scholarly journals Global Analysis of a Discrete Nonlocal and Nonautonomous Fragmentation Dynamics Occurring in a Moving Process

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
E. F. Doungmo Goufo ◽  
S. C. Oukouomi Noutchie
Keyword(s):  
Global Analysis ◽  
Semigroup Theory ◽  
Strong Solutions ◽  
Approximation Technique ◽  
Existence Of A Solution ◽  
Size Dependent ◽  
Evolution Semigroup ◽  
Time Position ◽  
Fragmentation Dynamics ◽  
Moving Process

We use a double approximation technique to show existence result for a nonlocal and nonautonomous fragmentation dynamics occurring in a moving process. We consider the case where sizes of clusters are discrete and fragmentation rate is time, position, and size dependent. Our system involving transport and nonautonomous fragmentation processes, where in addition, new particles are spatially randomly distributed according to some probabilistic law, is investigated by means of forward propagators associated with evolution semigroup theory and perturbation theory. The full generator is considered as a perturbation of the pure nonautonomous fragmentation operator. We can therefore make use of the truncation technique (McLaughlin et al., 1997), the resolvent approximation (Yosida, 1980), Duhamel formula (John, 1982), and Dyson-Phillips series (Phillips, 1953) to establish the existence of a solution for a discrete nonlocal and nonautonomous fragmentation process in a moving medium, hereby, bringing a contribution that may lead to the proof of uniqueness of strong solutions to this type of transport and nonautonomous fragmentation problem which remains unsolved.

scholarly journals Global Analysis of a Blood Flow Model with Artificial Boundaries

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
S. C. Oukouomi Noutchie
Keyword(s):  
Blood Flow ◽  
Fixed Point ◽  
Weak Solution ◽  
Flow Model ◽  
Global Analysis ◽  
Stationary Problem ◽  
Energy Estimates ◽  
Well Posedness ◽  
Existence Of A Solution ◽  
Artificial Boundaries

A theoretical model for blood flow in ramifying arteries was introduced and studied numerically (Quarteroni and Veneziani, 2003). A special experimental condition was considered on the artificial boundaries. In this paper, the aim is to analyze the well-posedness of this model, with the focus on the stilted boundary conditions. We use Brouwer’s fixed point theorem to show the existence of a solution to the stationary problem. For the evolutionary version, we use some energy estimates and Galerkin’s method to prove global existence, uniqueness, and stability of a weak solution.

scholarly journals Global Existence of Strong Solutions to a Class of Fully Nonlinear Wave Equations with Strongly Damped Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Zhigang Pan ◽  
Hong Luo ◽  
Tian Ma
Keyword(s):  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Galerkin Approximation ◽  
Strong Solutions ◽  
Nonlinear Wave Equations ◽  
Existence Of A Solution ◽  
Fully Nonlinear ◽  
Sequence Techniques ◽  
Strongly Damped

We consider the global existence of strong solutionu, corresponding to a class of fully nonlinear wave equations with strongly damped termsutt-kΔut=f(x,Δu)+g(x,u,Du,D2u)in a bounded and smooth domainΩinRn, wheref(x,Δu)is a given monotone inΔunonlinearity satisfying some dissipativity and growth restrictions andg(x,u,Du,D2u)is in a sense subordinated tof(x,Δu). By using spatial sequence techniques, the Galerkin approximation method, and some monotonicity arguments, we obtained the global existence of a solutionu∈Lloc∞((0,∞),W2,p(Ω)∩W01,p(Ω)).

scholarly journals Existence and uniqueness of mild and strong solutions of nonlinear volterra integrodifferential equations in Banach spaces

2010 ◽  
Vol 43 (3) ◽  
Author(s):  
H. L. Tidke ◽  
M. B. Dhakne
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Semigroup Theory ◽  
Strong Solutions ◽  
Banach Fixed Point Theorem ◽  
Volterra Integrodifferential Equation

AbstractIn this paper we prove the existence and uniqueness of mild and strong solutions of a nonlinear Volterra integrodifferential equation with nonlocal condition. Our analysis is based on semigroup theory and Banach fixed point theorem and inequalities are established by Gronwall and B. G. Pachpatte.

Production and STEM examination of controlled-size silver clusters

1983 ◽  
Vol 41 ◽  
pp. 338-339
Author(s):  
M. A. Listvan ◽  
R. P. Andres
Keyword(s):  
Cluster Size ◽  
Metal Clusters ◽  
Experimental Parameter ◽  
Carbon Films ◽  
Metal Species ◽  
Silver Clusters ◽  
Free Jet ◽  
Size Dependent ◽  
Cluster Properties ◽  
Controllable Size

Knowledge of the function and structure of small metal clusters is one goal of research in catalysis. One important experimental parameter is cluster size. Ideally, one would like to produce metal clusters of regulated size in order to characterize size-dependent cluster properties.A source has been developed which is capable of producing microscopic metal clusters of controllable size (in the range 5-500 atoms) This source, the Multiple Expansion Cluster Source, with a Free Jet Deceleration Filter (MECS/FJDF) operates as follows. The bulk metal is heated in an oven to give controlled concentrations of monomer and dimer which were expanded sonically. These metal species were quenched and condensed in He and filtered to produce areosol particles of a controlled size as verified by mass spectrometer measurements. The clusters were caught on pre-mounted, clean carbon films. The grids were then transferred in air for microscopic examination. MECS/FJDF was used to produce two different sizes of silver clusters for this study: nominally Ag6 and Ag50.

Transfer Technique for Electron Microscopy of Membrance Filter Samples

1974 ◽  
Vol 32 ◽  
pp. 554-555
Author(s):  
Lawrence W. Ortiz ◽  
Bonnie L. Isom
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Pore Size ◽  
Membrane Filters ◽  
Size Dependent

A procedure is described for the quantitative transfer of fibers and particulates collected on membrane filters to electron microscope (EM) grids. Various Millipore MF filters (Millipore AA, HA, GS, and VM; 0.8, 0.45, 0.22 and 0.05 μm mean pore size) have been used with success. Observed particle losses have not been size dependent and have not exceeded 10%. With fibers (glass or asbestos) as the collected media this observed loss is approximately 3%.

Spindle scaling mechanisms

2020 ◽  
Vol 64 (2) ◽  
pp. 383-396
Author(s):  
Lara K. Krüger ◽  
Phong T. Tran
Keyword(s):  
Cell Size ◽  
Spindle Assembly ◽  
Dependent Manner ◽  
Post Translational Modification ◽  
Size Dependent ◽  
A Cell ◽  
Chromosome Separation ◽  
Spindle Elongation ◽  
Protein Gradients ◽  
Spindle Structure

Abstract The mitotic spindle robustly scales with cell size in a plethora of different organisms. During development and throughout evolution, the spindle adjusts to cell size in metazoans and yeast in order to ensure faithful chromosome separation. Spindle adjustment to cell size occurs by the scaling of spindle length, spindle shape and the velocity of spindle assembly and elongation. Different mechanisms, depending on spindle structure and organism, account for these scaling relationships. The limited availability of critical spindle components, protein gradients, sequestration of spindle components, or post-translational modification and differential expression levels have been implicated in the regulation of spindle length and the spindle assembly/elongation velocity in a cell size-dependent manner. In this review, we will discuss the phenomenon and mechanisms of spindle length, spindle shape and spindle elongation velocity scaling with cell size.

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