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We analyse the spread of COVID-19, a disease caused by a novel coronavirus, in various countries by proposing a model that exploits the scaling and other important concepts of statistical physics. Quite expectedly, for each of the considered countries, we observe that the spread at early times occurs exponentially fast. We show how the countries can be classified into groups, like universality classes in the literature of phase transitions, based on the rates of infections during late times. This method brings a new angle to the understanding of disease spread and is useful in obtaining a country-wise comparative picture of the effectiveness of lockdown-like social measures. Strong similarity, during both natural and lockdown periods, emerges in the spreads within countries having varying geographical locations, climatic conditions, population densities and economic parameters. We derive accurate mathematical forms for the corresponding scaling functions and show how the model can be used as a predictive tool, with instruction even for future waves, and, thus, as a guide for optimizing social measures and medical facilities. The model is expected to be of general relevance in the studies of epidemics.

This paper is concerned with the modified function projective synchronization of Cohen–Grossberg neural networks systems with parameter mismatch and mixed time-varying delays. Due to the existence of parameter mismatch between the drive and slave systems, complete modified function projective synchronization is not possible to achieve. So a new concept, viz., weak modified function projective synchronization, is discussed up to a small error bound. Several generic criteria are derived to show weak modified function projective synchronization between the systems. The estimation of error bound is done using matrix measure and Halanay inequality. Simulation results are proposed graphically for different particular cases to show the synchronization between parameter-mismatched systems, which validate the effectiveness of our proposed theoretical results.

Light detection and ranging (LiDAR) sensor technology for people detection offers a significant advantage in data protection. However, to design these systems cost- and energy-efficiently, the relationship between the measurement data and final object detection output with deep neural networks (DNNs) has to be elaborated. Therefore, this paper presents augmentation methods to analyze the influence of the distance, resolution, noise, and shading parameters of a LiDAR sensor in real point clouds for people detection. Furthermore, their influence on object detection using DNNs was investigated. A significant reduction in the quality requirements for the point clouds was possible for the measurement setup with only minor degradation on the object list level. The DNNs PointVoxel-Region-based Convolutional Neural Network (PV-RCNN) and Sparsely Embedded Convolutional Detection (SECOND) both only show a reduction in object detection of less than 5% with a reduced resolution of up to 32 factors, for an increase in distance of 4 factors, and with a Gaussian noise up to μ=0 and σ=0.07. In addition, both networks require an unshaded height of approx. 0.5 m from a detected person’s head downwards to ensure good people detection performance without special training for these cases. The results obtained, such as shadowing information, are transferred to a software program to determine the minimum number of sensors and their orientation based on the mounting height of the sensor, the sensor parameters, and the ground area under consideration, both for detection at the point cloud level and object detection level.

Starting from configurations having homogeneous spatial density, we study kinetics in a two-dimensional system of inelastically colliding hard particles, a popular model for cooling granular matter. Following an initial time period, the system exhibits a crossover to an inhomogeneous regime that is characterized by the formation and growth of particle-rich clusters. We present results on the time dependence of average mass of the clusters and that of average kinetic energy, obtained via event-driven molecular dynamics simulations, for a wide range of values for the coefficient of restitution ( e ), by fixing the overall density of particles in the system to a constant number. The time of onset of crossover from homogeneous to the inhomogeneous regime, as is well known, strongly increases as one moves towards the elastic limit. Nevertheless, our presented results suggest that the asymptotic growth is independent of e , for uniform definition of cluster, onset of which has a different e -dependence than the onset of above-mentioned crossover. In other words, not only the exponent but also the amplitude of the power-law growth, which is widely believed to be the form of the evolution, is at the most very weakly sensitive to the choice of e . While it is tempting to attribute this fact to the similar feature in the decay of energy, we caution that our current understanding is not matured enough to draw such a connection between cluster growth and energy decay in a meaningful manner.

Understanding why hotter water can freeze faster than colder water — a phenomenon known as the Mpemba effect — is important for gaining deeper insights into systems far from equilibrium. Despite growing interest, this effect has not been demonstrated in computer simulations of ice formation. Using the TIP4P/Ice model, we show that the Mpemba effect appears in our simulated systems and observe its manifestation also during fluid-to-solid transitions in the case of simpler Lennard-Jones systems. We extend this investigation to magnetic transitions, revealing that the effect can arise from different mechanisms: for the TIP4P/Ice model, the effect arises from how long the system remains in a metastable state, while for other systems, it results from differences in critical fluctuations in the initial states. These findings suggest a universal behavior and are contrary to the common belief that metastability is a necessary requirement. The Mpemba effect — the counterintuitive phenomenon where a hotter system can freeze more rapidly than a cooler one — challenges conventional thermodynamic principles and stimulates ongoing inquiry. Using molecular dynamics simulations, this study demonstrates the Mpemba effect during ice formation in the TIP4P/Ice model, as well as for a similar transition in a Lennard-Jones model, and investigates the roles of metastability and critical fluctuations

Diffusion equations play a crucial role in various scientific and technological domains, including mathematical biology, physics, electrical engineering, and mathematics. This article presents a new formulation of the diffusion equation in the context of electrical engineering. Specifically, the behaviour of the physical quantity of charge carriers (such as concentration) is examined within semiconductor materials. The primary focus of this work is to solve the two-dimensional, time-fractional, nonlinear drift reaction–diffusion equation by applying an appropriate numerical scheme. In recent years, researchers working on nonlinear diffusion equations have proposed several numerical methods, with the shifted airfoil collocation method being one such efficient technique for solving nonlinear partial differential equations. This collocation approach effectively reduces the considered two-dimensional, time-fractional, nonlinear drift reaction–diffusion equation to a system of algebraic equations. The efficiency and effectiveness of the proposed method are validated through an error analysis, comparing the exact solution and the proposed numerical solution for a specific form of the considered mathematical model. The variations in the concentration of charge carriers, driven by the effects of drift and reaction terms, are displayed graphically as the system transitions from a fractional order to an integer order.

A study was undertaken to investigate the effects of non-antibiotic additives—citric acid, synbiotics, and probiotics—administered through drinking water on broiler growth performance, carcass characteristics, and blood biochemical profiles. A total of 400 one-day-old Cobb 500 broiler chicks were randomly divided into four treatment groups: Control; no additives administered (CON); Citric acid @2.5 g/L water (CA); Synbiotic @0.2 g/L water (SB); Probiotic @0.5 g/L water (PB) and with each group having 4 replicates of 25 chicks. Growth performance metrics, such as body weight (BW), body weight gain (BWG), feed intake (FI), and feed conversion ratio (FCR), were recorded weekly. At the end of the trial, the probiotic-fed group had significantly higher BW (p = 0.018), BWG (p = 0.027), and an improved FCR (1.62) compared to the CON (1.74), CA (1.66), and SB (1.70) groups (p = 0.042). Biochemical parameters showed significant differences in total cholesterol (p = 0.013) and low-density lipoprotein (LDL) levels (p = 0.039), with the PB group showing higher levels. These results suggest that citric acid, synbiotics, and probiotic additives provided through drinking water can enhance broiler growth performance, with probiotics offering the most promising benefits.

Acute hemorrhagic leucoencephalitis (AHLE) is a rare inflammatory disease of the brain. Literature on the presentation and management of this rare disease is limited. A Mycoplasma pneumoniae infection is considered a possible trigger for acute hemorrhagic leucoencephalitis (Weston-Hurst syndrome). We report a case of a 58-year-old man presenting with an altered level of consciousness following a history of acute respiratory tract infection. He had also clinical and laboratory features of disseminated intravascular coagulation (DIC). Brain imaging was suggestive of hemorrhagic encephalitis involving both the fronto-temporo-parieto-occipital lobes involving the cortical, subcortical, and splenium of the corpus callosum and the posterior limb of the right internal capsule. Antibodies against Mycoplasma were strongly positive in serum. The patient was treated with fresh frozen plasma, broad-spectrum antibiotics, and methylprednisolone. However, the patient died after 17 days of hospitalization probably due to multiorgan failure and brain herniation.

The article contains the solution of a semi-infinite crack present at the interface of two dissimilar orthotropic strips sandwiched between dissimilar orthotropic strips. The crack is moving with a constant velocity, and the surface is under shear wave disturbance. Using the Fourier integral transform, the standard form for the Wiener–Hopf (W–H) equation is obtained for the proposed mathematical model, which is solved using the W–H method. The approximate analytic expressions for stress intensity factor, normalised stress intensity factor (NSIF) and the crack energy have been obtained for the considered crack problem. The behaviour of NSIF and normalised crack energy has been graphically presented for different crack propagation velocities and various ratios of depths of the strips of the composite material for different particular cases. The novelty of the article lies in finding the approximate analytic solutions of the proposed mathematical model using the W–H method, finding the expression for the length of the contact region near the crack tip and the pictorial presentations of the impact of exterior strips on the two dissimilar bonded strips containing the crack through finding the stress magnification factor.

The fracture behavior of a functionally graded magneto-elastic plane with multiple parallel cracks is examined in this article. Under anti-plane mechanical, in-plane electric, and magnetic loadings, it is assumed that the cracks are either of the magneto-electrically impermeable or permeable types. Here, three distinct crack configurations are taken into consideration. For each of the three crack configuration cases, the boundary collocation and least square methods are used to obtain the semi-analytical expressions of the stress intensity factors (SIFs) at the crack tips. SIFs are used to calculate the stress magnification factors (SMFs). The novelty of the article is the study of shielding and amplification tendencies of cracks under the impact of functionally graded parameter, geometric size, and electric and magnetic loads. The graphical illustrations of SMFs as a function of gradient parameter, the distance between the cracks, and electric and magnetic loadings for three different crack configurations are the key features of the article.