Problem Of Compression Research Articles

Weighted ghost fluid discontinuous Galerkin method for two-medium problems

A new interface treating method is proposed to simulate compressible two-medium problems with the Runge-Kutta discontinuous Galerkin (RKDG) method. In the present work, both the Euler equation and the level-set equation are discretized with the RKDG method which is compact and of high-order accuracy. The linearized interface inside an interface cell is recovered by the level-set function. The new solution of this cell is taken as a convex combination of two auxiliary solutions. One is the solution obtained by the RKDG method for a single-medium cell with proper numerical fluxes, and the other one is the intermediate state of the two-medium Riemann problem constructed in the normal direction. The weights of the two auxiliary solutions are carefully chosen according to the location of the interface inside the cell. Thus, it ensures a smooth transition when the interface leaves one cell and enters a neighboring cell. The entropy-fix technique is adopted to minimize the overshoots or undershoots in problems with large entropy ratio across the interface. The scheme is justified in a 1-dimensional situation and extended to 2-dimensional problems. Several 1-dimensional two-medium problems, including both smooth and discontinuous examples, are simulated and compared with exact solutions. Also, three 2-dimensional benchmark problems are simulated to validate the present method in two-medium problems.

Variational multiscale method for fully coupled thermomechanical interface contact and debonding problems

In this study, a computational framework is proposed for thermomechanical contact and debonding problems with proper thermal resistance at the interface. Using the Variational Multiscale (VMS) framework, we present a fully coupled thermomechanical formulation with an explicit expression of the pressure at the contact interface. The formulation considers the quasi-static balance of the momentum and the transient heat transfer problem in a fully coupled fashion. At the interface, two different contact constitutive models are utilized for tension and compression. For tensile problems, in the mechanical phase, a tensile debonding model is employed, whereas in the thermal phase, the displacement-dependent model is employed. For compressive problems, in the mechanical phase, a Coulomb frictional model is employed while in the thermal phase, a pressure-dependent model is embedded. Because of the naturally derived interface stability terms that possess area- and stress-weighting, the proposed VMS formulation accommodates contact/debonding and contact/frictional sliding at the interface due to both thermal and mechanical loading without losing numerical stability. The proposed method is applied to a class of numerical test problems with discontinuity at the interfaces, and good agreement with analytical and numerical data is achieved.

An efficient secure data compression technique based on chaos and adaptive Huffman coding

Data stored in physical storage or transferred over a communication channel includes substantial redundancy. Compression techniques cut down the data redundancy to reduce space and communication time. Nevertheless, compression techniques lack proper security measures, e.g., secret key control, leaving the data susceptible to attack. Data encryption is therefore needed to achieve data security in keeping the data unreadable and unaltered through a secret key. This work concentrates on the problems of data compression and encryption collectively without negatively affecting each other. Towards this end, an efficient, secure data compression technique is introduced, which provides cryptographic capabilities for use in combination with an adaptive Huffman coding, pseudorandom keystream generator, and S-Box to achieve confusion and diffusion properties of cryptography into the compression process and overcome the performance issues. Thus, compression is carried out according to a secret key such that the output will be both encrypted and compressed in a single step. The proposed work demonstrated a congruent fit for real-time implementation, providing robust encryption quality and acceptable compression capability. Experiment results are provided to show that the proposed technique is efficient and produces similar space-saving (%) to standard techniques. Security analysis discloses that the proposed technique is susceptible to the secret key and plaintext. Moreover, the ciphertexts produced by the proposed technique successfully passed all NIST tests, which confirm that the 99% confidence level on the randomness of the ciphertext.

Parallel discontinuous Galerkin finite element method for computing hyperbolic conservation law on unstructured meshes

PurposeThe discontinuous Galerkin finite element method (DGFEM) is very suited for realizing high order resolution approximations on unstructured grids for calculating the hyperbolic conservation law. However, it requires a significant amount of computing resources. Therefore, this paper aims to investigate how to solve the Euler equations in parallel systems and improve the parallel performance.Design/methodology/approachDiscontinuous Galerkin discretization is used for the compressible inviscid Euler equations. The multi-level domain decomposition strategy was used to deal with the computational grids and ensure the calculation load balancing. The total variation diminishing (TVD) Runge–Kutta (RK) scheme coupled with the multigrid strategy was employed to further improve parallel efficiency. Moreover, the Newton Block Gauss–Seidel (GS) method was adopted to accelerate convergence and improve the iteration efficiency.FindingsNumerical experiments were implemented for the compressible inviscid flow problems around NACA0012 airfoil, over M6 wing and DLR-F6 configuration. The parallel acceleration is near to a linear convergence. The results indicate that the present parallel algorithm can reduce computational time significantly and allocate memory reasonably, which has high parallel efficiency and speedup, and it is well-suited to large-scale scientific computational problems on multiple instruction stream multiple data stream model.Originality/valueThe parallel DGFEM coupled with TVD RK and the Newton Block GS methods was presented for hyperbolic conservation law on unstructured meshes.

Transported PDF modeling of compressible turbulent reactive flows by using the Eulerian Monte Carlo fields method

Although the transported probability density function (PDF) method has been developed for decades, its application has been mainly focused on the low-Mach number flow problems. This work extends the transported PDF method to compressible flow problems. The Eulerian Monte Carlo fields (EMCF) solution method is employed to solve the transported PDF equation for compressible flow problems. A pseudo stagnation enthalpy is introduced and its stochastic partial differential equation is derived to ensure total energy conservation numerically. A new mixing model called interaction by partial exchange with mean (IPEM) is introduced to expand the available choices of mixing models for the EMCF method. The consistency of the EMCF method is examined for solving the transported PDF equation. Numerical implementation details are discussed, such as the density coupling between the compressible flow solver and the EMCF solver, discretization schemes for the mixing terms and the stochastic terms. The implemented compressible flow solver coupled with the EMCF solver is verified and validated in a series of test cases with increasing level of complexity, ranging from a statistically one-dimensional turbulent mixing layer to a self-excited resonance model rocket combustor. It is observed that in general with the increase of compressibility, there is an increase in the sensitivity of the modeling results to the different models and algorithms. This makes it necessary to develop a thorough understanding of the model sensitivity in order to develop a robust and accurate simulation solver for highly compressible turbulent reactive flows. The thermo-acoustic instability inside the model rocket combustor case is captured reasonably, which demonstrates the overall capability of the developed compressible turbulent combustion solver based on the transported PDF method.

A fast transient solver for low-Mach number aerodynamics and aeroacoustics

The fractional step method is an efficient time advancement scheme for problems involving transient incompressible flow. The method is desirable over traditional SIMPLE-like algorithms for its non-iterative nature. This paper presents a technique that extends the fractional step method to low-Mach number compressible flow problems. The proposed pressure-velocity coupling and a transient SIMPLEC algorithm are validated and verified for a 1D acoustic wave propagation and a convective isentropic vortex to qualitatively evaluate their convergence properties. Next, both algorithms are used to predict aerodynamic and aeroacoustic behaviour of flow past a wall-mounted side mirror. The proposed scheme is stable at acoustic CFL number greater than one, and at convective Co number equal one. The L2 error norms of both schemes exhibit second order accuracy as grids are refined, while the new scheme requires significantly less computation effort for an equal error. The new fractional step method consumes only 20% to 35% of the computation effort that is required by the transient SIMPLEC algorithm for the same error, and is easily scalable to a greater number of CPU processors.

A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics

This paper describes a space-time parallel algorithm with space-time adaptive mesh refinement (AMR). AMR with subcycling is added to multigrid reduction-in-time (MGRIT) in order to provide solution efficient adaptive grids with a reduction in work performed on coarser grids. This algorithm is achieved by integrating two software libraries: XBraid (Parallel time integration with multigrid. https://computation.llnl.gov/projects/parallel-timeintegration-multigrid ) and Chombo (Chombo software package for AMR applications—design document, 2014). The former is a parallel time integration library using multigrid and the latter is a massively parallel structured AMR library. Employing this adaptive space-time parallel algorithm is Chord (Comput Fluids 123:202–217, 2015), a computational fluid dynamics (CFD) application code for solving compressible fluid dynamics problems. For the same solution accuracy, speedups are demonstrated from the use of space-time parallelization over the time-sequential integration on Couette flow and Stokes’ second problem. On a transient Couette flow case, at least a $$1.5\times $$ speedup is achieved, and with a time periodic problem, a speedup of up to $$13.7\times $$ over the time-sequential case is obtained. In both cases, the speedup is achieved by adding processors and exploring additional parallelization in time. The numerical experiments show the algorithm is promising for CFD applications that can take advantage of the time parallelism. Future work will focus on improving the parallel performance and providing more tests with complex fluid dynamics to demonstrate the full potential of the algorithm.

Compression of Vehicle Trajectories with a Variational Autoencoder

The perception and prediction of the surrounding vehicles’ trajectories play a significant role in designing safe and optimal control strategies for connected and automated vehicles. The compression of trajectory data and the drivers’ strategic behavior’s classification is essential to communicate in vehicular ad-hoc networks (VANETs). This paper presents a Variational Autoencoder (VAE) solution to solve the compression problem, and as an added benefit, it also provides classification information. The input is the time series of vehicle positions along actual real-world trajectories obtained from a dataset containing highway measurements, which also serves as the target. During training, the autoencoder learns to compress and decompress this data and produces a small, few element context vector that can represent vehicle behavior in a probabilistic manner. The experiments show how the size of this context vector affects the performance of the method. The method is compared to other approaches, namely, Bidirectional LSTM Autoencoder and Sparse Convolutional Autoencoder. According to the results, the Sparse Autoencoder fails to converge to the target for the specific tasks. The Bidirectional LSTM Autoencoder could provide the same performance as the VAE, though only with double context vector length, proving that the compression capability of the VAE is better. The Support Vector Machine method is used to prove that the context vector can be used for maneuver classification for lane changing behavior. The utilization of this method, considering neighboring vehicles, can be extended for maneuver prediction using a wider, more complex network structure.

Additive Tree-Structured Conditional Parameter Spaces in Bayesian Optimization: A Novel Covariance Function and a Fast Implementation.

Bayesian optimization (BO) is a sample-efficient global optimization algorithm for black-box functions which are expensive to evaluate. Existing literature on model based optimization in conditional parameter spaces are usually built on trees. In this work, we generalize the additive assumption to tree-structured functions and propose an additive tree-structured covariance function, showing improved sample-efficiency, wider applicability and greater flexibility. Furthermore, by incorporating the structure information of parameter spaces and the additive assumption in the BO loop, we develop a parallel algorithm to optimize the acquisition function and this optimization can be performed in a low dimensional space. We demonstrate our method on an optimization benchmark function, on a neural network compression problem and on pruning pre-trained VGG16 and ResNet50 models. Experimental results show our approach significantly outperforms the current state of the art for conditional parameter optimization including SMAC, TPE and Jenatton et al. (2017).

Distributed Compression of Correlated Classical-Quantum Sources or: The Price of Ignorance

We resume the investigation of the problem of independent local compression of correlated quantum sources, the classical case of which is covered by the celebrated Slepian-Wolf theorem. We focus specifically on classical-quantum (cq) sources, for which one edge of the rate region, corresponding to the compression of the classical part, using the quantum part as side information at the decoder, was previously determined by Devetak and Winter [Phys. Rev. A 68, 042301 (2003)]. Whereas the Devetak-Winter protocol attains a rate-sum equal to the von Neumann entropy of the joint source, here we show that the full rate region is much more complex, due to the partially quantum nature of the source. In particular, in the opposite case of compressing the quantum part of the source, using the classical part as side information at the decoder, typically the rate sum is strictly larger than the von Neumann entropy of the total source. We determine the full rate region in the generic case, showing that, apart from the Devetak-Winter point, all other points in the achievable region have a rate sum strictly larger than the joint entropy. We can interpret the difference as the price paid for the quantum encoder being ignorant of the classical side information. In the general case, we give an achievable rate region, via protocols that are built on the decoupling principle, and the principles of quantum state merging and quantum state redistribution. Our achievable region is matched almost by a single-letter converse, which however still involves asymptotic errors and an unbounded auxiliary system.

Sublinear-Time Algorithms for Compressive Phase Retrieval

In the problem of compressed phase retrieval, the goal is to reconstruct a sparse or approximately $k$ -sparse vector $x \in \mathbb {C} ^{n}$ given access to $y= |\Phi x|$ , where $|v|$ denotes the vector obtained from taking the absolute value of $v\in \mathbb {C} ^{n}$ coordinate-wise. In this paper we present sublinear-time algorithms for a few for-each variants of the compressive phase retrieval problem which are akin to the variants considered for the classical compressive sensing problem in theoretical computer science. Our algorithms use pure combinatorial techniques and near-optimal number of measurements.

Conference matrices from Legendre C-pairs

Introduction: There are just a few known methods for the construction of symmetric C-matrices, due to the lack of a universal structure for them. This obstruction is fundamental, in addition, the structure of C-matrices with a double border is incompletely described in literature, which makes its study especially relevant. The purpose: To describe the two-border two-circulant construction in detail with the proposal of the concept of C-pairs Legendre. Results: The paper deals with C-matrices of order n=2v+2 with two borders and extends the so called generalized Legendre pairs, v odd, to a wider class of Legendre C-pairs with even and odd v, defined on a finite abelian group G of order v. Such a pair consists of two functions a, b: G→Z, whose values are +1 or −1 except that a(e)=0, where e is the identity element of G and Z is the ring of integers. To characterize the Legendre C-pairs we use the subsets X={xÎG: a(x)=–1} and Y={xÎG: b(x)=–1} of G. We show that a(x−1)=(−1)v a(x) for all x. For odd v we show that X and Y form a difference family, which is not true for even v. These difference families are precisely the so called Szekeres difference sets, used originally for the construction of skew-Hadamard matrices. We introduce the subclass of the special Legendre C-pairs and prove that they exist whenever 2v+1 is a prime power. In the last two sections of the paper we list examples of special cyclic Legendre C-pairs for lengths v<70. Practical relevance: C-matrices are used extensively in the problems of error-free coding, compression and masking of video information. Programs for search of conference matrices and a library of constructed matrices are used in the mathematical network “mathscinet.ru” together with executable on-line algorithms.

A new discontinuous Galerkin mixed finite element method for compressible miscible displacement problem

A new combined discontinuous Galerkin method is proposed for compressible miscible displacement problem in porous media. Here, a splitting positive definite mixed finite element method is used for the pressure and Darcy velocity, while an interior penalty discontinuous Galerkin (IPDG) method is used for the transport equation. The stability and convergence of this algorithm are considered, and the optimal a priori error estimate in l∞(L2) for velocity, pressure and concentration are given. Finally we provide some numerical results to confirm our theoretical analysis, and simulate compressible fluid flows through homogeneous and isotropic porous media.

On Asymptotic Behavior of HLL-Type Schemes at Low Mach Numbers

The HLLEM approximate Riemann solver can capture discontinuities sharply, maintain positive definiteness, and satisfy the entropy condition automatically. These attractive properties make the HLLEM scheme widely used in the simulations of many compressible fluid problems. However, in the simulations of low Mach incompressible flow, the accuracy of HLLEM solver cannot be guaranteed. In the current study, a detailed discrete asymptotic analysis is conducted on the HLLEM scheme and the responsible terms for the loss of accuracy are identified. This allows us to develop two modified methods to solve this low Mach number problem. The first method is to add a low Mach number correction term on the basis of the original HLLEM scheme. The second is to simply rescale the responsible terms with a Mach number-based function. The asymptotic analysis of these two low Mach correction methods shows that the difference between the continuous system and the discrete system disappears, which means the resulting LM-HLLEM and LM-HLLEM2 schemes are both capable of obtaining physically correct solutions in low Mach limit. The results obtained from various test cases demonstrate that both these two HLLEM-type schemes can simulate incompressible and compressible fluid problems accurately and robustly.

Radar Pulse Compression Methods Based on Nonlinear and Quadratic Optimization

This article addresses the problem of radar pulse compression. First, a matched filter at the receiver is assumed and a method to design a transmit waveform characterized by an autocorrelation function with a narrow mainlobe and low sidelobes is proposed. After that, a mismatched filter is considered and a method to design the optimum linear filter receiver is proposed. In both cases, the pursued objectives are minimum sidelobe energy and peak level through a strategy based on quadratic and nonlinear optimization. In this article, we focus particularly on the case of ground weather radars, where the problem of pulse compression is particularly challenging.

The Incidence of Thoracic Outlet Syndrome

Thoracic outlet syndrome (TOS) refers to a constellation of compressive problems that occur at the thoracic outlet. TOS has been recognized since the 19th century, and the "modern" era of treatment, especially for neurogenic TOS, dates from at least the 1970s. Despite this, however, the incidence and prevalence of these syndromes are almost completely unknown. To attempt to answer this fundamental question, we established a prospective database of all patients who presented to our clinic with a diagnosis of potential TOS, as described below. We established a database of all patients referred to our clinic from July 1, 2014 to May 2018. All subjective data, the tentative diagnosis, and plan at the time of the office visit were prospectively recorded. For patients with neurogenic TOS (NTOS), a standardized workup sheet was used based on the Society for Vascular Surgery's recently published reporting standards document. For patients with venous TOS (VTOS), diagnosis was made by clinical examination and ultrasound, and for those with arterial TOS (ATOS), by clinical examination, ultrasound, and cross-sectional imaging when needed. From July 1, 2014, to May 1, 2018, 526 patients were referred to our institution with a diagnosis of possible TOS. Of these, 432 (82%) were referred with symptoms suggestive of NTOS, 84 (16%) with symptoms suggestive of VTOS, and 10 (2%) with findings and/or symptoms suggestive of ATOS. NTOS: After evaluation as per the algorithm previously mentioned, 234 patients (54%) were judged high suspicion for NTOS, 126 (30%) moderate suspicion, and 72 (17%) low suspicion; 360 (83%) of those originally referred were felt to potentially have NTOS. Of the 84 patients with VTOS, 25 (30%) presented with acute Paget-Schroetter syndrome, 41 (48%) with subacute or chronic occlusion, and 18 (21%) with McCleery's syndrome. Finally, 8 of the 10 limbs had true ATOS; of these, 6 (75%) underwent decompression and repair and 2 (25%) endovascular intervention only. Based on referral assumptions and population density in our area, the incidence of NTOS seems to be between 2 and 3 cases per 100,000 people per year and that of VTOS between 0.5 and 1 per 100,000 people per year, ATOS being sporadic. The ratio of those with decent suspicion for NTOS and VTOS, respectively, is about 80:20, whereas that of those undergoing surgical decompression is about 75:25. The rates of NTOS and VTOS, as aforementioned, are approximately 25 and 8 per year in a metropolitan area of 1,000,000, respectively. Although a rare disease, these numbers are not insignificant, although are much lower than prior estimates.

Optimal Coding and the Origins of Zipfian Laws

ABSTRACT The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding – under an arbitrary coding scheme – and show that it predicts Zipf’s law of abbreviation, namely a tendency in natural languages for more frequent words to be shorter. We apply this result to investigate optimal coding also under so-called non-singular coding, a scheme where unique segmentation is not warranted but codes stand for a distinct number. Optimal non-singular coding predicts that the length of a word should grow approximately as the logarithm of its frequency rank, which is again consistent with Zipf’s law of abbreviation. Optimal non-singular coding in combination with the maximum entropy principle also predicts Zipf’s rank-frequency distribution. Furthermore, our findings on optimal non-singular coding challenge common beliefs about random typing. It turns out that random typing is in fact an optimal coding process, in stark contrast with the common assumption that it is detached from cost cutting considerations. Finally, we discuss the implications of optimal coding for the construction of a compact theory of Zipfian laws more generally as well as other linguistic laws.

Properties of a multi-layer multi-span corrugated package

In this article we deal with the problem of cyclic compression of a multilayer multi-span corrugated package by using the finite element method (FEM) and a three-dimensional model (3-D model) of deformation in Ansys. We take into account plastic deformation of the package, as well as the complex law of its propagation and mutual elastic slippage with dry friction over tops of corrugation and in local regions at the tops of corrugation along the package tapes, valid for any geometrical shape of corrugation. This solution can be considered as the second part of the general complex nonlinear problem of cyclic compression of a multilayer multi-span corrugated package with dry friction on contact surfaces. The solution obtained makes it possible to construct any loading processes in the field of elastic-hysteresis package loops. The comparison of elastic-frictional characteristics of the package (EFCs) obtained by calculation and the experimental ones showed their good agreement. The influence of the corrugated package parameters on its EFCs was studied. A number of properties of the package were determined allowing us to draw conclusions and formulate recommendations that make it possible to define the number of package tapes, the required accuracy in the manufacture of corrugations of its tapes, and the choice of the geometric shape of corrugations in almost all cases of practical use of corrugated packages. The solution obtained can be used to determine the effectiveness of a bumper and other protective devices during crash tests of a car for frontal and side impacts and to determine the optimal parameters of these devices by calculating. Certain results and recommendations of this paper can be useful for the calculation of parameters of damping elements of a blisk, hollow wide-chord blades of aircraft GTE fans, ring dampers of rocket engine rotors, as their damping elements are made in the form of multilayer, multi-span corrugated packages.

NUMERICAL SCHEME OF MULTI-MATERIAL COMPRESSIBLE FLOW WITH SHARP INTERFACE ON EULERIAN GRIDS

Numerical simulation of multi-material compressible flow problem is of great importance in both the national defense and industry areas, such as weapon design and blast wave defense. Due to the property of large deformation and high nonlinearity, the efficient simulation of multi-material compressible flow becomes a quite challenging problem. A numerical scheme is developed to carry out the simulation of an immiscible multi-material compressible flow with sharp phase interface on two dimensional and three dimensional unstructured Eulerian grids, which can handle the large deformation of compressible fluid and elastoplastic solid under the extreme conditions. We use the level set method to depict the phase interface numerically, and explicitly reconstruct the phase interface in a piecewise linear manifold. The topological structure of the phase interface is constructed explicitly, which can handle any number of media in the whole computational domain and three media in a single cell. The traditional finite volume method is used to calculate the edge numeircal flux between the same material in adjacent cells, while the phase interface flux is calculated by exactly solving a one dimensional multi-material Riemann problem on the normal direction of the phase interface. The above procedures can keep the conservation of the phase interface flux, and the interaction between two media across the phase interface can keep consistent with the real situation. A robust aggregation algorithm is adopted to build cell patches and adjust the conservation variables around the phase interface, which can effectively remove the numerical instability due to the breakdown of the CFL constraint by the cell fragments. Some classical examples and application problems, such as one-dimensional multi-material Riemann problem, gas-bubble interaction problem, intensive airblast problem, sub-surface blast problem, and blast wave propagation in three dimensional sap, which have a good agreement with the corresponding analytical and experimental results, are presented to validate our numerical scheme.

Non-standard contact conditions in generalized continua: microblock contact model for a Cosserat body

Generalized continuum theories involve non-standard boundary conditions that are associated with the additional kinematic variables introduced in those theories, e.g., higher gradients of the displacement field or additional kinematic degrees of freedom. Accordingly, formulation of a contact problem for such a continuum necessarily requires that adequate contact conditions are formulated for the additional kinematic variables and/or for the respective generalized tractions. In this paper, we address several related open problems, namely, how to enhance the classic contact conditions to include the effects of the additional kinematic variables, how to link the enhanced contact model to the underlying microstructure of the solid, and how to do it in a consistent manner. As a first step towards a new class of contact models for generalized continua, a microblock contact model is derived for a Cosserat solid based on simple micromechanical considerations. To illustrate the non-trivial effects introduced by the non-standard boundary conditions, the problem of compression of an infinite strip with nonaligned microblocks is considered, and the analytical solution is derived for the corresponding boundary layers. A Hertz-like contact problem is also solved numerically with the focus on non-standard features of the solution and on the related size effects.