A unified approach for numerical simulation of viscous compressible and incompressible flows over adiabatic and isothermal walls

A new formulation (including the choice of variables, their non-dimensionalization, and the form of the artificial viscosity) is proposed for the numerical solution of the full Navier-Stokes equations for compressible and incompressible flows with heat transfer. With the present approach, the same code can be used for constant as well as variable density flows. The changes of the density due to pressure and temperature variations are identified and it is shown that the low Mach number approximation is a special case. At zero Mach number, the density changes due to the temperature variation are accounted for, mainly through a body force term in the momentum equation. It is also shown that the Boussinesq approximation of the buoyancy effects in an incompressible flow is a special case. To demonstrate the new capability, three examples are tested. Flows in driven cavities with adiabatic and isothermal walls are simulated with the same code as well as incompressible and supersonic flows over a wall with and without a groove. Finally, viscous flow simulations of an oblique shock reflection from a flat plate are shown to be in good agreement with the solutions available in literature

An entropy correction method for unsteady full potential flows with strong shocks

An entropy correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to account for entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Comparisons between the present method and solutions of the Euler equations and between the present method and experimental data are presented. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation

Adrenocortical status in infants and children with sepsis and septic shock

AbstractBackgroundThe benefit from corticosteroids remains controversial in sepsis and septic shock and the presence of adrenal insufficiency (AI) has been proposed to justify steroid use.AimTo determine adrenal state and its relation with outcome in critical children admitted with sepsis to PICU of Cairo University, Children Hospital.MethodsThirty cases with sepsis and septic shock were studied. Cortisol levels (CL) were estimated at baseline and after high-dose short ACTH stimulation in those patients and in 30 matched controls. Absolute AI was defined as basal CL<7μg/dl and peak CL<18μg/dl. Relative AI was diagnosed if cortisol increment after stimulation is <9μg/dl.ResultsOverall mortality of cases was 50%. The mean CL at baseline in cases was higher than that of controls (51.39μg/dl vs. 12.83μg/dl, p=0.000). The mean CL 60min after ACTH stimulation was higher than that of controls (73.38μg/dl vs. 32.80μg/dl, p=0.000). The median of %rise in cases was lower than that of controls (45.3% vs. 151.7%). There was a positive correlation between basal and post-stimulation cortisol with number of system failure, inotropic support duration, mechanical ventilation days, and CO2 level in blood. There was a negative correlation between basal and post stimulation cortisol with blood pH and HCO3.ConclusionRAI is common with severe sepsis/septic shock. It is associated with more inotropic support and has higher mortality. Studies are warranted to determine whether corticosteroid therapy has a survival benefit in children with RAI and catecholamine resistant septic shock

Classical Analogue of the Ionic Hubbard Model

In our earlier work [M. Hafez, {\em et al.}, Phys. Lett. A {\bf 373} (2009) 4479] we employed the flow equation method to obtain a classic effective model from a quantum mechanical parent Hamiltonian called, the ionic Hubbard model (IHM). The classical ionic Hubbard model (CIHM) obtained in this way contains solely Fermionic occupation numbers of two species corresponding to particles with \up and \down spin, respectively. In this paper, we employ the transfer matrix method to analytically solve the CIHM at finite temperature in one dimension. In the limit of zero temperature, we find two insulating phases at large and small Coulomb interaction strength, $U$, mediated with a gap-less metallic phase, resulting in two continuous metal-insulator transitions. Our results are further supported with Monte Carlo simulations.Comment: 12 figure

From Gapped Excitons to Gapless Triplons in One Dimension

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.Comment: 18 pages, 10 figure

Detecting Heart Attacks Using Learning Classifiers

Cardiovascular diseases (CVDs) have emerged as a critical global threat to human life. The diagnosis of these diseases presents a complex challenge, particularly for inexperienced doctors, as their symptoms can be mistaken for signs of aging or similar conditions. Early detection of heart disease can help prevent heart failure, making it crucial to develop effective diagnostic techniques. Machine Learning (ML) techniques have gained popularity among researchers for identifying new patients based on past data. While various forecasting techniques have been applied to different medical datasets, accurate detection of heart attacks in a timely manner remains elusive. This article presents a comprehensive comparative analysis of various ML techniques, including Decision Tree, Support Vector Machines, Random Forest, Extreme Gradient Boosting (XGBoost), Adaptive Boosting, Multilayer Perceptron, Gradient Boosting, K-Nearest Neighbor, and Logistic Regression. These classifiers are implemented and evaluated in Python using data from over 300 patients obtained from the Kaggle cardiovascular repository in CSV format. The classifiers categorize patients into two groups: those with a heart attack and those without. Performance evaluation metrics such as recall, precision, accuracy, and the F1-measure are employed to assess the classifiers’ effectiveness. The results of this study highlight XGBoost classifier as a promising tool in the medical domain for accurate diagnosis, demonstrating the highest predictive accuracy (95.082%) with a calculation time of (0.07995 sec) on the dataset compared to other classifiers