Narrow Results

A lattice model is used to simulate the dependence of the condensation temperature of ternary mixtures (water-oil-surfactants) on varying tail length. Nonionic single-tailed amphiphiles are assumed. We have obtained the result that the longer the tail length, the higher is the condensation temperature. We also discuss the influence of the head–head interaction on that temperature.

The standard perturbation theory in QFT and lattice models leads to the asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the convergence. In the earlier studies, this approach was applied to the purely bosonic systems. Here, using bosonization, we develop the convergent perturbation theory for a toy lattice model with interacting fermionic and bosonic fields.

We discuss application of Wigner–Weyl formalism to the lattice models of condensed matter physics and relativistic quantum field theory. For the noninteracting models our technique relates Wigner transformation of the fermionic Green’s function with the Weyl symbol $Q_W$ of lattice Dirac operator. We take as an example of the model defined on rectangular lattice the model of Wilson fermions. It represents the regularization of relativistic quantum field theory and, in addition, describes qualitatively certain topological materials in condensed matter physics. In this model we derive expression for $Q_W$ in the presence of the most general case of external $U(1)$ gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of $Q_W$.

Using a lattice equation of state combined with the D-dimensional Tolman–Oppenheimer–Volkoff equation and the Friedmann equations, we investigate the possibility of the formation of compact objects as well as the time evolution of the scale factor and the density profile of a self-gravitating material cluster. The numerical results show that in a ($2+1$)-dimensional space–time, the mass is independent of the central pressure. Hence, the formation of only compact objects with a finite constant mass similar to the white dwarf is possible. However, in a ($3+1$)-dimensional space–time, self-gravity leads to the formation of compact objects with a large gap of mass and the corresponding phase diagram has the same structure as the one for Neutron Star. The results also show that beyond certain critical central pressure, the star is unstable against gravitational collapse, and it may end in a black hole. Analysis of space–times of higher dimensions shows that gravity has the stronger effect in $3+1$ dimensions. Numerical solutions of the Friedmann equations show that the effect of the curvature of space–time increases with the increasing temperature, but decreases with the increasing dimensionality beyond $D=3$.

We have considered a classical lattice-gas model, consisting of a three-dimensional simple-cubic lattice, whose sites host three-component unit vectors; pairs of nearestneighboring sites interact via the nematogenic potential

Recent advances in single molecule experiments have made it possible to investigate the mechanical anisotropy of protein stability in greater detail. It has been found that proteins can exhibit a diverse range of responses when pulled in different directions. We review some of the experimental and numerical work related to the study of the resistance of proteins to force-induced mechanical unfolding. Based on model studies in the framework of statistical mechanics, we discuss the possible molecular origin of the anisotropy of protein resistance to unfolding.

In this paper, we propose a numerical option pricing method based on an arbitrarily given stock distribution. We first formulate a European call option pricing problem as an optimal hedging problem by using a lattice based incomplete market model. A dynamic programming technique is then applied to solve the mean square optimal hedging problem for the discrete time multi-period case by assigning suitable probabilities on the lattice, where the underlying stock price distribution is derived directly from empirical stock price data which may possess "heavy tails". We show that these probabilities are obtained from a network flow optimization which can be solved efficiently by quadratic programming. A computational complexity analysis demonstrates that the number of iterations for dynamic programming and the number of parameters in the network flow optimization are both of square order with respect to the number of periods. Numerical experiments illustrate that our methodology generates the implied volatility smile.

We consider the free evolution of systems of granular particles whose dynamics is characterized by a collision rule which preserves the total momentum, but dissipates the kinetic energy. Starting from an inelastic version of a minimal model proposed by Ulam for a gas of Maxwell molecules, we introduce a new lattice model aimed at investigating the role of dynamical correlations and the onset of spatial order induced by the inelasticity of the interactions. We study, in one- and two-dimensional cases, the velocity distribution, the decay of the energy, the formation of spatial structures and topological defects. Finally, we relate our findings to other models known in other fields.

Our model of shaken sand, presented in earlier work, has been extended to include a more realistic 'glassy' state, i.e. when the sandbox is shaken at very low intensities of vibration. We revisit some of our earlier results, and compare them with our new results on the revised model. Our analysis of the glassy dynamics in our model shows that a variety of ground states is obtained; these fall into two categories, which we argue are representative of regular and irregular packings.

It is known that folding a protein chain into a cubic lattice is an NP-complete problem. We consider a seemingly easier problem: given a three-dimensional (3D) fold of a protein chain (coordinates of its C_α atoms), we want to find the closest lattice approximation of this fold. This problem has been studied under names such as "lattice approximation of a protein chain", "the protein chain fitting problem", and "building of protein lattice models". We show that this problem is NP-complete for the cubic lattice with side close to 3.8 Å and coordinate root mean square deviation.

We consider the free evolution of systems of granular particles whose dynamics is characterized by a collision rule which preserves the total momentum, but dissipates the kinetic energy. Starting from an inelastic version of a minimal model proposed by Ulam for a gas of Maxwell molecules, we introduce a new lattice model aimed at investigating the role of dynamical correlations and the onset of spatial order induced by the inelasticity of the interactions. We study, in one- and two-dimensional cases, the velocity distribution, the decay of the energy, the formation of spatial structures and topological defects. Finally, we relate our findings to other models known in other fields.

Our model of shaken sand, presented in earlier work, has been extended to include a more realistic ‘glassy’ state, i.e. when the sandbox is shaken at very low intensities of vibration. We revisit some of our earlier results, and compare them with our new results on the revised model. Our analysis of the glassy dynamics in our model shows that a variety of ground states is obtained; these fall into two categories, which we argue are representative of regular and irregular packings.

We suggest how versions of Schramm's SLE can be used to describe the scaling limit of some off-critical 2D lattice models. Many open questions remain.

Causal dynamical triangulations allows for a non perturbative approach to quantum gravity. In this article a solution for dimers coupled to CDT is presented and some of the conceptual problems that arise are reflected upon.