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At least 559 records · Page 31

Global properties and bifurcation analysis of an HIV-1 infection model with two target cells

In this paper, the authors consider a four-compartmental HIV epidemiological model, which describes the interaction between HIV virus and two target cells, CD4 T cells and macrophages in vivo. It is proved that the bilinear incidence can cause the backward bifurcation, where a locally asymptotically stable disease-free equilibrium co-exists with a locally asymptotically stable endemic equilibrium when the basic reproduction number (R{sub 0}) is less than unity. It is shown that a sequence of Hopf bifurcations occur at the endemic equilibrium by choosing one parameter of the model as the bifurcation parameter. Meanwhile, the global asymptotic stabilities of the equilibria are established by constructing suitable Lyapunov functions under some conditions. Furthermore, the authors develop an extended model by incorporating with the intracellular delays and derive global asymptotic stability of the delayed model by constructing Lyapunov functions. Some numerical simulations for justifying the theoretical analysis results are also given.

60 APPLIED LIFE SCIENCES↗

Low-mass molecular dynamics simulation: A simple and generic technique to enhance configurational sampling

Highlights: • Reducing atomic masses by 10-fold vastly improves sampling in MD simulations. • CLN025 folded in 4 of 10 × 0.5-μs MD simulations when masses were reduced by 10-fold. • CLN025 folded as early as 96.2 ns in 1 of the 4 simulations that captured folding. • CLN025 did not fold in 10 × 0.5-μs MD simulations when standard masses were used. • Low-mass MD simulation is a simple and generic sampling enhancement technique. - Abstract: CLN025 is one of the smallest fast-folding proteins. Until now it has not been reported that CLN025 can autonomously fold to its native conformation in a classical, all-atom, and isothermal–isobaric molecular dynamics (MD) simulation. This article reports the autonomous and repeated folding of CLN025 from a fully extended backbone conformation to its native conformation in explicit solvent in multiple 500-ns MD simulations at 277 K and 1 atm with the first folding event occurring as early as 66.1 ns. These simulations were accomplished by using AMBER forcefield derivatives with atomic masses reduced by 10-fold on Apple Mac Pros. By contrast, no folding event was observed when the simulations were repeated using the original AMBER forcefields of FF12SB and FF14SB. The results demonstrate that low-mass MD simulation is a simple and generic technique to enhance configurational sampling. This technique may propel autonomous folding of a wide range of miniature proteins in classical, all-atom, and isothermal–isobaric MD simulations performed on commodity computers—an important step forward in quantitative biology.

60 APPLIED LIFE SCIENCES↗

A new scheme of causal viscous hydrodynamics for relativistic heavy-ion collisions: A Riemann solver for quark–gluon plasma

In this article, we present a state-of-the-art algorithm for solving the relativistic viscous hydrodynamics equation with the QCD equation of state. The numerical method is based on the second-order Godunov method and has less numerical dissipation, which is crucial in describing of quark–gluon plasma in high-energy heavy-ion collisions. We apply the algorithm to several numerical test problems such as sound wave propagation, shock tube and blast wave problems. In sound wave propagation, the intrinsic numerical viscosity is measured and its explicit expression is shown, which is the second-order of spatial resolution both in the presence and absence of physical viscosity. The expression of the numerical viscosity can be used to determine the maximum cell size in order to accurately measure the effect of physical viscosity in the numerical simulation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Multiple-time-stepping generalized hybrid Monte Carlo methods

Performance of the generalized shadow hybrid Monte Carlo (GSHMC) method [1], which proved to be superior in sampling efficiency over its predecessors [2–4], molecular dynamics and hybrid Monte Carlo, can be further improved by combining it with multi-time-stepping (MTS) and mollification of slow forces. We demonstrate that the comparatively simple modifications of the method not only lead to better performance of GSHMC itself but also allow for beating the best performed methods, which use the similar force splitting schemes. In addition we show that the same ideas can be successfully applied to the conventional generalized hybrid Monte Carlo method (GHMC). The resulting methods, MTS-GHMC and MTS-GSHMC, provide accurate reproduction of thermodynamic and dynamical properties, exact temperature control during simulation and computational robustness and efficiency. MTS-GHMC uses a generalized momentum update to achieve weak stochastic stabilization to the molecular dynamics (MD) integrator. MTS-GSHMC adds the use of a shadow (modified) Hamiltonian to filter the MD trajectories in the HMC scheme. We introduce a new shadow Hamiltonian formulation adapted to force-splitting methods. The use of such Hamiltonians improves the acceptance rate of trajectories and has a strong impact on the sampling efficiency of the method. Both methods were implemented in the open-source MD package ProtoMol and were tested on a water and a protein systems. Results were compared to those obtained using a Langevin Molly (LM) method [5] on the same systems. The test results demonstrate the superiority of the new methods over LM in terms of stability, accuracy and sampling efficiency. This suggests that putting the MTS approach in the framework of hybrid Monte Carlo and using the natural stochasticity offered by the generalized hybrid Monte Carlo lead to improving stability of MTS and allow for achieving larger step sizes in the simulation of complex systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Stable explicit coupling of the Yee scheme with a linear current model in fluctuating magnetized plasmas

This work analyzes the stability of the Yee scheme for non-stationary Maxwell's equations coupled with a linear current model with density fluctuations. We show that the usual procedure may yield unstable scheme for physical situations that correspond to strongly magnetized plasmas in X-mode (TE) polarization. We propose to use first order clustered discretization of the vectorial product that gives back a stable coupling. We validate the schemes on some test cases representative of direct numerical simulations of X-mode in a magnetic fusion plasma including turbulence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Particle-in-cell simulations of collisionless shock formation via head-on merging of two laboratory supersonic plasma jets

We describe numerical simulations, using the particle-in-cell (PIC) and hybrid-PIC code lsp[T. P. Hughes et al., Phys. Rev. ST Accel. Beams 2, 110401 (1999)], of the head-on merging of two laboratory supersonic plasma jets. The goals of these experiments are to form and study astrophysically relevant collisionless shocks in the laboratory. Using the plasma jet initial conditions (density ∼10{sup 14}–10{sup 16} cm{sup −3}, temperature ∼ few eV, and propagation speed ∼20–150 km/s), large-scale simulations of jet propagation demonstrate that interactions between the two jets are essentially collisionless at the merge region. In highly resolved one- and two-dimensional simulations, we show that collisionless shocks are generated by the merging jets when immersed in applied magnetic fields (B∼0.1–1 T). At expected plasma jet speeds of up to 150 km/s, our simulations do not give rise to unmagnetized collisionless shocks, which require much higher velocities. The orientation of the magnetic field and the axial and transverse density gradients of the jets have a strong effect on the nature of the interaction. We compare some of our simulation results with those of previously published PIC simulation studies of collisionless shock formation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An improved Monte Carlo (MC) dose simulation for charged particle cancer therapy

Heavy-particle therapy such as carbon ion therapy are more popular nowadays because of the nature characteristics of charged particle and almost no side effect to patients. An effective treatment is achieved with high precision of dose calculation, in this research work, Geant4 based Monte Carlo simulation method has been used to calculate the radiation transport and dose distribution. The simulation have the same setting with the treatment room in Heavy Ion Medical Accelerator, HIMAC. The carbon ion beam at the isocentric gantry nozzle for the therapeutic energy of 290 MeV/u was simulated, experimental work was carried out in National Institute of Radiological Sciences, NIRS, Chiba, Japan by using the HIMAC to confirm the accuracy and qualities dose distribution by MC methods. The Geant4 based simulated dose distribution were verified with measurements for Bragg peak and spread out Bragg peak (SOBP) respectively. The verification of results shows that the Bragg peak depth-dose and SOBP distributions in simulation has good agreement with measurements. In overall, the study showed that Geant4 based can be fully applied in the heavy-ion therapy field for simulation, further works need to be carry on to refine and improve the Geant4 MC simulations.

61 RADIATION PROTECTION AND DOSIMETRY↗

A direct underground measurement of the {sup 17}O(p,α){sup 14}N reaction cross-section at energies of astrophysical interest

The {sup 17}O(p,α){sup 14}N reaction plays a key role in many stellar sites, including classical novae and massive stars. Our knowledge of these scenarios might be improved by a precise measurement of the reaction’s cross-section at astrophysical energies. A direct attempt is currently underway in the Gran Sasso Laboratory, Italy, using the underground LUNA 400kV accelerator. The background reduction afforded by the underground environment is essential to the success of this challenging measurement. A purpose-built experimental setup has been simulated and commissioned. Preliminary results are presented.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Systematic approach of nanoparticle design to enhance the broadband plasmonic scattering effect

To overcome low conversion efficiency of thin film solar cells, using the localized surface plasmon effect caused by the interaction between the incident beam and metallic nanoparticles inserted in or on the absorbing layer can be a promising alternative to overcome the low efficiency problem. Detail shape and size of nanoparticles are directly related with the localized surface plasmon effect as well as optical properties; however, their detail shape and size are hard to be determined depending only on the theoretical or experimental approach. Therefore, the method focusing on defining structural boundaries would be a useful method for nano or microscale design to generate simple and clear shape. In this study, we adopted the structural optimization scheme based on the phase field method to determine the optimal shape of a silver (Ag) nanoparticle positioned on the upper surface of the absorbing layer. We carried out the design process for broadband wavelength to be taken into account and verified the plasmonic scattering effect enhancement in the absorbing layer by numerical simulations.

30 DIRECT ENERGY CONVERSION↗

Inequalities for quantum marginal problems with continuous variables

We consider a mixed continuous-variable bosonic quantum system and present inequalities which must be satisfied between principal values of the covariances of a complete set of observables of the whole system and the principal values of the covariances of a complete set of observables of a subsystem. We use several classical results for the proof: the Courant-Fischer-Weyl min-max theorem for Hermitian operators and its consequence, the Cauchy interlacing theorem, and prove their analogues in the symplectic setting. For the case of passive transformations of Gaussian mixed states we also prove that the obtained inequalities are, in a sense, the best possible. The obtained mathematical results are applied to the system of n uncorrelated thermal modes of the electromagnetic field. Finally, we present the results of numerical simulations of the problem, suggesting avenues of further research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Improving the efficiency of configurational-bias Monte Carlo: A density-guided method for generating bending angle trials for linear and branched molecules

A new method has been developed to generate bending angle trials to improve the acceptance rate and the speed of configurational-bias Monte Carlo. Whereas traditionally the trial geometries are generated from a uniform distribution, in this method we attempt to use the exact probability density function so that each geometry generated is likely to be accepted. In actual practice, due to the complexity of this probability density function, a numerical representation of this distribution function would be required. This numerical table can be generated a priori from the distribution function. This method has been tested on a united-atom model of alkanes including propane, 2-methylpropane, and 2,2-dimethylpropane, that are good representatives of both linear and branched molecules. It has been shown from these test cases that reasonable approximations can be made especially for the highly branched molecules to reduce drastically the dimensionality and correspondingly the amount of the tabulated data that is needed to be stored. Despite these approximations, the dependencies between the various geometrical variables can be still well considered, as evident from a nearly perfect acceptance rate achieved. For all cases, the bending angles were shown to be sampled correctly by this method with an acceptance rate of at least 96% for 2,2-dimethylpropane to more than 99% for propane. Since only one trial is required to be generated for each bending angle (instead of thousands of trials required by the conventional algorithm), this method can dramatically reduce the simulation time. The profiling results of our Monte Carlo simulation code show that trial generation, which used to be the most time consuming process, is no longer the time dominating component of the simulation.

2-2-DIMETHYLPROPANE↗

Two-dimensional simulation research of secondary electron emission avalanche discharge on vacuum insulator surface

Based on the secondary electron emission avalanche (SEEA) model, the SEEA discharge on the vacuum insulator surface is simulated by using a 2D PIC-MCC code developed by ourselves. The evolutions of the number of discharge electrons, insulator surface charge, current, and 2D particle distribution are obtained. The effects of the strength of the applied electric field, secondary electron yield coefficient, rise time of the pulse, length of the insulator on the discharge are investigated. The results show that the number of the SEEA electrons presents a quadratic dependence upon the applied field strength. The SEEA current, which is on the order of Ampere, is directly proportional to the field strength and secondary electron yield coefficient. Finally, the electron-stimulated outgassing is included in the simulation code, and a three-phase discharge curve is presented by the simulation, which agrees with the experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria

Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces in non-axisymmetric ideal MHD equilibria. These include the force-free singular current density represented by a Dirac δ-function, which presumably prevents the formation of islands, and the Pfirsch-Schlüter 1/x singular current, which arises as a result of finite pressure gradient. An analytical model based on linearized MRxMHD is derived that can accurately (1) describe the formation of magnetic islands at resonant rational surfaces, (2) retrieve the ideal MHD limit where magnetic islands are shielded, and (3) compute the subsequent formation of singular currents. The analytical results are benchmarked against numerical simulations carried out with a fully nonlinear implementation of MRxMHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The ensemble switch method for computing interfacial tensions

We present a systematic thermodynamic integration approach to compute interfacial tensions for solid-liquid interfaces, which is based on the ensemble switch method. Applying Monte Carlo simulations and finite-size scaling techniques, we obtain results for hard spheres, which are in agreement with previous computations. The case of solid-liquid interfaces in a variant of the effective Asakura-Oosawa model and of liquid-vapor interfaces in the Lennard-Jones model are discussed as well. We demonstrate that a thorough finite-size analysis of the simulation data is required to obtain precise results for the interfacial tension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation onto that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

WEIGHING GALAXY CLUSTERS WITH GAS. I. ON THE METHODS OF COMPUTING HYDROSTATIC MASS BIAS

Mass estimates of galaxy clusters from X-ray and Sunyeav-Zel'dovich observations assume the intracluster gas is in hydrostatic equilibrium with their gravitational potential. However, since galaxy clusters are dynamically active objects whose dynamical states can deviate significantly from the equilibrium configuration, the departure from the hydrostatic equilibrium assumption is one of the largest sources of systematic uncertainties in cluster cosmology. In the literature there have been two methods for computing the hydrostatic mass bias based on the Euler and the modified Jeans equations, respectively, and there has been some confusion about the validity of these two methods. The word 'Jeans' was a misnomer, which incorrectly implies that the gas is collisionless. To avoid further confusion, we instead refer these methods as 'summation' and 'averaging' methods respectively. In this work, we show that these two methods for computing the hydrostatic mass bias are equivalent by demonstrating that the equation used in the second method can be derived from taking spatial averages of the Euler equation. Specifically, we identify the correspondences of individual terms in these two methods mathematically and show that these correspondences are valid to within a few percent level using hydrodynamical simulations of galaxy cluster formation. In addition, we compute the mass bias associated with the acceleration of gas and show that its contribution is small in the virialized regions in the interior of galaxy clusters, but becomes non-negligible in the outskirts of massive galaxy clusters. We discuss future prospects of understanding and characterizing biases in the mass estimate of galaxy clusters using both hydrodynamical simulations and observations and their implications for cluster cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗

Mass transport and turbulence in gravitationally unstable disk galaxies. I. The case of pure self-gravity

The role of gravitational instability-driven turbulence in determining the structure and evolution of disk galaxies, and the extent to which gravity rather than feedback can explain galaxy properties, remains an open question. To address it, we present high-resolution adaptive mesh refinement simulations of Milky Way-like isolated disk galaxies, including realistic heating and cooling rates and a physically motivated prescription for star formation, but no form of star formation feedback. After an initial transient, our galaxies reach a state of fully nonlinear gravitational instability. In this state, gravity drives turbulence and radial inflow. Despite the lack of feedback, the gas in our galaxy models shows substantial turbulent velocity dispersions, indicating that gravitational instability alone may be able to power the velocity dispersions observed in nearby disk galaxies on 100 pc scales. Moreover, the rate of mass transport produced by this turbulence approaches ∼1 M{sub ⊙} yr{sup −1} for Milky Way-like conditions, sufficient to fully fuel star formation in the inner disks of galaxies. In a companion paper, we add feedback to our models, and use the comparison between the two cases to understand which galaxy properties depend sensitively on feedback and which can be understood as the product of gravity alone. All of the code, initial conditions, and simulation data for our model are publicly available.

79 ASTRONOMY AND ASTROPHYSICS↗

MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

This report describes a new magnetohydrodynamic numerical model based on a hexagonal spherical geodesic grid. The model is designed to simulate astrophysical flows of partially ionized plasmas around a central compact object, such as a star or a planet with a magnetic field. The geodesic grid, produced by a recursive subdivision of a base platonic solid (an icosahedron), is free from control volume singularities inherent in spherical polar grids. Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model. Our numerical scheme uses piecewise linear reconstruction on a surface of a sphere in a local two-dimensional 'Cartesian' frame. The code employs Haarten-Lax-van-Leer-type approximate Riemann solvers and includes facilities to control the divergence of the magnetic field and maintain pressure positivity. Several test solutions are discussed, including a problem of an interaction between the solar wind and the local interstellar medium, and a simulation of Earth's magnetosphere.

79 ASTRONOMY AND ASTROPHYSICS↗