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Trotter's theorem forms the theoretical basis of most modern molecular dynamics. In essence this theorem states that a time displacement operator (a Lie operator) constructed by exponentiating a sum of noncommuting operators can be approximated by a product of single operators provided the time interval is 'very small.' In theory 'very small' implies infinitesimally small (at which point the approximate product becomes exact), while in practical analysis a finite time interval is divided into several small subintervals or steps. It follows, therefore, that the larger the number of steps the better the approximation to the exact time displacement operator. The question therefore arises: How many steps are sufficient? For bounded operators, standard theorems are available to provide the answer. In this paper we show that a very simple combinatorial formula can be derived which allows the computation of the global differences (as a function of the number of steps) between the Taylor coefficients of the exact time displacement operator and an approximate one constructed by using a finite number of steps. The formula holds for both bounded and nonbounded operators and shows, quantitatively, what is qualitatively expected-that the error decreases with increasing number of steps. Furthermore, the formula applies irrespective of the complexity of the system, boundary conditions, or the thermodynamic ensemble employed for averaging the initial conditions. The analysis yields explicit expressions for the Taylor coefficients which are then used to compute the errors. In the case of the algorithmically based practical numerical simulations in which fixed, albeit small, steps are repeatedly applied, the rise in the number of steps does not reduce the size of the steps but increases the total time of interest. The combinatorial formula shows that, here, the errors diverge. Furthermore, this work can be used to supplement other efforts such as the use of shadow Hamiltonians where the truncation of the series expansion of the latter will produce errors in the higher order propagator moments. [ABSTRACT FROM AUTHOR]

Tau leaping methods enable efficient simulation of discrete stochastic chemical systems. Stiff stochastic systems are particularly challenging since implicit methods, which are good for stiffness, result in noninteger states. The occurrence of negative states is also a common problem in tau leaping. In this paper, we introduce the implicit Minkowski-Weyl tau (IMW-τ) methods. Two updating schemes of the IMW-τ methods are presented: implicit Minkowski-Weyl sequential (IMW-S) and implicit Minkowski-Weyl parallel (IMW-P). The main desirable feature of these methods is that they are designed for stiff stochastic systems with molecular copy numbers ranging from small to large and that they produce integer states without rounding. This is accomplished by the use of a split step where the first part is implicit and computes the mean update while the second part is explicit and generates a random update with the mean computed in the first part. We illustrate the IMW-S and IMW-P methods by some numerical examples, and compare them with existing tau methods. For most cases, the IMW-S and IMW-P methods perform favorably. [ABSTRACT FROM AUTHOR]

Over the last number of years several simulation methods have been introduced to study rare events such as nucleation. In this paper we examine the crystal nucleation rate of hard spheres using three such numerical techniques: molecular dynamics, forward flux sampling, and a Bennett-Chandler-type theory where the nucleation barrier is determined using umbrella sampling simulations. The resulting nucleation rates are compared with the experimental rates of Harland and van Megen [Phys. Rev. E 55, 3054 (1997)], Sinn et al. [Prog. Colloid Polym. Sci. 118, 266 (2001)], Schätzel and Ackerson [Phys. Rev. E 48, 3766 (1993)], and the predicted rates for monodisperse and 5% polydisperse hard spheres of Auer and Frenkel [Nature 409, 1020 (2001)]. When the rates are examined in units of the long-time diffusion coefficient, we find agreement between all the theoretically predicted nucleation rates, however, the experimental results display a markedly different behavior for low supersaturation. Additionally, we examined the precritical nuclei arising in the molecular dynamics, forward flux sampling, and umbrella sampling simulations. The structure of the nuclei appears independent of the simulation method, and in all cases, the nuclei contains on average significantly more face-centered-cubic ordered particles than hexagonal-close-packed ordered particles. [ABSTRACT FROM AUTHOR]

This paper attempts to quantify the effects of contaminants on electrical contact resistance. Based on an idealized model, simple and explicit scaling laws for the electrical contact resistance with dissimilar materials are constructed. The model assumes arbitrary resistivity ratios and aspect ratios in the current channels and their contact region, for both Cartesian and cylindrical geometries. The scaling laws have been favorably tested in several limits, and in sample calculations using a numerical simulation code. From the scaling laws and a survey of the huge parameter space, some general conclusions are drawn on the parametric dependence of the contact resistance on the geometry and on the electrical resistivity in different regions. [ABSTRACT FROM AUTHOR]

As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus–Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient B4 predicted by the HNC and PY approximations via the virial route differ from those obtained via the compressibility route. Despite this, it is shown in this paper that the value of B4 obtained from the virial route in the HNC theory is exactly three halves the value obtained from the compressibility route in the PY theory, irrespective of the interaction potential (whether isotropic or not), the number of components, and the dimensionality of the system. This simple relationship is confirmed in one-component systems by analytical results for the one-dimensional penetrable-square-well model and the three-dimensional penetrable-sphere model, as well as by numerical results for the one-dimensional Lennard-Jones model, the one-dimensional Gaussian core model, and the three-dimensional square-well model. [ABSTRACT FROM AUTHOR]

The importance of molecular electrostatic interactions in aqueous solution has motivated extensive research into physical models and numerical methods for their estimation. The computational costs associated with simulations that include many explicit water molecules have driven the development of implicit-solvent models, with generalized-Born (GB) models among the most popular of these. In this paper, we analyze a boundary-integral equation interpretation for the Coulomb-field approximation (CFA), which plays a central role in most GB models. This interpretation offers new insights into the nature of the CFA, which traditionally has been assessed using only a single point charge in the solute. The boundary-integral interpretation of the CFA allows the use of multiple point charges, or even continuous charge distributions, leading naturally to methods that eliminate the interpolation inaccuracies associated with the Still equation. This approach, which we call boundary-integral-based electrostatic estimation by the CFA (BIBEE/CFA), is most accurate when the molecular charge distribution generates a smooth normal displacement field at the solute-solvent boundary, and CFA-based GB methods perform similarly. Conversely, both methods are least accurate for charge distributions that give rise to rapidly varying or highly localized normal displacement fields. Supporting this analysis are comparisons of the reaction-potential matrices calculated using GB methods and boundary-element-method (BEM) simulations. An approximation similar to BIBEE/CFA exhibits complementary behavior, with superior accuracy for charge distributions that generate rapidly varying normal fields and poorer accuracy for distributions that produce smooth fields. This approximation, BIBEE by preconditioning (BIBEE/P), essentially generates initial guesses for preconditioned Krylov-subspace iterative BEMs. Thus, iterative refinement of the BIBEE/P results recovers the BEM solution; excellent agreement is obtained in only a few iterations. The boundary-integral-equation framework may also provide a means to derive rigorous results explaining how the empirical correction terms in many modern GB models significantly improve accuracy despite their simple analytical forms. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to propagating the density matrix based on a time stepping procedure arising from a Trotter factorization and combining the forward and backward incremental propagators. The sums over intermediate states of the discrete quantum subsystem are implemented by a Monte Carlo surface hopping-like procedure, while the integrals over the continuous variables are performed using a linearization in the difference between the forward and backward paths of these variables leading to classical-like equations of motion with forces determined by the quantum subsystem states. The approach is tested on several models and numerical convergence is explored. [ABSTRACT FROM AUTHOR]

A new type of cooperativity termed temporal cooperativity [Biophys. Chem. 105, 585 (2003); Annu. Rev. Phys. Chem. 58, 113 (2007)] emerges in the signal transduction module of phosphorylation-dephosphorylation cycle (PdPC). It utilizes multiple kinetic cycles in time, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein. In the present paper, we thoroughly investigate both the deterministic (microscopic) and stochastic (mesoscopic) models and focus on the identification of the source of temporal cooperativity via comparing with allosteric cooperativity. A thermodynamic analysis confirms again the claim that the chemical equilibrium state exists if and only if the phosphorylation potential ΔG=0, in which case the amplification of sensitivity is completely abolished. Then we provide comprehensive theoretical and numerical analysis with the first-order and zero-order assumptions in PdPC, respectively. Furthermore, it is interestingly found that the underlying mathematics of temporal cooperativity and allosteric cooperativity are equivalent, and both of them can be expressed by “dissociation constants,” which also characterizes the essential differences between the simple and ultrasensitive PdPC switches. Nevertheless, the degree of allosteric cooperativity is restricted by the total number of sites in a single enzyme molecule that cannot be freely regulated, while temporal cooperativity is only restricted by the total number of molecules of the target protein that can be regulated in a wide range and gives rise to the ultrasensitivity phenomenon. [ABSTRACT FROM AUTHOR]

A numerical solution for the quantum dynamics of the spin boson problem is obtained using the semiclassical initial value series representation approach to the quantum dynamics. The zeroth order term of the series is computed using the new forward-backward representation for correlation functions presented in the preceding adjacent paper. This leads to a rapid convergence of the Monte Carlo sampling, as compared to previous attempts. The zeroth order results are already quite accurate. The first order term of the series is small, demonstrating the rapid convergence of the semiclassical initial value representation series. This is the first time that the first order term in the semiclassical initial value representation series has been converged for systems with the order of 50 degrees of freedom. [ABSTRACT FROM AUTHOR]

A method for constructing diabatic potential-energy matrices from ab initio quantum chemistry data is described and tested for use in exact quantum reactive scattering. The method is a refinement of that presented in a previous paper, in that it accounts for the presence of the nonremovable derivative coupling. The accuracy of quantum dynamics on this type of diabatic potential is tested by comparison with an analytic model and for an ab initio description of the two lowest-energy states of H3. [ABSTRACT FROM AUTHOR]

We present an adaptive time stepping scheme based on the extrapolative method of Barth and Schlick [LN, J. Chem. Phys. 109, 1633 (1998)] to numerically integrate the Langevin equation with a molecular-dynamics potential. This approach allows us to use (on average) a time step for the strong nonbonded force integration corresponding to half the period of the fastest bond oscillation, without compromising the slow degrees of freedom in the problem. We show with simple examples how the dynamic step size stabilizes integration operators, and discuss some of the limitations of such stability. The method introduced uses a slightly more accurate inner integrator than LN to accommodate the larger steps. The adaptive time step approach reproduces temporal features of the bovine pancreatic trypsin inhibitor (BPTI) test system (similar to the one used in the original introduction of LN) compared to short-time integrators, but with energies that are shifted with respect to both LN, and traditional stochastic versions of Verlet. Although the introduction of longer steps has the effect of systematically heating the bonded components of the potential, the temporal fluctuations of the slow degrees of freedom are reproduced accurately. The purpose of this paper is to display a mechanism by which the resonance traditionally associated with using time steps corresponding to half the period of oscillations in molecular dynamics can be avoided. This has theoretical utility in terms of designing numerical integration schemes—the key point is that by factoring a propagator so that time steps are not constant one can recover stability with an overall (average) time step at a resonance frequency. There are, of course, limitations to this approach associated with the complicated, nonlinear nature of the molecular-dynamics (MD) potential (i.e., it is not as straightforward as the linear test problem we use to motivate the method). While the basic notion remains in the full Newtonian problem, it is easier to see the effects when damping is considered to be physical—that is, we do not view our method as a perturbation of Newtonian dynamics, we associate the damping with the environment, for example, a water bath (with γ≈90 ps-1) [Zagrovic and Pande, J. Comp. Chem. 24, 1432 (2003)]. All stochastic approaches to MD are stabilized by large physical damping, but here, we are really using it only to show that the resonance frequency can be obtained. Another simplifying assumption used in this paper is “heavy” hydrogen (we take the hydrogen mass to be 10 amu)—the view here is that we are interested primarily in the slowest degrees of freedom, and this approach has effects similar to bond freezing and united atom treatments of hydrogen. So from the point of view of biomolecular applications, the method described here is best suited to studies in which water is not explicit (so that damping in the problem can really be viewed as environmental interaction), and the interest is in slow dynamics where the effects of hydrogen are neglectable. There are a number of parameters in the LN method and the one derived here, and we cannot in a short paper address all adjustments, so our primary goal as a first pass is to show that stability can be recovered for a set of numerically forced (and hence artificial) bond oscillations, and compare stability to fixed-step methods. [ABSTRACT FROM AUTHOR]

A local method is developed for estimating the effective conductivity for materials with varying deterministic or random conductivity on domains with mixed boundary conditions. The effective conductivity is the conductivity of a virtual homogeneous material which behaves globally as the original heterogeneous material. It is shown that the effective conductivity can be calculated from the values of the potential at a relatively small number of points in the specimen. A method is developed for calculating the potential at an arbitrary point in the specimen directly, rather than extracting its value from a field solution. The method is based on some technical concepts related to properties of diffusion processes and an extension of Itô’s formula for continuous semimartingales to the case of reflected diffusion processes. However, the application of the method is intuitive and uses elementary Monte Carlo simulation algorithms. The paper presents essential facts proving the validity of the proposed method and two numerical examples illustrating the calculation of the effective conductivity for specimens with deterministic and random conductivity fields. [ABSTRACT FROM AUTHOR]

This paper is devoted to a specific difficulty related to the electronic nonadiabatic coupling terms (NACT), namely, how to determine correctly their signs. It is well known that correct NACTs, including their signs, are crucial for any numerical treatment of the nuclear Schrödinger equation [see, i.e., A. Kuppermaan and R. Abrol, Adv. Chem. Phys. 124, 283 (2003)]. In most cases the derivation of the correct sign of the nonadiabatic coupling matrix (NACM) is done employing various continuity procedures. However, there are cases where these procedures do not suffice and for these cases we suggest to apply an additional procedure based on a mathematical lemma which asserts that the exponentiated line integral which yields the D matrix is invariant with respect to the initial point of the integration [M. Baer, J. Phys. Chem. A 104, 3181 (2000)]. In the numerical study we apply this lemma to determine the signs of the 3×3 NACM elements for the three excited states of the {H2,O} system (some of these NACTs are presented here for the first time). It turns out that the ab initio treatment yields results from which one can form eight different 3×3 NACMs. However the application of this lemma (which does not require any significant additional numerical effort) reduces this number to two. The final selection is done by an enhanced numerical study which requires more accurate calculations. [ABSTRACT FROM AUTHOR]

Based on a recently developed quantum dissipation formulation [R. X. Xu and Y. J. Yan, J. Chem. Phys. 116, 9196 (2002)], we present a reduced Liouville-space approach to evaluate the response and correlation functions of dissipative systems. The weak system-bath interaction is treated properly for its effects on the initial state, the evolution, and the correlation between coherent driving and non-Markovian dissipation. Numerical demonstration shows this correlated effect cannot be neglected even in the calculation of linear response quantities that do not explicitly depend on external fields. Highlighted in this paper is also the proper choice of theory among various formulations in the weak system-bath interaction regime. [ABSTRACT FROM AUTHOR]

A new approach, the hypothetical scanning Monte Carlo (HSMC), for calculating the absolute entropy, S, and free energy, F, has been introduced recently and applied first to fluids (argon and water) and later to peptides. In this paper the method is further developed for peptide chains in vacuum. S is calculated from a given MC sample by reconstructing each sample conformation i step-by-step, i.e., calculating transition probabilities (TPs) for the dihedral and bond angles and fixing the related atoms at their positions. At step k of the process the chain’s coordinates that have already been determined are kept fixed (the “frozen past”) and TP(k) is obtained from a MC simulation of the “future” part of the chain whose TPs as yet have not been determined; when the process is completed the contribution of conformation i to the entropy is, Si∼-ln Πk TP(k). In a recent paper we studied polyglycine chains, modeled by the AMBER force field with constant bond lengths and bond angles (the rigid model). Decaglycine [(Gly)10] was studied in the helical, extended, and hairpin microstates, while (Gly)16 was treated only in the first two microstates. In this paper the samples are increased and restudied, (Gly)16 is also investigated in the hairpin microstate, and for (Gly)10 approximations are tested where only part of the future is considered for calculating the TPs. We calculate upper and lower bounds for F and demonstrate that like for fluids, F can be obtained from multiple reconstructions of a single conformation. We also test a more realistic model of (Gly)10 where the bond angles are allowed to move (the flexible model). Very accurate results for S and F are obtained which are compared to results obtained by the quasiharmonic approximation and the local states method. Thus, differences in entropy and free energy between the three microstates are obtained within errors of 0.1–0.3 kcal/mol. The HSMC method can be applied to a macromolecule with any degree of flexibility, ranging from local fluctuations to a random coil. The present results demonstrate that the difference in stability, ΔFmn=Fm-Fn between significantly different microstates m and n, can be obtained from two simulations only without the need to resort to thermodynamic integration. Our long-term goal is to extend this method to any peptide and apply it to a peptide immersed in a box with explicit water. © 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H2O and N2. As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configuration-interaction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, the structure of the electric double layer in the presence of (mostly) multivalent counterions is investigated through Monte Carlo simulations. Unlike previous similar studies addressing this matter, the difference of this study lies in the use of realistic hydrated ion sizes. Additionally, two different methods for calculating energies in the Metropolis algorithm are applied. The obtained results show that the conclusions of preceding papers must be revised. In particular, our simulations suggest the existence of certain ion layering effects at high surface charge densities, which are not accounted for by integral equation theories in the case of divalent counterions. These layering effects could justify why the overcharging phenomena due to ion size correlations are hardly observable in real colloids with divalent counterions. The existence of charge inversion due to ion size correlations (and without requiring specific counterion adsorption) is probed for trivalent counterions. Moreover, the hypernetted-chain/mean-spherical-approximation is tested under conditions not studied yet. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper's goal is to investigate if a gob-side entry retention technique combined with a surrounding rock support system is feasible in three soft coal seams. Field engineering confirmed the results of numerical simulation tests and similar simulation tests, which were conducted in accordance with the actual geological conditions of Zhaojiazhai Mine. The following conclusions are reached after studying the technology and process parameter of the gob-side entry retaining in three soft coal seams in conjunction with theoretical calculations: the coal seam of Zhaojiazhai Coal Mine's 12 209 working face is a part of the soft coal seam, and its loose circle is approximately 1.8 m. The expansion roadway size is 3.5 m, and the potential loose circle range is 1.32 m, according to the same model and numerical simulation test. The support scheme after the expansion of the road working face is determined to be the "anchor rod + anchor cable + hydraulic lifting shed" support method. Furthermore, this article suggests a building method for the reinforcement and enlargement of gob-side entry retaining in three-soft thick coal seam by theoretical analysis and numerical simulation. Roadway shotcrete, advance grouting, building of a large deformation anchor cable and continuous resistance, single column lifting shed, hydraulic lifting shed, and roadway enlargement in advance are all steps in the procedure. Furthermore, an analysis is conducted on the deformation features of the surrounding rock in gob-side entry retention. The study highlights the significance of actively supporting the surrounding rock, fortifying the roof support, guaranteeing the stiffness compatibility between the shoulder filling body and the surrounding rock on the roof, boosting the wall's strength and stability, and enhancing the roadway's stability. [ABSTRACT FROM AUTHOR]

The development of hydrodynamic instabilities has a significant impact on the operation of laser fusion systems. During radiation compression, the shells of a target are accelerated, resulting in the growth of perturbations at their interfaces. In this paper, we study the influence of density perturbations on the stability of the contact boundary during accelerated motion. The analysis is performed in a two-dimensional planar formulation using the linear approximation and assuming a weak spatial dependence on the temperature near the contact boundary. Due to the consideration of small time intervals, the phenomenon of heat conduction is not taken into account. The cases of acceleration of a medium described by the Mie–Grüneisen equation of state (EoS) into a vacuum and of acceleration of two contacting media, each described by the ideal plasma EoS, are considered. The time dependence of the amplitude of the boundary perturbation on time is obtained. The obtained values are in agreement with the results of numerical analysis. It is shown that the boundary curvature occurs independently of the acceleration direction. The theoretical results are compared with numerical results for laser fusion systems. [ABSTRACT FROM AUTHOR]

This paper investigated the differences for the hydraulic characteristics in a single fracture between using the Navier–Stokes (N–S) equation and Darcy's law, which would be benefit to understand the seepage mechanism in the fracture. A numerical model of the radial flow was established considering the aperture size and water injection flow rate. Some conclusion could be given. First, the Darcy's law only described the seepage characteristics when the flow rate was small when the flow rate and pressure response have a linear relationship. While the N–S equation could describe the linear and nonlinear seepage characteristics, resulting in a better model of the actual fracture seepage flow. Second, the aperture size had a limited influence on the water pressure and seepage velocity inside the fracture when the flow rate was small. It began to have a significant impact influence on the seepage characteristics inside the fracture with the aperture increased. Third, the flow–pressure response conformed to the Forchheimer equation in the fracture. The critical Reynold number would decrease from 1.2 to 0.0116 when fracture aperture decreased from 3 to 0.5 mm using the N–S equation. The degree of nonlinearity of the fluid flow increases with fracture roughness increasing. This work gave a guidance to the difference in the two seepage theories and correction for the result by Darcy law, which was widely used in the engineering calculation. [ABSTRACT FROM AUTHOR]

This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution are efficient indicators (early-warning signals) of the presence of a tipping point. Precise time-dependent transitions with concave or d-concave variation in the state variable giving rise to scenarios of rate-induced tracking are shown. They are classified depending on the internal dynamics of the set of bounded solutions. Based on this classification, some representative features of these models are investigated by means of a careful numerical analysis. [ABSTRACT FROM AUTHOR]

The potential-based multiphase lattice Boltzmann models are widely used because they root in thermodynamics and evade the interface tracking or integrating. This paper investigates several potential-based models with the common equations of state (EOS) by the theoretical analyses and numerical computations of the thermodynamic consistency and spurious currents. Surprisingly, the Shan–Chen model presents a superior accuracy compared to the Zhang–Chen models, although they are mathematically equivalent. We find that the great improvement is attributed to the square root form of the pseudopotential model, which significantly lessens the error of numerical gradient calculation. Inspired by the improvement, a general formula φ ′ = n − 1 φ 1 − n ∂ x (φ n) is introduced for calculating the gradient, and the coefficient n = 0.1 yields better results than n = 0.5 , which is equal to the pseudopotential model. This scheme is further applied to optimize the evaluation of the chemical potential model. The improved chemical potential model displays lower numerical errors in the liquid–gas transition region and smaller spurious currents near the curved phase interface than the pseudopotential model. Additionally, the improved model is confirmed to meet the Young–Laplace law and Galilean invariance. [ABSTRACT FROM AUTHOR]

In this paper, the process of encapsulating solid particle(s) into liquid droplets in a high-throughput flow-focusing microchannel is investigated numerically. Open source software is used, which computes fluid flow in an Eulerian framework and particle dynamics with a Lagrangian approach. Previous studies have demonstrated that if no action is taken, particles suspended in a liquid passing through a flow-focusing microchannel will be encapsulated at random. This is perhaps unsurprising, but in one such study, less than 35% of droplets were found to contain exactly one particle. The two aims of this study are (i) to explore the flow patterns arising in a microfluidic channel and (ii) to elucidate the effect of salient governing parameters on encapsulation efficiency (i.e., the fraction of droplets encapsulating one particle) by focusing on ordering the particles before reaching the droplet generation section. Following validation against experimental reference data, the capillary number is varied across the three droplet generation regimes: squeezing, dripping, and jetting. We demonstrate that under certain conditions, an encapsulation frequency of 100% can be achieved with ordered particles, but in most cases, this is significantly lower. We examine the flow field to help understand how this non-uniform distribution of particles occurs. Notably, we find the dripping to be the best option for particle encapsulation and in this case extend the study to explore the effect of junction angle, finding that an angle of 60 ° is the most favorable. Improved understanding of the encapsulation process derived from this study can help to improve design of high-throughput droplet generation microfluidic systems. [ABSTRACT FROM AUTHOR]

The weld morphology of aluminum alloy oscillating laser welding has an important influence on the quality of welded joints. To understand the formation process of the weld morphology, the three-dimensional numerical simulation model and energy distribution model for circular shaped oscillating laser welding of 6061 aluminum alloy are developed in this paper to analyze the characteristics of weld morphology and the effect of the energy distribution on the weld width. The cross section of the weld and the energy distribution on the processing surface are obtained under the conditions of different oscillation frequencies. It is found that the left width of the weld is larger than the right width of the weld and the energy density on the left side of the weld is more concentrated than that on the right side of the weld. With the oscillation frequency increases, the weld width and peak of energy density decrease. Furthermore, the formation mechanism of the difference in weld width is revealed based on the energy distribution law of the oscillating laser welding process, which is of great significance for improving the quality of aluminum alloy oscillating laser welding. [ABSTRACT FROM AUTHOR]

This study explores the effects of wear and shaft-shape error defects on the tribo-dynamic responses of water-lubricated bearings under nonlinear propeller disturbance using a numerical model. The model proposed in this paper is verified by comparing the results from experiments and simulations in published studies. Numerical simulation studies reveal the effects of nonlinear propeller disturbance on the dynamic behavior and lubrication performance, such as hydrodynamic force, contact force, and journal trajectory, of the water-lubricated bearings with wear and shaft-shape errors. In addition, the effects of the critical factors for wear and shaft-shape errors, including wear depth, deviation angle, magnitude, and waviness order, on the tribo-dynamic responses of water-lubricated bearings are identified. The results of numerical spectrum analyses show that the nonlinear disturbance significantly affects the dynamic behavior (shown as the fluctuation range of the journal trajectory increases), and reasonable wear parameters can improve the lubrication performance of the water-lubricated bearing. Moreover, the effects of shaft-shape errors on the transient hydrodynamic force, contact force, film thickness, pressure, and journal trajectory are greater than that of wear. [ABSTRACT FROM AUTHOR]

The shear stress of a power-law fluid is exponentially related to the shear rate. Thus, unlike for Newtonian fluids, the Reynolds lubrication equation in the simplified differential form is nonlinear and cannot be solved analytically. This paper investigates the flow of a power-law fluid in comma-roll coating and planar blade coating. We establish an intermediate function F(x), defined as the ratio of the shear force τ(X,0) in the X-direction on the edge of the blade coater to the pressure gradient G(x). Using various flow patterns, the signs of F and G are determined, and expressions for ∂U/∂Y are obtained in terms of F and G. Combined with the velocity boundary condition, ∂U/∂Y is integrated and the explicit relation between the coating thickness H∞ and F is established. The pressure gradient is also obtained. Finally, dP/dX is integrated and combined with the inlet and outlet pressure conditions, and the bisection method is used to determine H∞. The coating thickness and pressure given by the proposed method for both comma-roll coating and flat blade coating are highly consistent with the exact results for n = 1, 1/2, and 1/3 calculated by Dien and Elrod's method. We deduce that the limiting thickness of comma-roll coating is (n + 1)/(2n + 1), and the limit of the pressure gradient is − [ n + 1 / n ] n . Moreover, we construct a phase diagram of the relationship between the shape parameter k of the blade coater and the power-law exponent n. These results have instructive significance and application value for guiding coating operations and applicator design. [ABSTRACT FROM AUTHOR]

A numerical analysis based on detached eddy simulations is conducted to investigate vortex dynamics of a pre-swirl pumpjet propulsor (PJP) in oblique inflow. In this paper, the working conditions of PJP operating in axisymmetric flow and drift with two angles (10° and 20°) are considered. The effects of incidence α and propeller loading on the wake dynamics of PJP as well as the mechanism leading to its destabilization are discussed. The results show that high hydrodynamic efficiency loss is found for PJP operating in drift. In addition, a different "secondary vortex structure" caused by the duct is found for PJP in both axisymmetric and oblique flow conditions. The instability mechanism of tip vortices shows obvious asymmetry. On the leeward side, it is dominated by the interaction caused by the duct-induced vortex, while it is dominated by the secondary vortices on the windward side. Furthermore, the fluctuation frequency of tip vortex for PJP is characterized by the rotor blade-passing frequency and the stator blade-passing frequency. In addition, the hub rotation frequency is important in oblique flow conditions. [ABSTRACT FROM AUTHOR]

The commercialization of GaN-based Schottky barrier diodes in middle- and high- voltage applications still faces many challenges, in which the lack of an effective selective area p-type doping method is one of the main obstacles. This paper proposes novel vertical GaN-based Schottky diodes with trench MIS structure and an embedded p-GaN protection layer (junction-trench MIS barrier Schottky diodes, J-TMBS). The trench structure and lateral p-n junctions can be achieved by selectively etching the very thin p-GaN and then regrowing n-GaN. Therefore, the fabrication technology avoids the selective area p-type doping process, and the dry etching damage and poor sidewall regrowth interface issue, which are serious in GaN Merged pn/Schottky (MPS) diodes, can also be alleviated for the proposed J-TMBS. Compared with the optimized GaN trench MIS barrier Schottky (TMBS) diodes, the surge current capability and dielectric reliability of the proposed J-TMBS are significantly improved (the electric field of the dielectric layer and maximum lattice temperature under the surge test can be reduced by 448% and 202%, respectively). In addition, the specific on-resistance (Ron,sp) and breakdown voltage remain basically unchanged compared with TMBS. Compared with the optimized GaN MPS diodes, the proposed structure improves the specific on-resistance by 17.2% benefiting from the reduced area of the JFET region without degrading the reverse I–V characteristics and surge current capability. The proposed J-TMBS exhibits potential in practical high voltage (>600 V) application of GaN Schottky power diodes. [ABSTRACT FROM AUTHOR]