Disparate Time Scales Research Articles

Recent hybrids recapitulate ancient hybrid outcomes

Genomic outcomes of hybridization depend on selection and recombination in hybrids. Whether these processes have similar effects on hybrid genome composition in contemporary hybrid zones versus ancient hybrid lineages is unknown. Here we show that patterns of introgression in a contemporary hybrid zone in Lycaeides butterflies predict patterns of ancestry in geographically adjacent, older hybrid populations. We find a particularly striking lack of ancestry from one of the hybridizing taxa, Lycaeides melissa, on the Z chromosome in both the old and contemporary hybrids. The same pattern of reduced L. melissa ancestry on the Z chromosome is seen in two other ancient hybrid lineages. More generally, we find that patterns of ancestry in old or ancient hybrids are remarkably predictable from contemporary hybrids, which suggests selection and recombination affect hybrid genomes in a similar way across disparate time scales and during distinct stages of speciation and species breakdown.

Quantification of Surface Receptor - Actin Cortex Interplay via Multiplexed Two-Color Imaging

The dynamic organization of receptors in the plasma membrane is crucial for ligand binding and downstream signaling. The actin cortex plays an important role in regulating cell surface receptor organization. However its role has been almost exclusively deduced via cell-wide actin perturbation experiments, which suffer from various caveats, such as lack of information about cortex dynamics and potential nonspecific effects. We have developed a quantitative imaging and computational analysis framework to derive perturbation free, explicit relationships between cell surface receptor organization and actin cortex dynamics. We use the receptor CD36 in endothelial cells as a model system, because its organization and signaling on the endothelial cell surface are thought to depend on actin. Briefly, to monitor both CD36 and actin cortex behavior at the same time in the same cell, we perform TIRF-based simultaneous single-molecule imaging of CD36 and fluorescent speckle microscopy (FSM) of actin, in live endothelial cells. Because of the disparate timescales of their dynamics, we image each at its relevant frame rate. Next, CD36 molecules are tracked to characterize their movement and clustering state to yield information about their dynamic organization, while neighboring actin behavior is characterized in the form of speckle density, movement and lifetime (reflecting actin turnover kinetics). Machine learning approaches are then applied to this multidimensional dataset to derive relationships between CD36 and actin cortex properties. Using this framework, we indeed find interdependence between CD36 and actin cortex properties. Interestingly, these inter-relationships vary based on subcellular location (cell side vs tip) and cell edge activity (actively ruffling vs quiescent). These observations highlight further the need for direct observation of these inter-relationships, instead of indirect deduction based on cell-wide perturbations that alter cell morphology and activity, leading to potentially difficult-to-interpret results.

Multi-scale dynamics of atmospheric-pressure discharges ignited over liquid electrodes

A multiphase computational model of atmospheric-pressure gas discharges ignited over liquid electrodes is developed. The model takes into account both the liquid electrode motion under applied electric fields and plasma generation in the gas phase. The influence of the applied voltage and liquid properties (density, viscosity, and surface tension) on the liquid surface deformation is analyzed. It is shown that the shape of dynamic cones formed on the liquid surface differs from the static Taylor's cones. The influence of the liquid surface protrusions on gas breakdown dynamics is demonstrated. It is shown that the breakdown develops in two stages: first, a fast ionization wave propagates from the cathode to the anode, and then the cathode sheath collapses due to secondary electron emission from the liquid surface. It is shown that dynamics of the multiphase system containing gas, plasma, and liquid states is characterized by three disparate time scales: the fast electron time scale, the intermediate ion time scale, and the slow liquid dynamics time scale.

Turning Drops into Bubbles: Cavitation by Vapor Diffusion through Elastic Networks.

Some members of the vegetal kingdom can achieve surprisingly fast movements making use of a clever combination of evaporation, elasticity, and cavitation. In this process, enthalpic energy is transformed into elastic energy and suddenly released in a cavitation event which produces kinetic energy. Here, we study this unusual energy transformation by a model system: A droplet in an elastic medium shrinks slowly by diffusion and eventually transforms into a bubble by a rapid cavitation event. The experiments reveal the cavity dynamics over the extremely disparate timescales of the process, spanning 9 orders of magnitude. We model the initial shrinkage as a classical diffusive process, while the sudden bubble growth and oscillations are described using an inertial-(visco)elastic model, in excellent agreement with the experiments. Such a model system could serve as a new paradigm for motile synthetic materials.

Reduced-order models for piezoelectric systems

Large-scale analysis of transducer arrays usually requires detailed, high-resolution modeling to represent the coupling effects of piezoelectric, elastic, and fluid media. However, reduced-order models, in the form of low-DOF lumped-parameter engineering models remain essential for system design. Here, we show how to bridge the gap between these model classes by deriving a simple means to compute the modes of an arbitrary piezoelectric system. Our approach exploits the intrinsic disparity in time scale between the electric and elastic fields to reduce the coupled problem into an augmented, elastic-only, system of equations. This system is shown to have the same mathematical characteristics as the elastic system, insofar as no new singularities appear. The piezoelectric-elastic modal system is fully general, and compatible with large-scale finite element representations of complex transducer designs. Numerical examples are shown to demonstrate the efficiency and practicality of the modal analysis.

The physics of cell-size regulation across timescales

The size of a cell is determined by a combination of synthesis, self-assembly, incoming matter and the balance of mechanical forces. Such processes operate at the single-cell level, but they are deeply interconnected with cell-cycle progression, resulting in a stable average cell size at the population level. Here, we examine this phenomenon by reviewing the physics of growth processes that operate at vastly different timescales, but result in the controlled production of daughter cells that are close copies of their mothers. We first review the regulatory mechanisms of size at short timescales, focusing on the contribution of fundamental physical forces. We then discuss the multiple relevant regulation processes operating on the timescale of the cell cycle. Finally, we look at how these processes interact: one of the most important challenges to date involves bridging the gap between timescales, connecting the physics of cell growth and the biology of cell-cycle progression. Cell size is regulated by processes ranging from rapid fluctuations to slower growth and division. Limited dialogue between communities studying these disparate timescales has hindered our understanding of size control—a gap bridged by this Review.

Closely coupled fluid-solid interface method with moving-average for LES based conjugate heat transfer solution

Fluid–solid coupled Conjugate Heat Transfer (CHT) simulations are relevant to many practical problems. Most existing interfacing methods have been developed for Reynolds averaged Navier-Stokes solvers. For high fidelity turbulence scale-resolved flow solvers however, the CHT interface methods face significant challenges arisen from a wide frequency spectrum of unsteady disturbances to be dealt with, compounded by the huge time scale disparity between fluid and solid domains.In this paper, a closely coupled non-partitioned (monolithic) CHT method is presented. The main issues of interest are the prohibitive time costs of direct time domain CHT methods and an extra mesh dependency in the solid domain when resolving high frequency turbulence disturbances. Based on a temporal Fourier spectral framework, the present CHT interface method entails a moving-average for the time-mean flow and a discrete Fourier transform on-the-fly at each time step. Taking advantage of a semi-analytical transfer function and harmonic balancing for the CHT interface, we can achieve solving the solid domain completely in its own time step (3–5 orders of magnitude larger than that of the fluid domain). The present interface method can effectively circumvent aliasing errors and extra solid domain mesh-dependence encountered by other time-domain coupling methods when applied to turbulence scale-resolved CHT solutions. Illustrative stability analyses also show that the numerical stability of the present CHT interface should require no more stringent conditions than that in either fluid or solid domain. The computational results and analyses highlight the advantages of the present methodology in terms of both the computational efficiency and accuracy, in comparison with a conventional directly coupled interface method. Furthermore, a case study aided by a simple interface response analysis highlights much augmented wall temperature fluctuations and higher sensitivity to the interface treatment when a low conductivity protection layer (Thermal Barrier Coating, TBC) is added. The present study underlines the relevance of accounting for fluid disturbances over a range of frequencies in an effective and accurate CHT interface treatment.

Simulating conical intersection dynamics in the condensed phase with hybrid quantum master equations

We present a framework for simulating relaxation dynamics through a conical intersection of an open quantum system that combines methods to approximate the motion of degrees of freedom with disparate time and energy scales. In the vicinity of a conical intersection, a few degrees of freedom render the nuclear dynamics nonadiabatic with respect to the electronic degrees of freedom. We treat these strongly coupled modes by evolving their wavepacket dynamics in the absence of additional coupling exactly. The remaining weakly coupled nuclear degrees of freedom are partitioned into modes that are fast relative to the nonadiabatic coupling and those that are slow. The fast degrees of freedom can be traced out and treated with second-order perturbation theory in the form of the time-convolutionless master equation. The slow degrees of freedom are assumed to be frozen over the ultrafast relaxation and treated as sources of static disorder. In this way, we adopt the recently developed frozen-mode extension to second-order quantum master equations. We benchmark this approach to numerically exact results in models of pyrazine internal conversion and rhodopsin photoisomerization. We use this framework to study the dependence of the quantum yield on the reorganization energy and the characteristic time scale of the bath in a two-mode model of photoisomerization. We find that the yield is monotonically increasing with reorganization energy for a Markovian bath but monotonically decreasing with reorganization energy for a non-Markovian bath. This reflects the subtle interplay between dissipation and decoherence in conical intersection dynamics in the condensed phase.

Effects of in-phase and anti-phase large amplitude nonlinear models for double-layer nanostructures

Double layer nano plates have magnificent applications in nanostructures such as, nano sensors, nano actuators and nano transistors. So, the main aim of the presented study is to propose an analytical model based on Reddy’s third-order shear deformation theory of plates which has a difficult procedure due to the great number of partial differential equations and nonlocal strain gradient theory. Due to the fact that numerical approaches aren’t good enough accurate and need more time to calculate, the multiple scales method which is a useful method in systems characterized by disparate time scales and in a variety of situations for extracting the slow time dependence of patterns or other systems is adopted. Based on von Karman equations as well as the theory of nonlocal strain gradient, the coupled nonlinear equations are derive. Compared to the other related published literature, acceptable agreement can be seen under different boundary conditions. Effect of size depended parameter on in-phase and anti-phase modes considering the SSSS and CCCC boundary condition is indescribable which means by increasing the nonlocal parameter nonlinear frequency and also the natural frequency of nanostructure reduces.

Coupled CFD and chemical-kinetics simulations of cellulosic-biomass enzymatic hydrolysis: Mathematical-model development and validation

Computational simulations of cellulosic-biomass enzymatic hydrolysis using a computational-fluid-dynamics (CFD) model coupled to a chemical-kinetics model are presented in this work. A time-step sub-cycling strategy was used to circumvent large disparities in time scales with respect to transport physics and chemical kinetics. The unknown reaction and transport parameters in the mathematical model were first fit to two canonical experiments: a well-mixed case that was limited by reaction kinetics and a settled-solids case that was limited by transport. The model was then validated against a benchtop experiment for an intermediate-mixing scenario, for which simulation results were in reasonable agreement with experimentally measured cellulose conversions. Settling of cellulose particles and diffusion of enzymes determine overall conversion rates for lower mixing rates, while reaction rates dominate conversion at higher mixing rates for which greater homogenization of substrates is achieved.

Stratified Flows over and around Long Dynamically Tall Mountain Ridges

AbstractUniformly stratified flows approaching long and dynamically tall ridges develop two distinct flow components over disparate time scales. The fluid upstream and below a “blocking level” is stagnant in the limit of an infinite ridge and flows around the sides when the ridge extent is finite. The streamwise half-width of the obstacle at the blocking level arises as a natural inner length scale for the flow, while the excursion time over this half-width is an associated short time scale for the streamwise flow evolution. Over a longer time scale, low-level horizontal flow splitting leads to the establishment of an upstream layerwise potential flow beneath the blocking level. We demonstrate through numerical experiments that for sufficiently long ridges, crest control and streamwise asymmetry are seen on both the short and long time scales. On the short time scale, upstream blocking is established quickly and the flow is well described as a purely infinite-ridge overflow. Over the long time scale associated with flow splitting, low-level flow escapes around the sides, but the overflow continues to be hydraulically controlled and streamwise asymmetric in the neighborhood of the crest. We quantify this late-time overflow by estimating its volumetric transport and then briefly demonstrate how this approach can be extended to predict the overflow across nonuniform ridge shapes.

A Practical Guide to Surface Kinetic Monte Carlo Simulations.

This review article is intended as a practical guide for newcomers to the field of kinetic Monte Carlo (KMC) simulations, and specifically to lattice KMC simulations as prevalently used for surface and interface applications. We will provide worked out examples using the kmos code, where we highlight the central approximations made in implementing a KMC model as well as possible pitfalls. This includes the mapping of the problem onto a lattice and the derivation of rate constant expressions for various elementary processes. Example KMC models will be presented within the application areas surface diffusion, crystal growth and heterogeneous catalysis, covering both transient and steady-state kinetics as well as the preparation of various initial states of the system. We highlight the sensitivity of KMC models to the elementary processes included, as well as to possible errors in the rate constants. For catalysis models in particular, a recurrent challenge is the occurrence of processes at very different timescales, e.g., fast diffusion processes and slow chemical reactions. We demonstrate how to overcome this timescale disparity problem using recently developed acceleration algorithms. Finally, we will discuss how to account for lateral interactions between the species adsorbed to the lattice, which can play an important role in all application areas covered here.

Sensitivity to luminosity, centrifugal force, and boundary conditions in spherical shell convection

ABSTRACTWe test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We find that varying the luminosity, which also controls the Mach number, has only a minor effect on the large-scale dynamics. A similar conclusion can also be drawn from the comparison of two formulations of the lower magnetic boundary condition with either vanishing electric field or current density. The centrifugal force has an effect on the solutions, but only if its magnitude with respect to acceleration due to gravity is by two orders of magnitude greater than in the Sun. Finally, we find that the parameterisation of the photospheric physics, either by an explicit cooling term or enhanced radiative diffusion, is more important than the thermal boundary condition. In particular, runs with cooling tend to lead to more anisotropic convection and stronger deviations from the Taylor-Proudman state. In summary, the fully compressible approach taken here with the Pencil Code is found to be valid, while still allowing the disparate timescales to be taken into account.

Mechanical Analysis of Vibrations in a Switched Reluctance Motor Using Experimental, Numerical, and Analytical Methodologies

Abstract Switched reluctance motors (SRM) are characterized by rotor/stator pole pairs, in which the wound field coils in the stator poles induce magnetic reluctance in the rotor poles to create torque. However, noise development during motor operation is a key issue for this class of motors and much of the work to understand the acoustics and vibrations of these systems is limited to comparing experimental measurements with high-performance, multiphysics simulations. This work focuses on mathematical analysis of these systems through reduced-order modeling using both numerical and analytical methods, and the results are compared against experimental measurements of a typical SRM. To describe the underlying response of the experimental system, a circular shell model is developed for the stator, and electromagnetic finite element analysis is utilized to develop a physically motivated forcing profile for the experimental system. A numerical simulation model is then constructed by applying the calculated electromagnetic forces to the stator, and effective system parameters are determined by calibrating the numerical model to match experimental measurements. An analytical approximation is then derived by leveraging disparate timescales in the problem, and it is shown that the analytical solution accurately recovers the numerical and experimental results while also providing insight into the underlying physics of the experimental system.

Physics-Constrained, Data-Driven Discovery of Coarse-Grained Dynamics

The combination of high-dimensionality and disparity of time scales encountered in many problems in computational physics has motivated the development of coarse-grained (CG) models. In this paper, we advocate the paradigm of data-driven discovery for extract- ing governing equations by employing fine-scale simulation data. In particular, we cast the coarse-graining process under a probabilistic state-space model where the transition law dic- tates the evolution of the CG state variables and the emission law the coarse-to-fine map. The directed probabilistic graphical model implied, suggests that given values for the fine- grained (FG) variables, probabilistic inference tools must be employed to identify the cor- responding values for the CG states and to that end, we employ Stochastic Variational In- ference. We advocate a sparse Bayesian learning perspective which avoids overfitting and reveals the most salient features in the CG evolution law. The formulation adopted enables the quantification of a crucial, and often neglected, component in the CG process, i.e. the pre- dictive uncertainty due to information loss. Furthermore, it is capable of reconstructing the evolution of the full, fine-scale system. We demonstrate the efficacy of the proposed frame- work in high-dimensional systems of random walkers.

A Class of Multirate Infinitesimal GARK Methods

Differential equations arising in many practical applications are characterized by multiple time scales. Multirate time integration seeks to solve them efficiently by discretizing each scale with a different, appropriate time step, while ensuring the overall accuracy and stability of the numerical solution. In a seminal paper Knoth and Wolke (APNUM, 1998) proposed a hybrid solution approach: discretize the slow component with an explicit Runge-Kutta method, and advance the fast component via a modified fast differential equation. The idea led to the development of multirate infinitesimal step (MIS) methods by Wensch et al. (BIT, 2009.)G\"{u}nther and Sandu (BIT, 2016) explained MIS schemes as a particular case of multirate General-structure Additive Runge-Kutta (MR-GARK) methods. The hybrid approach offers extreme flexibility in the choice of the numerical solution process for the fast component. This work constructs a family of multirate infinitesimal GARK schemes (MRI-GARK) that extends the hybrid dynamics approachin multiple ways. Order conditions theory and stability analyses are developed, and practical explicit and implicit methods of up to order four are constructed. Numerical results confirm the theoretical findings. We expect the new MRI-GARK family to be most useful for systems of equations with widely disparate time scales, where the fast process is dispersive, and where the influence of the fast component on the slow dynamics is weak.

Investigation of thermal inter-facial problems involving non-locality in space and time

The vastly disparate length and time scales existing in new devices and materials born out of micro-/nano- devices have made thermal modeling and simulation more important and more difficult. The heat transfer process in one certain micro-device is essentially a thermal contact problem that involves various scales of space and time in each of the sub-components. In this communication, we utilize a newly developed computational framework to investigate problems of thermal contact involving size-effects that span the ballistic, ballistic-diffusive, and diffusive heat transfer processes. The preliminary work regarding this generalized computational framework has been published in Xue, Zhang, and Tamma (2018) and has been proved to readily resolve the problem of thermal contact between Fourier-type and nonFourier-type sub-domains. The fashion of solving the thermal inter-facial problems from the perspective of differential-algebraic equations is extended to a broad range of thermal contact problems in the present work, including both the temporal and spatial non-locality. The numerical results demonstrate the prediction of thermal response of the bodies in contact at different scales. The proposed computational framework paves the way for investigating the thermal inter-facial problems in micro-/nano- devices.

Modeling a dry running twin-screw expander using a coupled thermal-fluid solver with automatic mesh generation

Understanding the details of the internal flow processes in screw compressors and expanders is very important for their efficient and robust design. Computational fluid dynamics (CFD) provides full access to a modeled three dimensional flow field and its variation in time. However, the application of CFD to screw compressors and expanders can be difficult because of the complicated geometries involved and the need to supply the computational grid on which the modeled equations are solved over a large number of time steps. While the majority of previous research on CFD applications to screw machines features inventive techniques for generating meshes that adequately resolve the flows in the small clearances, an alternate approach is demonstrated in this work. The screw expander SE 51.2 from TU Dortmund University is analyzed here through a CFD model which generates the grid automatically based on a modified Cartesian cut-cell approach. The grid is then adaptively refined based on local gradients of velocity and temperature. At each time step, the grid is regenerated based on the geometry motion. As opposed to resolving the flow in the clearances, a model is applied so that the cells in the clearance can remain relatively large. The detailed measurements of the screw expander are used to validate the model. The operating conditions investigated include the expansion of dry air at a four-to-one pressure ratio for four different rotational speeds. The measured internal chamber pressures are compared to the results from the model, as are the average mass flow rate, indicated power, and outlet temperature. A coupled thermal-fluid approach is used to model the rotor temperatures and corresponding thermal deformation of the rotors and housing. In this approach, the fluid and solid temperatures are solved together; to deal with the problem of the disparate time scales between the fluid and solid heat transfer, the solids are periodically solved to steady state using heat transfer coefficients and near-wall temperatures computed from an energy conserving averaging over several cycles. The effects of the various leakage flow paths in the model, including the rotor-to-rotor, rotor-tip-to-housing, and bearing leakage are demonstrated and quantified. Finally, simulation and experimental results are compared in terms of different rotor-tip-to-housing clearance heights. The model considering the appropriate thermal deformation of the rotors is shown to yield the best agreement with the measurements, however there is work remaining to reduce the model calculation time, especially at low rotational speeds.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

Efficient Fluid-Thermal-Structural Time Marching with Computational Fluid Dynamics

This study focuses on the development of time-marching procedures for efficient and accurate fluid-thermal-structural analysis with time-accurate computational fluid dynamics. The developed procedures are based on a loosely coupled, partitioned framework for the fluid, thermal, and structural solvers—each with different second-order time integrators. The procedures also implement subcycling, where disparate time scales between the solvers are leveraged to minimize communication between solvers. The first scheme uses a second-order predictor of fluid loads, along with second-order interpolations of structural and thermal solutions. The second scheme is an extension that adds a corrector step to the structural and thermal solvers. The two schemes are benchmarked against both a strongly coupled approach with subiterations and a basic loosely coupled approach that omits the use of predictors/correctors. The schemes are examined in the context of the aerothermoelastic response of a panel in high supersonic flow, and are found to maintain second-order time accuracy with and without subcycling. Furthermore the approaches compare favorably against a strongly coupled approach at significantly reduced computational times, with the predictor-corrector approach yielding speedups of 2–4 times. In comparison, a basic scheme can yield characteristically different behavior.