On Mechanical Response of Macro- and Microfiller-Reinforced Polymer: Young Modulus and Shear Wave Velocity

The problem of effective shear and bulk moduli, of an effective Poison's ratio and of an effective dielectric response in microcomposites of the ferroelastic-dielectric type was studied by us recently. Recently one of us, M. Hudak, studied static mechanical properties of the EVA material theoretically and experimentally. We extend our mentioned study of mechanical response of microcomposites of the type ferrolastics - dielectrics to study of Young modulus and shear wave velocity.Comment: 15 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:cond-mat/060459

On composites of the type: metal - dielectrics and superconductor - dielectrics

Composites of the type: metal - dielectrics and superconductor - dielectrics are studied in the quasistatic approximation. The dielectric response is described by the spectral function $G(n,x)$, which contains effects of the concentration x (of metallic resp. superconductive particles) on the dielectric function,and effects of the shape. The parameter n plays the role of the depolarisation factor for dielectric materials, in metals it is a factor which includes effects like shape, and a topology of the composite. There exists a percolation transition at $x_{c}= \frac{1}{3}$ which leads to a metallic-like for the composite with the concentration $x > x_{c}$. At low frequencies divergence with frequency remains even when there are present dielectric particles above the percolation concentration. In superconductor case the spectral function $G(n,x)$ may include also Josephson junction effects. We assume in both cases of composites two types of spheroidal particles, metal (superconducting) ones and dielectric ones. A dielectric function is constant in both cases for the dielectric material, and a dielectric function for the metal and for the superconductor are used with well known form for metals and a classical superconductor. A percolation transition at $x_{c}$ leads to a metallic-like absorption for the composite with $x>x_{c}$. Note that at low frequencies divergence in frequency remains even when there are present dielectric particles above $x_{c}$. Below the percolation threshold dielectric properties are modified by metalic particles. We obtain at very low temperatures and low concentrations x of the superconductor the effective dielectric constant. The absorption part is zero in our simple case. The real part of the dielectric function increases with the concentration of the superconducting spheres. The frequency dependence is quadratic, it gives low frequency tail.Comment: 4 pages, to be submitted to Modern Physics Letters

Transition of the uniform statistical field anyon state to the nonuniform one ar low particle densities

Using results of our exact description of the spinless fermion motion in a nonhomogeneous magnetic field ${\bf B} = B( 0, 0, 1/cosh^{2}( \frac{x-x_{0}}{ \delta }))$ we study a gas of these particles moving in this field. For lower densities $\nu < \nu_{c}(B, \delta )$ the corresponding total energy is lower than that of the uniform field state. Thus when the density of anyons decreases a transition from the uniform statistical field state to the nonhomogeneous field state is predicted.Comment: 12 pages, 0 figure

Displays and antiferroelectric liquid crystals

Recently we have formulated theory of bi-layer-dimerized chiral liquid antiferroelectric crystals. The spontaneous polarization has been increased owing to the strong interaction of the aromatic cores of the rod like liquid crystal molecules with the honey-comb pattern of the CNT walls The SmC*A ordering is improved around the CNTs. All relaxation modes in each phase are facilitated by dispersion of nanotubes whicg enhances the relaxation frequencies. This composite system with improvement in electro-optical properties can be exploited in modern display applications. SmC* LC were studied by one of t he authors (OH), namely their transition from the SmC phase. The role of disclinations in an applied electric field was studied by O. Hudak in the SmC* structure. While the role of fluctuations and of disclinations in the SmC* (FLC)was studied in the above papers, the role of fluctuations and disclinations in SmC*A and the role of addition of MWCNTs in SmC*A phaseis not well understood. Our theoretical description of (AFLC) including SmC*A introduced in may thus be used to study these effects.Comment: 4 pages, conference preprin

Third Harmonics and Defects in Modulated Phases of Structural Quantum Order-Disorder Systems

Influences of defects generating random fields on modulated phases in materials with the order-disorder type of phase transition are studied. It is shown that under appropriate conditions third harmonics of the ground state modulation may be suppressed by these defects.Comment: 21 page

Quantum Critical Phenomena, Entanglement Entropy and Hubbard Model in 1d with the Boundary Site with a Negative Chemical Potential -p and the Hubbard Coupling U Positive

Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed for an open chain with L sites. Authors considered the case when the boundary site has a negative chemical potential -p and the Hubbard coupling U is positive. They have shown by an analytic method that when p is larger than the transfer integral some of the ground-state solutions of the Bethe ansatz equations become complex-valued. They have found that there is a surface phase transition at some critical value p_c; when p < p_c all the charge excitations have the gap for this case, while there exists a massless charge mode when p > p_c. To find whether this surface phase transition is of the first order or of the second order we have used the entanglement entropy concept. The entropy and its derivative has a discontinuity there, so this transition is of the first order.Comment: 1d Hubbard Model, Exact Solution and Entanglement Entropy, QC

Social Behaviour of Agents: Capital Markets and Their Small Perturbations

We study social behaviour of agents on capital markets when these are perturbed by small perturbations. We use the mean field method. Social behaviour of agents on capital markets is described: volatility of the market, aversion constant and equilibrium states are discussed. Relaxation behaviour of agents on the capital market is studied. Equation of motion for the agent average number is of the relaxation type. Development of the group of agents in the states corresponding to minimum of the aim function is either linear either exponentially damped. There exist characteristic volatility constants $V_{c3}$ and $V_{c3}$. The constant b of verification of information contribution to the aversion constant A and the $A_{0}$ constant of aversion are distinguishing three types of dependencies of the minimum of the aim function on the expected volatility EV and on the expected returns E. Arbitrage trades and group forces lead the group into the equilibrium state. Verification of information intensity influences return back to the equilibrium state. The linear in time damping to the equilibrium state is characterized with the characteristic time $T_{3}$ and $T_{6}$, the exponential with a characteristic time $\tau$. Their dependence on the expected volatility, on the expected profit and characteristics of agents is discussed.Comment: LaTeX, sociophysics, agents on capital markets, perturbation of the marke

Anisotropic Vortices in High-Temperature Superconductors and the Onset of Vortex-like Excitations above the Critical Temperature

Recently we have found that a three-dimensional superconducting state with anisotropic vortices localized at the vortex-lattice points is a stable state in zero external magnetic field for the layered high temperature uperconductivity materials. There exists a phase transition at the temperature $T_{c}^{v}$ from the normal phase to the vortex superconducting state which is of the first order. The first order phase transition shows overheating and overcooling effects. Nucleation of the superconducting phase in the normal phase thus may occur at temperatures higher than the transition temperature $T_{c}^{v}$. Then the onset of the vortex-like excitations above the transition temperature $T_{c}^{v}$ occurs in our theory. The onset of the vortex-like excitations in Nerst signal and some other experimental evidence for these excitations above the transition temperature $T_{c}^{v}$ in LSCO, YBCO and in other high-temperature materials may be explained thus by our theory. The vortex-like excitations above and below the transition temperature $T_{c}^{v}$ in high temperature materials continuously evolve. This fact may be explained within our theory.Comment: LaTeX, high temperature superconductivity, anisotropic vortices, onset of vortex-like excitation

Topology and Behaviour of Agents: Capital Markets

On a capital market the social group is formed from traders. Individual behaviour of agents is influenced by the need to associate with other agents and to obtain the approval of other agents in the group. Making decisions an individual equates own needs with those of the other agents. Any two agents from the group may interact. The interaction consists of the exchange of information and it costs some money. We assume that agents give reference to the origin of the information if asked by other agents. Thus the agent may verify obtained private information. Hudak recently used methods described by Rivier to study social behaviour of such agents. He characterized the quantity which corresponds to verification of information. Quantity which characterizes verification of information contributes to an aversion of an agent with respect to a risk. The mix of investments of an agent in a given cell with an average measure A of risk aversion in the cell is found from minimum of the average per cell aim function . Absolute minimum corresponds to such a state in which there is an optimal mix of the exchange of information for a given expectations about the capital market. The crowd and personal /$\approx $/ contributions to the risk aversion of an agent are present in the aversion constant A. We have discussed a stable and metastable states of the market for different values of E, an expected return for a given investment period, of EV, an expected risk for a given investment period, and of b, a constant which characterizes contribution of the quantity to the risk aversion. Variance of n for the distribution of nonreducibile subgroups is found. Our model describes intermediary process effects.Comment: 14 pages, Latex, sociophysics, revised version (corrected typographical errors, extended discussion

Automated Trading Systems: Developed and Emerging Capital Markets

Automated trading systems on developed and emerging capital markets are studied in this paper. The standard for developed market is automated trading system with 40-days simple moving average. We tested it for the index SIX Industrial for 1000 and 730 trading days of the slovak emerging capital market. The Buy and Hold trading system was 7.80 times more profitable than this etalon trading system for active trading. Taking of profitable standard trading system from a developed capital market does not lead to optimal results on the emerging capital markets. We then studied optimized standard trading system based on the simple moving average. The parameter of optimization was the number of weeks. An optimal system was that with 5 weeks. This trading system has some of its characteristics comparable with the etalon trading system on the NYSE Composite Index. The emerging market is more risky than the developed market. The profit on the emerging market is also higher. The range of optimized system parameter is quite robust. Observed was increase of number of trades in the range from the 21 weeks to the 25 weeks. This indicates creation of a new optimal middle range trading system. Results of testing for liquid shares are quantitatively similar.Comment: LaTeX, econophysics, emerging capital market