Orientational Degrees Of Freedom Research Articles

Macroscopic behavior of systems with an axial dynamic preferred direction

We present the derivation of the macroscopic equations for systems with an axial dynamic preferred direction. In addition to the usual hydrodynamic variables, we introduce the time derivative of the local preferred direction as a new variable and discuss its macroscopic consequences including new cross-coupling terms. Such an approach is expected to be useful for a number of systems for which orientational degrees of freedom are important including, for example, the formation of dynamic macroscopic patterns shown by certain bacteria such a Proteus mirabilis. We point out similarities in symmetry between the additional macroscopic variable discussed here, and the magnetization density in magnetic systems as well as the so-called Î vector in superfluid (3)He-A. Furthermore we investigate the coupling to a gel-like system for which one has the strain tensor and relative rotations between the new variable and the network as additional macroscopic variables.

Effect of isospin on the fusion reaction cross section using various nuclear proximity potentials within the Wong model

Various versions of proximity potentials, with different isospin dependence, are used within the Wong model for fitting the fusion-evaporation cross sections from ${}^{58}$Ni + ${}^{58}$Ni, ${}^{64}$Ni + ${}^{64}$Ni, and ${}^{64}$Ni + ${}^{100}$Mo reactions in an intermediate mass region and capture cross sections from ${}^{48}$Ca + ${}^{238}$U, ${}^{244}$Pu, and ${}^{248}$Cm reactions in a superheavy mass region, known for fusion hindrance phenomena in coupled-channel calculations. It is found that proximity 1988 gives results close to experimental data in a comparison of proximity 1977 and proximity 2000 within the Wong formula, so this Proximity 1988 (Prox 1988) is then used within the extended Wong model. This combination can fit the cross sections for the ${}^{58}$Ni + ${}^{58}$Ni and ${}^{64}$Ni + ${}^{64}$Ni reactions but deviates a little from the experimental data for the ${}^{64}$Ni + ${}^{100}$Mo reaction at a center-of-mass energy below the Coulomb barrier. But the variation of ${\ensuremath{\ell}}_{\text{max}}$ with ${E}_{\text{c.m.}}$ at sub-barrier energies is absurd for these three reactions. So, a different type of strong nuclear interaction is required that accounts for isospin effect and asymmetry of the colliding nuclei, which is obtained here by a slight adjustment of the coefficient ${\ensuremath{\gamma}}_{0}$ of the nuclear surface energy constant of the Prox 1988 potential, in order to fit the experimental data for this reaction and named it mod-Prox 1988. The surface energy constant $\ensuremath{\gamma}$ depends on the neutron/proton excess, and change in one of its constants, ${\ensuremath{\gamma}}_{0}$, used in Prox 1988, introduces the required barrier modification for fitting the experimental data. Thus, change in $\ensuremath{\gamma}$ leads to change in barrier characteristics, i.e., barrier height (${V}_{B}^{\ensuremath{\ell}}$), position (${R}_{B}^{\ensuremath{\ell}}$), and oscillator frequency ($\ensuremath{\hbar}{\ensuremath{\omega}}_{\ensuremath{\ell}}$). Using this modified proximity potential within the extended Wong model, experimental data for all three Ni-induced reactions is fitted with a smooth variation of deduced ${\ensuremath{\ell}}_{\text{max}}({E}_{\text{c.m.}})$ at above- as well as below-barrier energies. The effect of isospin is more prominent at below-barrier energies. As an application, mod-Prox 1988 is then employed for the capture cross-section data from ${}^{48}$Ca + ${}^{238}$U, ${}^{244}$Pu, and ${}^{248}$Cm reactions in superheavy mass regions and it successfully fits the data point to point with a smooth variation of ${\ensuremath{\ell}}_{\text{max}}$ with ${E}_{\text{c.m.}}$. Thus, mod-Prox 1988 within the extended Wong model leads to a simultaneous explanation of several reactions displaying a hindrance to fusion. Thus, below the Coulomb barrier a stronger nuclear interaction is required as the $N/Z$ ratio increases and colliding nuclei become more and more asymmetric. The effects of multipole deformations are included here up to hexadecapole in the calculations, and orientation degrees of freedom are integrated for the coplanar configuration.

Monte Carlo and event-driven dynamics of Brownian particles with orientational degrees of freedom

Recently, a simple scaling argument was introduced that allows us to map, with some precautions, Brownian and Monte Carlo dynamics for spherical particles. Here, we extend the scaling to study systems that have orientational degrees of freedom and carefully asses its validity over a wide region of temperature and density. Our work allows us to devise a Brownian Monte Carlo algorithm that produces, to a good approximation, physically meaningful trajectories with a minimum programming effort, although at the expense of some sampling efficiency.

Three-dimensional ensemble averages for tensorial interactions in partially oriented, multi-particle systems

In a variety of three-dimensional, multi-particle systems, interactions of tensorial form occur between individual components and an applied stimulus that operates uniformly throughout the ensemble. When each material component has an identical, fixed orientation, its own response is replicated in the observed form of behaviour by the system as a whole, with respect to the angular disposition of the stimulus. The same complete correlation between microscopic and macroscopic response does not, however, operate in other systems where there is a degree of orientational freedom amongst the microscopic components. One limiting case is where the extent of such freedom allows random orientations, such conditions delivering a system that is macroscopically isotropic. When each particle has incomplete orientational freedom, the formulation is in general less mathematically tractable; here, the theory required to describe ensemble response yields analytically solvable equations only in cases where the distribution function takes a relatively simple form, such as a scalar product, and few explicit results are available. This paper addresses general systems in which there is an orientation-dependent complex exponential factor, weighting the response of each component. By means of irreducible tensor decomposition, results are determined for tensor interactions up to and including rank 2, where the weighting exponent is also of any rank up to the same order. Illustrative applications are drawn from the theory of laser particle orientation and photon absorption.

Efficient calculation of α- and β-nitrogen free energies and coexistence conditions via overlap sampling with targeted perturbation

A recently introduced solid-phase free-energy calculation method that is based upon overlap sampling with targeted free-energy perturbation is further developed and extended to systems with orientational degrees of freedom. Specifically we calculate the absolute free energy of the linear-molecular nitrogen model of Etter et al., examining both the low-temperature low-pressure α-N(2) structure and the orientationally disordered β-N(2) phase. In each perturbation (for the α-N(2) phase) to determine the free-energy difference between systems at adjacent temperatures, harmonic coordinate scaling is applied to both the translational and rotational degrees of freedom in the nitrogen molecule to increase the phase-space overlap of the two perturbing systems and consequently, improve the free-energy difference results. For the plastic β-N(2) phase, a novel method that requires several perturbation paths is introduced to calculate its absolute free energy. Through these methods, the absolute free energies for both the α-N(2) and β-N(2) phase can be accurately and precisely determined. We find again that the anharmonic contribution to the free energy has weak dependence on system size. The transition properties for the α-N(2) and β-N(2) phase are also investigated. The α-β phase transition for the model at atmospheric pressure (0.1 MPa) is found to occur at 40.35 ± 0.01 K with volumetric and entropy changes of 0.44 ± 0.01 cm(3)/mol and 1.99 ± 0.01 cal/mol.K respectively.

Modeling Anisotropic Elasticity of Fluid Membranes

AbstractThe biological membrane, which compartmentalizes the cell and its organelles, exhibits wide variety of macroscopic shapes of varying morphology and topology. A systematic understanding of the relation of membrane shapes to composition, external field, environmental conditions, etc. have important biological relevance. Here we review the triangulated surface model, used in the macroscopic simulation of membranes and the associated DTMC methods. New techniques to calculate surface quantifiers, that will facilitate the study of additional in‐plane orientational degrees of freedom, has been introduced. The mere presence of a polar and nematic fields, in the ordered phase, drives the ground state conformations of the membrane to a cylinder and tetrahedron, respectively. magnified image

Effect of the orientation degree of freedom on the rate and time of fission of highly excited nuclei

The effect of the dimensionality of the dynamical model used on the fission rate and mean time is studied within a multidimensional stochastic approach to fission dynamics. These features of fission of excited compound nuclei are calculated within four-dimensional Langevin dynamics, where the coordinate K, which is the projection of the total angular momentum onto the symmetry axis of the nucleus being considered, is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, a} parametrization. The evolution of this orientation degree of freedom (K mode) is described in terms of the Langevin equation in the overdamped regime. The effect of the orientation degree of freedom on the rate and mean time of fission of compound nuclei is studied. The introduction of the orientation degree of freedom is shown to lead to a substantial decrease in the fission rate and, accordingly, to an increase in the mean fission time upon going over from the three- to the four-dimensional model. The reactions induced by the interaction of 14N and 16O projectile ions with 197Au, 208Pb, 232Th, and 238U nuclei at energies above the Coulomb fusion barrier are considered. The effect of the increase in the fission time because of the introduction of the K mode is so strong that it compensates almost completely for an opposite effect from introducing, in the one-dimensional model, the second and third collective coordinates that take into account, respectively, the evolution of the neck in the nuclear shape and the mass asymmetry. Ultimately, the difference between the results in the four- and one dimensional problems is not more than 5 to 25% for the reactions considered here.

Non-Abelian monopoles in the Higgs phase

We use the moduli matrix approach to study the moduli space of 1/4 BPS kinks supported by vortices in the Higgs phase of N = 2 supersymmetric U ( N ) gauge theories when non-zero masses for the matter hypermultiplets are introduced. We focus on the case of degenerate masses. In these special cases vortices acquire new orientational degrees of freedom, and become “non-Abelian”. Kinks acquire new degrees of freedom too, and we will refer to them as “non-Abelian”. As already noticed for the Abelian case, non-Abelian kinks must correspond to non-Abelian monopoles of the unbroken phase of SU ( N ) Yang–Mills. We show, in some special cases, that the moduli spaces of the two objects are in one-to-one correspondence. We argue that the correspondence holds in the most general case. The consequence of our result is two-fold. First, it gives an alternative way to construct non-Abelian monopoles, in addition to other well-known techniques (Nahm transform, spectral curves, rational maps). Second, it opens the way to the study of the quantum physics of non-Abelian monopoles, by considering the simpler non-Abelian kinks.

Angular distribution of fission fragments of excited compound nuclei in multidimensional Langevin dynamics

Angular distributions of fission fragments were calculated within a multidimensional approach to the fission dynamics of excited nuclei, and the results of these calculations are presented. The evolution of the shape parameters of a fissile nucleus was described by the set of three-dimensional Langevin equations for collective coordinates introduced on the basis of the {c, h, a} parametrization. The evolution of the orientation degree of freedom (K mode, K being the projection of the total angular momentum on the symmetry axis of the nucleus under study) was described with the aid of the Langevin equation in an overdampedmode. The coupled Langevin equations for the shape and K-mode collective coordinates were integrated simultaneously. The friction parameter for the K mode was set to 0.077 (MeV × 10−21 s)−1/2, which is the estimate obtained previously for this quantity in calculating angular distributions of excited compound nuclei with allowance for the effects of the orientation degree of freedom. The developed model was used to analyze the anisotropy of angular distribution of fission fragments in 16O+208Pb, 16O+232Th, and 16O + 238U reactions over a broad interval of projectile-ion energies. The results of the calculations show that the developedmodel, usedwith the above value of the friction parameter for theK mode, leads to a rather good description of experimental data on the anisotropy of angular distributions of fission fragments. The effect of the dimensionality of the dynamicalmodel used to describe the evolution of the shape of a fissile nucleus on the results obtained by calculating the anisotropy of angular distributions is discussed.

Solution of an associating lattice-gas model with density anomaly on a Husimi lattice

We study a model of a lattice gas with orientational degrees of freedom which resemble the formation of hydrogen bonds between the molecules. In this model, which is the simplified version of the Henriques-Barbosa model, no distinction is made between donors and acceptors in the bonding arms. We solve the model in the grand-canonical ensemble on a Husimi lattice built with hexagonal plaquettes with a central site. The ground state of the model, which was originally defined on the triangular lattice, is exactly reproduced by the solution on this Husimi lattice. In the phase diagram, one gas and two liquid [high density liquid (HDL) and low density liquid (LDL)] phases are present. All phase transitions (GAS-LDL, GAS-HDL, and LDL-HDL) are discontinuous, and the three phases coexist at a triple point. A line of temperatures of maximum density in the isobars is found in the metastable GAS phase, as well as another line of temperatures of minimum density appears in the LDL phase, part of it in the stable region and another in the metastable region of this phase. These findings are at variance with simulational results for the same model on the triangular lattice, which suggested a phase diagram with two critical points. However, our results show very good quantitative agreement with the simulations, both for the coexistence loci and the densities of particles and of hydrogen bonds. We discuss the comparison of the simulations with our results.

Dynamic transitions in a three dimensional associating lattice gas model

We investigate the thermodynamic and dynamic properties of a three dimensional associating lattice gas (ALG) model through Monte Carlo simulations. The ALG model combines a soft core potential and orientational degrees of freedom. The competition of directional attractive forces and the soft core potential results in two coexisting liquid phases which are also connected through order-disorder critical transitions. The model presents structural order, density, and diffusion anomalies. Our study suggests that the dynamic fragile-to-strong transitions are associated to changes in structural order.

Effect of octupole and higher deformations on Coulomb barrier

The effect of octupole deformation, β 3 , and the higher multipole deformations, β 6 and β 8 , on the distribution of barriers in orientation degrees of freedom, is studied. Coulomb barriers are derived in the frame work of the double folding model with the realistic M3Y nucleon–nucleon interaction and its density dependent version. 48Ca + 244Pu spherical-deformed nuclear interacting pair is considered, as an example, to study the effect of deformation parameters on the height and position of the Coulomb barrier. Although the dependence of the Coulomb barrier parameters on the higher deformations is complicated, numerically, if it is treated in microscopic way, we found a simple linear variation of barrier parameters with the different orders of deformation. We found that the variation of the barrier parameters with deformation exactly follows the change of the half density radius of the deformed nucleus in the direction of the separation vector between the centers of mass of the interacting nuclei. This suggests a simple and straightforward way to predict the behavior of the barrier parameters with different orders of deformations. We compared the results of present work with a similar recent study of the same quantities based on simple expression derived by Wong for the Coulomb part and proximity approach for the nuclear part of heavy ion potential, respectively.

Dynamic transitions in a two dimensional associating lattice gas model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical lambda-line. The high density liquid phase and the fluid phases are separated by a second critical tau-line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong transition when the critical lambda-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the critical tau-line is crossed by decreasing the temperature at a constant chemical potential.

Statistical model of heavy-ion fusion-fission reactions

Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with the fission of fully equilibrated systems with fission lifetime estimates obtained via a Kramers-modified statistical model that takes into account the classical collective motion of the system about the ground state, the temperature dependence of the location and height of fission transition points, and the orientation degree of freedom. If the ``standard'' techniques for calculating fission lifetimes are used, then the calculated excitation-energy dependence of fission lifetimes is incorrect. We see no evidence to suggest that the nuclear viscosity has a temperature dependence. The strong increase in the nuclear viscosity above a temperature of $~1.3$ MeV deduced by others is an artifact generated by an inadequate fission model.

Phase transition in liquid crystal elastomers—A Monte Carlo study employing non-Boltzmann sampling

We investigate nematic-isotropic transition in liquid crystal elastomers employing a variant of Wang–Landau sampling. This technique facilitates calculation of the density of states from which other thermodynamic properties can be obtained. We consider a lattice model of a liquid crystal elastomer and a Hamiltonian which accounts for interactions among liquid crystalline units and interaction of local nematics with global strain. We investigate the effect of varying the strength of coupling between nematic and orientational degrees of freedom. When the local director is coupled strongly to the global strain, the transition is strongly first order. When the strength of the coupling decreases the transition becomes weakly first order. The transition temperature decreases when the coupling becomes weaker. We also report for the first time results on variation of free energy as a function of average energy at different temperatures and coupling constants.

Diffraction from the β -sheet crystallites in spider silk

We analyze the wide-angle X-ray scattering from oriented spider silk fibers in terms of a quantitative scattering model, including both structural and statistical parameters of the beta-sheet crystallites of spider silk in the amorphous matrix. The model is based on kinematic scattering theory and allows for rather general correlations of the positional and orientational degrees of freedom, including the crystallite's size, composition and dimension of the unit cell. The model is evaluated numerically and compared to experimental scattering intensities allowing us to extract the geometric and statistical parameters. We show explicitly that for the experimentally found mosaicity (width of the orientational distribution) intercrystallite effects are negligible and the data can be analyzed in terms of single-crystallite scattering, as is usually assumed in the literature.

Fission Decay Widths for Heavy-Ion Fusion-Fission Reactions

Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with a Kramers-modified statistical model which takes into account the collective motion of the system about the ground state, the temperature dependence of the location of fission transition points, and the orientation degree of freedom. The strong increase in the nuclear viscosity above a temperature of approximately 1 MeV deduced by others is an artifact generated by an inadequate fission model.

Subdiffusive dynamics of a liquid crystal in the isotropic phase

The isotropic phase dynamics of a system of 4-n-hexyl-4'-cyano-biphenyl (6CB) molecules has been studied by molecular dynamics computer simulations. We have explored the range of 275-330 K keeping the system isotropic, although supercooled under its nematic transition temperature. The weak rototranslational coupling allowed us to separately evaluate translational (TDOF) and orientational degrees of freedom (ODOF). Evidences of subdiffusive dynamics, more apparent at the lowest temperatures, are found in translational and orientational dynamics. Mean square displacement as well as self-intermediate center of mass and rotational scattering functions show a plateau, also visible in the orientational correlation function. According to the mode coupling theory (MCT), this plateau is the signature of the beta-relaxation regime. Three-time intermediate scattering functions reveal that the plateau is related to a homogeneous dynamics, more extended in time for the orientational degrees of freedom (up to 1 ns). The time-temperature superposition principle and the factorization property predicted by the idealized version of MCT hold, again for both kinds of dynamics. The temperature dependence of diffusion coefficient and orientational relaxation time is well described by a power law. Critical temperatures Tc are 244+/-6 and 258+/-6 K, respectively, the latter is some 10 K below the corresponding experimental values. The different values of Tc we obtained indicate that ODOF freezes earlier than TDOF. This appears due to the strongly anisotropic environment that surrounds a 6CB molecule, even in the isotropic phase. The lifetime of these "cages," estimated by time dependent conditional probability functions, is strongly temperature dependent, ranging from some hundreds of picoseconds at 320 K to a few nanoseconds at 275 K.

Strings in Yang-Mills-Higgs theory coupled to gravity

Non-Abelian strings for an Einstein-Yang-Mills-Higgs theory are explicitly constructed. We consider N_f Higgs fields in the fundamental representation of the U(1)xSU(N_c) gauge group in order to have a color-flavor SU(N_c) group remaining unbroken. Choosing a suitable ansatz for the metric, Bogomol'nyi-like first order equations are found and rotationally symmetric solutions are proposed. In the N_f = N_c case, solutions are local strings and are shown to be truly non-Abelian by parameterizing them in terms of orientational collective coordinates. When N_f > N_c, the solutions correspond to semilocal strings which, beside the orientational degrees of freedom, acquire additional collective coordinates parameterizing their transverse size. The low-energy effective theories for the correspondent moduli are found, showing that all zero modes are normalizable in presence of gravity, even in the semilocal case.

Demixing and orientational ordering in mixtures of rectangular particles

Using scaled-particle theory for binary mixtures of two-dimensional hard particles with orientational degrees of freedom, we analyze the stability of phases with orientational order and the demixing phase behavior of a variety of mixtures. Our study is focused on cases where at least one of the components consists of hard rectangles, or a particular case of these, hard squares. A pure fluid of hard rectangles has recently been shown to exhibit, aside from the usual uniaxial nematic phase, an additional oriented phase, called tetratic phase, possessing two directors, which is the analog of the biaxial or cubatic phases in three-dimensional fluids. There is evidence, based on computer simulation studies, that the tetratic phase might be stable with respect to phases with lower translational symmetry for rectangles with low aspect ratios. As hard rectangles are mixed, in increasing concentration, with other particles not possessing stable tetratic order by themselves, the tetratic phase is destabilized, via a first- or second-order phase transition, to uniaxial nematic or isotropic phases; for hard rectangles of low aspect ratio (hard squares, in particular), tetratic order persists in a relatively large range of volume fractions. The order of these transitions depends on the particle geometry and dimensions, and also on the thermodynamic conditions of the mixture. The second component of the mixture has been chosen to be hard disks or discorectangles, the geometry of which is different from that of rectangles, leading to packing frustration and demixing behavior, or simply rectangles of different aspect ratio but with the same particle area, or different particle area but with the same aspect ratio. These mixtures may be good candidates for observing thermodynamically stable tetratic phases in monolayers of hard particles. Finally, demixing between fluid (isotropic-tetratic or tetratic-tetratic) phases is seen to occur in mixtures of hard squares of different sizes when the size ratio is sufficiently large.