Formation of Superheavy Elements: Study Based on Dynamical Approach

Using multi-dimensional Langevin equations for the probability distribution of the distance between the surfaces of two approaching nuclei, we have studied the formation of superheavy elements via calculation of evaporation and fission cross sections of these elements. Evaporation residue cross sections have been calculated for the 1n, 2n, 3n, 4n, and 5n evaporation channels using one and four dimensional Langevin equations for the ⁴⁸Ca+²²⁶Ra, ²³²Th, ²³⁸U, ²³⁷Np, ^{239,240,242,244}Pu, ²⁴³Am, ^245,248Cm, ²⁴⁹Bk, and ²⁴⁹Cf reactions. Our results show that with increasing dimension of Langevin equations the evaporation residue cross section is increased. Also, obtained results based on fourdimensional Langevin are in better agreement with experimental data in comparison with one-dimensional model.     

Integrable discrete static Hamiltonian with a parametric double-well potential

A one-dimensional discrete conservative Hamiltonian with a generalized form of the Schmidt potential, is constructed with the help of a non-integrable discrete Hamiltonian whose parametrized double-well potential can be reduced to the ?⁴ potential. The new conservative Hamiltonian is completely integrable in the discrete static regime, and the associate exact nonlinear solution is shown to coincide with the continuum nonlinear periodic solution of the non-integrable Hamiltonian. Numerical simulations and nonlinear stability analysis suggest that the discrete mapping derived from the completely integrable Hamiltonian undergoes a bifurcation which does not leads to the chaotic phase with randomly pinned states, but instead to a phase where real solutions become rare forming a cluster of periodic points around an elliptic fixed point.     

The Langevin equation with fourier acceleration and its equilibrium action

We derive the Fokker-Planck equation of the Langevin equation for SU(N) models with nonlocal step size. We solve this equation for the SU(N) × SU(N) spin model and determine the rescaled coupling constant and the correction of observables.     

Newtonian versus Langevin dynamics: Example of ϕ4-model with infinite range interactions

The functional integral representation for the generating functional (GF) of the canonically averaged ensemble with an underlying Newtonian dynamics is obtained. It is shown that for this representation the non-linear fluctuation-dissipation theorem (NFDT) has the same form as for the Langevin dynamics case. This GF-representation is used for the investigation of the dynamics of the ϕ⁴-model with infinite range interactions at T > T_c. It is shown that the kinetic equation for the complete correlation function has the same form as for the Langevin dynamics case, which was considered before. All peculiarities of Newtonian dynamics are absorbed by one-particle (2-point and 4-point) correlator and response functions. The analysis of this equation shows that the 1/N-fluctuations (where N is the number of particles) restore the ergodicity of the system with the characteristicsrate τ⁻¹ ∼ μ²/N, where μ is a coupling constant.     

Mass-energy distribution of fragments within Langevin dynamics of fission induced by heavy ions

A stochastic approach based on four-dimensional Langevin fission dynamics is applied to calculating mass-energy distributions of fragments originating from the fission of excited compound nuclei. In the model under investigation, the coordinate K representing the projection of the total angular momentum onto the symmetry axis of the nucleus is taken into account in addition to three collective shape coordinates introduced on the basis of the {c, h, ??} parametrization. The evolution of the orientation degree of freedom (K mode) is described by means of the Langevin equation in the overdamped regime. The tensor of friction is calculated under the assumption of the reducedmechanismof one-body dissipation in the wall-plus-window model. The calculations are performed for two values of the coefficient that takes into account the reduction of the contribution from the wall formula: k _s = 0.25 and k _s = 1.0. Calculations with a modified wall-plus-window formula are also performed, and the quantity measuring the degree to which the single-particle motion of nucleons within the nuclear system being considered is chaotic is used for k _s in this calculation. Fusion-fission reactions leading to the production of compound nuclei are considered for values of the parameter Z ²/A in the range between 21 and 44. So wide a range is chosen in order to perform a comparative analysis not only for heavy but also for light compound nuclei in the vicinity of the Businaro-Gallone point. For all of the reactions considered in the present study, the calculations performed within four-dimensional Langevin dynamics faithfully reproduce mass-energy and mass distributions obtained experimentally. The inclusion of the K mode in the Langevin equation leads to an increase in the variances of mass and energy distributions in relation to what one obtains from three-dimensional Langevin calculations. The results of the calculations where one associates k _s with the measure of chaoticity in the single-particle motion of nucleons within the nuclear system under study are in good agreement for variances of mass distributions. The results of calculations for the correlations between the prescission neutron multiplicity and the fission-fragment mass, ??n _pre(M)??, and between, this multiplicity and the kinetic energy of fission fragments, ??n _pre(E _k )??, are also presented.     

An efficient local time-stepping scheme for solution of nonlinear conservation laws

We develop an efficient local time-stepping algorithm for the method of lines approach to numerical solution of transient partial differential equations. The need for local time-stepping arises when adaptive mesh refinement results in a mesh containing cells of greatly different sizes. The global CFL number and, hence, the global time step, are defined by the smallest cell size. This can be inefficient as a few small cells may impose a restrictive time step on the whole mesh. A local time-stepping scheme allows us to use the local CFL number which reduces the total number of function evaluations. The algorithm is based on a second order Runge–Kutta time integration. Its important features are a small stencil and the second order accuracy in the L² and L^∞ norms.     

A comment on chemical Langevin equations

It is noted that the diffusion Langevin stochastic sources in chemical reaction-diffusion theories should really arise from a stochastic source term added to the deterministic form of Fick's law. This gives rise to results for correlation functions which agree with those from stochastic master equations provided parameters are appropriately chosen.Some authors use the term Langevin force. Sinceg _i(x,t) is dimensionally not a force, we shall eschew this dangerous terminology.     

Fission dynamics of the compound nucleus 213Fr formed in heavy-ion-induced reactions

A stochastic approach based on one-dimensional Langevin equations was used to calculate the average pre-fission multiplicities of neutrons, light charged particles and the fission probabilities for the compound nucleus ²¹³Fr and the results are compared with the experimental data. In these calculations, a modified wall and window dissipation with a reduction coefficient, k _s , has been used in the Langevin equations. It was shown that the results of the calculations are in good agreement with the experimental data by using values of k _s in the range 0.3?≤?k _s ?≤?0.5.     

Modification of the magnetic properties of polyimide films by cobalt ion implantation

The magnetic characteristics of polyimide films implanted with Co⁺ ions with an energy of 40 keV in the dose range D = 2.50 × 10¹⁶?1.25 × 10¹⁷ cm^?2 at ion current densities j = 4, 8, and 12 μA/cm² have been investigated. It has been shown that, at implantation doses of less than 5 × 10¹⁶ cm^?2, the superparamagnetic properties of modified samples are described by the Langevin equation. At higher doses, there is an intercluster interaction. It has been found that, with an increase in the ion current, the cluster size decreases. The sizes of the formed clusters are determined and vary in the range from 3.9 to 11.0 nm, depending on the implantation dose.     

Asymptotic densities from the modified Montroll-Weiss equation for coupled CTRWs

We examine the bi-scaling behavior of Lévy walks with nonlinear coupling, where χ, the particle displacement during each step, is coupled to the duration of the step, τ, by χ?~?τ ^β . An example of such a process is regular Lévy walks, where β?=?1. In recent years such processes were shown to be highly useful for analysis of a class of Langevin dynamics, in particular a system of Sisyphus laser-cooled atoms in an optical lattice, where β?=?3/2. We discuss the well-known decoupling approximation used to describe the central part of the particles’ position distribution, and use the recently introduced infinite-covariant density approach to study the large fluctuations. Since the density of the step displacements is fat-tailed, the last travel event must be treated with care for the latter. This effect requires a modification of the Montroll-Weiss equation, an equation which has proved important for the analysis of many microscopic models.     

Finite temperature effective potential for the abelian Higgs model to the ordere 4,λ 2

A complete calculation of the finite temperature effective potential for the abelian Higgs model to the ordere ⁴, λ² is presented and the result is expressed in terms of physical parameters defined at zero temperature. The absence of a linear term is verified explicitly to the given order and proven to survive to all orders. The first order phase transition has weakened in comparison with lower order calculation, which shows up in a considerable decrease of the surface tension.     

Theoretical study of mesoscopic stochastic mechanism and effects of finite size on cell cycle of fission yeast

Based on a deterministic cell cycle model, the mesoscopic stochastic differential equations are theoretically derived from the biochemical reactions. The effects of the finite cell size on the cell cycle regulation in the wild type and wee1^-cdc25Δ double mutant type are numerically studied by virtue of the chemical Langevin equations. (i) When the system is driven only by the internal noise, our numerical results are in qualitative agreement well with some experimental observations and data. (ii) A parameter, which is sensitive to two resettings of M-phase promoting factor to G₂, is treated as a stochastic variable, and the system driven only by the external noise for double mutant type is investigated. (iii) When the system is driven by both the internal and external noise, a simple discussion about the combined effect for double mutant type is given. Our results imply some experimental results would be explained by introducing the appropriate internal or external noise into the cell cycle system.     

MCRG study of fixed-connectivity surfaces

We apply the Monte Carlo Renormalization group to the crumpling transition in random surface models of fixed connectivity. This transition is notoriously difficult to treat numerically. We employ here a Fourier accelerated Langevin algorithm in conjunction with a novel blocking procedure in momentum space which has proven extremely successful in λφ⁴. We perform two successive renormalizations in lattices with up to 64² sites. We obtain a result for the critical exponent ν in general agreement with previous estimates and similar error bars, but with much less computational effort. We also measure with great accuracy η. As a by-product we are able to determine the fractal dimension d_H of random surfaces at the crumpling transition.     

Study of fission dynamics with the three-dimensional Langevin equations

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei ²¹⁰Po and ²²⁴Th formed in the fusion-fission reactions ⁴He + ²⁰⁶Pb , ¹⁶O + ²⁰⁸Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data.     

Carbon clusters near the step of Rh surface: implication for the initial stage of graphene nucleation

To understand the initial nucleation of graphene by chemical vapor deposition along metal step, carbon clusters (N = 1 ～ 24) near Rh (4 3 3) stepwise surface were systemically explored by first-principles calculations. Carbon chains are always more stable than carbon rings on stepped metal surface. Starting from C₆, carbon chains prefer two-end passivation on the metal step. A structural transition of carbon clusters from one-dimensional sp chains to two-dimensional s p ² networks are found at C₁₀, which corresponds to the nucleation size at a wide range of chemical potentials. According to these theoretical results, we proposed that appropriately controlling the chemical potential may be helpful for observing the four stable carbon clusters along metal step and improving the quality of graphene.     

What lattice calculations can tell us about the gluon gas

Higher order perturbative and nonperturbative corrections to the grand potential of hot QCD are considered qualitatively Comparing with lattice results, it is argued that the nonperturbative parts are small but that the O(g⁴) term in $\text{Ω}$ is large and positive.     

Effect of aluminum substitution on the structural and magnetic properties of cobalt ferrite synthesized by sol-gel auto combustion process

Aluminum substituted cobalt ferrite powders (CoFe_2−xAl_xO₄) with varying composition from 0.0 to 1.0 in the step of 0.2 have been obtained by sol-gel auto combustion technique using citric acid as a fuel. The metal nitrate to fuel ratio was maintained 1:4 throughout the synthesis of CoFe_2−xAl_xO₄. The thermal analysis of as prepared samples is done by TGA technique. The compositional stoichiometry of the prepared samples is confirmed by Energy dispersive X-ray analysis technique. Single phase cubic spinel structure and nano phase structure of the synthesized powders were confirmed by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The crystallite size of 16-26 nm was obtained using Scherrer formula. SEM analysis shows the formation of uniform grain growth. The grain size obtained from SEM results is of the order of 30 nm. Maximum specific surface area was observed to be of the order of 52 m²/gm. The highest value of saturation magnetization and coercivity was observed for pure cobalt ferrite sample and it decreases as the aluminum content x increases. A strong co-relation between the saturation magnetization and aluminum content was observed. The decrease in magnetic properties is due to the substitution of aluminum ions in place of Fe³⁺.