Propagation of laser beams through curved interfaces of transparent media

Abstract Mathematical models of propagation of Gaussian, collimated and structured laser beams in transparent optically homogeneous media in the presence of curved interfaces are presented. Experimental techniques which are used for reconstruction of the interfaces profiles are described.

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Experimental techniques to verify mathematical models of non-Newtonian flow

Food Manufacturing Efficiency ◽

10.1616/fme.2006.1.1.45 ◽

2006 ◽

Vol 1 (1) ◽

pp. 45-50

Author(s):

Stephen T. Beckett

Keyword(s):

Mathematical Models ◽

Experimental Techniques ◽

Newtonian Flow

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Application of Raman Spectroscopy to Ancient Materials: Models and Results from Archaeometric Analyses

Materials ◽

10.3390/ma13112456 ◽

2020 ◽

Vol 13 (11) ◽

pp. 2456

Author(s):

Daniele Chiriu ◽

Francesca Assunta Pisu ◽

Pier Carlo Ricci ◽

Carlo Maria Carbonaro

Keyword(s):

Raman Spectroscopy ◽

Cultural Heritage ◽

Mathematical Models ◽

Structural Properties ◽

Statistical Models ◽

Experimental Techniques ◽

Pigment Degradation ◽

Properties Of Materials

Numerous experimental techniques of analysis find applications in many branches of the archaeometry. Among them, Raman spectroscopy carved out a niche in the field of diagnostic and conservation of cultural heritage. The exceptional ability to predict and discover the structural properties of materials set for Raman spectroscopy, an exclusive role among the analytic techniques, is further boosted when it is coupled with mathematical or statistical models able to deepen the studied phenomena. In this work, we present a review of recent studies where pairing Raman spectroscopy and mathematical models allowed achieving important results in the case of potteries, porcelains, ancient and modern paper, ancient jewelry, and pigment degradation. The potentialities of this approach are evidenced and analyzed in detail.

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Vibration of Soils and Foundations: Literature Review

Design Engineering, Parts A and B ◽

10.1115/imece2005-81506 ◽

2005 ◽

Author(s):

Albert C. J. Luo ◽

Mohammad Dehghani ◽

Hamid R. Hamidzadeh

Keyword(s):

Literature Review ◽

Mathematical Models ◽

Experimental Techniques ◽

Current State ◽

Dynamically Loaded ◽

Soil Media ◽

State Of Practice ◽

Soil Foundation

Research on vibration of soils and foundations has yielded several fundamental methods for formulation of interaction problems. This paper is intended to survey the development of the current state-of-practice for design and analysis of dynamically loaded foundations. Extensive studies in this field utilize various linear mathematical models for interaction between foundations and different soil media. The effective analytical, numerical and experimental techniques and their methodologies which are well established for treating problems in dynamic soil-foundation interaction are outlined. Described techniques are categorized based upon formulation procedures and their applications. Some areas are indicated where further research is needed.

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Matrix Fourier Transforms for Consistent Mathematical Models

Chinese Journal of Mathematics ◽

10.1155/2016/1975493 ◽

2016 ◽

Vol 2016 ◽

pp. 1-10

Author(s):

Oleg Yaremko ◽

Natalia Yaremko

Keyword(s):

Mathematical Models ◽

Fourier Transforms ◽

Integral Form ◽

Integral Transforms ◽

Mathematical Physics ◽

Discontinuous Coefficients ◽

Piecewise Homogeneous Media ◽

Fourier Matrix ◽

Matrix Transforms ◽

Homogeneous Media

We create a matrix integral transforms method; it allows us to describe analytically the consistent mathematical models. An explicit constructions for direct and inverse Fourier matrix transforms with discontinuous coefficients are established. We introduce special types of Fourier matrix transforms: matrix cosine transforms, matrix sine transforms, and matrix transforms with piecewise trigonometric kernels. The integral transforms of such kinds are used for problems solving of mathematical physics in homogeneous and piecewise homogeneous media. Analytical solution of iterated heat conduction equation is obtained. Stress produced in the elastic semi-infinite solid by pressure is obtained in the integral form.

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A model laser-compression experiment

Journal of Plasma Physics ◽

10.1017/s002237780002612x ◽

1975 ◽

Vol 13 (2) ◽

pp. 367-376

Author(s):

J. E. Crow ◽

I. J. Spalding ◽

J. A. Wesson

Keyword(s):

Light Absorption ◽

Thermal Transport ◽

University Research ◽

Experimental Techniques ◽

Laser Beams ◽

Diagnostic Equipment ◽

End Effects ◽

Time Resolved ◽

Simple Apparatus

The compression of plasmas by laser beams to produce a significant thermonuclear energy requires very sophisticated experimental techniques and equipment, costing millions of dollars. We review here comparatively simple techniques which should permit a time-resolved demonstration of an isentropic density compression, using low-powered lasers of a type commonly encountered in university research laboratories, and diagnostic equipment of modest cost. Althoughthermonuclear burn cannot be investigatedwith such simple apparatus, many aspects of flux-limited thermal transport, light absorption, and end-effects (i.e. intensity assymmetries) could be conveniently and quantitatively investigated.

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Experimental techniques and mathematical models in the study of waste pyrolysis and gasification

Conservation & Recycling ◽

10.1016/0361-3658(79)90012-2 ◽

1979 ◽

Vol 3 (1) ◽

pp. 1-23 ◽

Cited By ~ 9

Author(s):

A.G. Buekens ◽

J.J.R. Mertens ◽

J.G.E. Schoeters ◽

P.C. Steen

Keyword(s):

Mathematical Models ◽

Experimental Techniques

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Mathematical Models of Serotonin, Histamine, and Depression

10.5772/intechopen.96990 ◽

2021 ◽

Author(s):

Janet Best ◽

Anna Marie Buchanan ◽

Herman Frederik Nijhout ◽

Parastoo Hashemi ◽

Michael C. Reed

Keyword(s):

Mathematical Models ◽

Serotonin Release ◽

Experimental Techniques ◽

Joint Research ◽

Brain Histamine ◽

Biological Phenomena ◽

Serotonin Autoreceptors ◽

Neuropsychiatric Diseases ◽

Working Together ◽

The Brain

The coauthors have been working together for ten years on serotonin, dopamine, and histamine and their connection to neuropsychiatric illnesses. Hashemi has pioneered many new experimental techniques for measuring serotonin and histamine in real time in the extracellular space in the brain. Best, Reed, and Nijhout have been making mathematical models of brain metabolism to help them interpret Hashemi’s data. Hashemi demonstrated that brain histamine inhibits serotonin release, giving a direct mechanism by which inflammation can cause a decrease in brain serotonin and therefore depression. Many new biological phenomena have come out of their joint research including 1) there are two different reuptake mechanisms for serotonin; 2) the effect of the serotonin autoreceptors is not instantaneous and is long-lasting even when the extracellular concentrations have returned to normal; 3) that mathematical models of serotonin metabolism and histamine metabolism can explain Hashemi’s experimental data; 4) that variation in serotonin autoreceptors may be one of the causes of serotonin-linked mood disorders. Here we review our work in recent years for biological audiences, medical audiences, and researchers who work on mathematical modeling of biological problems. We discuss the experimental techniques, the creation and investigation of mathematical models, and the consequences for neuropsychiatric diseases.

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Integrating mathematical models with experimental data to investigate the within-host dynamics of bacterial infections

Pathogens and Disease ◽

10.1093/femspd/ftaa001 ◽

2019 ◽

Vol 77 (8) ◽

Cited By ~ 1

Author(s):

Myrto Vlazaki ◽

John Huber ◽

Olivier Restif

Keyword(s):

Experimental Data ◽

Mathematical Models ◽

Bacterial Infections ◽

Vaccine Development ◽

Bacterial Colonization ◽

Experimental Techniques ◽

Efficient Design ◽

Mortality And Morbidity ◽

Bacterial Dynamics

ABSTRACT Bacterial infections still constitute a major cause of mortality and morbidity worldwide. The unavailability of therapeutics, antimicrobial resistance and the chronicity of infections due to incomplete clearance contribute to this phenomenon. Despite the progress in antimicrobial and vaccine development, knowledge about the effect that therapeutics have on the host–bacteria interactions remains incomplete. Insights into the characteristics of bacterial colonization and migration between tissues and the relationship between replication and host- or therapeutically induced killing can enable efficient design of treatment approaches. Recently, innovative experimental techniques have generated data enabling the qualitative characterization of aspects of bacterial dynamics. Here, we argue that mathematical modeling as an adjunct to experimental data can enrich the biological insight that these data provide. However, due to limited interdisciplinary training, efforts to combine the two remain limited. To promote this dialogue, we provide a categorization of modeling approaches highlighting their relationship to data generated by a range of experimental techniques in the area of in vivo bacterial dynamics. We outline common biological themes explored using mathematical models with case studies across all pathogen classes. Finally, this review advocates multidisciplinary integration to improve our mechanistic understanding of bacterial infections and guide the use of existing or new therapies.

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