Sharif Digital Repository

A diverse range of natural and artificial self-propelled particles are known and are used nowadays. Among them, active Brownian particles (ABPs) and run-and-tumble particles (RTPs) are two important classes. We numerically study non-interacting ABPs and RTPs strongly confined to different maze geometries in two dimensions. We demonstrate that by means of geometrical confinement alone, ABPs are separable from RTPs. By investigating Matryoshka-like mazes with nested shells, we show that a circular maze has the best filtration efficiency. Results on the mean first-passage time reveal that ABPs escape faster from the center of the maze, while RTPs reach the center from the rim more easily.... 

Consideration is given to the buoyancy effects on fully developed gaseous slip flow in vertical microducts of constant but arbitrary geometry. The thermal boundary condition is assumed to be the constant wall heat flux of the first kind, H1. The rarefaction effects are treated using the first-order slip velocity and temperature jump boundary conditions. The method of solution being considered, in which the governing equations in cylindrical coordinates and three of the boundary conditions are exactly satisfied, is mainly analytical. The remaining slip boundary conditions on the duct wall are applied to the solution through the least-squares matching method. As an application of the method,... 

In this paper, we consider a special version of the well-known line-simplification problem for simplifying the boundary of a region illuminated by a point light source q, or its visibility polygon VP(q). In this simplification approach, we should take the position of q as an essential factor into account to determine the quality of the resulting simplification. For this purpose, we redefine the known distance- and area-distortion error criteria as the main simplification criteria to take into account the distance between the observer q and the boundary of VP(q). Based on this, we propose algorithms for simplifying VP(q). More precisely, we propose simplification algorithms of O(n2) and... 

We study a class of compactifications of open complex analytic surfaces which appear naturally in the study of the singularities of Calabi-Yau metrics. We obtain a new degenerate Hodge theory as well as a degenerate Dolbeault lemma for these surfaces. To cite this article: A. Bahraini, C. R. Acad. Sci. Paris, Ser. I 344 (2007). © 2007 Académie des sciences  

From ancient times to 19th century geometry symbolized the essence of mathematical thinking and method, but modern philosophy of mathematics seems to have marginalized the philosophical status of geometry. The roots of this transformation will be sought in the ascendance of logical foundations in place of intuitive primacy as the cornerstone of mathematical certainty in the late 19th century. Nevertheless, geometry and geometrical thinking, in multiple manifestations, have continued to occupy a central place in the practice of mathematics proper. We argue that this, together with advances in the neuroscience of mathematical processes, calls for an expansion of the present limited remit of... 

We obtain an exact analytical expression for magnetoresistance using noncommutative geometry and quantum groups. We then show there is a deep relationship between magnetoresistance and the quantum group suq(2), from which we understand the quantum interpretation of the quantum corrections to the conductivity  

We obtain an exact analytical expression for magnetoresistance using noncommutative geometry and quantum groups. Then we will show that there is a deep relationship between magnetoresistance and the quantum group su q(2), from which we understand the quantum interpretation of the quantum corrections to the conductivity. © 2003 Elsevier B.V. All rights reserved  

Concrete is a heterogeneous material with a wide variety of usage in structural design. Concrete under tension exhibits strain softening, i.e., a negative slope in the stress-deformation diagrams. Different softening curves have been proposed in the literature to interpret this phenomenon. In current research, a new softening curve for concrete has been proposed by using the newly introduced concept of fractal geometry. This new softening curve is denominated a 'Quasi-fractal' softening curve and consists of two parts, a linear portion at the beginning and an exponential portion in the rest of the curve. A comparison of a "Quasi-fractal" softening curve with a set of proposed experimental... 

We consider the problem of walking a robot in an unknown polygon called “street”, starting from a point (Formula presented.) to reach a target (Formula presented.). The robot is assumed to have minimal sensing capability in a way that cannot infer any geometric properties of the environment, such as its coordinates, angles or distances; but it is equipped with a sensor that can only detect the discontinuities in the depth information (or gaps). Our robot can also locate the target point (Formula presented.) as soon as it enters in robot’s visibility region. In addition, one pebble is assumed to be available to the robot to be used as an identifiable point and to mark any position of the... 

In this paper we provide the correct tight constant to a data-processing inequality claimed by Erkip and Cover. The correct constant turns out to be a particular hypercontractivity parameter of (X,Y), rather than their squared maximal correlation. We also provide alternate geometric characterizations for both maximal correlation as well as the hypercontractivity parameter that characterizes the data-processing inequality  

In tissue engineering, the development of a tissue essentially depends on supply of an adequate amount of nutrients and the design of a proper biophysical micro-environment for cells. The limitation of the available initial number of cells, expensive substances and time consuming experiments are the main bottlenecks in this type of processes. In this regard, mathematical modelling and computational fluid dynamics simulation (CFD) are powerful tools to identify an efficient and optimized design by providing reliable insights of the process. This study presents a mathematical model and CFD simulation of cartilage cell culture under a perfusion flow, which allows not only to characterize the... 

In this paper, several numerical simulations are performed to study the failure of epoxy adhesive joining composite plates. Different geometries for the joint and its edge are considered, and the effects of these geometries on the failure load are investigated. Moreover, the joints are subjected to different types of loading in order to determine the failure load. The failure theories of composite materials are implemented into the finite element software ABAQUS, and the failure propagation in the joint is studied. © 2020, Shiraz University  

In this paper we consider maintaining the visibility of a segment observer moving inside a simple polygon. A practical instance of this problem is to identify the regions of a planar scene illuminated by a fluorescent lamp while the lamp moves around. We consider both strong and weak visibility in this paper. Our method is based on the shortest path tree which builds a linear-sized data structure in O(n) time, where n is the number of the vertices of the underlying simple polygon P. We first compute VP(st̄), the initial view of the segment observer st̄. Then, as st̄ moves, each change of VP(st̄) can be computed in O(log2(|V P(st̄)|)) time when the observer is allowed to change its direction,... 

The sensor-source geometry has a significant effect on accuracy of source localization problems. In a sensor placement problem, one attempts to optimally place the sensors in the surveillance area so as to optimize a performance criterion. Sensor placement methods mainly solve the associated problems without taking any specific constraint on permissible location of sensors into account. In practical applications, however, possible location for deployment of the sensors are subject to such limitations as environmental, industrial, and communication constraints, which affects the optimal sensor-source geometry. In this article, we consider the problem of optimal sensor placement, based on time... 

We study a constrained version of the shortest path problem in simple polygons, in which the path must visit a given target polygon. We provide a worst-case optimal algorithm for this problem and also present a method to construct a subdivision of the simple polygon to efficiently answer queries to retrieve the shortest polygon-meeting paths from a single-source to the query point. The algorithms are linear, both in time and space, in terms of the complexity of the two polygons. © 2004 Elsevier B.V. All rights reserved  

The creation of massless scalar particles from the quantum vacuum by spherical shell with time varying radius is studied. In the general case of motion the equations are derived for the instantaneous basis expansion coefficients. The examples are considered when the mean number of particles can be explicitly evaluated in the adiabatic approximation  

We apply the Dirac bracket quantization to open strings attached to branes in the presence of background antisymmetric field and recover an inherent noncommutativity in the internal coordinates of the brane. © 2000 Elsevier Science B.V. All rights reserved  

Give a triangulation of a set of points on the plane, dilation of any two points is defined as the ratio between the length of the shortest path of these points and their Euclidean distance. Minimum dilation triangulation is a triangulation in which the maximum dilation between any pair of the points is minimized. We give upper bounds on the dilation of the minimum dilation triangulation for two kinds of point sets: An upper bound of nsin⁡(π/n)/2 for a centrally symmetric convex point set containing n points, and an upper bound of 1.19098 for a set of points on the boundary of a semicircle. © 2018 Elsevier B.V  

A plunge pool is one of the energy dissipater structures for high head dams, which ensures stability of the dam under extreme hydrodynamic pressure, due to falling jet impacts. The excess energy of the jet is dissipated, together with significant impact pressure exerted on the floor and pool walls. Thus, appropriate assessment of jet dynamic characteristics in the plunge pool is essential. This research presents experimental results focusing on. the distribution of mean and extreme pressure fluctuations on the sidewalls, due to circular and rectangular plunging jets, and the effects of pool dimension, especially in narrow valleys. The experimental variables are discharge, geometry of jet,... 

Purpose - One major challenge in turbulent flow applications is to control the recirculation zone behind the backward-facing step (BFS). One simple idea to do so is to modify the original BFS geometry, of course, without causing adverse or undesirable impacts on the original characteristics of the primary stream. The main objective of this work is to examine the solidity of the recirculation zone behind several different geometries which are slightly to moderately different from the original BFS geometry. Design/methodology/approach - The implemented modifications cause complicated irregularities at the boundaries of the domain. The experience shows that the mesh distribution around these...