Arbitrary Force Field Research Articles

Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator.

The nonequilibrium Fokker-Planck dynamics in an arbitrary force field f[over ⃗](x[over ⃗]) in dimension N is revisited via the correspondence with the non-Hermitian quantum mechanics in a real scalar potential V(x[over ⃗]) and in a purely imaginary vector potential [-iA[over ⃗](x[over ⃗])] of real amplitude A[over ⃗](x[over ⃗]). The relevant parameters of irreversibility are then the N(N-1)/2 magnetic matrix elements B_{nm}(x[over ⃗])=-B_{mn}(x[over ⃗])=∂_{n}A_{m}(x[over ⃗])-∂_{m}A_{n}(x[over ⃗]), while it is enlightening to explore the corresponding gauge transformations of the vector potential A[over ⃗](x[over ⃗]). This quantum interpretation is even more fruitful to study the statistics of all the time-additive observables of the stochastic trajectories, since their generating functions correspond to the same quantum problem with additional scalar and/or vector potentials. Our main conclusion is that the analysis of their large deviations properties and the construction of the corresponding Doob conditioned processes can be drastically simplified via the choice of an appropriate gauge for each purpose. This general framework is then applied to the special time-additive observables of Ornstein-Uhlenbeck trajectories in dimension N, whose generating functions correspond to quantum propagators involving quadratic scalar potentials and linear vector potentials, i.e., to quantum harmonic oscillators in constant magnetic matrices. As simple illustrative example, we finally focus on the Brownian gyrator in dimension N=2 to compute the large deviations properties of the entropy production of its stochastic trajectories and to construct the corresponding conditioned processes having a given value of the entropy production per unit time.

Simulation of dense random packings of ellipsoidal bodies by mechanical analogy

The statistical properties of dense random packings of ellipsoidal bodies in cylindrical vessels created under the effect of the gravity force are investigated by the numerical method developed from the equations of mechanics of a rigid body. The body-to-body and body-to-wall interaction is described by elastic forces. It has been found that the influence of the gravity force in the presence of walls specifies the statistically meaningful anisotropy of the orientation of ellipsoids. According to the method of the formation of a packing and the spatial separation of bodies by size can be found; this causes a local narrowing of the size spectrum. The method is naturally generalized by including friction forces, arbitrary force fields, and walls of an arbitrary shape.

The nonextensive parameter for the rotating astrophysical systems with power-law distributions

We study the nonextensive parameter for the rotating astrophysical systems with power-law distributions, including both the rotating self-gravitating system and the rotating space plasma. We extend the equation of the nonextensive parameter to a complex system with arbitrary force field , and derive a general equation of the q-parameter, most generally including both the rotating self-gravitating systems and the rotating space plasmas. At the same time, we reproduce the κ-distribution in space plasmas and obtain equations of the κ-parameter. We show that the q-parameter is related not only to the temperature gradient, the gravitational force and the electromagnetic force, but also to the inertial centrifugal force and Coriolis force. Thus, the rotation introduces a significant effect on the nonextensivity in the systems. Several examples are given to illustrate the nonextensive effect introduced by the rotation.

Non-Markovian Brownian motion in a magnetic field and time-dependent force fields

Abstract This work focuses on the derivation of the velocity and phase-space generalized Fokker–Planck equations for a Brownian charged particle embedded in a memory thermal bath and under the action of force fields: a constant magnetic field and arbitrary time-dependent force fields. To achieve the aforementioned goal we use a Gaussian but non-Markovian generalized Langevin equation with an arbitrary friction memory kernel. In a similar way, the generalized diffusion equation in the zero inertia limit is also derived. Additionally we show, in the absence of the time-dependent external forces, that, if the fluctuation–dissipation relation of the second kind is valid, then the generalized Langevin dynamics associated with the charged particle reaches a stationary state in the large-time limit. The consistency of our theoretical results is also verified when they are compared with those derived in the absence of the force fields and in the Markovian case.

Prediction of Stereochemistry using Q2MM.

ConspectusThe standard method of screening ligands for selectivity in asymmetric, transition metal-catalyzed reactions requires experimental testing of hundreds of ligands from ligand libraries. This “trial and error” process is costly in terms of time as well as resources and, in general, is scientifically and intellectually unsatisfying as it reveals little about the underlying mechanism behind the selectivity. The accurate computational prediction of stereoselectivity in enantioselective catalysis requires adequate conformational sampling of the selectivity-determining transition state but has to be fast enough to compete with experimental screening techniques to be useful for the synthetic chemist. Although electronic structure calculations are accurate and general, they are too slow to allow for sampling or fast screening of ligand libraries. The combined requirements can be fulfilled by using appropriately fitted transition state force fields (TSFFs) that represent the transition state as a minimum and allow fast conformational sampling using Monte Carlo.Quantum-guided molecular mechanics (Q2MM) is an automated force field parametrization method that generates accurate, reaction-specific TSFFs by fitting the functional form of an arbitrary force field using only electronic structure calculations by minimization of an objective function. A key feature that distinguishes the Q2MM method from many other automated parametrization procedures is the use of the Hessian matrix in addition to geometric parameters and relative energies. This alleviates the known problems of overfitting of TSFFs. After validation of the TSFF by comparison to electronic structure results for a test set and available experimental data, the stereoselectivity of a reaction can be calculated by summation over the Boltzman-averaged relative energies of the conformations leading to the different stereoisomers.The Q2MM method has been applied successfully to perform virtual ligand screens on a range of transition metal-catalyzed reactions that are important from both an industrial and an academic perspective. In this Account, we provide an overview of the continued improvement of the prediction of stereochemistry using Q2MM-derived TSFFs using four examples from different stages of development: (i) Pd-catalyzed allylation, (ii) OsO4-catalyzed asymmetric dihydroxylation (AD) of alkenes, (iii) Rh-catalyzed hydrogenation of enamides, and (iv) Ru-catalyzed hydrogenation of ketones. In the current form, correlation coefficients of 0.8–0.9 between calculated and experimental ee values are typical for a wide range of substrate–ligand combinations, and suitable ligands can be predicted for a given substrate with ∼80% accuracy. Although the generation of a TSFF requires an initial effort and will therefore be most useful for widely used reactions that require frequent screening campaigns, the method allows for a rapid virtual screen of large ligand libraries to focus experimental efforts on the most promising substrate–ligand combinations.

Global well-posedness of strong solutions to the magnetohydrodynamic equations of compressible flows

This paper is concerned with the global well-posedness of strong solutions to the compressible MHD equations in a bounded domain Ω⊂R3. We first establish the local existence and uniqueness of strong solutions with arbitrary initial data and external force field. Based on the local existence result and some a priori estimates, the global existence and large time behavior of strong solutions are proved, under the assumptions that the initial data and external force field are small enough. Furthermore, the existence of the time periodic solution is also obtained when the external force field is time periodic.

Kinect the dots: 3D control of optical tweezers

Holographically generated optical traps confine micron- and sub-micron sized particles close to the center of focused light beams. They also provide a way of trapping multiple particles and moving them in three dimensions. However, in many systems the user interface is not always advantageous or intuitive especially for collaborative work and when depth information is required. We discuss and evaluate a set of multi-beam optical tweezers that utilize off the shelf gaming technology to facilitate user interaction. We use the Microsoft Kinect sensor bar as a way of getting the user input required to generate arbitrary optical force fields and control optically trapped particles. We demonstrate that the system can also be used for dynamic light control.

Erratum to: Brachistochrone with limited reaction of constraint in an arbitrary force field

Erratum to: Brachistochrone with limited reaction of constraint in an arbitrary force field

Brachistochrone with limited reaction of constraint in an arbitrary force field

The paper considers brachistochronic motion of a particle along a curve y=y(x) in an arbitrary force field in the vertical plane of Cartesian coordinate system. The curve is treated as a bilateral or unilateral constraint that can be smooth or rough. The projection of the reaction force of the curve onto the normal to the curve is confined to the fixed limits. A control variable u is given as the second derivative of the function y(x) relative to the horizontal coordinate x of the particle, i.e., u=d2y/dx2. Applying Pontryagin’s maximum principle and singular optimal control theory, the problem is reduced to numerical solving of the corresponding two-point boundary value problem. The procedure based on the shooting method is used to solve the boundary value problem. Two examples with friction forces of the viscous friction and Coulomb friction type have been solved.

A rigid-body Newtonian propagation scheme based on instantaneous decomposition into rotation and translation blocks

The rotation and translation block (RTB) method of Durand et al. [Biopolymers 34, 759 (1994)] and Tama et al. [Proteins 41, 1 (2000)] provides an appealing way to calculate low-frequency normal modes of large biomolecules by restricting the space of motions to exclude internal motions of preselected rigid fragments within the molecule. These fragments are modeled essentially as rigid bodies and the need to calculate high-frequency relative motions of the atoms that form them is obviated in a natural way. Here we extend the RTB approach into a method for computing the classical (Newtonian) dynamics of a biomolecule, or any large molecule, with effective rigid-body constraints applied to a prechosen set of internal molecular fragments. This method, to be termed RTB dynamics, is easy to implement, conserves the total energy of the system, does not require the construction of the matrix of second spatial derivatives of the potential-energy function (Hessian matrix), and can be used to compute the classical dynamics of a system moving in an arbitrary anharmonic force field. An elementary numerical application to signal propagation in the small membrane-bound polypeptide gramicidin-A is presented for illustration purposes.

Plane poloidal-toroidal decomposition of doubly periodic vector fields. Part 2. The Stokes equations

AbstractWe continue our study of the adaptation from spherical to doubly periodic slot domains of the poloidal-toroidal representation of vector fields. Building on the successful construction of an orthogonal quinquepartite decomposition of doubly periodic vector fields of arbitrary divergence with integral representations for the projections of known vector fields and equivalent scalar representations for unknown vector fields (Part 1), we now present a decomposition of vector field equations into an equivalent set of scalar field equations. The Stokes equations for slow viscous incompressible fluid flow in an arbitrary force field are treated as an example, and for them the application of the decomposition uncouples the conservation of momentum equation from the conservation of mass constraint. The resulting scalar equations are then solved by elementary methods. The extension to generalised Stokes equations resulting from the application of various time discretisation schemes to the Navier-Stokes equations is also solved.

Control of Nanoparticles with Arbitrary Two-Dimensional Force Fields

An anti-Brownian electrophoretic trap is used to create arbitrary two-dimensional force fields for individual nanoscale objects in solution. The trap couples fluorescence microscopy with digital particle tracking and real-time feedback to generate a position-dependent electrophoretic force on a single nanoparticle. The force may vary over nanometer distances and millisecond times and need not be the gradient of a potential. As illustrations of this technique, I study Brownian motion in harmonic, power-law, and double-well potentials.

Finite burn maneuver modeling for a generalized spacecraft trajectory design and optimization system.

The modeling, design, and optimization of finite burn maneuvers for a generalized trajectory design and optimization system is presented. A generalized trajectory design and optimization system is a system that uses a single unified framework that facilitates the modeling and optimization of complex spacecraft trajectories that may operate in complex gravitational force fields, use multiple propulsion systems, and involve multiple spacecraft. The modeling and optimization issues associated with the use of controlled engine burn maneuvers of finite thrust magnitude and duration are presented in the context of designing and optimizing a wide class of finite thrust trajectories. Optimal control theory is used examine the optimization of these maneuvers in arbitrary force fields that are generally position, velocity, mass, and are time dependent. The associated numerical methods used to obtain these solutions involve either, the solution to a system of nonlinear equations, an explicit parameter optimization method, or a hybrid parameter optimization that combines certain aspects of both. The theoretical and numerical methods presented here have been implemented in copernicus, a prototype trajectory design and optimization system under development at the University of Texas at Austin.

Measuring viscous dissipative interactions in dynamic force microscopy

The periodic motion of a harmonic pendulum in an arbitrary force field including viscous damping is studied as it pertains to dynamic force microscopy. It is shown that the damping constant as a function of tip–sample distance and thus the dissipative force can be obtained unambiguously by measuring the driving-force amplitude versus displacement of the force sensor. This methodology provides the basis for quantitative force spectroscopy of dissipative interactions.

Interaction sensing in dynamic force microscopy

A first-order perturbative theory of the motion of a harmonic oscillator interacting with a weak arbitrary force field is presented, as it pertains to dynamic force microscopy. In essence the theory corresponds to a Born approximation for the scattering of standing waves trapped in a perturbed parabolic potential. In particular, it is shown that the scattering amplitudes are related to corresponding moments, involving Chebyshev polynomials and associated metrics of the conservative interaction force, and of a generalized friction coefficient accounting for irreversible interactions. Implications for dynamic force microscopy are discussed.

Fluid Mechanics Model and Analysis for the Photofabrication of Surface Relief Grating on Azo Polymers

ABSTRACTThe mass transporting properties of the surface relief grating (SRG) photofabrication on azobenzene polymer films is discussed precisely using an existing fluid mechanics model. Formulation for the SRG inscription rate is derived analytically from Navier-Stokes equation. In consequence, the dependence of inscription rate of the SRG on the experimental and geometrical parameters was explained very well by the model. The photoinduced surface deformation with an onedimensional Gaussian laser beam was also carried out in order to establish the validity and the generality of our fluid mechanics model. The experimentally obtained surface deformation profile is well reproduced by the theoretical model generalized for arbitrary force field profile.

Anomalous transport in external fields: Continuous time random walks and fractional diffusion equations extended

The continuous time random walk (CTRW) in a homogeneous velocity field and in arbitrary force fields is studied. Within the extended CTRW scheme, anomalous transport properties due to long-tailed waiting time or jump length distributions are consistently introduced. The connections with generalised diffusion equations in a potential field are discussed, these equations being of fractional order. In particular, the problems of a constant and a Hookean (linear) force, i.e., of a linear and a parabolic potential, are worked out.

Geometrical relationship between the classical and quantum descriptions of arbitrary force interactions

The paper is a continuation of a series papers by the author in which it is shown that the equations of contemporary quantum theory (the Klein-Gordon equation and the Dirac integral equation) can be interpreted as conditions of harmonicity of linear form in the manifoldsV4. In this paper, geometrization of classical and quantum interactions of a physical object is performed for the case of an arbitrary external force field in the manifoldkV4. This manifold is constructed on the same set of surfaces as the manifoldsV4. The equation representing conditions of harmonicity of linear form inkV4 is derived and is analogous to the KleinGordon equation.

Stress state of a transversely isotropic medium with an anisotropic inclusion. Arbitrary linear force field at infinity

Stress state of a transversely isotropic medium with an anisotropic inclusion. Arbitrary linear force field at infinity

A Singular Perturbation Approach to Non-Markovian Escape Rate Problems

We employ singular perturbation methods to examine the generalized Langevin equation which describes the dynamics of a Brownian particle in an arbitrary potential force field, acted on by a fluctuating force describing collisions between the Brownian particle and lighter particles comprising a thermal bath. In contrast to models in which the collisions occur instantaneously, and the dynamics are modeled by a Langevin stochastic equation, we consider the situation in which the collisions do not occur instantaneously, so that the process is no longer a Markov process and the generalized Langevin equation must be employed. We compute expressions for the mean exit time of the Brownian particle from the potential well in which it is confined.