Heat flow method to Lichnerowicz type equation on closed manifolds

In this paper, we establish existence results for positive solutions to the Lichnerowicz equation of the following type in closed manifolds -\Delta u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M, where $p>1, q>0$, and $A(x)>0$, $B(x)\geq0$ are given smooth functions. Our analysis is based on the global existence of positive solutions to the following heat equation {ll} u_t-\Delta u=A(x)u^{-p}-B(x)u^{q},\quad in\quad M\times\mathbb{R}^{+}, u(x,0)=u_0,\quad in\quad M with the positive smooth initial data $u_0$.Comment: 10 page

An iterative method for solving Fredholm integral equations of the first kind

The purpose of this paper is to give a convergence analysis of the iterative scheme: \bee u_n^\dl=qu_{n-1}^\dl+(1-q)T_{a_n}^{-1}K^*f_\dl,\quad u_0^\dl=0,\eee where $T:=K^*K,\quad T_a:=T+aI,\quad q\in(0,1),\quad a_n:=\alpha_0q^n, \alpha_0>0,$ with finite-dimensional approximations of $T$ and $K^*$ for solving stably Fredholm integral equations of the first kind with noisy data.Comment: 29 page

Stress concentration analysis of plate with circular hole : elasticity theory and finite element comparison

Stress concentration factor for a plate with circular free stress hole subjected to a uniform far field tension in single was investigated in this study. The stress concentration level along X and Y axis was determined by the elasticity theoritical method. Finite element analysis using LISA free source software was validate by the elasticity theoritical results. It was found that finite element analysis stress concentration factor results shows similar pattern as theoretical but higher near of the hole. Plain strain analysis with Quad 8 element type showed better results compared to plain stress with Quad 4 element type and plain strain with Quad 4 element type

Computational fluid dynamics model of a quad-rotor helicopter for dynamic analysis

The control and performance of a quad-rotor helicopter UAV is greatly influenced by its aerodynamics, which in turn is affected by the interactions with features in its remote environment. This paper presents details of Computational Fluid Dynamics (CFD) simulation and analysis of a quadrotor helicopter. It starts by presenting how SolidWorks software is used to develop a 3-D Computer Aided Design (CAD) model of the quad-rotor helicopter, then describes how CFD is used as a computer based mathematical modelling tool to simulate and analyze the effects of wind flow patterns on the performance and control of the quadrotor helicopter. For the purpose of developing a robust adaptive controller for the quad-rotor helicopter to withstand any environmental constraints, which is not within the scope of this paper; this work accurately models the quad-rotor static and dynamic characteristics from a limited number of time-accurate CFD simulations

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

solveME: fast and reliable solution of nonlinear ME models.

BackgroundGenome-scale models of metabolism and macromolecular expression (ME) significantly expand the scope and predictive capabilities of constraint-based modeling. ME models present considerable computational challenges: they are much (>30 times) larger than corresponding metabolic reconstructions (M models), are multiscale, and growth maximization is a nonlinear programming (NLP) problem, mainly due to macromolecule dilution constraints.ResultsHere, we address these computational challenges. We develop a fast and numerically reliable solution method for growth maximization in ME models using a quad-precision NLP solver (Quad MINOS). Our method was up to 45 % faster than binary search for six significant digits in growth rate. We also develop a fast, quad-precision flux variability analysis that is accelerated (up to 60× speedup) via solver warm-starts. Finally, we employ the tools developed to investigate growth-coupled succinate overproduction, accounting for proteome constraints.ConclusionsJust as genome-scale metabolic reconstructions have become an invaluable tool for computational and systems biologists, we anticipate that these fast and numerically reliable ME solution methods will accelerate the wide-spread adoption of ME models for researchers in these fields