying the monomer and initiator concentrations. The characterization of the products were achieved using ¹H-NMR, Fourier-transform infrared spectroscopy (FTIR), gel-permeation chromatography (GPC), thermogravimetric analysis (TGA), and fractional precipitation (γ) techniques.     

Relationships between unfolded configurations of proteins and dynamics of folding to the native state

We compare folding trajectories of chymotrypsin inhibitor (CI2) using a dynamic Monte Carlo scheme with Go-type potentials. The model considers the four backbone atoms of each residue and a sphere centered around C^β the diameter of which is chosen according to the type of the side group. Bond lengths and bond angles are kept fixed. Folding trajectories are obtained by giving random increments to the φ and ψ torsion angles with some bias toward the native state. Excluded volume effects are considered. Two sets of 20 trajectories are obtained, with different initial configurations. The first set is generated from random initial configurations. The initial configurations of the second set are generated according to knowledge-based neighbor dependent torsion probabilities derived from triplets in the Protein Data Bank. Compared to chains with randomly generated initial configurations, those generated with neighbor-dependent probabilities (i) fold faster, (ii) have better defined secondary structure elements, and (iii) have less number of non-native contacts during folding. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3667–3678, 2006     

Fibonacci and Lucas congruences and their applications

In this paper we obtain some new identities containing Fibonacci and Lucas numbers. These identities allow us to give some congruences concerning Fibonacci and Lucas numbers such as L _2mn+k ≡ (−1)^(m+1)n L _k (mod L _m ), F _2mn+k ≡ (−1)^(m+1)n F _k (mod L _m ), L _2mn+k ≡ (−1) ^mn L _k (mod F _m ) and F _2mn+k ≡ (−1) ^mn F _k (mod F _m ). By the achieved identities, divisibility properties of Fibonacci and Lucas numbers are given. Then it is proved that there is no Lucas number L _n such that L _n = L ₂ ^k t L _m x ² for m > 1 and k ≥ 1. Moreover it is proved that L _n = L _m L _r is impossible if m and r are positive integers greater than 1. Also, a conjecture concerning with the subject is given.