Elastic stability of DNA configurations. II. Supercoiled plasmids with self-contact

Configurations of protein-free DNA miniplasmids are calculated with the effects of impenetrability and self-contact forces taken into account by using exact solutions of Kirchhoff's equations of equilibrium for elastic rods of circular cross section. Bifurcation diagrams are presented as graphs of excess link, DeltaL, versus writhe, W, and the stability criteria derived in paper I of this series are employed in a search for regions of such diagrams that correspond to configurations that are stable, in the sense that they give local minima to elastic energy. Primary bifurcation branches that originate at circular configurations are composed of configurations with D(m) symmetry (m=2,3,...). Among the results obtained are the following. (i) There are configurations with C2 symmetry forming secondary bifurcation branches which emerge from the primary branch with m=3, and bifurcation of such secondary branches gives rise to tertiary branches of configurations without symmetry. (ii) Whether or not self-contact occurs, a noncircular configuration in the primary branch with m=2, called branch alpha, is stable when for it the derivative dDeltaL/dW, computed along that branch, is strictly positive. (iii) For configurations not in alpha, the condition dDeltaL/dW>0 is not sufficient for stability; in fact, each nonplanar contact-free configuration that is in a branch other than alpha is unstable. A rule relating the number of points of self-contact and the occurrence of intervals of such contact to the magnitude of DeltaL, which in paper I was found to hold for segments of DNA subject to strong anchoring end conditions, is here observed to hold for computed configurations of protein-free miniplasmids.     

Gauge fields and interactions in matrix string theory

It is shown that all possible N sheeted coverings of the cylinder are contained in type IIA matrix string theory as non-trivial gauge field configurations. Using these gauge field configurations as backgrounds the large N limit is shown to lead to the type IIA conformal field theory defined on the corresponding Riemann surfaces. The sum over string diagrams is identified as the sum over non-trivial gauge backgrounds of the SYM theory.     

Algorithms for computing preimages of cellular automata configurations

This paper investigates pre-images (ancestors or past configurations) of specified configurations of one-dimensional cellular automata. Both counting and listing of pre-images are discussed. The main graphical tools used are the de Bruijn diagram, and its extension the pre-image network, which is created by concatenating de Bruijn diagrams. The counting of pre-images is performed as the multiplication of topological matrices of de Bruijn diagrams. Listing of pre-images is described using two algorithms. The first algorithm traces paths in the pre-image network and focuses on local knowledge of the network. The second performs a complete analysis of the network before proceeding with listing.     

Two-loop vertices in quantum field theory: infrared convergent scalar configurations

A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different topologies and comparisons with analytical results, whenever available, are performed. An internal cross-check, based on alternative procedures, is also applied. The analysis of infrared divergent configurations, as well as the treatment of tensor integrals, will be discussed in two forthcoming papers.     

Sandwiched trilayer of Bethe lattices in the form of spin-(1/2,1,1/2)

The sandwiched trilayer of Bethe lattices in the form of the spins with spin-(1/2,1,1/2) Ising model is studied in terms of the recursion relations with either ferromagnetic or antiferromagnetic type bilinear interactions between the nearest-neighbor (NN) spins. The ground-state (GS) phase diagrams are obtained and it was found that the model presents six different GS phase configurations. In order to obtain the phase diagrams, the thermal variations of the order-parameter, spin-spin correlation functions and free energy are analyzed and different topological phase diagrams are obtained. It was found that the system exhibits different critical behaviors such as, second- and first-order phase transitions, tricritical and bicritical points for the values of the coordination numbers q=3,4 and 6.     

Dissipative photonic lattice solitons

We show that discrete dissipative optical lattice solitons are possible in waveguide array configurations that involve periodically patterned semiconductor optical amplifiers and saturable absorbers. The characteristics of these low-power soliton states are investigated, and their propagation constant eigenvalues are mapped on Floquet-Bloch band diagrams. The prospect of observing such low-power dissipative lattice solitons is discussed in detail.     

Conservative spatial chaos of buckled elastic linkages

Buckling of an elastic linkage under general loading is investigated. We show that buckling is related to an initial value problem, which is always a conservative, area-preserving mapping, even if the original static problem is nonconservative. In some special cases, we construct the global bifurcation diagrams, and argue that their complicated structure is a consequence of spatial chaos. We characterize spatial chaos by the associated initial value problem's topological entropy, which turns out to be related to the number of buckled configurations.     

磁性薄膜自旋重取向行为的Monte Carlo模拟

利用Monte Carlo方法模拟了二维简单立方结构磁性薄膜的自旋重取向行为，重点研究了各向异性和偶极相互作用对系统自旋取向的影响．通过计算，获得了系统的相图以及系统组态、磁分量、比热等随偶极相互作用和温度的变化规律．模拟结果表明，在一定的参数范围内，随着温度的升高，系统的自旋取向将由垂直向平行方向转变。     

Strong Asymmetric Coupling of Two Parallel Exclusion Processes

This paper studies asymmetric strong coupling effect in two parallel exclusion processes, which is a generalization of previous works of Kolomeisky group (Pronina and Kolomeisky in Physica A 372:12, 2006; Tsekouras and Kolomeisky in J. Phys. A 41:465001, 2008). It is shown that with different configurations of hopping rates, the two-lane system exhibits diverse phase diagram and density profiles. Specifically, it shows how the phase diagram changes from having seven phases, via six phases, to three phases. Moreover, it shows that the phase diagram could have only one phase, which exhibits quadrilateral or triangular density profile. The vertical cluster mean-field approach is used to get the stationary-state bulk densities and phase diagrams. Extensively Monte Carlo simulations are carried out, and theoretical predictions are in excellent agreement with simulation results.     

Penrose diagrams for the Schwartzschild-Friedman model in Kruskal coordinates

The unified Schwartzschild-Friedman model is studied in Kruskal coordinates. Expressions for Schwartzschild time-like geodesics are obtained in Schwartzschild space. Penrose diagrams are constructed for various configurations of the model.Ukraine and Russia Reunion Tercentenary State University, Dnepropetrovsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 87–91, July, 1992.     

The mixed spin-1/2 and spin-1 Ising system on a two-layer Bethe lattice

Two layered magnetic Bethe lattice with varying coordination number q is introduced and numerically studied via exact recursion relations within a pairwise approach. The system is influenced by competing interlayer and intralayer nearest-neighbour (NN) coupling interactions and also by the crystal and external magnetic fields. Cases where both layers are ferromagnetic or one is ferro and the other antiferromagnetic are considered. System configurations’ energy calculations are used to devise some ground state phase diagrams that have proven useful for the investigation of the very low temperature behaviour of the model. Analysis of the thermal behaviours of the total magnetization within the model parameters’ space yield interesting phase diagrams which display fascinating properties, in particular the presence of tricritical points. Increasing negative values of the crystal field strength stabilizes the disordered paramagnetic phase and sometimes gives rise to wavy transition lines.     

Elastic and photoelastic properties of KGd(WO4)2 single crystals

The elastic and photoelastic properties of a potassium-gadolinium tungstate KGd(WO₄)₂ crystal are determined. A complete matrix of elastic constants for the material is obtained for the first time and the velocity diagrams in the five most practically important planes are constructed on its basis. The coefficients of acoustooptic quality M ₂ are measured for the first time for the crystal in the case of isotropic diffraction for all basic configurations of acoustooptic interaction, which makes it possible to reveal the directions of the most effective interaction.     

Trilayer Bethe lattices in the form of spin-(1/2,3/2,1/2)

The critical behaviors of the trilayer Bethe lattice in the form of spin-(1/2,3/2,1/2) with the exterior two layers consisting of spin-1/2 and the interior one having only spin-3/2 Ising spins are studied in terms of the recursion relations with either ferromagnetic or antiferromagnetic bilinear exchange interactions between the nearest-neighbor spins. The ground-state phase diagrams are calculated and it is found that the model presents six different ground state phase configurations. The thermal variations of the order-parameter and free energy are investigated, therefore, topologically different phase diagrams of the model are obtained. It is found that the model exhibits second- and first-order phase transitions, tricritical and bicritical points for the values of the coordination numbers q=3, 4 and 6 and, the reentrant behavior for q=4 and 6, respectively.     

Regular and chaotic dynamics of the dipole moment of square dipole arrays

Dipole lattices, which represent square dipole arrays, are investigated. Various types of equilibrium configurations of arrays are obtained, and conditions are shown under which these configurations are established. On the basis of parametric bifurcation diagrams, the main types of regular and chaotic oscillation regimes of the total dipole moment of a system are considered and their dependence on the amplitude, frequency, and polarization of an alternating field, as well as on the initial equilibrium configuration of arrays, is analyzed. Scenarios of the onset of chaotic regimes are demonstrated, including those that occur via the establishment and variation of quasiperiodic oscillations of the dipole moment of a system. The dynamic bistability state is revealed in which a stochastic resonance—an increase in the response of a system to a harmonic signal in the presence of noise—can be implemented.     

Spin configurations in the absence of an external magnetic field in a magnetic bilayer with in-plane cubic or uniaxial anisotropies

The spin configurations in the absence of an external magnetic field have been systematically investigated for a magnetic bilayer system consisting of two ferromagnetic layers separated by a non-magnetic layer with interlayer exchange coupling. Based on a phenomenological model, the conditions for the existence of collinear and non-collinear spin structures were derived for three kinds of magnetic bilayers with different combinations of in-plane cubic and uniaxial anisotropies for the two ferromagnetic layers. The phase diagrams of the spin configurations at zero field were drawn, taking into account the lowest-order anisotropy parameters of both the ferromagnetic layers. The values of the canting angle have been derived analytically and then numerically plotted.     

The phase diagram for coexisting d-wave superconductivity and charge-density waves: cuprates and beyond

Phase diagrams of d-wave superconductivity characterized by an order parameter Δ coexisting with charge-density waves (CDWs) characterized by an order parameter Σ were constructed for the two-dimensional Fermi surface (FS) appropriate to, e.g., cuprates. CDWs were considered as an origin of the pseudogap appearing at antinodal FS sections of the d(x2-y2) superconductor. Two types of the Σ-reentrance were found: with the temperature, T, and with the opening of the CDW sector, 2α. The angular plots in the momentum space for the resulting gap profile over the FS ('gap roses') were obtained. The gap patterns are rather involved, giving insight into the difficulties of the interpretation of photoemission spectra. It was shown that the Σ-Δ coexistence region exists even for the complete dielectric gapping due to the distinction between the superconducting and CDW order parameter symmetries. The checkerboard and unidirectional CDW configurations were examined, and both the phase diagrams and the behavior with T and α of the order parameters were found to differ. A more general case with a non-zero mismatch angle β between the superconducting lobes and the CDW sectors was analyzed, the case β = π/4 corresponding to the d(xy) symmetry of the superconducting order parameter. The phase diagrams were found to be sensitive to β-variations, showing that internal strains and external pressure can drastically affect the behavior of Σ(T) and Δ(T).     

Quantum-chemical study of the spectral properties of stilbene isomers

Calculations of absorption spectra of cis-and trans-forms of stilbene by the quantum-chemical method of intermediate neglect of differential overlap with spectroscopy parametrization were carried out. The electron structure of a stilbene molecule was studied and energy-level diagrams were drawn and analyzed. Rate constants of different photophysical processes occurring in a stilbene molecule after absorption of a photon were calculated in relation to the molecule conformation. On the basis of the obtained results, possible configurations of photoisomer molecules were considered and the most probable configurations of excited stilbene molecules were determined. It was shown how the change in the configurations of cis-and trans-forms of stilbene affects its spectral properties.     

Metallic magnetism in amorphous TM-Y (TM = Mn,Fe, Co,Ni) alloys

Systematic variations of magnetic properties in amorphous TM-Y (TM = Mn, Fe, Co, Ni) alloys are investigated on the basis of a finite temperature theory of amorphous metallic magnetism which takes into account both thermal spin fluctuations and the fluctuations due to structural and configurations disorder. It is shown that the magnetic phase diagrams calculated in the most random atomic configuration explain qualitatively the spinglass (SG) in Mn-Y, the SG ferromagnetism (F) transition in Fe-Y, and the F-paramagnetism transition in Co-Y and Ni-Y alloys. Magnetization vs concentration curves and susceptibility vs concentration curves as well as the effective Bohr magneton numbers are also shown to be explained qualitatively or semi-quantitatively by the theory. Their miscroscopic mechanisms are elucidated by means of their electronic structures, magnetic couplings, and atomic short range order. It is found that the magnetism in Fe-Y and Mn-Y amorphous alloys is strongly influenced by the atomic short range order. The result explains different magnetic phase diagrams in amorphous Fe-Y alloys and experimental SG transition temperatures in amorphous Mn-Y alloys.