Sharif Digital Repository

In this article, we find a lower bound for the blow-up time of solutions to some nonlinear parabolic equations under Robin boundary conditions in bounded domains of Rn  

We consider the chemotaxis system:. {ut=δu-∇;{dot operator}(uχ(v)∇;v)+f(u),x∈Ω,t>0,vt=δv-v+ug(u),x∈Ω,t>0, under homogeneous Neumann boundary conditions in a bounded domain Ω⊂Rn, n≥ 1, with smooth boundary and function f is assumed to generalize the logistic source:. f(u)=au-bu2,u≥0, with a>0,b>0. Moreover, χ( s) and g( s) are nonnegative smooth functions and satisfy:. χ(s)≤κ script(1+θ symbols)k,s≥0, with some κ script>0,θ symbol>0 and k>1,g(s)≤h0(1+hs)δ,s≥0,withh0>0,h≥0,δ≥0. We prove that for all positive values of κ script, a and b, classical solutions to the above system are uniformly-in-time bounded. This result extends a recent result by C. Mu, L. Wang, P. Zheng and Q. Zhang (2013)... 

This paper deals with the blow-up of solutions to some nonlinear divergence form parabolic equations with nonlinear boundary conditions. We obtain a lower bound for the blow-up time of solutions in a bounded domain Ω⊆Rn, n≥. 3. L'article traite d'un problème d'explosion des solutions d'équations paraboliques non linéaires sous forme de divergence, avec des conditions aux limites non linéaires. On obtient une estimation d'une borne inférieure du temps d'explosion des solutions dans le cas d'un domaine borné Ω⊆Rn, n≥. 3  

This paper deals with the blow-up phenomena for a system of parabolic equations with nonlinear boundary conditions. We show that under some conditions on the nonlinearities, blow-up occurs at some finite time. We also obtain upper and lower bounds for the blow-up time when blow-up occurs. Copyright  

In this paper, we study the mathematical model proposed by Owen and Sherratt in 1997. We prove that the classical solutions to this model are uniformly-in-time bounded. © World Scientific Publishing Company  

This letter is concerned with the blow-up of the solutions to a semilinear parabolic problem with a reaction given by a variable exponent. Lower bounds for the time of blow-up are derived if the solutions blow up  

In this paper, we describe the design, development and preliminary evaluation of a novel animation tool for smartphones and tablets, with the goal of improving creativity and problem-solving ability among novice users, mainly young children. The user first draws the objects with markers and crayons on paper and takes a photo with their mobile or tablet to import their drawings into the app as game sprites. They then design their animation scene and point to a part of the character and selecting its animation type from existing buttons. Hence the selected part is animated in a vertex shader while ensuring a smooth transition with the non-pointed part. The results of a preliminary evaluation... 

A tanks-in-series model was applied for mathematical modeling of the unsteady state performance of 70 and 100 liters airlift bioreactor for the production of lactic acid by fermentation. A set of first-order differential equations for the material balances of micro-organism, substrate, product, and dissolved oxygen around hypothetically well mixed stages was solved simultaneously utilizing computer program in MATLAB. The kinetic model utilized considered the effect of two substrates (glucose and dissolved oxygen) on the growth rate. The effect of air velocity on the lactic acid production was investigated. Results of this model have been validated with experimental data  

One of the methods to increase the hardness of metals, mostly used in aerospace and automobile industries, where light parts with high strength is needed, is precipitation hardening. Nano-precipitates can strongly influence the mechanical properties of materials, especially in a dynamic case. In the present work, attempts have been made so as to make Nano-particles dynamically precipitate in IF steels. Investigating the structure by the means of SEM and AFM resulted in understanding that the precipitates were in nano-size. The micro-hardness of samples was measured as well. © BHR Group 2007 Industrial Processes for Nano and Micro Products  

Detection of rolling bearing faults by vibration analysis is an important part of condition monitoring programs. In this paper a new method for detection of bearing defects based on a new concept of local surface roughness, is proposed. When a defect in the bearing grows then roughness of the defective surface increases and measurement of the roughness can be a good indicator of the bearing defect. In this paper a method of indirectly measuring surface roughness by using vibration signal is introduced. Several attached examples including both numerically simulated signals and actual experimental data show the effectiveness of the new, easy-to-implement method  

In this study, the energy method has been used to develop a finite-element code for studying the effects of loose rotating discs on the rotor-bearing systems' response. A mathematical model of the loose disc has resulted in terms similar to unbalance and gyroscopic effects in the equation of motion of the system. Results of this study show that rotor response and beating phenomena are a function of measurement location, loose disc mass and inertia, ratio of rotating speed to the speed of loose disc, and clearance between the loose disc and shaft considering constant speed for loose disc and shaft. The developed finite-element model can numerically give the response of rotors with any number... 

During backward rub in a turbomachine, rotor is compelled by frictional forces into a severe precessional sliding motion inside stationary parts such as seals or journal bearings in opposite direction of rotor's rotation. Backward rub occurs with high frequency and high amplitude of vibration and can deteriorates rubbing surfaces just for few moments. This paper presents and investigates the idea of clearance profile alteration from annular form to non-annular 3-lobed form in order to affect the reverse rub's characteristics. For this purpose, a test setup consisting of a lightly damped rotor-stator system is designed and built in SUT's condition-monitoring laboratory for testing the... 

Today, turbomachinery designers are trying to attain zero clearances for optimizing performance and efficiency of machine by designing advanced compliant-segmented seals. This trend involves secondary issues such as rotor-to-stator contact interaction which is to be treated with more technical knowledge in rotordynamic design and condition monitoring programs. The aim of this paper is to gain insight into dynamic interaction between a flexible rotor and a set of compliant arc-shaped segments as stator system. Specifically, the unbalanced-induced forward rubbing response is investigated in tight clearance condition during resonance-passing situations. A Jeffcott rotor modeling is used for... 

This paper presents the experimental results of an investigation on the response and efficiency of floating pontoon type breakwaters. Random waves modeled by the Pierson Moskowits wave spectrum are used for various configurations of floating breakwaters. The experimental results are presented in graphs for the transmission coefficient as a function of incident wave length and height for breakwaters used in this study. The obtained results for the breakwaters of this study show that by increasing the wave period and length, the transmission coefficient increases, while increase in the mass and draft of the floating breakwater causes the transmission coefficient to reduce. © Shiraz University