Search Results (11)

Ultrasonic wave attenuation in biological tissues arises from complex interactions between mechanical, structural, and fluidic properties, making it essential to identify dominant mechanisms for accurate simulation and device design. This work introduces a novel integration of experimentally measured tissue parameters into time-explicit nonlinear acoustic wave simulations, in which the equations are directly solved in the time domain using an explicit solver. This approach captures the full transient waveform without relying on frequency-domain simplifications, offering a more realistic representation of ultrasound propagation in heterogeneous media. The study estimates both sound diffusivity and viscous damping parameters (dynamic and bulk viscosity) for a broad range of ex vivo tissues (skin, adipose tissue, skeletal muscle, trabecular/cortical bone, liver, myocardium, kidney, tendon, ligament, cartilage, and gray/white brain matter). Four regression models (power law, linear, exponential, logarithmic) were applied to characterize their frequency dependence between 0.5 and 5 MHz. Results show that attenuation is more strongly driven by bulk viscosity than dynamic viscosity, particularly in fluid-rich tissues such as liver and myocardium, where compressional damping dominates. The power-law model consistently provided the best fit for all attenuation metrics, revealing a scale-invariant frequency relationship. Tissues such as cartilage and brain showed weaker viscous responses, suggesting the need for alternative modeling approaches. These findings not only advance fundamental understanding of attenuation mechanisms but also provide validated parameters and modeling strategies to improve predictive accuracy in therapeutic ultrasound planning and the design of non-invasive, tissue-specific acoustic devices. Full article

The sea surface displays dynamic characteristics, such as waves and various formations. As a result, images of the sea surface usually have few stable feature points, with a background that is often complex and variable. Moreover, the sea surface undergoes significant changes due to variations in wind speed, lighting conditions, weather, and other environmental factors, resulting in considerable discrepancies between images. These variations present challenges for identification using traditional methods. This paper introduces an algorithm based on the phase-consistency model. We utilize image data collected from a specific maritime area with a high-frame-rate surface array infrared camera. By accurately detecting images with identical names, we focus on the subtle texture information of the sea surface and its rotational invariance, enhancing the accuracy and robustness of the matching algorithm. We begin by constructing a nonlinear scale space using a nonlinear diffusion method. Maximum and minimum moments are generated using an odd symmetric Log–Gabor filter within the two-dimensional phase-consistency model. Next, we identify extremum points in the anisotropic weighted moment space. We use the phase-consistency feature values as image gradient features and develop feature descriptors based on the Log–Gabor filter that are insensitive to scale and rotation. Finally, we employ Euclidean distance as the similarity measure for initial matching, align the feature descriptors, and remove false matches using the fast sample consensus (FSC) algorithm. Our findings indicate that the proposed algorithm significantly improves upon traditional feature-matching methods in overall efficacy. Specifically, the average number of matching points for long-wave infrared images is 1147, while for mid-wave infrared images, it increases to 8241. Additionally, the root mean square error (RMSE) fluctuations for both image types remain stable, averaging 1.5. The proposed algorithm also enhances the rotation invariance of image matching, achieving satisfactory results even at significant rotation angles. Full article

Full waveform inversion (FWI) is recognized as a leading data-fitting methodology, leveraging the detailed information contained in physical waveform data to construct accurate, high-resolution velocity models essential for crosshole surveys. Despite its effectiveness, FWI is often challenged by its sensitivity to data quality and inherent nonlinearity, which can lead to instability and the inadvertent incorporation of noise and extraneous data into inversion models. To address these challenges, we introduce the scale-aware edge-preserving FWI (SAEP-FWI) technique, which integrates a cutting-edge nonlinear anisotropic hybrid diffusion (NAHD) filter within the gradient computation process. This innovative filter effectively reduces noise while simultaneously enhancing critical small-scale structures and edges, significantly improving the fidelity and convergence of the FWI inversion results. The application of SAEP-FWI across a variety of experimental and authentic crosshole datasets clearly demonstrates its effectiveness in suppressing noise and preserving key scale-aware and edge-delineating features, ultimately leading to clear inversion outcomes. Comparative analyses with other FWI methods highlight the performance of our technique, showcasing its ability to produce images of notably higher quality. This improvement offers a robust solution that enhances the accuracy of subsurface imaging. Full article

This paper is concerned with intriguing possibilities for non-conventional critical behavior that arise when a nearly critical strongly non-equilibrium system is subjected to chaotic or turbulent motion of the environment. We briefly explain the connection between the critical behavior theory and the quantum field theory that allows the application of the powerful methods of the latter to the study of stochastic systems. Then, we use the results of our recent research to illustrate several interesting effects of turbulent environment on the non-equilibrium critical behavior. Specifically, we couple the Kazantsev–Kraichnan “rapid-change” velocity ensemble that describes the environment to the three different stochastic models: the Kardar–Parisi–Zhang equation with time-independent random noise for randomly growing surface, the Hwa–Kardar model of a “running sandpile” and the generalized Pavlik model of non-linear diffusion with infinite number of coupling constants. Using field-theoretic renormalization group analysis, we show that the effect can be quite significant leading to the emergence of induced non-linearity or making the original anisotropic scaling appear only through certain “dimensional transmutation”. Full article

The aim of the present work is to investigate the efficiency of flat-plate solar panels in Greece for delivering solar energy. In this study, the solar panels are mounted on a two-axis tracker, which follows the daily path of the sun. In this context, the annual energy sums are estimated on such surfaces from hourly solar horizontal radiation values at forty-three locations, covering all of Greece. The solar horizontal radiation values are embedded in the typical meteorological years of the sites obtained from the PVGIS tool. All calculations use near-real surface-albedo values for the sites, and isotropic and anisotropic models are used to estimate the diffuse-inclined radiation. The analysis provides non-linear regression expressions for the energy sums as a function of time (month, season). The annual energy sums are found to vary between 2247 kWhm⁻² and 2878 kWhm⁻² under all-sky conditions with the anisotropic transposition model. Finally, maps of Greece showing the distribution of the annual and seasonal solar energy sums under all- and clear-sky conditions are derived for the first time, and these maps constitute the main innovation of this work. Full article

When treating geomaterials, fractional derivatives are used to model anomalous dispersion or diffusion phenomena that occur when the mass transport media are anisotropic, which is generally the case. Taking into account anomalous diffusion processes, a revised Fick’s diffusion law is to be considered, where the fractional derivative order physically reflects the heterogeneity of the soil medium in which the diffusion phenomena take place. The solutions of fractional partial differential equations can be computed by using the so-called semi-analytical methods that do not require any discretization and linearization in order to obtain accurate results, e.g., the Adomian Decomposition Method (ADM). Such a method is innovatively applied for overcoming the critical issue of geometric nonlinearities in coupled saturated porous media and the potentialities of the approach are studied, as well as findings discussed. Full article

In this paper we propose a new mathematical model for describing the complex interplay between skin cell populations with fibroblast growth factor and bone morphogenetic protein, occurring within deformable porous media describing feather primordia patterning. Tissue growth, in turn, modifies the transport of morphogens (described by reaction-diffusion equations) through diverse mechanisms such as advection from the solid velocity generated by mechanical stress, and mass supply. By performing an asymptotic linear stability analysis on the coupled poromechanical-chemotaxis system (assuming rheological properties of the skin cell aggregates that reside in the regime of infinitesimal strains and where the porous structure is fully saturated with interstitial fluid and encoding the coupling mechanisms through active stress) we obtain the conditions on the parameters—especially those encoding coupling mechanisms—under which the system will give rise to spatially heterogeneous solutions. We also extend the mechanical model to the case of incompressible poro-hyperelasticity and include the mechanisms of anisotropic solid growth and feedback by means of standard Lee decompositions of the tensor gradient of deformation. Because the model in question involves the coupling of several nonlinear PDEs, we cannot straightforwardly obtain closed-form solutions. We therefore design a suitable numerical method that employs backward Euler time discretisation, linearisation of the semidiscrete problem through Newton–Raphson’s method, a seven-field finite element formulation for the spatial discretisation, and we also advocate the construction and efficient implementation of tailored robust solvers. We present a few illustrative computational examples in 2D and 3D, briefly discussing different spatio-temporal patterns of growth factors as well as the associated solid response scenario depending on the specific poromechanical regime. Our findings confirm the theoretically predicted behaviour of spatio-temporal patterns, and the produced results reveal a qualitative agreement with respect to the expected experimental behaviour. We stress that the present study provides insight on several biomechanical properties of primordia patterning. Full article

Owing to the fact that heat transfer during the thermally induced phase separation process is limited, a quench rate is inevitably entailed, which leads to the existence of temporal and spatial variations in temperature. Hence, it is of great importance to take into account the nonisothermality during the phase separation process, especially in high viscosity polymer solutions. In this study, the influence of conductive heat transfer on the morphology formation during the thermally induced phase separation process was investigated theoretically in terms of quench depth, boundary conditions, and enthalpy of demixing to elucidate the interaction between temperature and concentration through incorporating the nonlinear Cahn-Hilliard equation and the Fourier heat transfer equation in two dimensions. The Flory-Huggins free energy theory for the thermodynamics of phase separation, slow mode theory, and Rouse law for polymer diffusion without entanglements were taken into account in the model development. The simulation results indicated a strong interaction between heat transfer and phase separation, which impacted the morphology formation significantly. Results confirmed that quench depth had an indispensable impact on phase separation in terms of higher characteristic frequency by increasing the driving force for heat transfer. Applying quench from various boundaries led to a difference in the quench rate due to the high viscosity of the polymer solution. This led to a gradation in pore size and anisotropic morphology formation. The degree and direction of anisotropy depended on quench depth and rate, quench time, heat conduction rate inside the solution, solution viscosity, temperature evolution, and the enthalpy of demixing. It was also verified that the influence of enthalpy of demixing on phase separation could not be neglected as it increased the solution temperature and led to phase separation being accomplished at a higher temperature than the initial quench temperature. Full article

Due to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier–Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations. Full article

A novel unsupervised texture classification technique is proposed in this research work. The proposed method clusters automatically the textures of an image collection in similarity classes whose number is not a priori known. A nonlinear diffusion-based multi-scale texture analysis approach is introduced first. It creates an effective scale-space by using a well-posed anisotropic diffusion filtering model that is proposed and approximated numerically here. A feature extraction process using a bank of circularly symmetric 2D filters is applied at each scale, then a rotation-invariant texture feature vector is achieved for the current image by combining the feature vectors computed at all these scales. Next, a weighted similarity graph, whose vertices correspond to the texture feature vectors and the weights of its edges are obtained from the distances computed between these vectors, is created. A novel weighted graph clustering technique is then applied to this similarity graph, to determine the texture classes. Numerical simulations and method comparisons illustrating the effectiveness of the described framework are also discussed in this work. Full article

In this paper we are addressing two main topics, as follows. First, a rigorous qualitative study is elaborated for a second-order parabolic problem, equipped with nonlinear anisotropic diffusion and cubic nonlinear reaction, as well as non-homogeneous Cauchy-Neumann boundary conditions. Under certain assumptions on the input data: $f(t,x)$, $w(t,x)$ and $v_0\left(x\right)$, we prove the well-posedness (the existence, a priori estimates, regularity, uniqueness) of a solution in the Sobolev space $W_p^{1,2}\left(Q\right)$, facilitating for the present model to be a more complete description of certain classes of physical phenomena. The second topic refers to the construction of two numerical schemes in order to approximate the solution of a particular mathematical model (local and nonlocal case). To illustrate the effectiveness of the new mathematical model, we present some numerical experiments by applying the model to image segmentation tasks. Full article