Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

This paper proposes a survey and critical analysis focused on a variety of chemotaxis models in biology, namely the classical Keller–Segel model and its subsequent modifications, which, in several cases, have been developed to obtain models that prevent the non-physical blow up of solutions. The presentation is organized in three parts. The first part focuses on a survey of some sample models, namely the original model and some of its developments, such as flux limited models, or models derived according to similar concepts. The second part is devoted to the qualitative analysis of analytic problems, such as the existence of solutions, blow-up and asymptotic behavior. The third part deals with the derivation of macroscopic models from the underlying description, delivered by means of kinetic theory methods. This approach leads to the derivation of classical models as well as that of new models, which might deserve attention as far as the related analytic problems are concerned. Finally, an overview of the entire contents leads to suggestions for future research activities.

Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

A Well-Balanced Partial Relaxation Scheme for the Two-Dimensional Saint-Venant System

The possibility of reuse of heavy residues (oily sludge) of low-sulfur, highly paraffinic Mangyshlak oils as a basis for fuel with improved environmental characteristics for engines to marine, river and railway transport, gas turbine and boiler plants, steam boilers and industrial furnaces was shown. A variant of the joint application of the methods of nuclear magnetic resonance, laser confocal microscopy and rheology for study of micro- and mesoscopic structure and some physicochemical properties of crude oil products has been developed. It has been shown that preliminary heating to 90 ° C leads to disruption of the structure and hydrogen bonds between oil associates and complexes, increasing sample homogeneity due to precipitation of solid impurities, partial removal of water content, air bubbles and dissolved gases. The addition of medium distillate diesel fractions to preliminary heated oil residues will make it possible to obtain a higher quality version of the fuel with a reduced resinous and asphaltene substances, lower pour point, good energy content and low sulfur content. Thus, valuable energy-containing raw materials can be reused. It should also be noted that the reuse of accumulated oil waste will reduce the harmful effects of landfills, will preserve the natural landscape, and will cut the cost of extracting natural resources.

Paraffinic oil residues after heating as a basis for fuel

Photoisomerization of 1,2-di(4-pyridyl)ethylene under UV irradiation was studied by NMR and UV spectroscopy in solutions of acetone, acetonitrile and chloroform. It has been established that in the studied solutions under irradiation, geometric photoisomerization occurs: the trans-isomer transforms into the cis-isomer and then cyclization occurs. DFT modeling of the listed processes, states and UV absorption spectra of the sample in an acetonitrile solution was performed.

Photoisomerization of 1,2-Di(4-pyridyl)ethylene According to NMR and UV Spectroscopy Data and Density Functional Modeling.

https://doi.org/10.1016/j.jcp.2023.111987

Stochastic Galerkin method for cloud simulation. Part II: a fully random Navier-Stokes-cloud model

Influence of the Structure of (О-Phenylenoxymethylene)diphosphine Dioxides on Their Extraction Ability to U(VI), Th(IV), and REE(III) in Nitric Acid Media

Alexander Kurganov

Papers

A Well-Balanced Partial Relaxation Scheme for the Two-Dimensional Saint-Venant System

Paraffinic oil residues after heating as a basis for fuel

Photoisomerization of 1,2-Di(4-pyridyl)ethylene According to NMR and UV Spectroscopy Data and Density Functional Modeling.

Stochastic Galerkin method for cloud simulation. Part II: a fully random Navier-Stokes-cloud model

Influence of the Structure of (О-Phenylenoxymethylene)diphosphine Dioxides on Their Extraction Ability to U(VI), Th(IV), and REE(III) in Nitric Acid Media