A Review of Time Relaxation Methods

The time relaxation model has proven to be effective in regularization of Navier–Stokes Equations. This article reviews several published works discussing the development and implementations of time relaxation and time relaxation models (TRMs), and how such techniques are used to improve the accuracy and stability of fluid flow problems with higher Reynolds numbers. Several analyses and computational settings of TRMs are surveyed, along with parameter sensitivity studies and hybrid implementations of time relaxation operators with different regularization techniques

Numerical analysis and phenomenology of homogeneous, isotropic turbulence generated by higher order models of turbulence

Turbulence appears in many processes in the nature and it is connected with many engineering, biophysical and climate applications. Therefore, the accurate, efficient and reliable simulation of turbulent flows is an essential difficulty in many current applications. Fundamental and universal (i.e. mathematical) insights into fluid structures will enable such simulations. To that end, we apply the phenomenology of homogeneous, isotropic turbulence to a family of Large Eddy Simulation (LES) models, the so-calledfamily of Approximate Deconvolution Models (ADM). We establish that the models themselves have an energy cascade with two asymptotically different inertial ranges. Delineation of these gives insight into the resolution requirements of using ADM. A correct prediction of a 3D turbulent flow means getting the energy balance and rotational structures correct, i.e., it means (in the large) matching the energy and helicity statistics. Thus, we consider the prediction of energy and helicity statistics of the family of Approximate Deconvolution Models of turbulence. We show that the family of ADM has a helicity cascade that it is linked to its energy cascade and predicted correctly over the large/resolved scales. Turbulent flows are very rich in scales and to be able to capture all of them, we need to use a very fine mesh. Unfortunately, even with the amazing development of the computer power, we are not able to perform such simulations. Thus, many numerical regularization (aiming to truncate the small scales) have been explored in computational fluid dynamics. We investigated one of such regularization, called the Time Relaxation Model (TRM). We apply the phenomenology of homogeneous, isotropic turbulence to understand how the time relaxation term, by itself, acts to truncate solution scales and to use this understanding to give insight into coefficient selection. We also study the stability and convergence analysis of a finite element discretization of TRM. Next we complement this with an experimentalstudy of the convergence rates and of the effect the time relaxation term has on the large scales of a flow near a transitional point

Efficient simulation of fluid flow

We are computationally investigating fluid flow models for physically correct predictions of flow structures. Models based on the idea of filtering the small scales/structures and also the Navier-Stokes equations which are the fundamental equations of fluid flow, are numerically solved via the continuous finite element method. Crank-Nicolson and fractional-step theta scheme are used for the discretization of the time derivative, while the Taylor-Hood and Mini elements are used for the discretization is space. The effectiveness of these numerical discretizations in time and space are examined by studying the accuracy of fluid characteristics, such as drag, lift and pressure drop

Mathematical analysis and applications of logistic differential equation

Logistic differential equation has a way to measure the proportionality of various resources with respect to time. This equation has been used in many research areas, such as, biology, medicine, psychology, economics, etc. A mathematical description, analysis and solution of the logistic type differential equation is studied. Besides the mathematical part, the poster will contain biological examples, graphs of the direction fields for different parameter settings and logistic plots for specific species population. The logistic growth function will also be applied to learning curves in area of psychology, as a rate at which performance improves

UNLV enrollment forecasting

Our project investigates the future enrollment of undergraduates at UNLV in the entire university, the College of Science, and the Department of Mathematical Sciences. The method used for the forecast, is the well-known least-squares method, for which a mathematical description will be presented. Studies for the numerical error are pursued too. The study will include graphs that describe the past and future behavior for different parameter settings. Mathematical results obtained show that the university will continue to grow given the current trends of enrollment

Interweaving Research and Teaching

This work describes a teaching practice that is based on creating an assignment for students to work on a research project. The students will use methods learned in the class to solve a research problem and then present their findings though a class presentation.https://digitalscholarship.unlv.edu/btp_expo/1183/thumbnail.jp

Computational Study of the Time Relaxation Model With High Order Deconvolution Operator

This paper presents a computational investigation for a time relaxation regularization of Navier–Stokes equations known as Time Relaxation Model, TRM, and its corresponding sensitivity equations. The model generates a regularization based on both filtering and deconvolution. We discretize the equations of TRM and the corresponding sensitivity equations using finite element in space and Crank–Nicolson in time. The step problem and the shear layer roll-up benchmark is used to computationally test the performance of TRM across different orders of deconvolution operator as well as the sensitivity of the shear layer computations of the model with respect to the variation of time relaxation parameter in those cases

Sources of Infection in Childhood Tuberculosis in a Region of East Croatia

Possible sources of tuberculosis (TBC) infection in children have been assessed in a retrospective epidemiological study covering a north-east region of Croatia in which the incidence of childhood tuberculosis has been increasing since the war in 1991–1995. During the past decade (1993–2003), 271 children up to 18 years of age have been referred for hospital care because of known contacts with tuberculosis (142 children, group A) or because of indicative clinical signs and symptoms (129 children, group B). Possible sources of infection were identified on the basis of medical documentation and field investigations. Frequencies of source identification for different age groups were compared. In group A, the exposure took place most often within the family (parents, grandparents, siblings, 129 of 142 children, 90.8%). Relatives, neighbors, friends and schoolmates accounted for 9.2%. In group B, possible sources of infection were identified for 44 of 129 children (34.1%) and were within the family for 16 of those 44 (36.4%). Evidenced contact with tuberculosis was more usual among younger children (0–9 years of age, 65.5%) in group A than among the older ones (10–18 years of age, 34.5%). In group B, contacts with tuberculosis were equally distributed (50.0%) among younger and older children. High proportion of unrecognized contacts in children having clinical signs and symptoms indicative of tuberculosis (group B, 85 of 129, 65.9%) opens the possibility that extra-familial exposure to tuberculosis occurs more often than expected regardless of the age of children

Intestinal B cells license metabolic T-cell activation in NASH microbiota/antigen-independently and contribute to fibrosis by IgA-FcR signalling

BACKGROUND & AIMS: The progression of non-alcoholic steatohepatitis (NASH) to fibrosis and hepatocellular carcinoma (HCC) is aggravated by auto-aggressive T cells. The gut-liver axis contributes to NASH, but the mechanisms involved and the consequences for NASH-induced fibrosis and liver cancer remain unknown. We investigated the role of gastrointestinal B cells in the development of NASH, fibrosis and NASH-induced HCC. METHODS: C57BL/6J wild-type (WT), B cell-deficient and different immunoglobulin-deficient or transgenic mice were fed distinct NASH-inducing diets or standard chow for 6 or 12 months, whereafter NASH, fibrosis, and NASH-induced HCC were assessed and analysed. Specific pathogen-free/germ-free WT and μMT mice (containing B cells only in the gastrointestinal tract) were fed a choline-deficient high-fat diet, and treated with an anti-CD20 antibody, whereafter NASH and fibrosis were assessed. Tissue biopsy samples from patients with simple steatosis, NASH and cirrhosis were analysed to correlate the secretion of immunoglobulins to clinicopathological features. Flow cytometry, immunohistochemistry and single-cell RNA-sequencing analysis were performed in liver and gastrointestinal tissue to characterise immune cells in mice and humans. RESULTS: Activated intestinal B cells were increased in mouse and human NASH samples and licensed metabolic T-cell activation to induce NASH independently of antigen specificity and gut microbiota. Genetic or therapeutic depletion of systemic or gastrointestinal B cells prevented or reverted NASH and liver fibrosis. IgA secretion was necessary for fibrosis induction by activating CD11b+CCR2+F4/80+CD11c-FCGR1+ hepatic myeloid cells through an IgA-FcR signalling axis. Similarly, patients with NASH had increased numbers of activated intestinal B cells; additionally, we observed a positive correlation between IgA levels and activated FcRg+ hepatic myeloid cells, as well the extent of liver fibrosis. CONCLUSIONS: Intestinal B cells and the IgA-FcR signalling axis represent potential therapeutic targets for the treatment of NASH. IMPACT AND IMPLICATIONS: There is currently no effective treatment for non-alcoholic steatohepatitis (NASH), which is associated with a substantial healthcare burden and is a growing risk factor for hepatocellular carcinoma (HCC). We have previously shown that NASH is an auto-aggressive condition aggravated, amongst others, by T cells. Therefore, we hypothesized that B cells might have a role in disease induction and progression. Our present work highlights that B cells have a dual role in NASH pathogenesis, being implicated in the activation of auto-aggressive T cells and the development of fibrosis via activation of monocyte-derived macrophages by secreted immunoglobulins (e.g., IgA). Furthermore, we show that the absence of B cells prevented HCC development. B cell-intrinsic signalling pathways, secreted immunoglobulins, and interactions of B cells with other immune cells are potential targets for combinatorial NASH therapies against inflammation and fibrosis