Deterministic Field Research Articles

Quantum radiation and dissipation in relation to classical radiation and radiation reaction

This work continues the investigation of radiation phenomena from atom-field interactions, extending our earlier study of quantum radiation from a stationary atom's internal degree of freedom, modeled by a harmonic oscillator, to the emittance of classical radiation. By assuming that the atom interacts with a quantum scalar field initially in a coherent state, we show how a stochastic component of the internal dynamics of the atom arises from the vacuum fluctuations of the field, resulting in the emittance of quantum radiation, whose reaction induces quantum dissipation in the internal dynamics. We also show how the deterministic mean field drives the internal classical mean component to emit classical radiation and receive classical radiation reaction. Both components are statistically distinct and fully decoupled. It is clearly seen that the effects of the vacuum fluctuations of the field are matched with those of quantum radiation reaction, not with classical radiation reaction, as the folklore goes. In contrast to the quantum component of the atom's internal dynamics, which always equilibrates, the relaxation dynamics of the classical component largely depends on the late-time behavior of the mean field. For the values of the parameters defining the coherent state of the field much greater than unity, if the mean field remains periodic, then the internal dynamics of the atom will appear classical and periodic. If the mean field diminishes with time, then the classical component of the atom's internal dynamics subsides but the quantum component will abide and dynamically equilibrate. This also explains why quantum radiation from a stationary atom is not observed, and a probe located far away only sees classical radiation. Our analysis therefore paints a continuum landscape starting from vacuum fluctuations in the quantum field to classical radiation and radiation reaction.

Global well-posedness of the 3D Navier–Stokes equations perturbed by a deterministic vector field

We are concerned with the problem of global well-posedness of the 3D Navier–Stokes equations on the torus with unitary viscosity. While a full answer to this question seems to be out of reach of the current techniques, we establish a regularization by a deterministic vector field. More precisely, we consider the vorticity form of the system perturbed by an additional transport type term. Such a perturbation conserves the enstrophy and therefore a priori it does not imply any smoothing. Our main result is a construction of a deterministic vector field v=v(t,x) which provides the desired regularization of the system and yields global well-posedness for large initial data outside arbitrary small sets. The proof relies on probabilistic arguments developed by Flandoli and Luo, tools from rough path theory by Hofmanová, Leahy and Nilssen and a new Wong–Zakai approximation result, which itself combines probabilistic and rough path techniques.

Toward Large-Scale Hybrid Edge Server Provision: An Online Mean Field Learning Approach

The efficiency of a large-scale edge computing system primarily depends on three aspects: i) edge server provision, ii) task migration, and iii) computing resource configuration. In this paper, we study the dynamic resource configuration for hybrid edge server provision under two decentralized task migration schemes. We formulate the dynamic resource configuration as an online cost minimization problem, aiming to jointly minimize performance degradation and operation expenditure. Due to the stochastic nature, it is an online learning problem with partial feedback. To address it, we derive a deterministic mean field model to approximate the stochastic edge computing system. We show that the mean field model provides the increasingly accurate full feedback as the system scales. We then propose a learning policy based on the mean field model, and show that our proposed policy performs asymptotically as well as the offline optimal configuration. We provide two ways of setting the policy parameters, which achieve a constant competitive ratio (under certain mild conditions) and a sub-linear regret, respectively. Numerical results show that the mean field model significantly improves the convergence speed. Moreover, our proposed policy under the decentralized task migration schemes considerably reduces the operating cost (by 23%) and incurs little communication overhead.

Statistical Analysis of Electric-Field Distribution and Radiation Characteristics From a Perforated Enclosure Excited by Built-In Devices

The electronic devices working inside the enclosure will affect the internal electromagnetic (EM) environment, and their radiated EM energy will also be coupled out through the apertures, which could affect the surrounding equipment. In this article, the built-in transmission line and printed circuit board are considered, respectively, to analyze their influence on the deterministic and statistical distribution of the internal EM environment at different frequencies and positions. Second, based on the radiation power of the built-in device, combined with the coupling cross-section of the aperture, the statistical method is used to quickly calculate the leaking power outward the perforated enclosure. Finally, a three-dimensional positioning system is developed to measure the statistical characteristics of the internal electric field and the outward radiation power, which are in good agreement with the calculation ones. It is revealed that when the device is working at a high frequency, the field modes excited simultaneously increases, the complexity of the EM environment increases, and the field distribution is complex and chaotic. The change of the frequency or position will cause drastic changes in the deterministic field distribution. However, from the probability density functions of the electric field, the position of the built-in device has little effect on the statistical characteristics.

Nanoscale light field imaging with graphene

Modern nano-optics and nanophotonics rely heavily on the precise formation of nanostructured light fields. Accurate and deterministic light field formation and characterization are indispensable for device operation as well as for revealing the underlying physical mechanisms involved. Despite a significant progress made in detection of scattered light with extremely high precision down to 1 nm resolution, there are only a limited number of techniques for direct subwavelength light mapping which do not rely on measurements of light scattering, fluorescence, or non-linear light conversion. Hence, techniques for direct conversion of light to electrical signals with precise and non-destructive imaging of nanoscale light would be of great benefit. Here, we report a nanoscale light field imaging approach based on photodetection with a p-n junction that is induced and moved inside a graphene probe by gate voltage, formed by a set of external electrodes. The spatial resolution of this electrical scanning technique is determined by p-n junction width, reaching ~ 20 nm. The developed approach is demonstrated with mapping the electric field distribution of a plasmonic slot-waveguide at telecom wavelengths. Our method provides a non-invasive nanoscale light field imaging that ensures extremely high spatial resolution and precision.

Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research.

Indirect-imaging methods involve at least two steps, namely optical recording and computational reconstruction. The optical-recording process uses an optical modulator that transforms the light from the object into a typical intensity distribution. This distribution is numerically processed to reconstruct the object’s image corresponding to different spatial and spectral dimensions. There have been numerous optical-modulation functions and reconstruction methods developed in the past few years for different applications. In most cases, a compatible pair of the optical-modulation function and reconstruction method gives optimal performance. A new reconstruction method, termed nonlinear reconstruction (NLR), was developed in 2017 to reconstruct the object image in the case of optical-scattering modulators. Over the years, it has been revealed that the NLR can reconstruct an object’s image modulated by an axicons, bifocal lenses and even exotic spiral diffractive elements, which generate deterministic optical fields. Apparently, NLR seems to be a universal reconstruction method for indirect imaging. In this review, the performance of NLR isinvestigated for many deterministic and stochastic optical fields. Simulation and experimental results for different cases are presented and discussed.

Impacts of wind field characteristics and non-steady deterministic wind events on time-varying main-bearing loads

Abstract. This work considers the characteristics and drivers of the loads experienced by wind turbine main bearings. Simplified load response models of two different hub and main-bearing configurations are presented, representative of both inverting direct-drive and four-point-mounted geared drivetrains. The influences of deterministic wind field characteristics, such as wind speed, shear, yaw offset, and veer, on the bearing load patterns are then investigated for similarity scaled 5, 7.5, and 10 MW reference wind turbine models. Main-bearing load response in cases of deterministic gusts and extreme changes in wind direction are also considered for the 5 MW model. Perhaps surprisingly, veer is identified as an important driver of main-bearing load fluctuations. Upscaling results indicate that similar behaviour holds as turbines become larger, but with mean loads and load fluctuation levels increasing at least cubically with the turbine rotor radius. Strong links between turbine control and main-bearing load response are also observed.

Deterministic Mean Field Games with Control on the Acceleration and State Constraints

We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure on trajectories. The main results of the paper concern the existence of relaxed equilibria under suitable assumptions. The fact that the optimal trajectories of the related optimal control problem solved by the agents do not form a compact set brings a difficulty in the proof of existence. The proof also requires closed graph properties of the map which associates to initial conditions the set of optimal trajectories.

Observation of in-plane exciton–polaritons in monolayer WSe2 driven by plasmonic nanofingers

Abstract The transition metal dichalcogenides (TMDs) have drawn great research attention, motivated by the derived remarkable optoelectronic properties and the potentials for high-efficient excitonic devices. The plasmonic nanocavity, integrating deep-sub wavelength confinement of optical mode with dramatic localized field enhancement, provides a practical platform to manipulate light–matter interaction. In order to obtain strong exciton–plasmon coupling effects, it’s crucial to match the vibration direction of exciton to the available strong localized in-plane electric field. Herein, we demonstrate the coupling effect of in-plane exciton in monolayer tungsten diselenide (WSe2) to deterministic gap-plasmon field which is produced by nanometrically gapped collapsed nanofingers. The gap-plasmon field which is completely parallel to the in-plane excitons in WSe2 will drive a strong exciton–plasmon coupling at room temperature. More interestingly, it is experimentally observed that the luminescence of exciton–polariton cannot be influenced by the temperature in the range from 77 K to 300 K due to the presence of nanofingers. According to the theoretical analysis results, we attribute this finding to the dielectric screening effect arising from the extremely strong localized electric field of plasmonic nanofingers. This work proposes a feasible way to harness and manipulate the exciton of low-dimensional semiconductor, which might be potential for quantum optoelectronics.

Dispersion of particles in two-dimensional monopolar and dipolar vortices using a Lagrangian stochastic model

The dispersion of particles in two-dimensional vortices, two circular monopoles, and the Chaplygin–Lamb dipole is studied numerically with a Lagrangian stochastic model. The monopoles are the Rankine and the steady Oseen vortex, whose azimuthal velocity profile is irrotational at a long radial distance. The total velocity of each particle is divided into two parts: the deterministic field due to the vortex plus a stochastic velocity representing homogeneous turbulence. The experiments are carried out with thousands of particles to calculate the dispersion as a function of time. The dispersion in the monopoles grows rapidly and then increases at a lower rate as the particles transit toward the potential region. This transition occurs more quickly in the Rankine vortex, so the Oseen vortex has a wider time-lapse to generate a more significant dispersion. In the case of the Chaplygin–Lamb dipole, having an internal and external flow, the dispersion has different behavior depending on which region the particles depart. The dispersion curves describe the exchange of particles between the poles and the outer flow as the dipole drifts. We discuss the capacity of the dipole to transport particles through long distances.

Quantum spin-flavour memory of ultrahigh-energy neutrino

There are two types of uncertainties related to the measurements done on a quantum system: statistical and those related to non-commuting observables and incompatible measurements. The latter indicates the quantum system’s inherent nature and is in the scope of the present study. We explore uncertainties related to the interstellar ultrahigh-energy neutrino and introduce a novel concept: quantum spin-flavour memory. Advanced uncertainty measures are entropic measures, and the effect of the quantum memory reduces the uncertainty. The problem in question corresponds to a real physical event: high-energy Dirac neutrinos emitted by some distant source and propagating towards the earth. The neutrino has a finite magnetic moment and interacts with both deterministic and stochastic interstellar magnetic fields. To describe the effect of a noisy environment, we exploit the Lindblad master equation for the neutrino density matrix. Quantum spin-flavour memory is quantified in terms of the generalized Kraus’s trade-off relation. This trade-off relation converts to the equality when quantum memory is absent. We discovered that while most measures of quantum correlations show their irrelevance, the quantum spin-flavour discord is the quantifier of the quantum spin-flavour memory.

Single-shot mid-infrared incoherent holography using Lucy-Richardson-Rosen algorithm

In recent years, there has been a significant transformation in the field of incoherent imaging with new possibilities of compressing three-dimensional (3D) information into a two-dimensional intensity distribution without two-beam interference (TBI). Most of the incoherent 3D imagers without TBI are based on scattering by a random phase mask exhibiting sharp autocorrelation and low cross-correlation along the depth. Consequently, during reconstruction, high lateral and axial resolutions are obtained. Imaging based on scattering requires an astronomical photon budget and is therefore precluded in many power-sensitive applications. In this study, a proof-of-concept 3D imaging method without TBI using deterministic fields has been demonstrated. A new reconstruction method called the Lucy-Richardson-Rosen algorithm has been developed for this imaging concept. We believe that the proposed approach will cause a paradigm-shift in the current state-of-the-art incoherent imaging, fluorescence microscopy, mid-infrared fingerprinting, astronomical imaging, and fast object recognition applications.

Dimension reduction techniques in deterministic mean field games

We present examples of equations arising in the theory of mean field games that can be reduced to a system in smaller dimensions. Such examples come up in certain applications, and they can be used as modeling tools to numerically approximate more complicated problems. General conditions that bring about reduction phenomena are presented in both the finite and infinite state-space cases. We also compare solutions of equations with noise with their reduced versions in a small-noise expansion.

Label-Free Isolation of Exosomes Using Microfluidic Technologies.

Exosomes are cell-derived structures packaged with lipids, proteins, and nucleic acids. They exist in diverse bodily fluids and are involved in physiological and pathological processes. Although their potential for clinical application as diagnostic and therapeutic tools has been revealed, a huge bottleneck impeding the development of applications in the rapidly burgeoning field of exosome research is an inability to efficiently isolate pure exosomes from other unwanted components present in bodily fluids. To date, several approaches have been proposed and investigated for exosome separation, with the leading candidate being microfluidic technology due to its relative simplicity, cost-effectiveness, precise and fast processing at the microscale, and amenability to automation. Notably, avoiding the need for exosome labeling represents a significant advance in terms of process simplicity, time, and cost as well as protecting the biological activities of exosomes. Despite the exciting progress in microfluidic strategies for exosome isolation and the countless benefits of label-free approaches for clinical applications, current microfluidic platforms for isolation of exosomes are still facing a series of problems and challenges that prevent their use for clinical sample processing. This review focuses on the recent microfluidic platforms developed for label-free isolation of exosomes including those based on sieving, deterministic lateral displacement, field flow, and pinched flow fractionation as well as viscoelastic, acoustic, inertial, electrical, and centrifugal forces. Further, we discuss advantages and disadvantages of these strategies with highlights of current challenges and outlook of label-free microfluidics toward the clinical utility of exosomes.

Epidemics on hypergraphs: spectral thresholds for extinction.

Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible–infected–susceptible setting, spectral conditions characterize whether the disease vanishes. However, modelling human interactions using a graph is a simplification which only considers pairwise relationships. This does not fully represent the more realistic case where people meet in groups. Hyperedges can be used to record higher order interactions, yielding more faithful and flexible models and allowing for the rate of infection of a node to depend on group size and also to vary as a nonlinear function of the number of infectious neighbours. We discuss different types of contagion models in this hypergraph setting and derive spectral conditions that characterize whether the disease vanishes. We study both the exact individual-level stochastic model and a deterministic mean field ODE approximation. Numerical simulations are provided to illustrate the analysis. We also interpret our results and show how the hypergraph model allows us to distinguish between contributions to infectiousness that (i) are inherent in the nature of the pathogen and (ii) arise from behavioural choices (such as social distancing, increased hygiene and use of masks). This raises the possibility of more accurately quantifying the effect of interventions that are designed to contain the spread of a virus.

Probabilistic stability assessment of tunnel-support system considering spatial variability in weak rock mass

Analysis of tunnel-support system stability with uncertain rock mass properties is conducted in this paper. A horseshoe shaped tunnel driven in weak rock mass is analyzed through deterministic, random variable and random field approaches. Performance of the tunnel in probabilistic analysis was assessed by defining three limit states which ensure that tunnel convergence remained below a safe threshold level, the rock bolts installed are embedded sufficiently beyond the depth of yielded rock mass and load induced on liner support does not exceed its capacity. Both unsupported and supported tunnels were analyzed with deterministic, random variable and random field approaches. Fourier series method was applied to discretize the random fields, and random finite difference analysis was conducted using Monte Carlo simulations. Scale of fluctuation (SOF) for isotropic random fields and horizontal and vertical SOF ratios for anisotropic random fields were varied to study their effect on performance of the tunnel and failure mechanisms involved. It was found that SOF significantly influences the output statistics and Pf of the limit states. It was observed that, random variable approach underestimates the performance of the tunnel-support system; however, it can be adopted as conservative option in absence of data required for random field characterization.

Scattered Acoustic Field Above a Rectangular Cavity in a Rigid Plane Insonified by a Deterministic Field

Scattered Acoustic Field Above a Rectangular Cavity in a Rigid Plane Insonified by a Deterministic Field

Sensitivity and robustness of Lagrangian coherent structures in coastal water systems

In coastal water systems, horizontal chaotic dispersion plays a significant role in the distribution and fate of pollutants. Lagrangian Coherent Structures (LCSs) provide useful tools to study the problem of the transport of pollutants and have only recently been applied to coastal waters. While the fundamentals of the LCS approach using idealised analytical flow fields are well established in the literature, there are limited studies on their practical implementations in coastal waters where effects of boundaries and bathymetry frequently become significant. Due to their complex bathymetry and boundaries, unstructured grid systems are commonly used in modelling of coastal waters. For convenient derivation of LCS diagnostics, structured grids are commonly used. Here we examine the effect of mesh resolution, interpolation schemes and additive random noise on the LCS diagnostics in relation to coastal waters. Two kinematic model flows, the double gyre and the meandering jet, as well as validated outputs of a hydrodynamic model of Moreton Bay, Australia, on unstructured grids are used. The results show that LCSs are quite robust to the errors from interpolation schemes used in the data conversion from unstructured to structured grid. Attributed to the divergence in the underlying flow field, the results show that random errors in the order of 1–10% cause a breakdown in the continuity of ridges of maximum finite-time Lyapunov exponents and closed orbit elliptic LCSs. The result has significant implications on the suitability of applying LCS formulations based on a deterministic flow field to diffusive coastal waters.

A stability property in mean field type differential games

The paper is concerned with the feedback approach to the deterministic mean field type differential games. Previously, it was shown that suboptimal strategies in the mean field type differential game can be constructed based on functions of time and probability satisfying the stability condition. This property realizes the dynamic programming principle for the constant control of one player. We present the infinitesimal form of this condition involving analogs of the directional derivatives. In particular, we obtain the characterization of the value function of the deterministic mean field type differential game in the terms of directional derivatives and the set of directions feasible by virtue of the dynamics of the game.

Aerodynamic Data Fusion Toward the Digital Twin Paradigm

This paper considers the fusion of two aerodynamic data sets originating from differing types of physical or computer experiments. This paper specifically addresses the fusion of 1) noisy and in-complete fields from wind-tunnel measurements and 2) deterministic but biased fields from numerical simulations. These two data sources are fused in order to estimate the true field that best matches measured quantities that serve as the ground truth. For example, two sources of pressure fields about an aircraft are fused based on measured forces and moments from a wind-tunnel experiment. A fundamental challenge in this problem is that the true field is unknown and cannot be estimated with 100% certainty. A Bayesian framework is employed to infer the true fields conditioned on measured quantities of interest; essentially a statistical correction to the data is performed. The fused data may then be used to construct more accurate surrogate models suitable for early stages of aerospace design. An extension of the proper orthogonal decomposition with constraints is also introduced to solve the same problem. Both methods are demonstrated on fusing the pressure distributions for flow past the RAE2822 airfoil and the Common Research Model wing at transonic conditions. Comparison of both methods reveals that the Bayesian method is more robust when data are scarce and capable of also accounting for uncertainties in the data. Furthermore, given adequate data, the proper-orthogonal-decomposition-based and Bayesian approaches lead to surprisingly similar results.