Some Comments on the Matter Wave-light Wave Hypothesis

From the de Broglie matter wave hypothesis and Planck’s energy quantization law, and assuming conservation of energy in the absorption of a photon and its consequent conversion to kinetic energy of motion by a material particle initially at rest, one can deduce a simple mathematical relationship between the wavelength λ (or frequency ν), of the photon absorbed by the particle at rest, and the resulting de Broglie matter wave length, λ_D, of the particle with kinetic energy of motion of mv²/2. The relationship so deduced, λ_D∝√λ, suggests that visible wavelengths of light, from about 4000 ?, in the violet, to beyond about 7000 ?, in the red, on absorption by an electron at rest, lead to material electron wavelengths, λ_D, of the order of the size of the electron transfer proteins seen in the photosynthetic reaction centers of photosynthesizing organisms, at about a size of 50–100 ?. In addition to understanding the mechanism of photosynthesis as a material wave mediated phenomenon, further areas of importance of the relations pointed out in this paper are in the design of experiments to gain a deeper understanding of the basic tenets of wave mechanics, and in the use of tunable lasers to probe various properties of material waves, and to precisely control their properties for applications including lithography.     

Scaling Function Between the Exponential-6 and the Generalized Lennard-Jones Potential Functions

The van der Waals forces for non-bonded interaction can be expressed either by the Exponential-6 or by the Lennard-Jones(m-n) potential functions, whereby m > n. Hitherto a relationship exists between the Exponential-6 and the Lennard-Jones(12-6) potential functions, with a scaling factor = 13.772 at or near the equilibrium and = 12.0 for long range interaction. This paper attempts to develop relationships between Exponential-6 and a more generalized Lennard-Jones(m-n). Analysis reveals that the relationship exists only when n = 6 and that two sets of scaling factors (as functions of index m) applies for the relationship between Exponential-6 and the Lennard-Jones(m-6), whereby m > 6.     

Fractal phenomena in molecular mechanics calculation

It is proposed that in molecular mechanics calculation points belonging to various stable or meta-sta-ble conformtrs are mixed up and form fractal structures in conformation space.The calculation results show the following two phenomena:(i)Two levels of structure with fractal feature were observed.Around the conformer without mirror symmetry points belonging to the conformer and its enantiomer are mixed up and form the first level of fractal structure; on the boundary of the attractive basin o{ each atlractor,points belonging to different attractors form the second level of fractal structure.(ii) The variation of molecular mechanics parameters will influence the structure and area of each attractive basin significantly The above phenomena may become the basis of a new method for solving the troublesome multi-minimum-point problem in molecular mechanics calculation.     

Minimax principles for elliptic mixed hemivariational–variational inequalities

In this paper, minimax principles are explored for elliptic mixed hemivariational–variational inequalities. Under certain conditions, a saddle-point formulation is shown to be equivalent to a mixed hemivariational–variational inequality. While the minimax principle is of independent interest, it is employed in this paper to provide an elementary proof of the solution existence of the mixed hemivariational–variational inequality. Theoretical results are illustrated in the applications of two contact problems.     

Structural optimization with parameter-transfer finite element

A mathematical method to solve structural problems, using parameter-transfer finite elements (P-TFE) was recently proposed by the authors [1] [2] [3]. The proposed transfer finite element approach is able to create a mathematical model of a structure, taking into account directly the whole behaviour of the structure under dynamic, aerodynamic, and thermal actions, and not by assembling, in a separate fashion, the stiffness and the mass matrix on one side and the external load vector as performed by the classical finite element procedure.The purpose of this paper is to apply the above methodology to optimization problems, in particular to obtain the minimum structural weight for a beam, under primary constraints on buckling load or natural frequencies.The use of P-TFE in the field of structural optimization overcomes most difficulties of the usual techniques of solution and the element is particularly useful in the evaluation of the sensitivity matrix.The formulation of the optimization problem based on P-TFE is presented and some applications are studied. The numerical results obtained are compared with other existing methodologies and briefly discussed.

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Sommario Gli autori hanno già proposto un metodo per studiare problemi strutturali [1] [2] [3], introducendo una nuova metodologia di discretizzazione, basata sull'impiego di elementi finiti di trasferimento, funzioni esplicite di un parametro, indicati come P-TFE. Tali elementi sono in grado di rappresentare, in similitudine alla funzione di trasferimento, il comportamento completo dell'elemento strutturale in esame, soggetto ad azioni dinamiche, aerodinamiche e termiche; sono parimenti in grado di produrre, in similitudine al metodo degli elementi finiti, un modello matematico discreto di un continuo.Scopo del presente lavoro è di applicare detta metodologia a problemi di ottimizzazione, in particolare alla ricerca del minimo peso per una trave che mantenga inalterate le sue caratteristiche di carico critico o le frequenze naturali di vibrazione.Vengono quindi presentati alcuni risultati numerici dei casi esaminati e confrontati con quelli ottenuti da altri autori con l'impiego di altre metodologie.

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List of Symbols {B} _m vector of the generalized state variables - {C} _m vector of integration constants - [I] unit matrix - EI bending stiffness - A cross-sectional area - u adimensional thickness - l beam length - M,M bending moment - [N] _m shape function ofm-th order - [N*] shape function atx ₀ - P axial load - [R] _i transfer matrix of thei-th element - T,T shear force - w transverse displacement - x adimensional independent variable - x ₀ value ofx at the left of the element - {Y} vector of state variables - {Y*} imposed condition atx ₀ - _0m Kronecker delta with the first pedix always set equal to zero - normalized eigenfrequency - normalized buckling load - mass density     

Lattice-BGK approach to simulating granular flows

Many continuum theories for granular flow produce an equation of motion for the fluctuating kinetic energy density (granular temperature) that accounts for the energy lost in inelastic collisions. Apart from the presence of an extra dissipative term, this equation is very similar in form to the usual temperature equation in hydrodynamics. It is shown how a lattice-kinetic model based on the Bhatnagar-Gross-Krook (BGK) equation that was previously derived for a miscible two-component fluid may be modified to model the continuum equations for granular flow. This is done by noting that the variable corresponding to the concentration of one species follows an equation that is essentially analogous to the granular temperature equation. A simulation of an unforced granular fluid using the modified model reproduces the phenomenon of clustering instability, namely the spontaneous agglomeration of particles into dense clusters, which occurs generically in all granular flows. The success of the continuum theory in capturing the gross features of this basic phenomenon is discussed. Some shear flow simulations are also presented.     

Coulomb pair density matrix I

The Coulomb pair density matrixG (r, r) for attractive and repulsive potentials is not only interesting for determining the two-particle effective potentials, but it is also essential in numerical studies of quantum systems. A high-temperature approximation is obtained for logG (r, r), in the form of simple integrals or series expansions; large-distance expansions are also given.     

Positivity of entropy production in nonequilibrium statistical mechanics

We analyze different mechanisms of entropy production in statistical mechanics, and propose formulas for the entropy production ratee() in a state . When is steady state describing the long term behavior of a system we show thate()0, and sometimes we can provee()>0.     

18－冠－6及其碱金属配合物构象和稳定性的分子力学研究

１８－冠－６及其碱金属配合物构象和稳定性的分子力学研究张士国,李红,杨频（滨州师范专科学校滨州２５６６０４）（山西大学分子所太原０３０００６）关键词分子力学,冠醚,配合物,构象１８－冠－６及其大部分配合物的晶体结构已被测定,但由于存在晶体堆积能而使分...     

Polarographic study of Tl+, Li+, Na+, K+, and Cs+ complexes with monensin anion in dipolar aprotic solvents

Summary The stability constants,K _sof monensin complexes with Li⁺, Na⁺, K⁺ and Cs⁺ ions were studied by a competitive polarographic method using the Tl⁺/Tl(Hg) redox couple as a sensitive electrochemical probe. TheK _svalues are strongly influenced by the solvents (acetonitrile, propionitrile, acetone, N,N-dimethylformamide, N-methyl pyrolidinone, N,N-dimethylacetamide, dimethylsulfoxide, N,N-diethylformamide and N,N-diethylacetamide were used in experiments) and vary inversely with the Gutmann donicity scale. Molecular mechanics computations revealed the probable structures of the complexes.

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Polarographische Untersuchung von Tl⁺-, Li⁺-, Na⁺- und Cs⁺-Komplexen mit Monesin-Anion in dipolaren aprotischen Lösungsmitteln

Zusammenfassung Es wurden die StabilitätskonstantenK _svon Monesin-Komplexen mit Li⁺-, Ma⁺- und Cs⁺-Ionen mittels einer competitiven polarographischen Methode unter Verwendung der Tl⁺/Tl(Hg)-Redoxelektrode als sensitiver elektrochemischer Sonde bestimmt. DieK _s-Werte werden stark vom Lösungsmittel (Acetonitril, Propionitril, Aceton, N,N-Dimethylformamid, N-Methylpyrrolidinon, N,N-Dimethylacetamid, Dimethylsulfoxid, N,N-Diethylformamid und N,N-Diethylacetamid) beeinflußt, wobei sie invers zurGutmann schen Donizitätsskala variieren. Die wahrscheinliche Struktur der Komplexe wurde mittels molekularmechanischer Berechnungen ermittelt.