Variational Principles and Methods in Theoretical Physics and Chemistry

Method of Mathematical Physics which has strong applicability is an important basic course in colleges of engineering.However, in the process of teaching this course, most teachers only focus on theoretical derivation, ignoring the practical application.This inappropriate teaching method greatly weakens the students' interest in learning, which hinders the improvement of students' ability to solve the practical problem.With the development of Multimedia and network technology, more and more teaching methods have been applied in class.As a discipline with strong application, "Method of Mathematical Physics" should be taught in a new way the modern technology is fully used.In this article, several ideals are discussed for the curriculum reform in terms of teaching content and teaching methods.We make a special mention of the innovation based of Network and Multimedia technology in this article.Combined with authors teaching practice, applied teaching methods are put forward.

Mathematical Methods in Physics

Zusammenfassender Bericht über die Tagung in Bonn vom 3. bis 6. 7. 1973 über die neuen theoretischen Arbeiten von Kostant und Souriau.

Mathematical Methods in Physics and Engineering (J. W. Dettman)

Proceedings of the 7th International Conference on Mathematical Methods in Physics. April 16-21, 2012. CBPF, Rio de Janeiro, Brasil

The XXVIIIth International Colloquium on Group-Theoretical Methods in Physics (ICGTMP), also known as the GROUP 28 conference, took place in Newcastle upon Tyne from 26–30 July 2010. There were 128 attendees from 22 countries – physicists, mathematicians, chemists and engineers who use mathematical and numerical methods based on geometry and symmetry in their work. The conference was organised jointly by Northumbria and Durham Universities. The conference website is http://group28.northumbria.ac.uk.

Learning physics mathematics is one of the subjects in the physics education study program at the University of Jambi. Based on the results of the questionnaire, students' needs regarding learning mathematics and physics are considered difficult to understand the material taught by lecturers. This is due to the less varied teaching materials and the books used are only sourced from the book Mathematical Methods in Physics written by Mary L. Boas with a thickness of 839 pages consisting of 15 chapters with the language used in English. This is why this research was conducted with the aim of being able to help students with problems when learning mathematics and physics, especially in the material of coordinate transformation using e-modules created using Flip PDF Professional software. The method used is a mixed method with an explanatory design where quantitative data in the form of questionnaire results are strengthened by qualitative data in the form of interviews. Based on the research results, the existence of e-modules can be an alternative in learning that can be used by lecturers and students who are used for independent study with a flexible design that can be used.

Generalized Fourier methods in mathematical physics – a software for education

In this work, we apply a new variational principle that allows us to find the distribution function of electron in an arbitrary atom. This principle is based on the method of density matrix. Using the density matrix, we found the energy of the electrons in an atom, entropy and thermodynamic potential. The main idea of this article is that all two-electron matrices must be anti-symmetric. This refers to the two-electron Hamiltonian. This applies to Slater two-particle wave function. We found the equation for the distribution function of electrons at the quantum orbits. This equation can be obtained in two cases. In the first case, based on the density matrix of the first order, this equation is obtained only for the distribution function. In the second case two equations are obtained, which include distribution function and correlation function. The distribution function of electrons in the atom is similar to the function of Fermi–Dirac for electrons in a solid. In this work we apply a new approach to calculate the energy levels of electron in an arbitrary atom. This approach is also based on the method of density matrix.

Studies in physical and theoretical chemistry, Vol. 19, field theoretical methods in chemical physics: by R. Paul, Elsevier, Amsterdam, 1982, pp. vii + 414, price US $107.00

The presented study examines various methods for phase-averaging the naturally oscillating flow field of an enlarged fluidic oscillator acquired by a high-speed PIV system. Because of the absence of an external trigger, phase-averaging the acquired data is challenging. Mathematical and physical methods are categorized and described. The results of these methods are evaluated for their accuracy in capturing the natural flow field. It is found that the mathematical methods, especially the method of proper orthogonal decomposition, produce reasonable qualitative results. However, compared to the physical methods, shortcomings in quantitative accuracy are revealed. The physical methods require a time-resolved reference signal. Two possibilities to identify the oscillation periods in the reference signal are described and compared. It is found that applying an autocorrelation on the reference signal improves the period identification due to consideration of a locally fluctuating mean value. This period identification method and according phase-averaging yields the best results regarding the minimum fluctuation of the oscillation period lengths. The according procedure is described in detail and applied to the internal and external flow field of the fluidic oscillator.

Supercomputing has been widely implemented in theoretical physics, theoretical chemistry, climate modeling, biology simulation and medicine research for high-performance and energy-efficient computing. Many of scientific applications are I/O sensitive and users have to tolerate high latency when supercomputing center storage processes thousands of I/O requests. In this paper, IMFSSC, an in-memory distributed file system framework for super computing is proposed, which is supposed to improve latency performance for I/O sensitive applications and relieves the congestion when I/O requests burst. IMFSSC consists of modules for multiple master-slave supports, load balance among huge amount computing nodes, and uses memory space to store data to minimize the latency. Additional features will be added in the near future and it is supposed to provide better support for large scaled computer systems. Finally, the performance is tested under the framework for evaluation, which shows high scalability and good I/O performance.

A classical problem of digital sequence design, first studied in the 1950s but still not well understood, is to determine those binary sequences whose aperiodic autocorrelations are collectively small according to some suitable measure. The merit factor is an important such measure, and the problem of determining the best value of the merit factor of long binary sequences has resisted decades of attack by mathematicians and communications engineers. In equivalent guise, the determination of the best asymptotic merit factor is an unsolved problem in complex analysis proposed by Littlewood in the 1960s that until recently was studied along largely independent lines. The same problem is also studied in theoretical physics and theoretical chemistry as a notoriously difficult combinatorial optimisation problem. The best known value for the asymptotic merit factor has remained unchanged since 1988. However recent experimental and theoretical results strongly suggest a possible improvement. This survey describes the development of our understanding of the merit factor problem by bringing together results from several disciplines, and places the recent results within their historical and scientific framework.

How and why should physicians translate qualitative impressions into quantitative values? This chapter analyzes some answers to that question in early modern British mathematical medicine. Focusing on the geometrical medicine of Archibald Pitcairne and the British followers of the mathematical experimentalism of Santorio Santori (Sanctorius), I ask how mathematical physicians attempted to quantify the medical concept of temperament or complexion by adopting the method of Newtonian mathematical physics and re-trying Sanctorius’s static weighing experiments. I argue that, insofar as Pitcairne’s program called for the imitation of Newtonian astronomers, it had difficulty translating temperament into a useful and meaningful quantity. The restaging of Sanctorius’s experiments, however, gave mathematical physicians practical opportunities to quantify temperament through the externalization and systematic recording of body weight, food intake, and bodily excreta.

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