A quantum mechanical evaluation of the intermediate scattering function

In the last 25 years, mathematical and numerical modeling of cardiovascular problems has experienced a spectacular progress. Moving progressively from the stage of idealized models supporting traditional in vitro and in vivo approaches – basically with proofs of concept – Cardiovascular Mathematics has been transforming into a unique tool for patient-specific analysis. This has been made possible by the strong integration with imaging devices. Nowadays, the work pipeline starting from a medical image in the Digital Imaging and Communications in Medicine (DICOM) format to retrieve the patient-specific geometry of an artery or the left ventricle to be used as computational domain in a numerical simulation is well established. This has initiated a paradigm shift in the interactions between mathematicians, bioengineers, and medical doctors. The latter are progressively getting used to in silico analysis as an important component of their research [3]. The introduction of numerical procedures as a part of an established clinical routine and more in general of a consolidated support to the decision-making process of physicians still requires some steps both in terms of infrastructures (to bring computational tools to the operating room or the bedside) and methods. In particular, the quality of the numerical results needs to be assessed and certified. The reliability of simulations calls for an accurate quantification and possibly reduction of uncertainty. In this scenario and in view of terrific advancements of measuring techniques, an important research line – quite established in other fields – is data assimilation [4,6,9], that is, the integration of numerical simulations and measurements. We may say that numerical models provide a background knowledge (based on physical principles and constitutive laws, not patient-specific), whereas measures give a foreground (individual) information; accuracy of in silico procedures relies on the correct integration of these two levels of knowledge of the problem [9,10]. As a matter of fact, numerical models depend on parameters and boundary/initial conditions. Their knowledge is in practice usually incomplete, inaccurate, and noisy. In some cases, the sensitivity itself of the final results to these parameters is unclear and needs to be quantified. Such an uncertainty may be significantly reduced by the availability of patient-specific measures; on the other hand, the quality of measures can be strongly enhanced by comparison with mathematical models (after all, noise is in general not educated, it does not know PDEs . . . ) [4,5,7,8,9,11]. We think therefore that, in the future, a crucial step for the clinical application of Cardiovascular Mathematics will be the passage from numerical simulation to data assimilation. To be concrete, borrowing a motto by Michel Fortin supporting mesh adaptivity in finite element simulations, stating that a ‘grid should not be considered a data, but an unknown of the problem’, we think that many parameters currently tuned on the basis of nonpatient specific criteria (even in patient-specific geometries) should be considered part of the unknowns to be found by assimilation procedures.

Dualities are widely used in quantum field theories and string theory to obtain correlation functions at high accuracy. Here we present examples where dual data representations are useful in supervised classification, linking machine learning and typical tasks in theoretical physics. We then discuss how such beneficial representations can be enforced in the latent dimension of neural networks. We find that additional contributions to the loss based on feature separation, feature matching with respect to desired representations, and a good performance on a ‘simple’ correlation function can lead to known and unknown dual representations. This is the first proof of concept that computers can find dualities. We discuss how our examples, based on discrete Fourier transformation and Ising models, connect to other dualities in theoretical physics, for instance Seiberg duality.

We present the first application of full‐waveform ambient noise inversion to observed correlation functions that jointly constrains 3‐D Earth structure and heterogeneous noise sources. For this, we model and interpret ambient noise correlations as recordings of correlation wavefields, which completely eliminates the limiting assumptions of Green's function retrieval, such as equipartitioning and homogeneous random noise sources. Our method accounts for seismic wave propagation physics in 3‐D heterogeneous and attenuating media and also for the heterogeneous and nonstationary nature of the ambient noise field. Designed as a proof of concept, the study considers long periods from 100 to 300 s, thus focusing on the Earth's hum. Treating correlations as self‐consistent observables allows us to make separate measurements on the causal and acausal branches of correlation functions, without any need to choose one of them or form the average. We validate our approach by assessing the quality of the obtained models and by comparing them to previous studies. This work is a step toward the establishment of full‐waveform ambient noise inversion as a tomographic technique with the goal to go beyond ambient noise tomography based on Green's function retrieval.

Energy absorbers and energy-harvesting devices have been under the scope of scientists and engineers for decades to fulfill specific technological needs, mainly concerned with sound and vibration absorbers, and efficient mechanical energy converters. In this paper, as a proof of concept, we build a mass-in-mass device to study the response of a linear absorber immersed in one of the spheres composing a linear array of equal elastic spheres. Spheres barely touch one another and can thus sustain nonlinear solitary wave propagation only. The linear intruder absorbs a given amount of energy depending on the frequency content of the incident solitary wave. A numerical simulation is developed to account for the experimental finding. The validation of the numerical model allows for the theoretical study of the energy absorbed by any number of intruders, and to demonstrate that the former increases exponentially with the latter, indicating that only ten of the intruders is enough to absorb the system energy. A detailed study of the transmitted energy from an external source into the chain reveals that, due to nonlinearity, the array of spheres is able to convert almost any mechanical shock to a well-defined solitary or trains of solitary waves, whose frequency content is nearly independent on the excitation amplitude. This property leads to the design of a device, which is optimized to absorb energy over a broad frequency range.

In this paper we overcome a key problem in an otherwise highly potential approach to study turbulent flows, ODTLES (One‐Dimensional Turbulence Large Eddy Simulation). From a methodological point of view, ODTLES is an approach in between Direct Numerical Simulations (DNS) and averaged/filtered approaches like RANS (Reynolds Averaged Navier‐Stokes) or LES (Large Eddy Simulations). In ODTLES, a set of 1D ODT models is embedded in a coarse grained 3D LES. On the ODT scale, the turbulent advection is modeled as a sequence of stochastic eddy events, also known as triplet maps, while the other (deterministic) terms are fully resolved in space (along the ODT‐line) and time. Schmidt et al. first (2008) introduced ODTLES and Gonzalez et al. (2011) applied the model for a variety of wall‐bounded flow problems. Although the results were notable for a first proof of concept, the numerical methods used are subject to debate. First of all, an unstable discretization for the large scale 3D advective terms was used, as shown by Glawe (2015). This scheme can be stabilized by reducing the CFL number for the explicitly discretized LES terms down to the order of the small scale ODT time step, but this of course reduces the advantage of the ODTLES multi‐scale approach. The stochastic ODT eddies were also allowed to overlap two LES cells introducing an artificial smoothing (stabilizing) effect. Glawe (2015) limited the overlap consistently to one LES cell and used a stable Runge Kutta (RK) discretization, maintaining, however the low CFL number problem. In this paper we adapt a new implicit/explicit (IMEX) time scheme to ODTLES in order to remedy the small CFL number issue. For the problems investigated, the results indicate a performance increase of the IMEX scheme by a factor of 17 based on the ratio of applied CFL numbers. This allowed simulations of a turbulent channel flow with characteristic friction Reynolds number on one Banana Pi single board computer. We compare results to available DNS data and discuss in general the efficiency and potential of ODTLES for high Reynolds number flows.

We introduce a new semirelativistic quantum operator for the length of the worldline a particle traces out as it moves. In this article the operator is constructed in a heuristic way and some of its elementary properties are explored. The operator ends up depending in a very complicated way on the potential of the system it is to act on so as a proof of concept we use it to analyze the expected distance traveled by a free Gaussian wave packet with some initial momentum. It is shown in this case that the distance such a particle travels becomes light-like as its mass vanishes and agrees with the classical result for macroscopic masses. This preliminary result has minor implications for the Weak Equivalence Principle (WEP) in quantum mechanics. In particular it shows that the logical relationship between two formulations of the WEP in classical mechanics extends to quantum mechanics. That our result is qualitatively consistent with the work of others emboldens us to start the task of evaluating the new operator in nonzero potentials. However, we readily acknowledge that the looseness in the definition of our operator means that all of our so-called results are highly speculative. Plans for future work with the new operator are discussed in the last section.

Weakly nonintegrable many-body systems can restore ergodicity in distinctive ways depending on the range of the interaction network in action space. Action resonances seed chaotic dynamics into the networks. Long-range networks provide well connected resonances with ergodization controlled by the individual resonance chaos time scales. Short-range networks instead yield a dramatic slowing down of ergodization in action space, and lead to rare resonance diffusion. We use Josephson junction chains as a paradigmatic study case. We exploit finite time average distributions to characterize the thermalizing dynamics of actions. We identify an action resonance diffusion regime responsible for the slowing down. We extract the diffusion coefficient of that slow process and measure its dependence on the proximity to the integrable limit. Independent measures of correlation functions confirm our findings. The observed fragile diffusion is relying on weakly chaotic dynamics in spatially isolated action resonances. It can be suppressed, and ergodization delayed, by adding weak action noise, as a proof of concept.

Stochastic simulations of spatiotemporal patterns of hydroclimatic processes, such as precipitation, are needed to build alternative but equally plausible inputs for water‐related design and management, and to estimate uncertainty and assess risks. However, while existing stochastic simulation methods are mature enough to deal with relatively small domains and coarse spatiotemporal scales, additional work is required to develop simulation tools for large‐domain analyses, which are more and more common in an increasingly interconnected world. This study proposes a methodological advancement in the CoSMoS framework, which is a flexible simulation framework preserving arbitrary marginal distributions and correlations, to dramatically decrease the computational burden and make the algorithm fast enough to perform large‐domain simulations in short time. The proposed approach focuses on correlated processes with mixed (zero‐inflated) Uniform marginal distributions. These correlated processes act as intermediates between the target process to simulate (precipitation) and parent Gaussian processes that are the core of the simulation algorithm. Working in the mixed‐Uniform space enables a substantial simplification of the so‐called correlation transformation functions, which represent a computational bottle neck in the original CoSMoS formulation. As a proof of concept, we simulate 40 years of daily precipitation records from 1,000 gauging stations in the Mississippi River basin. Moreover, we extend CoSMoS incorporating parent non‐Gaussian processes with different degrees of tail dependence and suggest potential improvements including the separate simulation of occurrence and intensity processes, and the use of advection, anisotropy, and nonstationary spatiotemporal correlation functions.

The quantum transition state concept provides an intuitive and numerically efficient framework for the description of quantum state-resolved reactive scattering and thermal reaction processes. Combining multiconfigurational time-dependent Hartree wave packet dynamics calculations with a flux correlation function based analysis, rigorous full-dimensional calculations of initial state-selected and state-to-state reaction probabilities for six atom reactions are feasible. In these calculations, a set of wave packets is generated in the transition state region, propagated into the asymptotic area, and analyzed. In the present work, an alternative approach which employs counter-propagating sets of wave packets is introduced. Outgoing wave packets started in the transition state region are matched with incoming wave packets generated in the reactant (or product) asymptotic area. Studying the H + CH4 → H2 + CH3 reaction as a prototypical example, one finds that the incoming wave packets can be propagated closely up to the transition state region with minor numerical effort. Employing cross correlation functions of incoming and outgoing wavefunctions, the propagation times required for the outgoing wave packet and thus the numerical costs of the entire calculation can be reduced significantly. Detailed full-dimensional calculations studying initial state-selected reaction probabilities for the H + CH4 → H2 + CH3 reaction are presented to illustrate the new approach. It is found that converged results can be obtained using shorter propagation times of the outgoing wave packets and less single-particle functions.

For the disadvantages of the traditional NDT methods for coating defects, Thermal Wave Nondestructive Testing (TWNDT) technology was used to detect coating debonding defect on composite Materials matrix. Numerical simulation method was used to simulate the heat transfer process of thermal wave in the coating material with defects. The factors influencing the testing sensitivity were in-depth studied, including the debonding defect size and coating thickness. Simulation results show that: TWNDT technology can quickly and efficiently identify the size of the coating debonding defects, while the thickness of the coating is an important factor influencing the inspection sensitivity for the thermal wave detection.

The "bad" Jaulent-Miodek (JM) equation serves to describe the motion of non-viscous shallow water wave packets in a flat-bottomed domain subject to shear forces. The "bad" JM equation exhibits poor properties, characterized by the linear instability of nonlinear waves on the zero-plane background, rendering it challenging to solve through traditional analytical and numerical methods. In this paper, two classic physics-driven deep learning approaches, namely, Physics-Informed Neural Networks (PINN) and Physics and Equality-Constrained Artificial Neural Networks (PECANN), are combined into a two-stage "PINN+PECANN" neural network to address the nonlinear wave evolution on the zero-plane background for the "bad" JM equation. The two-stage "PINN+PECANN" neural network method employs PINN in the first stage to pre-train the neural network, followed by fine-tuning of the network parameters using PECANN in the second stage. This approach not only correctly obtains solutions to the "bad" JM equation but also enhances computational efficiency. Specifically, we present the evolutionary behavior of nonlinear waves for the common initial values of the "bad" JM equation: Gauss wave packets, sech wave packets, and rational wave packets. Furthermore, the nonlinear interactions between two Gauss, sech, rational wave packets are provided. The results in this paper validate the advantages of physics-driven deep learning methods in solving equations with poor properties and open up a new pathway for obtaining unstable solutions of nonlinear equations.

In robotics, high gear reductions are often required when using an electromagnetic motor to drive revolute joints, as in a humanoid robot. Strain wave gears (SWGs), also known as harmonic drives, are often used. However, these transmissions are relatively expensive and have a fixed gear ratio. Here, we present a low-cost transmission that maintains the high reduction of the SWG and enables a continuously variable gear ratio. We achieve this by, first, replacing the teeth of an SWG with a smooth frictional contact to enable continuous gear variation and, second, inverting the gear elements to enable high frictional torque transfer with a low preload via the capstan effect. We choose a gecko-inspired dry adhesive as the frictional material because it has high friction at low normal forces, and is not inherently tacky. We present a model describing the transmission, as well as experimental data gathered from a prototype device that verifies this model and establishes a proof of concept. Our transmission expands the possibilities for low-cost robotic systems.

A novel formal equivalence between thermal averages of coherent properties (e.g., conductance) and time averages of a single wave packet arises for Fermi gases and certain geometries. In the case of one open channel in a quantum point contact (QPC), only one wave packet history, with the wave packet width equal to the thermal length, completely determines the thermally averaged conductance. The formal equivalence moreover allows very simple physical interpretations of interference features surviving under thermal averaging. Simply put, pieces of the thermal wave packet returning to the QPC along independent paths must arrive at the same time in order to interfere. Remarkably, one immediate result of this approach is that higher temperature leads to narrower wave packets and therefore better resolution of events in the time domain. In effect, experiments at 4.2 K are performing time-gated experiments at better than a gigahertz. Experiments involving thermally averaged ballistic conductance in 2DEGS are presented as an application of this picture.

This paper presents a numerical solution of the hyperbolic heat conduction equation in a thermal barrier coating (TBC) structure under an imposed heat flux on the exterior of the TBC. The non-Fourier heat conduction equation is used to model the heat conduction in the TBC system that predicts the heat flux and the temperature distribution. This study presents a more realistic approach to evaluate in-service performance of thin layers of TBCs typically found in hot sections of land based and aircraft gas turbine engines. In such ultrafast heat conduction systems, the orders of magnitude of the time and space dimensions are extremely short which renders the traditional Fourier conduction law, with its implicit assumption of infinite speed of thermal propagation, inaccurate. There is, therefore, the need for an advanced modeling approach for the thermal transport phenomenon taking place in microscale systems. A hyperbolic heat conduction model can be used to predict accurately the transient temperature distribution of thermal barrier structures of turbine blades. The hyperbolic heat conduction equations are solved numerically using a new numerical scheme codenamed the mean value finite volume method (MVFVM). The numerical method yields minimal numerical dissipation and dispersion errors and captures the discontinuities such as the thermal wave front in the solution with reliable accuracy. Compared with some traditional numerical methods, the MVFVM method provides the ability to model the behavior of the single phase lag thermal wave following its reflection from domain boundary surfaces. In addition, parametric studies of properties of the substrate on the temperature and the heat flux distributions in the TBC revealed that relaxation time of the substrate material, unlike the thermal diffusivity and thermal conductivity has very little effect on the transient thermal response in the TBC. The study further showed that for thin film structures subject to short time durations of heat flux, the hyperbolic model yields more realistic results than the parabolic model.

We investigate the effects of linearly polarized optical radiation on the cyclotron motion of an electron wave packet, considering the full quantum dynamics of the system. Analysis of the Landau-level (LL) spectrum reveals that only intra band cyclotron oscillation frequencies contribute to the effective oscillation frequency of the motion, whereas scattering between electron and hole Landau levels are forbidden. We find that the wave packet dynamics is significantly affected by varying the polarization direction of the electromagnetic radiation. The optical radiation is also affected by its interaction with electrons. Interestingly, we find that chaotic effects are induced by radiation in the dynamics of electron wave packet in an applied uniform magnetic field. Chaotic signatures in the dynamics are diagnosed by computing the relevant out-of-time-order correlation function and analyzed by using Poincaré maps. We attribute the appearance of such chaotic transport of electron wave packet to the nonlinear interaction between the optical radiation and internal cooperative oscillating mode produced by the interplay of relativistic (zitterbewegung) and cyclotron oscillations.