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We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. We are interested in deriving rigorously the upscaled model equations and the corresponding effective coefficients for the case when the microscopic dynamics are linked to a particular choice of characteristic length and time scales that lead to an exploding nonlinear drift. The main mathematical difficulty lies in proving the two-scale compactness and strong convergence results needed for the passage to the homogenization limit. To cope with the situation, we use the concept of two-scale compactness with drift, which is similar to the more classical two-scale compactness result but it is defined now in moving coordinates. We provide as well a strong convergence result for the corrector function, starting this way the search for the order of the convergence rate of the homogenization process for our target nonlinear drift problem., 37 pages

We study the question of periodic homogenization of a variably scaled reaction-diffusion equation with non-linear drift of polynomial type. The non-linear drift was derived as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) for a population of interacting particles crossing a domain with obstacle. We consider three different geometries: (i) Bounded domain crossed by a finitely thin flat composite layer; (ii) Bounded domain crossed by an infinitely thin flat composite layer; (iii) Unbounded composite domain.\end{itemize} For the thin layer cases, we consider our reaction-diffusion problem endowed with slow or moderate drift. Using energy-type estimates as well as concepts like thin-layer convergence and two-scale convergence, we derive homogenized evolution equations and the corresponding effective model parameters. Special attention is paid to the derivation of the effective transmission conditions across the separating limit interfaces. As a special scaling, the problem with large drift is treated separately for an unbounded composite domain. Because of the imposed large drift, this nonlinearity is expected to explode in the limit of a vanishing scaling parameter. To deal with this special case, we employ two-scale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder's fixed point Theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in the unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials which are resistant to slow, moderate, and high velocity impacts. We study the question of periodic homogenization of a variably scaled reaction-diffusion equation with non-linear drift of polynomial type. The non-linear drift was derived as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) for a population of interacting particles crossing a domain with obstacle. We consider three different geometries: (i) Bounded domain crossed by a finitely thin composite layer; (ii) Bounded domain crossed by an infinitely thin composite layer; (iii) Unbounded composite domain. For the thin layer cases, we consider our reaction-diffusion problem endowed with slow or moderate drift. Using energy-type estimates, concepts like thin-layer convergence and two-scale convergence, we derive homogenized equations. Special attention is paid to the derivation of the effective transmission conditions across the separating limit interfaces. The problem with large drift is treated separately for an unbounded composite domain. Because of the imposed large drift, this nonlinearity is expected to explode in the limit of a vanishing scaling parameter. This study wants to contribute with theoretical understanding needed when designing thin composite materials which are resistant to slow, moderate, and high velocity impacts.

We study a reaction-diffusion-convection problem with nonlinear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. Because of the imposed large drift scaling, this nonlinearity is expected to explode in the limit of a vanishing scaling parameter. As main working techniques, we employ two-scale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder's fixed point theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in an unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials that are resistant to high velocity impacts., Comment: 27 pages, 3 figures

Metaplastic breast carcinoma (MBC) is a rare malignant neoplasm of the breast which is highly aggressive and is known for its early recurrence and poor prognosis. Concurrent detection of a MBC and tuberculosis of the axillary lymph node is a rarity. To the best of our knowledge, there is no such case report in the literature. A 35-year-old premenopausal woman was diagnosed as a case of left carcinoma breast with a left axillary lymph node. Core-needle biopsy of the breast was suggestive of squamous cell carcinoma. The patient underwent modified radical mastectomy with a latissimus dorsi myocutaneous flap. The postoperative biopsy of the breast and axilla revealed MBC and tuberculous lymphadenitis of the axillary lymph node. The patient received antitubercular therapy and radiotherapy, followed by chemotherapy and had no recurrence on follow-up. This case report emphasizes that metaplastic carcinoma breast can coexist with tuberculous axillary lymphadenopathy.

An autonomous vehicle has to understand the surrounding dynamic environment to make the driving decisions such as lane change by giving way to the dynamic obstacles. Motion planning is a challenging problem for an autonomous vehicle while changing a lane in the complex dynamic environment, as the optimal solution for routing must be computed in real time. This thesis provides a framework for an autonomous vehicle to analyse the lane change possibilities. Information from the digital map and estimation of the surrounding objects evaluate a method to find the trajectory for a lane change. The method involves constrained optimization problem of trajectory planning by incorporating interpolated optimal route as the sampling points. Numerical simulations show the effectiveness of the proposed technique in a scenario emulating a driving context for the autonomous vehicle. The result shows that, in a complex dynamic environment, the innovation of deploying model of the road descriptions, graph search and trajectory planning together makes the proposed method far better than the other methods applied in the researches done before for the lane change.

Objective: The purpose of this video is to present robotic excision of a complex adrenal mass with retrocaval extension and encasement of renal hilum in a 16 year old boy. Biochemical screening was negative for metabolically active component. Computerized tomographic scan with contrast revealed a homogenous mass of approximately 10.8 cm x 6.2 cm x 4.2 cm in the suprarenal area on right side that was extend-ing behind inferior vena cava and encasing renal hilar vessels. Imaging findings were that of a classical ganglioneuroma. Material and methods: Robot assisted laparoscopic adrenalectomy with sparing of renal hilar vasculature was performed. With patient in lateral position, five ports were used, including one for liver retraction. Da Vinci® system with four arms was docked from over the right shoulder. The displaced renal hilar structures were identified by opening Gerota's fascia. Mass was dissected completely and removed through Pfan-nensteil incision. Results: Duration of procedure was 345 minutes and console time was 290 minutes. Blood loss was 250 mL. Post-operative renal doppler showed normal blood flow. He was discharged on post-operative day three. Histopathologic examination of specimen revealed ganglioneuroma arising from adrenal gland. Conclusion: Ganglioneuroma is a rare adrenal tumor with good prognosis on surgical removal. The advent of robotic surgery has made complex surgical procedures involving vital structures like inferior vena cava be performed using minimally invasive techniques without compromising oncologic principles.