Space Dependent Mean Field Approximation Modelling

It is shown that the self-consistency condition which is the basic equation for calculating the mean-field order parameter of any mean-field model Hamiltonian can be replaced by the standard Metropolis Monte Carlo scheme. The advantage of this method is its ease of implementation for both the homogeneous mean-field order parameter and the heterogeneous one. To be specific, the mean-field version of the Ising model spin system is discussed in detail and the resulting magnetization is the same as in the case of solving the respective mean-field self-consistency equation. In addition, it is shown that if a high temperature phase of such system is quenched below critical temperature then the mean field experienced by spins develops into a network of domains in analogous way as it happens with the spins in the case of the exact many-body Hamiltonian system and the coarsening processes start to take place. To show that the introduced Metropolis Monte Carlo method works also in case of the continuous variables the order parameter for the Maier-Saupe model for nematic liquid crystals has been calculated.     

Polymerization of 1,1,1-trifluoroacetone with aliphatic secondary amines. A proton and fluorine magnetic resonance investigation

The polymerization of 1,1,1-trifluoroacetone with aliphatic secondary amines is reported. The polymerization product is found to be a mixture of four diastereoisomers of the cyclic trimer, the structure of which has been determined using proton and fluorine magnetic resonance spectroscopy. The proportions of the isomers have been estimated to be 70:19:8:3 from the ¹⁹F resonance spectrum. A comparative study of the reaction products of trifluoroacetone with metallic sodium and diethylamine is also discussed.     

An efficient implementation of a QM�CMM method in SIESTA

We present the major features of a new implementation of a QM?CMM method that uses the DFT code Siesta to treat the quantum mechanical subsystem and the AMBER force field to deal with the classical part. The computation of the electrostatic interaction has been completely revamped to treat periodic boundary conditions exactly, using a real-space grid that encompasses the whole system. Additionally, we present a new parallelization of the Siesta grid operations that provides near-perfect load balancing for all the relevant operations and achieves a much better scalability, which is important for efficient massive QM?CMM calculations in which the grid can potentially be very large.     

Magnetic properties for the Cu2MnSnSe4 and Cu2FeSnSe4 compounds

Magnetic susceptibility χ measurements in the range from 2 to 300 K were carried out on samples of the Cu₂FeSnSe₄ and Cu₂MnSnSe₄ compounds. It was found that Cu₂FeSnSe₄ was antiferromagnetic showing ideal Curie-Weiss behavior with a Néel temperature T_N of about 19 K and Curie-Weiss temperature θ=−200 K, while for Cu₂MnSnSe₄ the behavior was spin-glass with a freezing temperature T_f of about 22 K and Curie-Weiss temperature θ=−25 K. The spin-glass order parameter q(T), determined from the susceptibility data, was found to be in agreement with the prediction of conventional spin-glass theory.     

Estimation risk and stability of optimal portfolio composition

The mean-variance portfolio models indicate that for optimal investment decisions, the ‘true’ ex-ante values of the model parameters should be used. Instead, in practice, ex-post parameter estimates are used. If in the estimation process, the probability distribution of estimators is not known, there is a problem of estimation risk. This paper investigates the impact of estimation risk on the composition of optimal portfolios. As the multivariance distribution of the vector of optimal portfolio weights allocated to risky assets is analytically intractable, a use of the Monte Carlo simulation experimental is made. This study suggests that the composition of optimal portfolio is relatively more stable when the estimates of model parameters are obtained from longer series of historical observations or the expected portfolio return is low.     

Auxetic metamaterials exhibiting giant negative Poisson's ratios

Auxetic metamaterials have generated a great deal of interest in recent years. In this letter, a novel approach which can be used to produce such auxetic metamaterials is presented. This method involves the introduction of patterned slit perforations within a sheet/block of material in order to create systems which resemble a large variety of auxetic systems ranging from rotating units to chiral honeycombs. These perforated systems have also been shown to have the potential to exhibit giant negative Poisson's ratios. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Steady-state fluctuations of a genetic feedback loop: an exact solution

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence, exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution [J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, and P. G. Wolynes, Phys. Rev. E 72, 051907 (2005), and subsequent studies]. We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.