Set Of Discrete Levels Research Articles

Discrete level set method enhanced by conformal mapping: an efficient approach for topology optimization of piezoelectric energy harvesters

Discrete level set method enhanced by conformal mapping: an efficient approach for topology optimization of piezoelectric energy harvesters

A mini immersed finite element method for two-phase Stokes problems on Cartesian meshes

Abstract This paper presents a mini immersed finite element (IFE) method for solving two- and three-dimensional two-phase Stokes problems on Cartesian meshes. The IFE space is constructed from the conventional mini element, with shape functions modified on interface elements according to interface jump conditions while keeping the degrees of freedom unchanged. Both discontinuous viscosity coefficients and surface forces are taken into account in the construction. The interface is approximated using discrete level set functions, and explicit formulas for IFE basis functions and correction functions are derived, facilitating ease of implementation.The inf-sup stability and the optimal a priori error estimate of the IFE method, along with the optimal approximation capabilities of the IFE space, are derived rigorously, with constants that are independent of the mesh size and the manner in which the interface intersects the mesh, but may depend on the discontinuous viscosity coefficients. Additionally, it is proved that the condition number has the usual bound independent of the interface. Numerical experiments are provided to confirm the theoretical results.

A novel discrete adjoint-based level set topology optimization method in B-spline space

A novel discrete adjoint-based level set topology optimization method in B-spline space

Atomic Emission Study of the Gross Composition of the Ash Residue of Deposits in Petroleum Refineries

The article discusses atomic emission spectroscopy as an elemental analysis method based on the analysis of optical line emission spectra of atoms in the gas phase. During the transition of one or more electrons from a low energy level (ground state) to a higher energy level (excited state), excess energy is released in the form of radiation, in this state the electron stays for a very short time (8-10 seconds), because it is not stable. Because an atom has only a discrete set of energy levels, then the emission corresponds to a specific value of energy (or frequency and wavelength) in the form of radiation.

An immersed Crouzeix–Raviart finite element method in 2D and 3D based on discrete level set functions

This paper is devoted to the construction and analysis of immersed finite element (IFE) methods in three dimensions. Different from the 2D case, the points of intersection of the interface and the edges of a tetrahedron are usually not coplanar, which makes the extension of the original 2D IFE methods based on a piecewise linear approximation of the interface to the 3D case not straightforward. We address this coplanarity issue by an approach where the interface is approximated via discrete level set functions. This approach is very convenient from a computational point of view since in many practical applications the exact interface is often unknown, and only a discrete level set function is available. As this approach has also not be considered in the 2D IFE methods, in this paper we present a unified framework for both 2D and 3D cases. We consider an IFE method based on the traditional Crouzeix–Raviart element using integral values on faces as degrees of freedom. The novelty of the proposed IFE is the unisolvence of basis functions on arbitrary triangles/tetrahedrons without any angle restrictions even for anisotropic interface problems, which is advantageous over the IFE using nodal values as degrees of freedom. The optimal bounds for the IFE interpolation errors are proved on shape-regular triangulations. For the IFE method, optimal a priori error and condition number estimates are derived with constants independent of the location of the interface with respect to the unfitted mesh. The extension to anisotropic interface problems with tensor coefficients is also discussed. Numerical examples supporting the theoretical results are provided.

Joint Estimation of Expertise and Reward Preferences From Human Demonstrations

When a robot learns from human examples, most approaches assume that the human partner provides examples of optimal behavior. However, there are applications in which the robot learns from nonexpert humans. We argue that the robot should learn not only about the human's objectives, but also about their expertise level. The robot could then leverage this joint information to reduce or increase the frequency at which it provides assistance to its human's partner or be more cautious when learning new skills from novice users. Similarly, by taking into account the human's expertise, the robot would also be able to infer a human's true objectives even when the human fails to properly demonstrate these objectives due to a lack of expertise. In this article, we propose to jointly infer the expertise level and the objective function of a human given observations of their (possibly) nonoptimal demonstrations. Two inference approaches are proposed. In the first approach, inference is done over a finite discrete set of possible objective functions and expertise levels. In the second approach, the robot optimizes over the space of all possible hypotheses and finds the objective function and the expertise level that best explain the observed human behavior. We demonstrate our proposed approaches both in simulation and with real user data.

Delocalized Spectra of Landau Operators on Helical Surfaces

On a flat surface, the Landau operator, or quantum Hall Hamiltonian, has spectrum a discrete set of infinitely-degenerate Landau levels. We consider surfaces with asymptotically constant curvature away from a possibly non-compact submanifold, the helicoid being our main example. The Landau levels remain isolated, provided the spectrum is considered in an appropriate Hilbert module over the Roe algebra of the surface delocalized away from the submanifold. Delocalized coarse indices may then be assigned to them. As an application, we prove that Landau operators on helical surfaces have no spectral gaps above the lowest Landau level.

Tracking Consensus of Multi-Agent Systems Under Switching Topologies via Novel SMC: An Event-Triggered Approach

This paper investigates the tracking consensus issue for second order multi-agent systems (MAS) under switching topologies by using a novel event-triggered sliding mode control strategy. First, in order to compensate for the effect brought by the information transmission caused by event-triggered sampling and the switching topologies respectively, the dynamic sliding mode control (SMC) mechanism is proposed based on two discrete level sets. By considering the event-triggered rules and the sliding mode method jointly, the corresponding limited-information-based protocol is constructed. This technology does not require the system dynamics to reach the sliding mode manifold compared to previous studies. In addition, with the help of the boundary layer technique, the control protocol is designed to be continuous, which can reduce the chattering of the system and increase the life of machine. Through strict mathematical derivation, when the dwell time of switching between different communication graph candidates is within a limited range, it is proved that the consensus error of the nonlinear multi-agent systems (NMAS) with disturbances converges to an adjustable bounded set, and the networked harmonic oscillator systems (NHOS) without disturbances asymptotically reaches zero. Finally, Zeno behavior can be avoided entirely, and several numerical examples are presented to evaluate the efficiency of the proposed algorithms.

A two-grid binary level set method for structural topology optimization

A binary level set method of two-grid type is proposed for structural topology optimization. The method allows both shape and topological changes during evolution with no need for reinitialization. The Galerkin finite element method is used to discretize the linear elasticity equation, the eigenvalue problem in structure and the semi-implicit time discrete level set equation. In order to improve the efficiency of the gradient-type algorithm as well as balance the computational efforts of solvers, a nested two-grid discretization strategy is proposed. The linear elasticity or eigenvalue problem is solved on a coarse mesh, while the level set equation and the smoothing step are both discretized on a fine mesh. A variety of numerical results are given to demonstrate both the efficiency and effectiveness of the algorithm.

Electron-phonon interaction in the dynamics of trap filling in quantum dots

We analyze theoretically the effects of electron-phonon interaction in the dynamics of an electron that can be trapped to a localized state and detrapped to an extended band state of a small quantum dot (QD) using a simple model system. It consists of a one-dimensional tight-binding linear chain of a few sites, having a discrete set of energy levels mimicking the discrete levels of the conduction band of the QD that is connected at its end to another site, the trap, having a single energy level well below the conduction band, where the electron is allowed to interact with a local phonon of a single frequency. In spite of its simplicity, the time-dependent model has no analytical solution but a numerically exact one can be found, producing a rich dynamics. The electronic motion is quasiperiodic in time, with oscillations around a mean value that are basic characteristics of the weak and strong coupling regimes of electron-phonon interaction and set the timescales of the system. Using values of the parameters appropriate for defects in semiconductor QDs, we find these timescales to range typically from tenths of picoseconds to a few picoseconds. The values of the time-averaged trap occupancy strongly depend on the the strength of the electron-phonon interaction and can be as large as $40%$ when the coupling is most efficient, independently of other parameters. An interesting result of the present paper is the formation of resonances at specific values of the electron-phonon coupling parameter that only exist when several levels are allowed to coherently cooperate in the filling of the trap. They are characterized by a trap occupancy that is a periodic function of time with large amplitude and period picturing an electron that is periodically trapped and detrapped. We conclude that the formation of these resonances is a robust consequence of electron-phonon interaction in small systems. Electron-phonon interaction is an efficient mechanism that can provide ca. $50%$ filling of a deep trap state on a subpicosecond to picosecond timescale, much faster than radiative decay occurring in timescales of tens of picoseconds to nanoseconds, while the occupancy of this state will be smaller than ca. $1%$ in the absence of electron-phonon coupling.

Image Texture Analysis and Edge Detection Algorithm Based on Anisotropic Diffusion Equation

This paper uses partial differential equation image processing techniques to establish image texture analysis models based on nonlinear anisotropic diffusion equations for image denoising, image segmentation, and image decomposition. This paper proposes a class of denoising models based on the hybrid anisotropic diffusion equation from the characteristics of different noise types. The model exhibits anisotropic diffusion near the image boundary, which can protect the boundary well, and isotropic diffusion inside the image; so, it can remove the noise effectively. We use the immovable point theory to prove the uniqueness of the model solution and further discuss other properties such as asymptotics of the solution. We propose a class of image texture analysis algorithms based on anisotropic diffusion equations and discrete gray level sets. First, a class of nonconvex generalized functions is proposed to remove the noise from the original image to obtain a smooth image while sharpening the edges. Then, an energy generalization function based on the gray level set is proposed, and the existence of the global minimum of this energy generalization function is discussed. Finally, an equivalent form of this energy generalization is given in the discrete case, and an image texture analysis algorithm is designed based on the equivalent form. The algorithm is improved by initial position optimization, dynamic adjustment of parameters, and adaptive selection of thresholds so that the ants can search along the real edges. Experiments show that the improved algorithm for image edge detection can obtain more complete edges and better detection results. The energy generalization function is calculated directly on the discrete gray level set instead of solving the corresponding partial differential equation, which can avoid the selection of the initial level set and the reinitialization of the level set, thus greatly improving the segmentation efficiency. The new algorithm has a high improvement in segmentation efficiency and can efficiently handle large size complex images.

Spectral collapse in anisotropic two-photon Rabi model

In this communication, based upon a squeezed-state trial wave function, we have performed a simple variational study of the spectral collapse in the anisotropic two-photon Rabi model. Our analysis indicates that the light-matter interaction and the spin-flipping (together with the anisotropy) effectively constitute two competing impacts upon the radiation mode. Whilst the former tries to decrease the radiation mode frequency, the latter may counteract or reinforce it. The light-matter interaction appears to dominate the frequency modulation as its coupling strengths go beyond the critical values, leading to the emergence of the spectral collapse. However, at the critical couplings the dominance of the light-matter interaction is not complete, and incomplete spectral collapse appears. Accordingly, at the critical couplings the eigenenergy spectrum comprises both a set of discrete energy levels and a continuous energy spectrum. The discrete eigenenergy spectrum can be derived via a simple one-to-one mapping to the bound state problem of a particle of variable effective mass in a finite potential well, and the number of bound states available is determined by the energy difference between the two atomic levels. Each of these eigenenergies has a twofold degeneracy corresponding to the spin degree of freedom.

Spectral collapse in two-mode two-photon Rabi model

We have investigated the eigenenergy spectrum of the two-mode two-photon Rabi model at the critical coupling, particularly the special feature “spectral collapse”. The eigenenergy spectrum is found to consist of both a set of discrete energy levels and a continuous energy spectrum. Each of these eigenenergies has a two-fold degeneracy corresponding to the spin degree of freedom. The discrete eigenenergy spectrum has a one-to-one mapping with that of a particle in an isotropic two-dimensional ”Lorentzian function” potential well, and the continuous energy spectrum can be derived from the scattering problem associated with an isotropic two-dimensional potential barrier. The number of bound states available at the critical coupling is determined by the energy difference between the two atomic levels so that the extent of the “spectral collapse” can be monitored straightforwardly.

Dual grid level set method based direct numerical simulations of nucleate boiling with oscillating base plate

We have used Direct Numerical Simulations to study the effect of base plate oscillations on nucleate boiling heat transfer at low super heat in the isolated bubble regime. A sharp interface dual grid level set method (SI-DGLSM) has been used to carry out the numerical simulations. Here, dual grid implies that the grid points for the discretized temperature and level set functions are twice as refined as that for the discretized velocity and pressure fields. A semi-implicit projection method is used to solve the mass, momentum and energy conservation equations. For nucleate boiling on oscillating plate with oscillations perpendicular to plate surface, a lock-on regime has been observed, during which the frequency of bubble departure synchronizes with the frequency of plate oscillation over a range of oscillation amplitude and frequencies. The size of the bubbles have been shown to be effectively controlled by the frequency of plate oscillation within this lock-on regime. The lock-on of bubble departure and plate oscillations is especially robust when the amplitude of plate oscillations is increased. The increase in oscillation amplitude also helps in increasing the average Nusselt number by around 22%. We use data from our simulations to show that the enhancement in Nusselt number can mainly be attributed to larger downflow in the liquid, and therefore thinner thermal boundary layer, due to plate oscillation.

Effects of taxes and safety net pensions on life-cycle labor supply, savings and human capital: The case of Australia

We structurally estimate a life-cycle model of consumption, labor supply and retirement, using data from the Australian HILDA panel. We use the model to evaluate effects of Australia’s Age Pension system and income tax policy on labor supply, consumption and retirement. Our model accounts for human capital, savings, uninsurable wage risk and credit constraints. We account for “bunching” of hours by assuming a discrete set of hours levels, and we investigate labor supply on both the intensive and extensive margins. Our model allows us to quantify the effects of anticipated and unanticipated tax and pension policy changes at different points of the life-cycle. Our results imply that Australia’s Age Pension system as currently designed is poorly targeted. Our simulations suggest that a doubling of taper rates, combined with a 5.9% reduction of income tax rates, would be budget neutral and Pareto improving.

Demystifying the spectral collapse in two-photon Rabi model

We have investigated the eigenenergy spectrum of the two-photon Rabi model at the critical coupling, particularly the special feature “spectral collapse”, by means of an elementary quantum mechanics approach. The eigenenergy spectrum is found to consist of both a set of discrete energy levels and a continuous energy spectrum. Each of these eigenenergies has a two-fold degeneracy corresponding to the spin degree of freedom. The discrete eigenenergy spectrum has a one-to-one mapping with that of a particle in a “Lorentzian function” potential well, and the continuous energy spectrum can be derived from the scattering problem associated with a potential barrier. The number of bound states available at the critical coupling is determined by the energy difference between the two atomic levels so that the extent of the “spectral collapse” can be monitored in a straightforward manner.

Ambiguous phase assignment of discretized 3D geometries in topology optimization

This paper considers topology optimization approaches where the geometry is described by a level set method and the system’s response is discretized on nonconforming meshes while providing a crisp definition of interface and external boundaries. Since the interface is explicitly tracked, the elements intersected by the interface are divided into sub-elements to which a phase needs to be assigned. Due to loss of information in the discretization of the level set field, certain geometrical configurations allow for ambiguous phase assignment of sub-elements, and thus ambiguous definition of the interface. The study presented here focuses on investigating these topological ambiguities in embedded geometries constructed from discretized level set fields on hexahedral meshes. Three-dimensional problems where several intersection configurations can significantly affect the problem’s topology are considered. This is in contrast to two-dimensional problems where ambiguous topological features exist only in one intersection configuration, and identifying and resolving them is straightforward. A set of rules that resolve these ambiguities for two-phase problems is proposed, and algorithms for their implementations are provided. The influence of these rules on the evolution of the geometry in the optimization process is investigated with linear elastic topology optimization problems. These problems are solved by an explicit level set topology optimization framework that uses the extended finite element method to predict physical responses. This study shows that the choice of a rule to resolve topological features can result in drastically different final geometries. However, for the problems studied in this paper, the performances of the optimized design do not differ.

Master equation approach for modeling diatomic gas flows with a kinetic Fokker-Planck algorithm

In recent years the kinetic Fokker-Planck approach for modeling gas flows has become increasingly popular. In the Fokker-Planck ansatz the collision integral of the Boltzmann equation is approximated by a Fokker-Planck operator in velocity space. Instead of solving the resulting Fokker-Planck equation directly, the underlying random process is modeled, which leads to an efficient stochastic solution algorithm. Despite the attention to the Fokker-Planck ansatz, the modeling of polyatomic gases has been addressed only in a few works. In this paper a scheme is presented to extend arbitrary monatomic Fokker-Planck models to model polyatomic species. A master equation approach is used to model internal energy relaxation, but instead of solving the master equation directly, the underlying random process is simulated. Three different models are suggested to describe internal particle energies as continuous scalars or as a set of discrete energy levels. The proposed models are applied on different test cases to demonstrate their accuracy. Within the bounds of expectations, a very good agreement with reference DSMC simulations is achieved.

Homoclinic dynamics in a spatial restricted four-body problem: blue skies into Smale horseshoes for vertical Lyapunov families

The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four-body problem admit certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection -- or homoclinic web. In the present work, the planar restricted four-body problem is viewed as an invariant subsystem of the spatial problem, and the influence of this planar homoclinic skeleton on the spatial dynamics is studied from a numerical point of view. Starting from the vertical Lyapunov families emanating from saddle focus equilibria, we compute the stable/unstable manifolds of these spatial periodic orbits and look for intersections between these manifolds near the fundamental planar homoclinics. In this way, we are able to continue all of the basic planar homoclinic motions into the spatial problem as homoclinics for appropriate vertical Lyapunov orbits which, by the Smale Tangle theorem, suggest the existence of chaotic motions in the spatial problem. While the saddle-focus equilibrium solutions in the planar problems occur only at a discrete set of energy levels, the cycle-to-cycle homoclinics in the spatial problem are robust with respect to small changes in energy.

Multiorbital Quantum Impurity Solver for General Interactions and Hybridizations.

We present a numerically exact inchworm MonteCarlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time hybridization expansion, fails due to the sign problem. Our method therefore enables simulations of impurity problems as they appear in embedding theories without further approximations, such as the truncation of the hybridization or interaction structure or a discretization of the impurity bath with a set of discrete energy levels, and eliminates a crucial bottleneck in the simulation of abinitio embedding problems.