Structure of Ti N (N = 6–15) titanium cluster isomers

The atomic structures of various isomers of free Ti _N (N = 6–15) titanium clusters have been studied by molecular dynamics using the many-body interaction potential in the tight binding model. The following parameters of the cluster structure have been calculated: average bond length and energy, coordination number, and frequencies (probabilities) of their appearance. An increase in the cluster size N is accompanied by increased values of these parameters. It is established that the frequency of appearance of an isomer with a given N value increases with the bond energy. The most probable structures of clusters with N = 10–15 correspond to maximum values of the atomic structure parameters among all isomers of a given size.     

Probing free xenon clusters from within

Inner-shell and valence-shell photoionization of van-der-Waals Xe clusters have been measured using both angle-resolved photoelectron spectroscopy and velocity map ion imaging technique. Both techniques have been used to probe the electronic properties and the fragmentation dynamics of clusters as a function of photon energy and cluster size. In particular, the evolution of the photoelectron angular distributions and partial cross sections as a function of photon energy and cluster size has revealed cluster size effects similar to the ones found in solids. Our cluster angular distribution parameters have been compared to the free atoms. In addition, the measurement of the fragmentation dynamic of the clusters seems to be photon energy dependent.     

Noise-Robust Image Reconstruction Based on Minimizing Extended Class of Power-Divergence Measures

The problem of tomographic image reconstruction can be reduced to an optimization problem of finding unknown pixel values subject to minimizing the difference between the measured and forward projections. Iterative image reconstruction algorithms provide significant improvements over transform methods in computed tomography. In this paper, we present an extended class of power-divergence measures (PDMs), which includes a large set of distance and relative entropy measures, and propose an iterative reconstruction algorithm based on the extended PDM (EPDM) as an objective function for the optimization strategy. For this purpose, we introduce a system of nonlinear differential equations whose Lyapunov function is equivalent to the EPDM. Then, we derive an iterative formula by multiplicative discretization of the continuous-time system. Since the parameterized EPDM family includes the Kullback–Leibler divergence, the resulting iterative algorithm is a natural extension of the maximum-likelihood expectation-maximization (MLEM) method. We conducted image reconstruction experiments using noisy projection data and found that the proposed algorithm outperformed MLEM and could reconstruct high-quality images that were robust to measured noise by properly selecting parameters.     

Variational principle for regular and random Ising models on the cactus tree or on the usual lattice in the “cactus approximation”

The distribution functions and the free energy are expressed in terms of the effective fields for the regular and random Ising models of an arbitrary spin S on the generalized cactus tree. The same expressions apply to systems on the usual lattice in the “cactus approximation” in the cluster variation method. For an ensemble of random Ising models of an arbitrary spin S on the generalized cactus tree, the equation for the probability distribution function of the effective fields is set up and the averaged free energy is expressed in terms of the probability distribution. The same expressions apply to the system on the usual lattice in the “cactus approximation”. We discuss the quantities on the usual lattice when the system or the ensemble of random systems has the translational symmetry. Variational properties of the free energy for a system and of the averaged free energy for an ensemble of random systems are noted. The “cactus approximations” are applicable to the Heisenberg model as well as to the Ising model of an arbitrary spin, and to ensembles of random systems of these models.     

Parallel cluster labeling for large-scale Monte Carlo simulations

We present an optimized version of a cluster labeling algorithm previously introduced by the authors. This algorithm is well suited for large-scale Monte Carlo simulations of spin models using cluster dynamics on parallel computers with large numbers of processors. The algorithm divides physical space into rectangular cells which are assigned to processors and combines a serial local labeling procedure with a relaxation process across nearest-neighbor processors. By controlling overhead and reducing inter-processor communication this method attains good computational speed-up and efficiency. Large systems of up to 65536² spins have been simulated at updating speeds of 11 nanosecs/site (90.7 × 10⁶ spin updates/sec) using state-of-the-art supercomputers. In the second part of the article we use the cluster algorithm to study the relaxation of magnetization and energy on large Ising models using Swendsen-Wang dynamics. We found evidence that exponential and power law factors are present in the relaxation process as has been proposed by Hackl et al. The variation of the power-law exponent λ_M taken at face value indicates that the value of Z_M falls in the interval 0.31–0.49 for the time interval analysed and appears to vanish asymptotically.     

Domain growth in chiral phase transitions

We study the kinetics of chiral phase transitions in quark matter. We discuss the phase diagram of this system in both a microscopic framework (using the Nambu-Jona-Lasinio model) and a phenomenological framework (using the Landau free energy). Then, we study the far-from-equilibrium coarsening dynamics subsequent to a quench from the chirally-symmetric phase to the massive quark phase. Depending on the nature of the quench, the system evolves via either spinodal decomposition or nucleation and growth. The morphology of the ordering system is characterized using the order-parameter correlation function, structure factor, domain growth laws, etc.     

Simulation of sputtering and desorption of gold nanoclusters under bombardment with 180-eV/atom Au400 nanoclusters using the classical molecular dynamics method

Computer simulation of the interaction of an Au₄₀₀ nanocluster (the total energy E = 72 keV) with free spherical Au _N nanoclusters (6 and 12 nm in diameter) and Au₆₀₅₁ clusters deposited on the (111) surface of an Al substrate is performed by means of the classical molecular dynamics method. The distributions of the absorbed energy (ε) converted to one atom of the bombarded nanocluster and the sputtering yield are analyzed. It has been ascertained that the most probable values are either the small (ε ? ε_max = E/N) or the maximum possible (ε ～ ε_max) values of absorbed energy. The total sputtering yield and the absorbed energy decrease with increasing impact parameter. It has been demonstrated that, with a probability of ～10%, a direct impact can lead to ejection of the entire bombarded nanocluster from the substrate. This event occurs in the case where an incident cluster initiates the secondary emission of target-cluster atoms mainly in the direction of the substrate. As a result, the nonsputtered part of the target cluster acquires the momentum in the opposite direction. This recoil effect can be regarded as one of the possible mechanisms by which nanoclusters deposited on substrate surfaces desorb under ion and cluster bombardment.     

Molecular dynamics simulations of nanopore processing in a graphene sheet by using gas cluster ion beam

The formation of a nanopore in a graphene sheet by collision with an argon cluster is simulated using molecular dynamics method. The number of removed carbon atoms and the size of the nanopore are obtained as a function of the kinetic energy of the cluster. In contrast to nanosculpting with a monomer ion beam, the size of the nanopore that is created by one shot of the cluster varies because of the variety of atom configuration. However, the mean size of the nanopore can be controlled over a wide range only by changing the kinetic energy of the cluster. This implies that the cleaning and processing of the graphene sheet may be realized simultaneously by changing the acceleration energy of the cluster.     

Reentrant adhesion behavior in nanocluster deposition

We simulate the collision of atomic clusters with a weakly attractive surface using molecular dynamics in a regime between soft landing and fragmentation, where the cluster undergoes large deformation but remains intact. As a function of incident kinetic energy, we find a transition from adhesion to reflection at low kinetic energies. We also identify a second adhesive regime at intermediate kinetic energies, where strong deformation of the cluster leads to an increase in contact area and adhesive energy.     

A Monte Carlo Sampling Scheme for the Ising Model

In this paper we describe a Monte Carlo sampling scheme for the Ising model and similar discrete-state models. The scheme does not involve any particular method of state generation but rather focuses on a new way of measuring and using the Monte Carlo data. We show how to reconstruct the entropy S of the model, from which, e.g., the free energy can be obtained. Furthermore we discuss how this scheme allows us to more or less completely remove the effects of critical fluctuations near the critical temperature and likewise how it reduces critical slowing down. This makes it possible to use simple state generation methods like the Metropolis algorithm also for large lattices.     

Adsorption of polymer chains by disordered traps

We study the adsorption cross-over of ideal polymer chains in an environment of disordered traps. Starting from the assumption of an optimal cluster size of traps (optimal fluctuation method) we derive a general scaling form of the free energy function for arbitrary spatial dimensions. For small concentrations of traps we find a cross-over from localized (adsorbed) behavior to delocalized behavior depending on the chain's length and on the depth of the traps; this is connected with the non-monotonic behavior of the chain's extension. In terms of the free energy of the chain this cross-over resembles a first order transition scenario, the chain gets localized at many traps at once. Received 18 November 1998     

Modeling and computation of two phase geometric biomembranes using surface finite elements

Biomembranes consisting of multiple lipids may involve phase separation phenomena leading to coexisting domains of different lipid compositions. The modeling of such biomembranes involves an elastic or bending energy together with a line energy associated with the phase interfaces. This leads to a free boundary problem for the phase interface on the unknown equilibrium surface which minimizes an energy functional subject to volume and area constraints. In this paper we propose a new computational tool for computing equilibria based on an L² relaxation flow for the total energy in which the line energy is approximated by a surface Ginzburg–Landau phase field functional. The relaxation dynamics couple a nonlinear fourth order geometric evolution equation of Willmore flow type for the membrane with a surface Allen–Cahn equation describing the lateral decomposition. A novel system is derived involving second order elliptic operators where the field variables are the positions of material points of the surface, the mean curvature vector and the surface phase field function. The resulting variational formulation uses H¹ spaces, and we employ triangulated surfaces and H¹ conforming quadratic surface finite elements for approximating solutions. Together with a semi-implicit time discretization of the evolution equations an iterative scheme is obtained essentially requiring linear solvers only. Numerical experiments are presented which exhibit convergence and the power of this new method for two component geometric biomembranes by computing equilibria such as dumbbells, discocytes and starfishes with lateral phase separation.     

Use of electron correlation to make attosecond measurements without attosecond pulses

We describe how correlations between electrons can be used to trace the dynamics of correlated two-electron ionization with attosecond precision, without using attosecond pulses. The approach is illustrated using the example of Auger or Coster-Kronig decay triggered by photoionization with an extreme ultraviolet pulse. It requires correlated measurements of angle-resolved energy spectra of both the photo- and Auger electrons in the presence of a laser pulse. To reconstruct the dynamics, we use not only classical time and energy correlation, but also entanglement between the two electrons.     

The Response of Glassy Systems to Random Perturbations: A Bridge Between Equilibrium and Off-Equilibrium

We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free energy. By exploiting this fact, we define a new order parameter function, and we relate it to the ratio between response and fluctuation, which is in principle measurable in an aging experiment. For a class of systems possessing stochastic stability, we show that this new order parameter function is intimately related to the static order parameter function, describing the distribution of overlaps between clustering states. The same method is applied to investigate the geometrical organization of pure states. We show that the ultrametric organization in the dynamics implies static ultrametricity, and we relate these properties to static separability, i.e., the property that the measure of the overlap between pure states is essentially unique. Our results, especially relevant for spin glasses, pave the way to an experimental determination of the order parameter function.     

Ab Initio Study of Electroweak Responses of 4He

In this contribution, we discuss the electroweak responses of ⁴He based on a full four-body calculation. The wave function of the ground state is obtained accurately using an explicitly correlated basis. Four-body final states are expressed in a superposition of many basis functions including configurations which have 3+1 and 2+1+1 cluster partitions of four-nucleon system explicitly. The continuum is properly treated by taking the two approaches: one is the complex scaling method and the other is the microscopic R-matrix method. The calculated photoabsorption cross sections agree up to the rest energy of a pion. The spin–dipole strength function is also presented and its relationship between the spectrum of ⁴He is discussed.     

Free energy computations by minimization of Kullback–Leibler divergence: An efficient adaptive biasing potential method for sparse representations

The present paper proposes an adaptive biasing potential technique for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells and estimating the free energy function, under the same objective of minimizing the Kullback–Leibler divergence between appropriately selected densities. It offers rigorous convergence diagnostics even though history dependent, non-Markovian dynamics are employed. It makes use of a greedy optimization scheme in order to obtain sparse representations of the free energy function which can be particularly useful in multidimensional cases. It employs embarrassingly parallelizable sampling schemes that are based on adaptive Sequential Monte Carlo and can be readily coupled with legacy molecular dynamics simulators. The sequential nature of the learning and sampling scheme enables the efficient calculation of free energy functions parametrized by the temperature. The characteristics and capabilities of the proposed method are demonstrated in three numerical examples.     

Theoretical investigation on isomer formation probability and free energy of small C clusters

Molecular dynamics simulations and free energy calculations are employed to investigate the evolution,formation probability,detailed balance,and isomerization rate of small C cluster isomer at 2500 K.For C10,the isomer formation probability predicted by free energy is in good agreement with molecular dynamics simulation.However,for C20,C30,and C36,the formation probabilities predicted by free energy are not in agreement with molecular dynamics simulations.Although the cluster systems are in equilibrium,detailed balance is not reached.Such results may be attributed to high transformation barriers between cage,bowl,and sheet isomers.In summary,for mesoscopic nanosystems the free energy criterion,which commonly holds for macroscopic systems in dynamic equilibrium,may not provide a good prediction for isomer formation probability.New theoretical criterion should be further investigated for predicting the isomer formation probability of a mesoscopic nanosystem.