Exploring mechanisms for pattern formation through coupled bulk-surface PDEs

This work explores mechanisms for pattern formation through coupled bulksurface partial differential equations of reaction-diffusion type. Reaction-diffusion systems posed both in the bulk and on the surface on stationary volumes are coupled through linear Robin-type boundary conditions. In this framework we study three different systems as follows (i) non-linear reactions in the bulk and surface respectively, (ii) non-linear reactions in the bulk and linear reactions on the surface and (iii) linear reactions in the bulk and non-linear reactions on the surface. In all cases, the systems are non-dimensionalised and rigorous linear stability analysis is carried out to determine the necessary and sufficient conditions for pattern formation. Appropriate parameter spaces are generated from which model parameters are selected. To exhibit pattern formation, a coupled bulk-surface finite element method is developed and implemented. We implement the numerical algorithm by using an open source software package known as deal.II and show computational results on spherical and cuboid domains. Theoretical predictions of the linear stability analysis are verified and supported by numerical simulations. The results show that non-linear reactions in the bulk and surface generate patterns everywhere, while non-linear reactions in the bulk and linear reactions on the surface generate patterns in the bulk and on the surface with a pattern-less thin boundary layer. However, linear reactions in the bulk do not generate patterns on the surface even when the surface reactions are non-linear. The generality, robustness and applicability of our theoretical computational framework for coupled system of bulk-surface reaction-diffusion equations set premises to study experimentally driven models where coupling of bulk and surface chemical species is prevalent. Examples of such applications include cell motility, pattern formation in developmental biology, material science and cancer biology

The patterns of abdominal trauma and factors associated with ICU admission in a major trauma center in Medina

BackgroundTrauma is a significant health problem in Saudi Arabia. In polytrauma victims, the abdomen is the second most affected body region following the head. In the Middle East, abdominal trauma prevalence ranges from 15 per cent to 82 per cent. AimsThis study aims to assess the patterns of blunt and penetrating abdominal traumas and to assess the factors associated with ICU admission.MethodsThis is a retrospective analytical study conducted at a major trauma centre in Medina, Saudi Arabia. Admitted abdominal trauma patients from 2015 to 2018 were included. Paediatric and isolated extra-abdominal traumas were excluded. Descriptive analysis was used to identify patterns of abdominal trauma. Chi-squared test and independent t-test were applied to evaluate the association of the mechanism of injury, solid abdominal organs, associated extra-abdominal injuries, and type of injury. Multiple regression analysis was conducted to assess factors associated with ICU admission in abdominal trauma. ResultsWe included a total of 218 patients with a mean age of 32.7±13.9 years. Males (78.4 per cent) were predominantly greater in number than females (21.6 per cent). The primary mechanisms of injury were motor vehicle collisions (MVCs) (76.6 per cent), followed by stab wounds (12.4 per cent) and falls (7 per cent). The liver and spleen were the most injured organs (31 per cent and 30 per cent, respectively). Chest injuries were the most associated extra-abdominal trauma (47.2 per cent). The majority of MVC patients (88.6 per cent) had BTA, while stab wound was the main mechanism of injury in penetrating trauma (12 per cent) (P < 0.001). Penetrating trauma patients required laparotomy more than BTA patients (52.9 per cent and 8 per cent; P < 0.05). Eighteen percent of patients needed ICU admission. Factors positively associated with ICU admission (P < 0.05) were head and neck, musculoskeletal, and thoracic injuries and a moderate Revised Trauma Score (RTS).ConclusionBlunt abdominal trauma was the dominant type of abdominal injury in this study. The majority of patients were young adult males. MVCs and stab wounds were the predominant mechanisms of injury. The most affected organs were the liver and spleen. Chest injuries were the most associated extra-abdominal trauma. Factors positively associated with ICU admission were head and neck, chest, and musculoskeletal injuries and a moderate RTS

Comparing the Numerical Solution of Fractional Glucose–Insulin Systems Using Generalized Euler Method in Sense of Caputo, Caputo–Fabrizio and Atangana–Baleanu

The purpose of this paper is to present a fractional nonlinear mathematical model with beta-cell kinetics and glucose–insulin feedback in order to describe changes in plasma glucose levels and insulin levels over time that may be associated with changes in beta-cell kinetics. We discuss the solution to the problem with respect to its existence, uniqueness, non-negativity, and boundedness. Using three different fractional derivative operators, the proposed model is examined. To approximate fractional-order systems, we use an efficient numerical Euler method in Caputo, Caputo–Fabrizio, and Atangana–Baleanu sense. Several asymptomatic behaviors are observed in the proposed models based on these three operators. These behaviors do not appear in integer-order derivative models. These behaviors are essential for understanding fractional-order systems dynamics. Our results provide insight into fractional-order systems dynamics. These operators analyze local and global stability and Hyers–Ulam stability. Furthermore, the numerical solutions for the proposed model are simulated using the three methods

Entropy Generation and MHD Convection within an Inclined Trapezoidal Heated by Triangular Fin and Filled by a Variable Porous Media

Analyses of the entropy of a thermal system that consists of an inclined trapezoidal geometry heated by a triangular fin are performed. The domain is filled by variable porosity and permeability porous materials and the working mixture is Al2O3-Cu hybrid nanofluids. The porosity is varied exponentially with the smallest distance to the nearest wall and the permeability is depending on the particle diameter. Because of using the two energy equations model (LTNEM), sources of the entropy are entropy due to the transfer of heat of the fluid phase, entropy due to the fluid friction and entropy due to the porous phase transfer of heat. A computational domain with new coordinates (ξ,η) is created and Finite Volume Method (FVM) in case of the non-orthogonal grids is used to solve the resulting system. Various simulations for different values of the inclination angle, Hartmann number and alumina-copper concentration are carried out and the outcomes are presented in terms of streamlines, temperature, fluid friction entropy and Bejan number. It is remarkable that the increase in the inclination angle causes a diminishing of the heat transfer rate. Additionally, the irreversibility due to the temperature gradients is dominant near the heated fins, regardless of the values of the Hartmann number

Numerical Study of Heat Transfer Enhancement within Confined Shell and Tube Latent Heat Thermal Storage Microsystem Using Hexagonal PCMs

Thermophoresis represents one of the most common methods of directing micromachines. Enhancement of heat transfer rates are of economic interest for micromachine operation. This study aims to examine the heat transfer enhancement within the shell and tube latent heat thermal storage system (LHTSS) using PCMs (Phase Change Materials). The enthalpy&ndash;porosity approach is applied to formulate the melting situation and various shapes of inner heated fins are considered. The solution methodology is based on the Galerkin finite element analyses and wide ranges of the nanoparticle volume fraction are assumed, i.e., (0% &le; &phi; &le; 6%). The system entropy and the optimization of irreversibility are analyzed using the second law of the thermodynamics. The key outcomes revealed that the flow features, hexagonal entropy, and melting rate might be adjusted by varying the number of heated fins. Additionally, in case 4 where eight heated fins are considered, the highest results for the average liquid percentage are obtained