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We investigate the transition between the overdamped and underdamped regimes in Langevin dynamics simulations with significant conservative forces by comparing direct simulations with theories of Kramers, Mel'nikov and Meshkov (MM), and Larson and Lightfoot (LL). The need for clarification is made evident by noting that the most commonly cited theories of Kramers and MM do not apply in the overdamped limit to escape times from a Lennard-Jones (LJ) potential, because Kramers and MM do not account for the flatness of the LJ potential at the escape position, which allows for a region of nearly free Brownian diffusion near the escape position. While the little-known LL approach does consider an LJ potential, it does not properly consider the underdamped regime, and so a complete description is only achieved by combining the LL and MM results into a single general equation, which we validate for the first time by an explicit comparison with Langevin simulations.

Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency, but with the caveat that they were designed for tensor contractions (matrix-matrix multiplications) using only low-precision floating point operations. In spite of this, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born-Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on the tensor cores of a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born-Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics., 20 pages, 9 figures

The principle of least action is a variational principle that states an object will always take the path of least action as compared to any other conceivable path. This principle can be used to derive the equations of motion of many systems, and therefore provides a unifying equation that has been applied in many fields of physics and mathematics. Hamilton’s formulation of the principle of least action typically only accounts for conservative forces, but can be reformulated to include non-conservative forces such as friction by using the approach suggested by Wang and co-workers (Lin and Wang, 2014; Wang, 2015). However, it turns out that this modified action is dependent upon the nature and amount of damping in the system and the optimality argument fails to hold for sufficiently large values of the damping coefficient. In this paper, we specifically investigate the modified action principle for the cases of a linearly and cubically damped, nonlinear pendulum.

We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system

In this paper, a discretization method for incorporating nonconservative forces in a class of geometric numerical integrators known as variational integrators and Galerkin variational propagators i...

In this paper, we justify of the low Mach number limit of the steady irrotational Euler flow through infinite multidimensional largely-open nozzles. Firstly, the existence and uniqueness of the incompressible flow are proved. Then, the uniform estimates on the compressibility parameter e, which is singular for the flows, are established via a variational approach based on the compressible-incompressible difference functions. The limit is in the Holder space and is unique. Moreover, the convergence rate is of order e 2 including the pressure. And, for the compressible case, the extra force influences the asymptotic behaver to the open end, while the effect vanishes in the limiting process from compressible flows to the incompressible ones. Also, for the compressible flows with general conservative forces, the well-posedness of subsonic solution are given, which leads to the existence of subsonic-sonic limit solutions.

Observed temperatures of transiently accreting neutron stars in the quiescent state are generally believed to be supported by deep crustal heating, associated with non-equilibrium exothermic reactions in the crust. Traditionally, these reactions are studied by considering nuclear evolution governed by compression of the accreted matter. Here we show that this approach has a basic weakness, that is that in some regions of the inner crust the conservative forces, applied for matter components (nuclei and neutrons), are not in mechanical equilibrium. In principle the force balance can be restored by dissipative forces, however the required diffusion fluxes are of the same order as total baryon flux at Eddington accretion. We argue that redistribution of neutrons in the inner crust should be involved in realistic model of accreted crust., Comment: Accepted for publication in MNRAS:Letters, 6 pages, 1 figure

This paper deals with the evaluation of eigenvalues of a linear damped elastic two-degrees-of-freedom system under a non- onservative loading. As a physical interpretation of a proposed mathematical model, a simplified disk brake model is considered. A spectral analysis is performed to predict an eigenvalues bifurcation, known as the Krein collision, leading to double eigenvalues, one of them having a positive real part causing a vibration instability of the mechanical systems. This defective behaviour of eigenvalues is studied with respect to a magnitude of non-conservative Coulomb friction force, through the variation of the friction coefficient. The influence of a proportional versus general damping on the system stability is further analysed. The generalized non-symmetric eigenvalue problem calculation is employed for spectral analyses, while a modal decomposition is performed to obtain a time-domain response of the system. The analyses are compared with an experiment.

Background: The impression given in the literature was that the net interaction potential energy, V is the difference between columbic-columbic and total weaker interaction energies. It is proposed however, that in aqueous solution all particles with full formal charges and partial charge (dipoles) contribute to the total interaction as applicable to conservative field but not to the exclusion of hydrophobic interaction if applicable. Objectives: The objectives are 1) To theoretically elucidate the basis of the intermolecular interaction, 2) To show that effectiveness of an osmolyte which may include inorganic ion to force macromolecular, (un)folding, the m-value, is a function of the implicit mobility (or translational velocity) of the cosolute, 3) To link the m-value to conservative forces (or potential energies, V) and 4) Quantitate the values of V. Methods: A major theoretical investigation and experimentation using Bernfeld method. Results and Discussion: There were higher velocities of amylolysis with salt than without it in the presence of ethanol. The magnitude of the calculated V and energy equivalent of the entropic term were higher with higher concentration of ethanol unlike was the case with graphically determined values which were generally higher in magnitude than calculated values. The values of the calculated V and intermolecular distance were respectively higher in magnitude and longer with higher concentration of the salt. Conclusion: The attractive interaction between a macromolecule and a cationic counter ion is due to long ranged ion-ion interaction which ultimately enhances the effect of short ranged interaction. Higher salt concentration promotes long ranged interaction. The translational velocity of the solvent and cosolute has a role in the quantification of intermolecular distance. A mathematical relationship exists between m-value and - V (or 2 K.E.). The values of V can be calculated based on the derived equations.

A new method is introduced for the simulation of multiple impacts in granular media using the Kuwabara-Kono (KK) contact model, a nonsmooth (not Lipschitz continuous) extension of Hertz contact that accounts for viscoelastic damping. We use the technique of modified equations to construct time-discretizations of the nondissipative Hertz law matching numerical dissipation with KK dissipation at different consistency orders. This allows us to simulate dissipative impacts with good accuracy without including the nonsmooth KK viscoelastic component in the contact force. This tailored numerical dissipation is developed in a general framework, for Newtonian dynamical systems subject to dissipative forces proportional to the time-derivative of conservative forces. Numerical tests are performed for the simulation of impacts in Newton’s cradle and on alignments of alternating large and small balls. Resulting wave phenomena (oscillator synchronization, propagation of dissipative solitary waves, oscillatory tails) are accurately captured by implicit schemes with tailored numerical dissipation, even for relatively large time steps.

In general, mechanical energy monotonically decreases in a physically consistent system, constructed with conservative force and dissipative force. This feature is important in designing a particle method, which is a discrete system approximating continuum fluid with particles. When the discretized system can be fit into a framework of analytical mechanics, it will be a physically consistent system which prevents instability like particle scattering along with unphysical mechanical energy increase. This is the case also in incompressible particle methods. However, most incompressible particle methods do not satisfy the physical consistency, and they need empirical relaxations to suppress the system instability due to the unphysical energy behavior. In this study, a new incompressible particle method with the physical consistency, moving particle full-implicit (MPFI) method, is developed, where the discretized interaction forces are related to an analytical mechanical framework for the systems with dissipation. Moreover, a new pressure evaluation technique based on the virial theorem is proposed for the system. Using the MPFI method, static pressure, droplet extension, standing wave and dam break calculations were conducted. The capability to predict pressure and motion of incompressible free surface flow was presented, and energy dissipation property depending on the particle size and time step width was studied through the calculations.

We address the dynamics of near-integrable Hamiltonian systems with 3 degrees of freedom in extended vicinities of unperturbed resonant invariant Liouville tori. The main attention is paid to the case where the unperturbed torus satisfies two independent resonance conditions. In this case the average dynamics is 4-dimensional, reduced to a generalised motion under a conservative force on the 2-torus and is generically non-integrable. Methods of differential topology are applied to full description of equilibrium states and phase foliations of the average system. The results are illustrated by a simple model combining the non-degeneracy and non-integrability of the isoenergetically reduced system.

In the context of multibody dissipative particle dynamics (MDPD), a closed-form mathematical expression is developed to analytically model a complex wall. MDPD is a modified version of dissipative particle dynamics (DPD), a particle-based mesh free method. There have been several attempts to analytically model the influence of solid walls and non-periodic boundary conditions in the DPD approach. However, there is a limited number of studies for these boundary conditions associated with MDPD that capture static and dynamic fluid-structure interactions through direct modeling of fluid-solid particle interactions. This work, for the first time, employs an analytical model (integral approach) for the solid wall boundary condition in MDPD that brings substantial gain in computational efficiency and thus expands the scope of its applicability to curved or complex walls. Furthermore, a modified model of conservative force is used in the current investigation. The model is first normalized to address the discrepancies in wetting that exist in the present literature and is then validated through several benchmark studies and test cases, such as a Wenzel model. Moreover, comparisons between both the fully numerical and the semi-analytical (integral force model) approaches are drawn. Time efficiency, accuracy, density fluctuation in vicinity of solid wall, and limitations of the proposed model are thoroughly discussed.

Like any physical quantity whose symmetry properties mimic its source, the optical force acting on a neutral spherical particle has a symmetry that mimics the incident field. The optical force cons...

The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the effects of the Winkler coefficient, Pasternak coefficient and damping coefficient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary differential equations with variable coefficients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verified through two numerical examples. The influences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with different taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.