Canonical Problem Research Articles

Modeling of turbulent flames with the large eddy simulation–probability density function (LES–PDF) approach, stochastic fields, and artificial neural networks

This work proposes a chemical mechanism tabulation method using artificial neural networks (ANNs) for turbulent combustion simulations. The method is employed here in the context of the Large-Eddy Simulation (LES)–Probability Density Function (PDF) approach and the method of stochastic fields for numerical solution, but can also be employed in other methods featuring real-time integration of chemical kinetics. The focus of the paper is on exploring an ANN architecture aiming at improved generalization, which uses a single multilayer perceptron (MLP) for each species over the entire training dataset. This method is shown to outperform previous approaches which take advantage of specialization by clustering the composition space using the Self-Organizing Map (SOM). The ANN training data are generated using the canonical combustion problem of igniting/extinguishing one-dimensional laminar flamelets with a detailed methane combustion mechanism, before being augmented with randomly generated data to produce a hybrid random/flamelet dataset with improved composition space coverage. The ANNs generated in this study are applied to the LES of a turbulent non-premixed CH4/air flame, Sydney flame L. The transported PDF approach is used for reaction source term closure, while numerical solution is obtained using the method of stochastic fields. Very good agreement is observed between direct integration (DI) and the ANNs, meaning that the ANNs can successfully replace the integration of chemical kinetics. The time taken for the reaction source computation is reduced 18-fold, which means that LES–PDF simulations with comprehensive mechanisms can be performed on modest computing resources.

Bottom-up and Layerwise Domain Adaptation for Pedestrian Detection in Thermal Images

Pedestrian detection is a canonical problem for safety and security applications, and it remains a challenging problem due to the highly variable lighting conditions in which pedestrians must be detected. This article investigates several domain adaptation approaches to adapt RGB-trained detectors to the thermal domain. Building on our earlier work on domain adaptation for privacy-preserving pedestrian detection, we conducted an extensive experimental evaluation comparing top-down and bottom-up domain adaptation and also propose two new bottom-up domain adaptation strategies. For top-down domain adaptation, we leverage a detector pre-trained on RGB imagery and efficiently adapt it to perform pedestrian detection in the thermal domain. Our bottom-up domain adaptation approaches include two steps: first, training an adapter segment corresponding to initial layers of the RGB-trained detector adapts to the new input distribution; then, we reconnect the adapter segment to the original RGB-trained detector for final adaptation with a top-down loss. To the best of our knowledge, our bottom-up domain adaptation approaches outperform the best-performing single-modality pedestrian detection results on KAIST and outperform the state of the art on FLIR.

Exceptional compound plasmon-polariton waves

Ordinarily, a trimaterial structure comprising a sufficiently thin metal film interposed between two homogeneous dielectric materials guides compound plasmon-polariton (CPP) waves, for which the fields on both sides of the metal film decay exponentially with distance from the nearest metal/dielectric interface. However, if one of the dielectric materials is anisotropic, then the trimaterial structure can guide an exceptional CPP wave for a particular propagation direction. On the side of the metal film occupied by the anisotropic dielectric material, the fields of the exceptional CPP wave decay as the product of a linear function and an exponential function of the distance from the nearest metal/dielectric interface. The canonical boundary-value problem for CPP-wave propagation has been analyzed and solved numerically; thereby, the spatial field profiles for exceptional CPP waves for a uniaxial-dielectric/metal/isotropic-dielectric structure have been established.

Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow

Thermal hydraulics, in certain components of nuclear reactor systems, involve complex flow scenarios, such as flows assisted by free jets and stratified flows leading to turbulent mixing and thermal fluctuations. These complex flow patterns and thermal fluctuations can be extremely critical from a reactor safety standpoint. The component-level lumped approximations (0D) or one-dimensional approximations (1D) models for such components and subsystems in safety analysis codes cannot capture the physics accurately, and may introduce a large degree of modeling uncertainty. On the other hand, high-fidelity computational fluid dynamics codes, which provide numerical solutions to the Navier–Stokes equations, are accurate but computationally intensive, and thus cannot be used for system-wide analysis. An alternate way to improve reactor safety analysis is by building reduced-order emulators from computational fluid dynamics (CFD) codes to improve system scale models. One of the key challenges in developing a reduced-order emulator is to preserve turbulent mixing and thermal fluctuations across different-length scales or time-scales. This paper presents the development of a reduced-order, non-linear, “Markovian” statistical surrogate for turbulent mixing and scalar transport. The method and its implementation are demonstrated on a canonical problem of differentially heated channel flow, and high-resolution direct numerical simulations (DNS) data are used for emulator or surrogate development. This statistical surrogate model relies on Kramers–Moyal expansion and emulates the turbulent velocity signal with a high degree of accuracy.

Modified Butterworth Filters in Solving the Inverse Problem of Analytical Design of Optimal Controllers

In this work, for linear stationary one-dimensional control objects, the inverse problem of analytical design of optimal controllers (ADOC) is considered, which consists in determining the weight coefficients of the quadratic functional of the optimality of the control process that provide the closed-loop control system with the specified values of the time of transient processes and overshoot. The time of the transient process (regulation time) of the synthesized system is understood in the sense of the classical theory of automatic control and is determined using a " tube" , the value of which is taken, in contrast to known works, equal to the required (desired) small value of the system overshoot of a few percent (2—5 %). The equality of the percentage values characterizing the " tube" and the desired overshoot of the synthesized system is a necessary condition for the maximum response rate of linear dynamic systems and, accordingly, ensures the unambiguity of the solution of the considered inverse ADOC problem in the class of fast-response systems. The proposed solution method provides for the transformation of the ADOC problem to the canonical form, in which the control object is described by a matrix differential equation in the Frobenius form, and the quality functional is defined as the integral of the sum of the products of the object’s canonical phase coordinates, as well as the square of the control signal with appropriate weight coefficients. It is shown that the solution of the inverse canonical ADOC problem is determined by the values of only three nonzero weight coefficients of the criterion, and one of them has a single value. The values of the other two coefficients are proposed to be found in the process of modeling the synthesized optimal control system from the conditions of providing for it a given control time and a given overshoot. To obtain numerical estimates of the two main weight coefficients of the quadratic quality criterion, the solution of the ADOC problem is considered with the limiting increase in the values of these weight coefficients. By the limiting solution of the ADOC problem, the transfer functions of dynamic systems with the limiting (maximum) speed are determined, which have a given overshoot of 4.321 %. The dynamical systems described by these transfer functions are called modified Butterworth filters due to the fact that the well-known Butterworth filters are obtained as their special case with a zero value of a certain constant. The parameters and indicators of the dynamics of these filters up to the sixth order are presented in the table. Using the indicators of Butterworth filters, numerical estimates of the weight coefficients of the quadratic quality criterion are established. Transfer functions of modified Butterworth filters are recommended to be used as reference transfer functions of synthesized high-speed control systems.

Provably Near-Optimal Simple Markdown Readjustment Pricing Policies

We consider a canonical revenue management problem wherein a monopolist seller seeks to maximize expected total revenues from selling a fixed inventory of a product to customers who arrive sequentially over time, and the seller is restricted to implement a pricing policy that is non-increasing over time (i.e., markdown pricing). Gallego and van Ryzin (1994) show that the simplest non-increasing price policy, the fixed price policy, is asymptotically optimal in the high-volume regime where both the seller's initial inventory and the length of the selling horizon are proportionally scaled. Specifically, the revenue loss of the fixed price policy is O( k^{1/2}), where k is the system's scaling parameter. In the present paper, we present a novel real-time pricing policy. This policy repeatedly updates the fixed price policy in Gallego and van Ryzin (1994) by taking into account the volatility of the historic sales and forcing the price process to be non-increasing over time. We show that if the seller updates the price for only a single time, then the revenue loss of our policy can be arbitrarily close to O( k^{1/3} \ln k). If the seller updates the prices with a frequency O( \ln k / \ln \ln k ), then the revenue loss of our policy can be arbitrarily close to O( ( \ln k )^3 ). These results are novel and show the power of dynamic pricing in the presence of the markdown restriction.

Deep learning or interpolation for inverse modelling of heat and fluid flow problems?

PurposeThe purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear and nonlinear behaviour.Design/methodology/approachA series of runs were conducted for a canonical test problem. These were used as databases or “learning sets” for both interpolation algorithms and deep neural networks. A second set of runs was conducted to test the prediction accuracy of both approaches.FindingsThe results indicate that interpolation algorithms outperform deep neural networks in accuracy for linear heat conduction, while the reverse is true for nonlinear heat conduction problems. For heat convection problems, both methods offer similar levels of accuracy.Originality/valueThis is the first time such a comparison has been made.

High-phase-speed Dyakonov surface waves

The canonical boundary-value problem for Dyakonov-surface-wave propagation in a fixed direction guided by the planar interface of a uniaxial dielectric material and an isotropic nondissipative dielectric material was solved. Both partnering materials were taken to be homogeneous and the constitutive parameters for both to lie within the ranges of available materials. Solutions were found for which the phase speed of the Dyakonov surface wave is greater than the phase speed of a plane wave in the bulk isotropic partnering material.

Hyperbolic discounting and the time‐consistent solution of three canonical environmental problems

AbstractIn this paper I propose a time‐consistent method of discounting hyperbolically and apply it to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, and (iii) economic growth and pollution. I show that, irrespective of potentially high initial discount rates, time‐consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time‐consistent hyperbolic discounting. This result is also confirmed for open‐access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the modified Green Golden Rule.

Hyperbolic Discounting and the Time-Consistent Solution of Three Canonical Environmental Problems

In this paper I propose a time-consistent method of discounting hyperbolically that contains the discount rate implied by Gamma discounting as a special case. I apply the discounting method to three canonical environmental problems: (i) optimal renewable resource use, (ii) the tragedy of the commons, (iii) economic growth and pollution. I then compare results with those for conventional exponential discounting using the normalization that both methods provide the same present value of an infinite constant flow. I show that, irrespective of potentially high initial discount rates, time-consistent hyperbolic discounting leads always to a steady state of maximum yield, or, if the environment enters the utility function, a steady state where the Green Golden Rule applies. While (asymptotic) extinction is a real threat under exponential discounting it is impossible under time-consistent hyperbolic discounting. This result is also confirmed for open access resources. In a model of economic growth and pollution, hyperbolic discounting establishes the Golden Rule of capital accumulation and the Modified Green Golden Rule.

Aggregative Efficiency of Bayesian Learning in Networks

When individuals in a social network learn about an unknown state from private signals and neighbors' actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are a log-linear function of observations and admit a signal-counting interpretation of accuracy. This generates a fine-grained ranking of networks based on their aggregative efficiency index. Networks where agents observe multiple neighbors but not their common predecessors confound information, and we show confounding can make learning very inefficient. In a class of networks where agents move in generations and observe the previous generation, aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Generations after the first contribute very little additional information due to confounding, even when generations are arbitrarily large.

Effects of Sampling and Prediction Horizon in Reinforcement Learning

Plain reinforcement learning (RL) may be prone to loss of convergence, constraint violation, unexpected performance, etc. Commonly, RL agents undergo extensive learning stages to achieve proper functionality. This is in contrast to classical control algorithms, which are typically model-based. A direction of research is the fusion of RL with such algorithms, especially model-predictive control (MPC). This, however, introduces new hyper-parameters related to the prediction horizon. Furthermore, RL is usually concerned with Markov decision processes. Nevertheless, most of the real environments are not time-discrete. The factual physical setting of RL consists of a digital agent and a time-continuous dynamical system. There is thus, in fact, yet another hyper-parameter – the agent sampling time. In this paper, we investigate the effects of prediction horizon and sampling of two hybrid RL-MPC agents in a case study with a mobile robot parking, which is, in turn, a canonical control problem. We benchmark the agents with a simple variant of MPC. The sampling showed a “sweet spot” behavior, whereas the RL agents demonstrated merits at shorter horizons.

Physics guided machine learning using simplified theories

Recent applications of machine learning, in particular deep learning, motivate the need to address the generalizability of the statistical inference approaches in physical sciences. In this Letter, we introduce a modular physics guided machine learning framework to improve the accuracy of such data-driven predictive engines. The chief idea in our approach is to augment the knowledge of the simplified theories with the underlying learning process. To emphasize their physical importance, our architecture consists of adding certain features at intermediate layers rather than in the input layer. To demonstrate our approach, we select a canonical airfoil aerodynamic problem with the enhancement of the potential flow theory. We include the features obtained by a panel method that can be computed efficiently for an unseen configuration in our training procedure. By addressing the generalizability concerns, our results suggest that the proposed feature enhancement approach can be effectively used in many scientific machine learning applications, especially for the systems where we can use a theoretical, empirical, or simplified model to guide the learning module.

A stochastic modeling strategy for intermittently unstable Ekman–Stokes boundary layers

AbstractWe numerically investigate stable and intermittently unstable Ekman–Stokes boundary layers (ESBLs) as canonical problem for oscillatory near‐surface flows in Earth's ocean and atmosphere. The configuration is given by a neutrally‐stratified Newtonian fluid above a horizontal wall that resides in a rotating frame of reference. A flow is excited relative to this frame by lateral wall oscillations with prescribed amplitude and frequency. We utilize the stochastic one‐dimensional turbulence (ODT) model and investigate it's capabilities for time‐resolved numerical simulations from the laminar to the turbulent flow regime. The results obtained so far suggest that the model is able to capture the leading‐order transient dynamics of the laminar and turbulent ESBL. We conclude that ODT is an economical and reasonably accurate tool for studying transient boundary layers.

A Surprising Observation in the Quarter-Plane Diffraction Problem

In this paper, we revisit Radlow's highly original attempt at a double Wiener-Hopf solution to the canonical problem of wave diffraction by a quarter-plane. Using a constructive approach, we reduce the problem to two equations, one containing his somewhat controversial ansatz, and an additional compatibility equation. We then show that despite Radlow's ansatz being erroneous, it gives surprisingly accurate results in the far-field, in particular for the spherical diffraction coefficient. This unexpectedly good result is established by comparing it to results obtained by the recently established modified Smyshlyaev formulae.

Analytical continuation of two-dimensional wave fields.

Wave fields obeying the two-dimensional Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing ideal boundary conditions. This is for example the case for the classical canonical problems of diffraction by a half-line or a segment. In the present work, it is shown that such wave fields admit an analytical continuation into the domain of two complex coordinates. The branch sets of such continuation are given and studied in detail. For a generic scattering problem, it is shown that the set of all branches of the multi-valued analytical continuation of the field has a finite basis. Each basis function is expressed explicitly as a Green’s integral along so-called double-eight contours. The finite basis property is important in the context of coordinate equations, introduced and used by the authors previously, as illustrated in this article for the particular case of diffraction by a segment.

3D elastic plane-wave diffraction by a stress-free wedge for incident skew angles below the critical angle in diffraction

Elastic plane wave diffraction by a stress-free wedge is a canonical problem of interest to researchers in many different fields. To our knowledge, no fully analytical resolution has been found and semi-analytical evaluations of asymptotic approximations have therefore become a common approach. In this paper, a method called the spectral functions method is developed in a 3D configuration, meaning that the incident ray is not necessarily in the plane normal to the wedge edge. The diffracted displacement field is expressed as an integral in terms of two unknown functions called the spectral functions. These functions are decomposed into two parts: one which can be computed analytically and the other which is approached numerically using a collocation method. The details of the corresponding numerical scheme are given and first numerical validations are presented. The presented method is valid for incident skew angles which are below the critical angle in diffraction.

Particle-resolved simulation of freely evolving particle suspensions: Flow physics and modeling

The objective of this study is to understand the dynamics of freely evolving particle suspensions over a wide range of particle-to-fluid density ratios. The dynamics of particle suspensions are characterized by the average momentum equation, where the dominant contribution to the average momentum transfer between particles and fluid is the average drag force. In this study, the average drag force is quantified using particle-resolved direct numerical simulation in a canonical problem: a statistically homogeneous suspension where an imposed mean pressure gradient establishes a steady mean slip velocity between the phases. The effects of particle velocity fluctuations, particle clustering, and mobility of particles are studied separately. It is shown that the competing effects of these factors could decrease, increase, or keep constant the drag of freely evolving suspensions in comparison to fixed beds at different flow conditions. It is also shown that the effects of particle clustering and particle velocity fluctuations are not independent. Finally, a correlation for interphase drag force in terms of volume fraction, Reynolds number, and density ratio is proposed. Two different approaches (symbolic regression and predefined functional forms) are used to develop the drag correlation. Since this drag correlation has been inferred from simulations of particle suspensions, it includes the effect of the motion of the particles. This drag correlation can be used in computational fluid dynamics simulations of particle-laden flows that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.

Study of Argon and Xenon gas properties on DC-glow discharge plasma

With the advances in the plasma technology in several fields as waste management, space technology and medical applications, non-thermal plasmas have become popular. They replace the combustion fuels for stationary hall thrusters and require minimal voltage to sustain longer duration. Generally, non-reactive gases such as Xenon, Argon, Krypton in a pure or mixture form is used to generate plasma, in order to have overall better performance of the system. Hence, the study of these gases and its properties becomes very crucial for further improvement in any kind of application. Xenon has proven to be most efficient in Hall thruster as compared to the other gases, but its limited availability and high cost has led to the idea of replacing it with other gases that are in abundant. As the DC glow discharge is considered to be canonical problem of interest, the paper focuses on modelling and simulation of 1-D and 2-D. DC glow discharge tubes using Argon and Xenon as gases to generate plasma and study its properties. The trend in distribution of electron density, electron temperature and electric potential have shown little variation. However, the magnitude on electron density is slightly higher for Argon relative to Xenon for given operating conditions in 1-D simulation and in the case of 2-D simulation the diffusive nature in lateral direction has shown higher peak value for Xenon.

A Scalable Platform for Distributed Object Tracking Across a Many-Camera Network

Advances in deep neural networks (DNN) and computer vision (CV) algorithms have made it feasible to extract meaningful insights from large-scale deployments of urban cameras. Tracking an object of interest across the camera network in near real-time is a canonical problem. However, current tracking platforms have two key limitations: 1) They are monolithic, proprietary and lack the ability to rapidly incorporate sophisticated tracking models, and 2) They are less responsive to dynamism across wide-area computing resources that include edge, fog, and cloud abstractions. We address these gaps using Anveshak, a runtime platform for composing and coordinating distributed tracking applications. It provides a domain-specific dataflow programming model to intuitively compose a tracking application, supporting contemporary CV advances like query fusion and re-identification, and enabling dynamic scoping of the camera network's search space to avoid wasted computation. We also offer tunable batching and data-dropping strategies for dataflow blocks deployed on distributed resources to respond to network and compute variability. These balance the tracking accuracy, its real-time performance, and the active camera-set size. We illustrate the concise expressiveness of the programming model for four tracking applications. Our detailed experiments for a network of 1000 camera-feeds on modest resources exhibit the tunable scalability, performance, and quality trade-offs enabled by our dynamic tracking, batching, and dropping strategies.