Dynamical Quantities Research Articles

A baseline for ensemble-based, time-resolved inflow reconstruction for a single turbine using large-eddy simulations and latent diffusion models

We are interested in reconstructing winds flowing through a turbine on a second-by-second basis over a 10 min window. Previously, we developed a machine learning algorithm that takes in a snapshot of wind speed measurements and generates ensembles of three-dimensional wind field estimates. Here, we use these estimates as initial conditions in large-eddy simulations and reconstruct atmospheric and turbine response dynamic quantities in a synthetic field campaign. In doing so, we establish a baseline for model validation that future time-aware data assimilation techniques will be compared to. In turbine-free case studies, ground truth wind speeds consistently fall within our estimated wind speed distribution for the first 100 s after the simulation start. In simulations with turbines, the wind estimates show a small bias of 0.10 m s−1 and good correlation of 0.80 during the first 100 s. During this window, our estimates of the Blade 1 bending moment and generator power typically span the ground truth, with the estimate of the former performing better overall. In summary, this approach shows promise as a stand-alone technique for reconstructing real-world inflow and turbine dynamics in 1−2 min windows and as a foundation for future time-aware data assimilation techniques.

Synthesizing Sea Surface Temperature and Satellite Altimetry Observations Using Deep Learning Improves the Accuracy and Resolution of Gridded Sea Surface Height Anomalies

AbstractGridded sea surface height (SSH) maps estimated from satellite altimetry are widely used for estimating surface ocean geostrophic currents. Satellite altimeters observe SSH along one‐dimensional tracks widely spaced in space and time, making accurately reconstructing the two‐dimensional (2D) SSH field challenging. Traditionally, SSH is mapped using optimal interpolation (OI). However, OI artificially smooths the SSH field leading to high mapping errors in regions with rapidly‐evolving mesoscale features such as western boundary currents. Motivated by the dynamical relation between SSH and sea surface temperature (SST) and the notion that even the chaotic evolution of mesoscale ocean turbulence may contain repeating patterns, we outline a deep learning (DL) approach where a neural network is trained to reconstruct 2D SSH by synthesizing altimetry and SST observations. In the Gulf Stream Extension region, dominated by mesoscale variability, our DL method substantially improves the SSH reconstruction compared to existing methods. Our SSH map has 17% lower root‐mean‐square error and resolves spatial scales 30% smaller than OI compared against independent altimeter observations. Surface geostrophic currents calculated from our map are closer to surface drifter observations and appear qualitatively more realistic, with stronger currents, a clearer separation between the Gulf Stream and neighboring eddies, and the appearance of smaller coherent eddies missed by other methods. Our map yields significant re‐estimations of important dynamical quantities such as eddy kinetic energy, vorticity, and strain rate. Applying our DL method to produce a global SSH product may provide a more accurate and higher resolution product for studying mesoscale ocean turbulence.

A semi-tetrad decomposition of the Kerr spacetime

In this paper we perform a semi-tetrad decomposition of the Kerr spacetime. We apply the 1+1+2 covariant method to the Kerr spacetime in order to describe its geometry outside the horizon. Comparisons are drawn between an observer belonging to the Killing frame and a ZAMO (zero angular momentum observer), a locally non-rotating observer in a zero angular momentum frame, and their resulting geometrical quantities that generate the evolution and propagation equations. This enhances the study of the Kerr geometry as the results are valid in the ergoregion from where energy can be extracted. Using this formalism allows us to present the kinematic and dynamic quantities in a transparent geometrical manner not present in alternate approaches. We find significant relationships between the properties of shear, vorticity and acceleration. Additionally we observe that in the Killing frame, the gravitational wave is a direct consequence of vorticity and in the ZAMO frame, the gravitational wave is a direct consequence of shear. To our knowledge, using the 1+1+2 formalism to investigate the Kerr spacetime is a novel approach, and this provides new insights into the spacetime geometry in an easier manner than alternate approaches. Furthermore we make corrections to earlier equations in the 1+1+2 formalism applied to the Kerr spacetime.

Spherical winding and helicity

In ideal magnetohydrodynamics, magnetic helicity is a conserved dynamical quantity and a topological invariant closely related to Gauss linking numbers. However, for open magnetic fields with non-zero boundary components, the latter geometrical interpretation is complicated by the fact that helicity varies with non-unique choices of a field’s vector potential or gauge. Evaluated in a particular gauge called the winding gauge, open-field helicity in Cartesian slab domains has been shown to be the average flux-weighted pairwise winding numbers of field lines, a measure constructed solely from field configurations that manifest its topological origin. In this paper, we derive the spherical analogue of the winding gauge and the corresponding winding interpretation of helicity, in which we formally define the concept of spherical winding of curves. Using a series of examples, we demonstrate novel properties of spherical winding and the validity of spherical winding helicity. We further argue for the canonical status of the winding gauge choice among all vector potentials for magnetic helicity by exhibiting equivalences between local coordinate changes and gauge transformations.

An embedded Hamiltonian dynamic evolutionary neural network model for high-dimensional data recognition

Aiming at the limitation of Hamiltonian neural network in high-dimensional data processing with non-observable physical quantity system, an embedded Hamiltonian dynamic evolutionary neural network model (EHDN) is proposed in this paper. First, the dynamic physical quantities of high dimensional nonlinear systems are represented by constructing Hamiltonian functions. Then a symplectic integrator is designed to realize the time-varying evolution of network features based on Hamiltonian regular equation and variational numerical integration. Finally, the Hamiltonian dynamic evolutionary neural network is embedded in the convolutional neural network (CNN) to realize the Hamiltonian simulation evolution of convolutional features. Experimental results on two different datasets, CIFAR and Fashion-Mnist, show that compared with existing state-of-the-art (SOTA) methods, EHDN model can combine the advantages of Hamiltonian dynamics and convolutional network to improve the recognition accuracy and training stability in high-dimensional image classification tasks.

A Unified Description of the Liquid Structure, Static and Dynamic Anomalies, and Criticality of TIP4P/2005 Water by a Hierarchical Two-State Model

Water has anomalous thermodynamic and kinetic properties distinct from ordinary liquids. The famous examples are the density maximum at 4 °C and the viscosity decrease upon pressurization. The presence of the second critical point has been considered to be responsible for these anomalies since its discovery in ST2 water. Recently, its existence has been confirmed firmly in TIP4P/2005, which is one of the most successful classical models of water, by Debenedetti et al. [Debenedetti et al. Science 2020, 369, 289]. Here, we study the water structure and thermodynamic and dynamic quantities in a wide temperature (T)-pressure (P) range, including the vicinity of the second critical point, by extensive molecular dynamics simulation of this water model. We reveal that a hierarchical two-state model with the cooperative formation of water tetrahedral structures via hydrogen bonding can describe the T, P-dependences of structure, thermodynamic and kinetic anomalies, and criticality of TIP4P/2005 water in a unified manner. TIP4P/2005 water shows very similar behaviors to real water in all these aspects, suggesting a possible existence of the second critical point in the water. Our physical description based on the two order parameters, the density and the fraction of locally favored tetrahedral structures, indicates that the latter is the relevant order parameter for the second critical point, which is supported by the analysis of the critical fluctuations. The different nature of the density and the fraction of tetrahedral arrangements, conserved and nonconserved, may be key to unambiguously identifying the relevant order parameter.

Girsanov Reweighting Enhanced Sampling Technique (GREST): On-the-Fly Data-Driven Discovery of and Enhanced Sampling in Slow Collective Variables.

Molecular dynamics simulations of microscopic phenomena are limited by the short integration time steps which are required for numerical stability but which limit the practically achievable simulation time scales. Collective variable (CV) enhanced sampling techniques apply biases to predefined collective coordinates to promote barrier crossing, phase space exploration, and sampling of rare events. The efficacy of these techniques is contingent on the selection of good CVs correlated with the molecular motions governing the long-time dynamical evolution of the system. In this work, we introduce Girsanov Reweighting Enhanced Sampling Technique (GREST) as an adaptive sampling scheme that interleaves rounds of data-driven slow CV discovery and enhanced sampling along these coordinates. Since slow CVs are inherently dynamical quantities, a key ingredient in our approach is the use of both thermodynamic and dynamical Girsanov reweighting corrections for rigorous estimation of slow CVs from biased simulation data. We demonstrate our approach on a toy 1D 4-well potential, a simple biomolecular system alanine dipeptide, and the Trp-Leu-Ala-Leu-Leu (WLALL) pentapeptide. In each case GREST learns appropriate slow CVs and drives sampling of all thermally accessible metastable states starting from zero prior knowledge of the system. We make GREST accessible to the community via a publicly available open source Python package.

Transition of a 2D crystal to a non-equilibrium two-phase coexistence state

In this paper, we present experimental observation of the transition of a 2D dust crystal to a non-equilibrium solid–liquid phase coexistence state. The experiments have been carried out in an L-shaped dusty plasma experimental device in a DC glow discharge argon plasma environment. Initially, a monolayer crystalline structure is formed, which is later transformed to a two-phase coexistence state using the background neutral pressure as a control parameter. Self-excited horizontal oscillations are found in the center of the monolayer prior to the appearance of the coexistence state. It is observed that a molten center coexists with a solid periphery. Various structural, thermodynamic, and dynamical quantities are used to characterize the phase state. The surface tension at the solid–liquid circular interface is also determined. A detailed parametric study is made to delineate the existence region of such a state. It is found that melting caused at the core is due to the onset of a localized Schweigert instability in the presence of a few stray particles beneath the top layer in that region.

Numerical investigation of the effects of model and operator uncertainties on component-based transfer path analysis methods with substructuring applied to aircraft-like components

Hydraulic pumps are considered to have a major contribution to the structure borne noise generated inside aircrafts. Methods such as Component-Based Transfer Path Analysis (CB-TPA) are promising tools for aircraft manufacturers to build internal processes for the specification, design and validation of the impact of vibrating systems on new aircrafts. However, the experimental applicability of these methods remains limited due to some experimental difficulties. CB-TPA' formulation is based on dynamical quantities, which require the determination of terms related to rotational degrees of freedom. Virtual Point (VP) or Equivalent Multi-Point Connection (EMPC) methods are commonly employed for this purpose, but both result in more cumbersome experimental set-ups and increased measurement uncertainties. The implementation of these methods is difficult in the case of a flat and thin receiving structure as commonly encountered in aircraft applications, since in-plane translational excitations have to be applied and the access to the vibrating system/structure interface points is limited. In this work, a decoupling procedure is used to overcome these issues. A numerical model is used to investigate the influence of model and operator uncertainties on the CB-TPA' predictions, when the dynamical quantities are provided by VP and EMPC methods including the decoupling procedure.

Quantum simulation of weak-field light-matter interactions

Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials, and for modeling next-generation non-linear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.

Accurate estimation of dynamical quantities for nonequilibrium nanoscale systems.

Fluctuations of dynamical quantities are fundamental and inevitable. For the booming research in nanotechnology, huge relative fluctuation comes with the reduction of system size, leading to large uncertainty for the estimates of dynamical quantities. Thus, increasing statistical efficiency, i.e., reducing the number of samples required to achieve a given accuracy, is of great significance for accurate estimation. Here we propose a theory as a fundamental solution for such problem by constructing auxiliary path for each real path. The states on auxiliary paths constitute canonical ensemble and share the same macroscopic properties (NVT) with the initial states of the real path. By implementing the theory in molecular dynamics simulations, we obtain a nanoscale Couette flow field with an accuracy of 0.2μm/s with relative standard error <0.1. The required number of samples is reduced by 12 orders compared to conventional method. The predicted thermolubric behavior of water sliding on a self-assembled surface is directly validated by experiment under the same velocity. This theory only assumes the system is initially in thermal equilibrium, then driven from that equilibrium by an external perturbation. It could serve as a general approach for extracting the accurate estimate of dynamical quantities from large fluctuations to provide insights on atomic level under experimental conditions, and benefit the studies on mass transport through (biological) nanochannels and fluid film lubrication of nanometer thickness.

Fines-controlled drainage in just-saturated, inertial column collapses

The wide particle size distributions, over several orders of magnitude, observed in debris flows leads to a diverse range of rheological behaviours controlling flow outcomes. This study explores the influence of different scale grains by conducting subaerial, fully saturated granular column collapse experiments with extreme, bimodal particle size distributions. The primary particles were of a size where their behaviour was controlled by their inertia while a suspension of kaolin clay particles within the fluid phase acts at spatial scales smaller than the pore space between the primary particles. The use of a geotechnical centrifuge allowed for the systematic variation of gravitational acceleration, inertial particle size and the degree of kaolin fines. Characteristic velocity- and time-scales of the acceleration phase of the collapse were quantified using high-speed cameras. Comparing tests containing fines to equivalent collapses with a glycerol solution mimicking the enhanced viscosity but not the particle behaviour of the fines, it was found that all characteristic dynamic quantities were dependent on the degree of fines, the system size, the grain fluid-density ratio and the column– and grain-scale Bond and Capillary numbers. We introduce a fine-scale Capillary number showing that, although surface tension effects at the column scale are negligible, fines do control the movement of fluid through the pore spaces.

Numerical Investigation of Very Low Reynolds Cross Orifice Jet for Personalized Ventilation Applications in Aircraft Cabins

This study focuses on the numerical analysis of a challenging issue involving the regulation of the human body's microenvironment through personalized ventilation. We intended to first concentrate on the main flow, namely, the personalized ventilation jet, before connecting the many interacting components that are impacting this microenvironment (human body plume, personalized ventilation jet, and the human body itself as a solid obstacle). Using the laminar model and the large eddy simulation (LES) model, the flow field of a cross-shaped jet with very low Reynolds numbers is examined numerically. The related results are compared to data from laser doppler velocimetry (LDV) and particle image velocimetry (PIV) for a reference jet design. The major goal of this study is to evaluate the advantages and disadvantages of the CFD approach for simulating the key features of the cross-shaped orifice jet flow. It was discovered that the laminar model overestimated the global jet volumetric flow rate and the flow expansion. LES looks more suitable for the numerical prediction of such dynamic integral quantities. In light of the computational constraints, it quite accurately mimics the mean flow behavior in the first ten equivalent diameters from the orifice, where the mesh grid was extremely finely tuned. From the perspective of the intended application, the streamwise velocity distributions, streamwise velocity decay, and volumetric flow rate anticipated by the LES model are rather well reproduced.

Integrable and Superintegrable 3D Newtonian Potentials Using Quadratic First Integrals: A Review

The determination of the first integrals (FIs) of a dynamical system and the subsequent assessment of their integrability or superintegrability in a systematic way is still an open subject. One method which has been developed along these lines for holonomic autonomous dynamical systems with dynamical equations q¨a=−Γbca(q)q˙bq˙c−Qa(q), where Γbca(q) are the coefficients of the Riemannian connection defined by the kinetic metric of the system and −Qa(q) are the generalized forces, is the so-called direct method. According to this method, one assumes a general functional form for the FI I and requires the condition dIdt=0 along the dynamical equations. This results in a system of partial differential equations (PDEs) to which one adds the necessary integrability conditions of the involved scalar quantities. It is found that the final system of PDEs breaks into two sets: a. One set containing geometric elements only and b. A second set with geometric and dynamical quantities. Then, provided the geometric quantities are known or can be found, one uses the second set to compute the FIs and, accordingly, assess the integrability of the dynamical system. The ‘solution’ of the system of PDEs for quadratic FIs (QFIs) has been given in a recent paper (M. Tsamparlis and A. Mitsopoulos, J. Math. Phys. 61, 122701 (2020)). In the present work, we consider the application of this ‘solution’ to Newtonian autonomous conservative dynamical systems with three degrees of freedom, and compute integrable and superintegrable potentials V(x,y,z) whose integrability is determined via autonomous and/or time-dependent QFIs. The geometric elements of these systems are the ones of the Euclidean space E3, which are known. Setting various values for the parameters determining the geometric elements, we determine in a systematic way all known integrable and superintegrable potentials in E3 together with new ones obtained in this work. For easy reference, the results are collected in tables so that the present work may act as an updated review of the QFIs of Newtonian autonomous conservative dynamical systems with three degrees of freedom. It is emphasized that, by assuming different values for the parameters, other authors may find more integrable potentials of this type of system.

Магнитная система одноосного инерционного магнитожидкостного акселерометра

Today, a physical problem of engineering design of inertial magnetic fluid accelerometers to measure dynamic processes is relevant. The main drawback of modern sensors is the nonlinear characteristic of the forced response, which limits the application area of the sensors to the case of quasi-static action (tilt angle sensor). The reason of nonlinearity is the design of the magneto-mechanical system of the elastic suspension of the inertial mass made in the form of a pair of permanent ring magnets. This drawback can be eliminated by designing an axisymmetric electromagnetic system that generates a magnetic field with a linear intensity gradient along the symmetry axis. Thus, the paper is devoted to this problem and experimental approvement of the results on a laboratory sensor prototype. The Monte Carlo algorithm is used to calculate electromagnetic system containing permanent magnets and magnetizing coils. The algorithm is implemented using the C++ programming language. Measurements of the most important parameters of the magnetic field from the point of view of the purpose of the study are carried out on the assembled model of the electromagnetic system of the accelerometer. The calculation of electromagnetic system that generate permanent magnetic field with linear intensity gradient along the symmetry axis is carried out. The applicability of the Monte Carlo method to solve similar engineering problems is shown. The measurements of the magnetic field strength of a given configuration have been made. The force of the magnetic field acting on the test sensitive element with a constant magnetic moment is measured. A comparison of the calculated magnetic field with the field of a real system is carried out. It shows satisfactory agreement between the calculated data and the real ones. A linear dependence of the restoring force on the displacement coordinate of a body with a constant magnetic moment from the equilibrium position is shown. The linearization of the response of the mechanical part of the magnetic fluid accelerometer is achieved by choosing the desired configuration of its electromagnetic system, which allows making reliable measurements of both static and dynamic quantities.

Soil Deformation after Water Drop Impact-A Review of the Measurement Methods.

Water erosion is an unfavorable phenomenon causing soil degradation. One of the factors causing water erosion is heavy or prolonged rainfall, the first effect of which is the deformation of the soil surface and the formation of microcraters. This paper presents an overview of research methods allowing the study of microcraters as well as the process of their formation. A tabular summary of work on the measurements of various quantities describing the craters is presented. The said quantities are divided into three groups: (i) static quantities, (ii) dynamic quantities, and (iii) dimensionless parameters. The most important measurement methods used to study crater properties, such as (i) basic manual measurement methods, (ii) photography, (iii) high-speed imaging, (iv) profilometers, (v) 3D surface modelling, and (vi) computed tomography (CT) and its possibilities and limitations are discussed. The main challenges and prospects of research on soil surface deformation are also presented.

Building Quantitative Bridges between Dynamics and Sequences of SARS-CoV-2 Main Protease and a Diverse Set of Thirty-Two Proteins.

Proteases are major drug targets for many viral diseases. However, mutations can render several antiprotease drugs inefficient rapidly even though these mutations may not alter protein structures significantly. Understanding relations between quickly mutating residues, protease structures, and the dynamics of the proteases is crucial for designing potent drugs. Due to this reason, we studied relations between the evolutionary information on residues in the amino acid sequences and protein dynamics for SARS-CoV-2 main protease. More precisely, we analyzed three dynamical quantities (Schlitter entropy, root-mean-square fluctuations, and dynamical flexibility index) and their relation to the amino acid conservation extracted from multiple sequence alignments of the main protease. We showed that a quantifiable similarity can be built between a sequence-based quantity called Jensen-Shannon conservation and those three dynamical quantities. We validated this similarity for a diverse set of 32 different proteins, other than the SARS-CoV-2 main protease. We believe that establishing these kinds of quantitative bridges will have larger implications for all viral proteases as well as all proteins.

Real tensor eigenvalue/vector distributions of the Gaussian tensor model via a four-fermi theory

Abstract Eigenvalue distributions are important dynamic quantities in matrix models, and it is an interesting challenge to study corresponding quantities in tensor models. We study real tensor eigenvalue/vector distributions for real symmetric order-three random tensors with a Gaussian distribution as the simplest case. We first rewrite this problem as the computation of a partition function of a four-fermi theory with R replicated fermions. The partition function is exactly computed for some small-N,R cases, and is shown to precisely agree with Monte Carlo simulations. For large-N, it seems difficult to compute it exactly, and we apply an approximation using a self-consistency equation for two-point functions and obtain an analytic expression. It turns out that the real tensor eigenvalue distribution obtained by taking R = 1/2 is simply the Gaussian within this approximation. We compare the approximate expression with Monte Carlo simulations, and find that, if an extra overall factor depending on N is multiplied to the the expression, it agrees well with the Monte Carlo results. It is left for future study to improve the approximation for large-N to correctly derive the overall factor.

Signed distributions of real tensor eigenvectors of Gaussian tensor model via a four-fermi theory

Eigenvalue distributions are important dynamical quantities in matrix models, and it is a challenging problem to derive them in tensor models. In this paper, we consider real symmetric order-three tensors with Gaussian distributions as the simplest case, and derive an explicit formula for signed distributions of real tensor eigenvectors: Each real tensor eigenvector contributes to the distribution by ±1, depending on the sign of the determinant of an associated Hessian matrix. The formula is expressed by the confluent hypergeometric function of the second kind, which is obtained by computing a partition function of a four-fermi theory. The formula can also serve as lower bounds of real eigenvector distributions (with no signs), and their tightness/looseness are discussed by comparing with Monte Carlo simulations. Large-N limits are taken with the characteristic oscillatory behavior of the formula being preserved.

Collision avoidance control for unmanned surface vehicle with COLREGs compliance

In this paper, a collision avoidance control algorithm for unmanned surface vehicle (USV) with COLREGs is studied. To solve the constraints of actuator and dynamics in the maneuvering characteristics and the estimation of velocity window parameters in dynamic window approach (DWA), a real-time collision avoidance control algorithm based on dynamic constraints is proposed according to the principle of DWA, which mainly includes the design of candidate control behavior space, feasible trajectory prediction, collision risk assessment, acquisition of optimal control quantities and so on. The candidate control behavior space designed according to DWA meets the actuator constraints; The feasible trajectory prediction method can meet the dynamic constraints and avoid the problem of velocity window parameters estimation in DWA; The optimal control quantity method constructs the collision avoidance control evaluation function according to the collision risk evaluation principle, and obtain the feasible dynamic trajectory and collision avoidance control quantities at the same time. In addition, the collision avoidance rule function is introduced into the collision avoidance control evaluation function to enable the USV to comply with the COLREGs. Finally, simulation results are provided to illustrate the efficacy of collision avoidance control algorithm.