Problem Of Compression Research Articles

On compressive self-calibration with structural constraints via alternating minimization

This paper considers the compressive bilinear self-calibration problem with explicit low-dimensional structural constraints. The celebrated proximal alternating linearized minimization (PALM) framework is adapted to simultaneously allow general sub-sampling schemes and structure-promoting regularizers. For the first time in literature, we refine the conditional convergence guarantees of PALM and show that the parameter commonly adopted to remove the scaling ambiguity as well as the structural penalties can ensure the unconditional convergence independent of strict assumptions on the statistical properties of the measurements, subspaces, number of snapshots, or initial iterates. In particular, we impose sparse and small total variation structures on the target signals and provide detailed numerical procedures for efficient computations. The extension to the complex-valued case is also made and extensive numerical experiments are carried out to corroborate the theoretical claims. Different choices of sub-sampling schemes and compression rates are simulated to support the effectiveness of the proposed algorithm under various settings. We also make comparisons with the state-of-art competing methods and the superiority of our proposed algorithm is empirically verified.

Physics-informed neural networks for weakly compressible flows using Galerkin–Boltzmann formulation

In this work, we study the Galerkin–Boltzmann formulation within a physics-informed neural network (PINN) framework to solve flow problems in weakly compressible regimes. The Galerkin–Boltzmann equations are discretized with second-order Hermite polynomials in microscopic velocity space, which leads to a first-order conservation law with six equations. Reducing the output dimension makes this equation system particularly well suited for PINNs compared with the widely used D2Q9 lattice Boltzmann velocity space discretizations. We created two distinct neural networks to overcome the scale disparity between the equilibrium and non-equilibrium states in collision terms of the equations. We test the accuracy and performance of the formulation with benchmark problems and solutions for forward and inverse problems with limited data. We compared our approach with the incompressible Navier–Stokes equation and the D2Q9 formulation. We show that the Galerkin–Boltzmann formulation results in similar L2 errors in velocity predictions in a comparable training time with the Navier–Stokes equation and lower training time than the D2Q9 formulation. We also solve forward and inverse problems for a flow over a square, try to capture an accurate boundary layer, and infer the relaxation time parameter using available data from a high-fidelity solver. Our findings show the potential of utilizing the Galerkin–Boltzmann formulation in PINN for weakly compressible flow problems.

Recovery of compaction resources in internal dump of gently inclined composite coal seam open-pit mine

In the production and construction process of a slowly inclined composite coal seam surface mine in China, the problem of coal compression by the non-working slope is common, but the research on coal recovery is usually conducted for the end slope compression problem. Due to the small economic and reasonable stripping ratio in the early stage of infrastructure construction in an open-pit mine, the buried deep coal seam has not yet been mined and is covered by internal dumping. In recent years, with the gradual increase of the economic and reasonable stripping ratio, the mining of coal seam covered by internal dumping site has become feasible. This paper puts forward the mining scheme for this problem. In this paper, a mathematical model is established, and the trench between the inner dump and the non-working side is used as the working platform for coal seam mining. The relationship between stripping height, working line length and mining width of coal seam is studied. The variation law of production stripping ratio, remining amount, repeated stripping amount and mining width is further analyzed. At the same time, the influence of production stripping cost on the economic and reasonable stripping ratio is studied, and the relationship between transportation cost and discharge distance is established, so as to indirectly determine the relationship between mining width and economic and reasonable stripping ratio. Finally, it is found that the relationship between mining net income and mining width is first proportional and then inversely proportional. Taking an open-pit mine as an example, through the quantitative analysis of economic indicators, the net income of coal mining under different mining widths is calculated. The results show that when the mining width is 271 m, the economic benefit of the inner row mining is the highest, and the net income reaches 2021.4575 million yuan. At this time, the production stripping ratio is 5.25, which is less than the economic and reasonable stripping ratio of 6.95. The practical significance of the results is to improve the overall economic benefits and recovery rate of mining enterprises, and ensure the safe, green and efficient mining of mines.

Сompression and Shear of an Ideal-plastic Wedge with a Rough Stamp (Frictional Contact Model)

The transfer of shear force through frictional contact on rough surfaces of precompressed plastic bodies is studied. As a contact model, we consider the problem of plastic compression of a wedge by a rough flat stamp with the condition of Prandtl friction on the contact surface. A technique is proposed for determining the maximum shear load perceived by frictional contact.

Modeling and performance estimation for L-shaped OWC wave energy converters with a theoretical correction for spring-like air compressibility

The investigation of Oscillating Water Columns (OWC) has gained significant attention in recent years thanks to their resilient structural design, allowing them to withstand harsh environmental conditions. This study focuses on the L-shaped OWC (L-OWC) due to its excellent energy capture efficiency. It should be noted that air compressibility plays a significant role in the plenum chamber of the OWC, especially at full scale. The present paper proposes a scaling-rematched approach, facilitating the evaluation of hydrodynamic coefficients and the performance estimation with a theoretical correction for the unmatched scaling problem of spring-like air compressibility. The methodology is applied successfully to a model-scale L-OWC design, employing three-dimensional, incompressible-flow simulations combined with an impeller model. The present study reveals the hydrodynamic characteristics (advantages) of the L-OWC: small fluid damping coefficient and large added mass, and hence the possibility that the spring-like air compressibility can be used to raise the efficiency of power capturing. Furthermore, there exists an interval where the air compressibility has a positive effect on the performance, not only having a significantly longer span than that of the conventional OWC but also much more directly matching the period range of high energy potential found in the wave climate of Northeastern Taiwan waters.

Symmetry and structure in the “Generalized Plasma Focus problem”

The “Generalized Plasma Focus problem” refers to a generic class of plasma propagation phenomena that share many features of a dense plasma focus device. Its recent theoretical development has been shown to predict some features of the pinch phase in PF-1000 and POSEIDON. The theory attempts to decompose the plasma propagation problem into two weakly interdependent subproblems. This is achieved by expressing every physical variable of an applicable continuum model of the plasma as the product of a scaling parameter, which contains device-related information and represents its numerical magnitude, and a scaled variable that is devoid of device-related information, is of order unity, and represents the spatiotemporal structure of that variable. The first subproblem seeks a traveling surface of revolution whose local normal velocity equals the scaling parameter for velocity and is aligned with the magnetic force density. Spatiotemporal distributions of all the scaled variables must move along with this reference surface by definition. This paper explores the resulting scaling theory and its symmetry properties. A new coordinate transformation results in a formula for the spatiotemporal distribution of the magnetic field of the curved and non-steady plasma sheath. New insights into the snowplow effect are obtained. A current sheath with a rear boundary exists only when the current is decreasing and only when the current carrying plasma is less dense than the fill gas. The current sheath thickness is the same for small and large devices. The geomagnetic flux compression problem has an exact solution.

Gaussian smoothed particle hydrodynamics: A high-order meshfree particle method

Smoothed particle hydrodynamics (SPH) has attracted significant attention in recent decades, and exhibits special advantages in modeling complex flows with multiphysics processes and complex phenomena. Its accuracy depends heavily on the distribution of particles, and will generally be lower if the particles are distributed non-uniformly. A high-order SPH scheme is proposed in the present work for simulating both compressible and incompressible flows. It uses a Gaussian quadrature rule to perform the particle approximation of SPH by introducing Gaussian nodes. Unfortunately, the Gaussian nodes hardly overlap with SPH particles due to the Lagrangian feature, and thus we use a high-order interpolation method to obtain the corresponding physical quantities at the Gaussian nodes. The accuracy and robustness of the proposed Gaussian SPH are demonstrated by several numerical tests, including the Sod problem, Poiseuille flow, Couette flow, cavity flow, Taylor–Green vortex and dam break flow, and a convergence analysis is also conducted to evaluate the effects of particle resolution and distribution for reconstructing a given function. The simulation results for each test case are in good agreements with the available analytical, experimental or numerical results, showing that the proposed Gaussian SPH method is accurate and reliable but expensive for simulating compressible and incompressible flow problems.

Theory and Modelling of Isotropic Turbulence: From Incompressible through Increasingly Compressible Flows

Homogeneous isotropic turbulence (HIT) has been a useful theoretical concept for more than fifty years of theory, modelling, and calculations. Some exact results are revisited in incompressible HIT, with special emphasis on the 4/5 Kolmogorov law. The finite Reynolds number effect (FRN), which yields corrections to that law, is investigated, using both Kármán–Howarth-type equations and a statistical spectral closure of the Eddy-Damped Quasi-Normal Markovian (EDQNM)-type. This discussion offers an opportunity to give an extended review of such spectral closures, from weak turbulence, as in wave turbulence theory, to a strong one. Extensions of the 4/5 or 4/3 Kolmogorov/Monin laws to anisotropic cases, such as stably stratified and MHD turbulence, are briefly touched on. Before addressing more recent work on compressible isotropic turbulence, the simplest case of quasi-incompressible turbulence subjected to externally imposed isotropic compression or dilatation is presented. Rapid distortion theory is found to be a poor model in this isotropic case, in contrast with its relevance in strongly anisotropic flow cases. Accordingly, a fully nonlinear approach based on a rescaling of all fluctuating variables is used, in order to show its interplay with the linear operator. This opens the discussion on the cases of homogeneous incompressible turbulence, where RDT and nonlinear models are relevant, provided that anisotropy is accounted for. Finally, isotropic compressible flows of increasing complexity are considered. Recent studies using weak turbulence theory, modelling, and DNS are discussed. A final unpublished study involves interactions between the solenoidal mode, inherited from incompressible turbulence, and the acoustic and entropic modes, which are specific to the compressible problem. An approach to acoustic wave turbulence, with resonant triads, is revisited on this occasion.

Strong observational support for the [formula omitted] timeline in the early universe

JWST’s recent discovery of well-formed galaxies and supermassive black holes only a few hundred Myr after the big bang seriously challenges the timeline predicted by ΛCDM. Now, the latest identification of polycyclic aromatic hydrocarbons (PAHs) at z=6.71, together with these earlier inconsistencies, makes the time compression problem in this model quite overwhelming. We consider the timeline associated with the formation and growth of PAH grains based on current astrophysical models and argue that their appearance at z=6.71 favors the structure formation history in Rh=ct rather than that of Planck-ΛCDM. We estimate the time at which they must have started growing in each case, and then trace their history through various critical events, such as the end of the ‘dark ages’, the beginning of Pop III star formation, and the onset of reionization. Together, these three distinct discoveries by JWST, viz. high-z galaxies, high-z quasars and the surprisingly early appearance of PAHs, all paint a fully consistent picture in which the timeline in ΛCDM is overly compressed at z≳6, while strongly supporting the expansion history in the early Universe predicted by Rh=ct.

Preferential evaluation of coal filling mining scheme under building pressure based on improved grey target decision-making model of game theory

The problem of coal compression under buildings is common in underground mining of coal mines in China. The selection of traditional mining programme is subjective and lacks scientific rationality. In order to solve this problem, this paper studies the evaluation index system and model applicable to the selection of coal filling mining scheme under buildings. A multi-objective evaluation index system integrating economic, technical and adaptive factors is constructed. And an integrated optimization model is established, which is based on the traditional grey target model, combining the game theory optimal combination of weights with the hierarchical analysis method, entropy weight method, Critic method to determine the weights, and then introducing the TOPSIS model and the Mars distance to establish an improved grey target decision-making model. The validity of the evaluation index system and model is verified by taking the example of coal mining under pressure of buildings in five mining areas of a coal mine, which provides technical support for decision makers. This study helps to scientifically and reasonably carry out the preferred mining scheme of coal filling under building pressure.

On immiscibility preservation conditions of material interfaces in the generic five-equation model

Interfaces separating pure materials and mixtures tend to be severely smeared with interface-capturing methods for compressible multi-material flows, necessitating the requirement of various interface-sharpening techniques. However, these techniques have various problems related to consistency, conservation, and thermodynamic compatibility. In this work, we derive a general theoretical formulation of interface-sharpening techniques for the generic five-equation model. This theoretical formulation is not only conservative in mass, momentum, and total energy but also asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed, and is independent of various specific numerical algorithms. We further propose a general numerical method to solve this theoretical formulation. The proposed method is consistent and conservative, and it prevents spurious errors at the interfaces. Examples of one- and two-dimensional multimaterial compressible flow problems, including shocks and interfaces, are considered to verify the analysis and demonstrate the efficiency of the method.

Multiobjective Evolutionary Generative Adversarial Network Compression for Image Translation

Generative Adversarial Networks (GANs) have achieved remarkable success in image translation tasks. However, its prohibitive computational overhead has been a major hurdle for deployment on resource constrained platforms. Due to the training instability and the complicated network architecture, existing model acceleration techniques cannot appropriately handle the GAN compression problem. To cope with these difficulties, we propose a multi-objective evolutionary algorithm to compress GAN models in the context of image translation tasks, which is termed as MEGC. Particularly, the conflict between the computational cost of the GAN model and the quality of generated image is explicitly modeled as a two-objective optimization problem, and the evolved Pareto set is utilized to guide the sampling process during supernet training, which can in turn divert the focus of the supernet training to well-performing compact subnets. Besides, an evaluation-free strategy is introduced to facilitate exploration in the search space while incurring no extra computational cost. Based on the above design, the proposed MEGC eliminates the requirement of subnet searching in the post-processing procedure. Experiments on image translation tasks under paired and unparied settings demonstrate the effectiveness of the proposed MEGC on reducing the computational cost of GANs while improving the quality of generated images compared to those of the full models.

Feasibility of Formulating Ecosystem Biogeochemical Models From Established Physical Rules

AbstractTo improve the predictive capability of ecosystem biogeochemical models (EBMs), we discuss the feasibility of formulating biogeochemical processes using physical rules that have underpinned the many successes in computational physics and chemistry. We argue that the currently popular empirically based approaches, such as multiplicative empirical response functions and the law of the minimum, will not lead to EBM formulations that can be continuously refined to incorporate improved mechanistic understanding and empirical observations of biogeochemical processes. Instead, we propose that EBM parameterizations, as a lossy data compression problem, can be better formulated using established physical rules widely used in computational physics and chemistry, and different biogeochemical processes can be more robustly integrated within a reactive‐transport framework. Through several examples, we demonstrate how mathematical representations derived from physical rules can improve understanding of relevant biogeochemical processes and enable more effective communication between modelers, observationalists, and experimentalists regarding essential questions, such as what measurements are needed to meaningfully inform models and how can models generate new process‐level hypotheses to test in empirical studies. Finally, while empirical models with more parameters are often less robust, physical rules‐based models can be more robust and show lower predictive equifinality, stemming from their enhanced consistency in representations of processes, interactions and spatial scaling.

Mannitol-coated hydroxypropyl methylcellulose as an alternative directly compressible controlled release excipient

One of the most common forms of controlled release technology for oral drug delivery comprises an active ingredient dispersed in a hydrophilic matrix forming polymer such as hydroxypropyl methylcellulose (HPMC), which is tableted via direct compression. However, HPMC may pose problems in direct compression due to its poor flowability. Hence, mannitol syrup was spray-coated over fluidized HPMC particles to produce co-processed HPMC–mannitol at ratios of 20:80, 50:50, and 70:30. Particles of pure HPMC, co-processed HPMC–mannitol, and their respective physical mixtures were evaluated for powder flowability, compression profiles, and controlled release performance. It was found that co-processed HPMC–mannitol consisted of particles with improved flow compared to pure HPMC particles. Sufficiently strong tablets of >2 MPa could be produced at moderate to high compression forces of 150–200 MPa. The dissolution profile could be tuned to obtain desired release profiles by altering HPMC–mannitol ratios. Co-processed HPMC–mannitol offers an interesting addition to the formulator’s toolbox in the design of controlled release formulations for direct compression.

Local Integrals of Motion in Dipole-Conserving Models with Hilbert Space Fragmentation.

Hilbert space fragmentation is an ergodicity-breaking phenomenon, in which the Hamiltonian shatters into exponentially many dynamically disconnected sectors. In many fragmented systems, these sectors can be labeled by statistically localized integrals of motion, which are nonlocal operators. We study the paradigmatic nearest-neighbor pair hopping model exhibiting the so-called strong fragmentation. We show that this model hosts local integrals of motion (LIOMs), which correspond to frozen density modes with long wavelengths. The latter modes become subdiffusive when longer-range pair hoppings are allowed. Finally, we make a connection with a tilted (Stark) chain. Contrary to the dipole-conserving effective models, the tilted chain is shown to support either a Hamiltonian or dipole moment as an LIOM. Numerical results are obtained from a numerical algorithm, in which finding LIOMs is reduced to a data compression problem.

Composite loss function for 3-D poststack seismic data compression

This work introduces composite functions to compute distortion in volumetric seismic data. Several loss functions, such as those based on Lp-functions, ignore the structure of 3-D seismic data, treating it as a unidimensional vector. Alternatively, applying distinct functions in each axis, properly designed for dimension reduction, can evaluate seismic data error according to its unity and magnitude. We thus propose a novel multidimensional composite loss function to evaluate through dimension reduction, suitable for seismic data compression within a method named 3DSC-GAN. It replaces the usual peak signal-to-noise ratio (PSNR) metric as the distortion function. An extensive study is conducted to analyze potential combinations of functions for the 3-D poststack seismic data compression problem. Results indicate that the new function contributes to improve the neural network learning step. Our method provides superior reconstructions, both quantitatively and qualitatively, when compared to the PSNR metric.

A two-grid characteristic block-centered finite difference method for Darcy-Forchheimer slightly compressible miscible displacement problem

In this paper, a two-grid characteristic block-centered finite difference method is developed for solving a nonlinear Darcy-Forchheimer slightly compressible miscible displacement problem in porous media. The method is proposed for solving the nonlinear system in two steps. In the first step, the nonlinear equations are approximated on a coarse grid using the characteristic block-centered finite difference method. In the second step, the nonlinear system is linearized using Newton's method with a small positive parameter to ensure the differentiability of the nonlinear term |u|u in the Darcy-Forchheimer equation. The proposed two-grid method is rigorously analyzed, in which a priori error estimates of the velocity, pressure, concentration and its flux are provided, and the rates of convergence are O(ε+Δt+H3+h2). Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods by comparing the efficiency, especially in terms of CPU time.

Semantic regularization of electromagnetic inverse problems

Solving ill-posed inverse problems typically requires regularization based on prior knowledge. To date, only prior knowledge that is formulated mathematically (e.g., sparsity of the unknown) or implicitly learned from quantitative data can be used for regularization. Thereby, semantically formulated prior knowledge derived from human reasoning and recognition is excluded. Here, we introduce and demonstrate the concept of semantic regularization based on a pre-trained large language model to overcome this vexing limitation. We study the approach, first, numerically in a prototypical 2D inverse scattering problem, and, second, experimentally in 3D and 4D compressive microwave imaging problems based on programmable metasurfaces. We highlight that semantic regularization enables new forms of highly-sought privacy protection for applications like smart homes, touchless human-machine interaction and security screening: selected subjects in the scene can be concealed, or their actions and postures can be altered in the reconstruction by manipulating the semantic prior with suitable language-based control commands.

Implementation of IDEAL algorithm based on Delaunay triangular mesh for 2D-compressible flows

PurposeTo present the detailed implementation processes of the IDEAL algorithm for two-dimensional compressible flows based on Delaunay triangular mesh, and compare the performance of the SIMPLE and IDEAL algorithms for solving compressible problems. What’s more, the implementation processes of Delaunay mesh generation and derivation of the pressure correction equation are also introduced.Design/methodology/approachProgramming completely in C++.FindingsFive compressible examples are used to test the SIMPLE and IDEAL algorithms, and the comparison with measurement data shows good agreement. The IDEAL algorithm has much better performance in both convergence rate and stability over the SIMPLE algorithm.Originality/valueThe detail solution procedure of implementing the IDEAL algorithm for compressible flows based on Delaunay triangular mesh is presented in this work, seemingly first in the literature.

ДОСЛІДЖЕННЯ МЕТОДУ ФРАКТАЛЬНОГО СТИСНЕННЯ ЗОБРАЖЕНЬ З МЕТОЮ ПОКРАЩЕННЯ ЯКОСТІ СТИСНЕННЯ

The development of the Internet, along with the availability of increasingly powerful computers and other digital devices, cameras, scanners and printers, has led to the wide-spread use of digital images. In this regard, interest in improving data compression algo-rithms, such as images, is growing. Data compression is important for both transfer speed and storage efficiency. In addition to many commercial uses, compression technologies are also of interest in the military industry, such as applications for processing telemetry data from missile inter-ceptors or for archiving terrain image data for defense simulations. Solving the problem of image compression, or, more generally, image coding, has used advances and stimulated the development of many fields of engineering and math-ematics. The article examines fractal image compression — a data compression method based on the use of self-similar patterns in an image. This method allows you to achieve a high degree of compression while preserving image details. Fractal image compression is a unique and efficient approach to data compression based on the mathematical theory of fractals. Nowadays, it has important applications and advantages that make it a valuable tool in image processing. The main advantages include: 1. Preservation of details during compression. One of the key advantages of fractal compression is its ability to preserve a high degree of image detail in a relatively small amount of storage. This is especially important in situations where image quality must be preserved with limited storage and data transfer resources. 2. Efficiency of transmission through the network. Fractal compression allows for compact images, making it suitable for image transmission over a low-bandwidth network. This is especially true for mobile devices, the Internet of Things, and other scenarios where high bandwidth is not always available. 3. Adaptive compression for different resolutions. Fractal compression allows you to adapt the level of compression depending on the resolution and details of the image. This means that it can be used to compress various image sizes without significant loss of quality. 4. Data archiving and storage. Fractal compression can be useful for archiving and long-term storage of images, as it allows you to effectively reduce the amount of data without losing important information. This is especially important for libraries, archives, research databases and other data repositories. Fractal image compression remains a relevant and valuable tool in today's envi-ronment, thanks to its ability to efficiently compress, preserve details, and adapt to dif-ferent usage scenarios. Therefore, the study of its efficiency, the optimization of the soft-ware code to obtain a faster and better compression result, is an urgent task.