On the Emergence of Simple Structures in Complex Phenomena: Concepts and Some Numerical Examples

2014 ◽  
pp. 97-118
Author(s):  
Martin Quack
Keyword(s):  
Numerical Examples ◽  
Complex Phenomena

Defects of Platelet Function Recognized by X-Ray Imaging and Scanning Electron Microscopy

1985 ◽  
Vol 43 ◽  
pp. 610-613
Author(s):  
M.G. Baldini ◽  
S. Morinaga ◽  
D. Minasian ◽  
R. Feder ◽  
D. Sayre ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
Cell Biology ◽  
Imaging Technique ◽  
Human Platelets ◽  
X Rays ◽  
X Ray ◽  
X Ray Imaging ◽  
Complex Phenomena ◽  
Scanning Electron

Contact X-ray imaging is presently developing as an important imaging technique in cell biology. Our recent studies on human platelets have demonstrated that the cytoskeleton of these cells contains photondense structures which can preferentially be imaged by soft X-ray imaging. Our present research has dealt with platelet activation, i.e., the complex phenomena which precede platelet appregation and are associated with profound changes in platelet cytoskeleton. Human platelets suspended in plasma were used. Whole cell mounts were fixed and dehydrated, then exposed to a stationary source of soft X-rays as previously described. Developed replicas and respective grids were studied by scanning electron microscopy (SEM).

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Stability of Implicit Difference Equations Generated by Parabolic Functional Differential Problems

2007 ◽  
Vol 7 (1) ◽  
pp. 68-82
Author(s):  
K. Kropielnicka
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Initial Boundary ◽  
Numerical Examples ◽  
Convergence Results ◽  
Nonlinear Parabolic ◽  
Implicit Difference Methods ◽  
Neumann Type ◽  
Difference Methods ◽  
Functional Differential

AbstractA general class of implicit difference methods for nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type is constructed. Convergence results are proved by means of consistency and stability arguments. It is assumed that given functions satisfy nonlinear estimates of Perron type with respect to functional variables. Differential equations with deviated variables and differential integral problems can be obtained from a general model by specializing given operators. The results are illustrated by numerical examples.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

Influence of Flexible Side-Chains on the Breathing Phase Transition of Pillared Layer MOFs: A Force Field Investigation

2020 ◽  
Author(s):  
Julian Keupp ◽  
Johannes P. Dürholt ◽  
Rochus Schmid
Keyword(s):  
First Principles ◽  
Good Accuracy ◽  
Field Investigation ◽  
Square Lattice ◽  
Side Chain ◽  
Second Step ◽  
Side Chains ◽  
Dynamics Simulations ◽  
Complex Phenomena ◽  
Closed Pore

The prototypical pillared layer MOFs, formed by a square lattice of paddle-<br>wheel units and connected by dinitrogen pillars, can undergo a breathing phase<br>transition by a “wine-rack” type motion of the square lattice. We studied this not<br>yet fully understood behavior using an accurate first principles parameterized force<br>field (MOF-FF) for larger nanocrystallites on the example of Zn 2 (bdc) 2 (dabco) [bdc:<br>benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)] and found clear indi-<br>cations for an interface between a closed and an open pore phase traveling through<br>the system during the phase transformation [Adv. Theory Simul. 2019, 2, 11]. In<br>conventional simulations in small supercells this mechanism is prevented by periodic<br>boundary conditions (PBC), enforcing a synchronous transformation of the entire<br>crystal. Here, we extend this investigation to pillared layer MOFs with flexible<br>side-chains, attached to the linker. Such functionalized (fu-)MOFs are experimen-<br>tally known to have different properties with the side-chains acting as fixed guest<br>molecules. First, in order to extend the parameterization for such flexible groups,<br>1a new parametrization strategy for MOF-FF had to be developed, using a multi-<br>structure force based fit method. The resulting parametrization for a library of<br>fu-MOFs is then validated with respect to a set of reference systems and shows very<br>good accuracy. In the second step, a series of fu-MOFs with increasing side-chain<br>length is studied with respect to the influence of the side-chains on the breathing<br>behavior. For small supercells in PBC a systematic trend of the closed pore volume<br>with the chain length is observed. However, for a nanocrystallite model a distinct<br>interface between a closed and an open pore phase is visible only for the short chain<br>length, whereas for longer chains the interface broadens and a nearly concerted trans-<br>formation is observed. Only by molecular dynamics simulations using accurate force<br>fields such complex phenomena can be studied on a molecular level.

Assessing maximal allowable levels for simultaneous skin and eyes exposure to laser irradiation of various wavelengths

2019 ◽  
pp. 35-38
Author(s):  
Boris N. Rakhmanov ◽  
Vladimir I. Kezik ◽  
Vladimir T. Kibovsky ◽  
Valentin M. Ponomarev
Keyword(s):  
Total Energy ◽  
Laser Irradiation ◽  
Customs Union ◽  
Economic Community ◽  
Laser Safety ◽  
Numerical Examples ◽  
Allowable Level ◽  
Correct Formula

Introduction.Evidences prove falseness of formula determining maximal allowable level of total energy of laser irradiation in case when eyes or skin are simultaneously exposed to several irradiation sources with various wavelengths. The formula was mentioned in actual «Sanitary rules and regulations for lasers construction and exploitation» Nо 5804–91 and in SanPiN 2.2.4.3359–16, that in a part of VIII section «Laser irradiation atworkplace» are latest acting regulation document on laser safety. SanPiN 2.2.4.13–2–2006 of Belarus Republic and regulation document Nо 299 of Customs Union Commission of Eurasia Economic Community on 28/05/2010 appeared to contain other, more correct formula determining the same maximal allowable level.Objectivewas to improve regulation basis in laser safety by correcting mistakes made previously in regulation documents.Deducing formulae.The article presents thorough and consistent deducing a formula to determine total energy of laser irradiation in case when eyes or skin are simultaneously and jointly exposed to several irradiation sources with various wavelengths. The efforts resulted in the formula that agreed with formulae presented in the regulation document on laser safety of Belarus Republic and in the regulation document Nо 299 of Customs Union Commission of Eurasia Economic Community on 28/05/2010.Discussion.Correctness of the obtained formula is supported by numerical examples and by comparison with other formulae used in regulation documents on hygienic regulation of other acting factors.Conclusion.Results of the work are summarized, and emphasis is made on its value for solving problems of improving regulation basis for laser safety.

Encapsulation and the C++ class

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Program Design ◽  
Internal Representation ◽  
Floating Point ◽  
Complex Class ◽  
Numerical Examples ◽  
Important Notion ◽  
Standard Library

Built-in datatypes and C++ classes are introduced in this chapter, and discussed in relation to the important notion of encapsulation, which refers to the separation between the internal representation of the datatype and the operations to which it responds. Encapsulation later becomes an important consideration in the design of custom C++ classes that programmers develop themselves. It is illustrated with built-in floating-point datatypes float and double and with the complex class from the C++ standard library. While a sophisticated programmer is aware of the internal representation of data and its resulting limitations, encapsulation allows one to consider these as details and frees one to think at a higher level of program design. Some simple numerical examples are discussed in the text and in the exercises.

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