On the stability of crystal lattices. I

Author(s):  
Max Born

The stability of lattices is discussed from the standpoint of the method of small vibrations. It is shown that it is not necessary to determine the whole vibrational spectrum, but only its long wave part. The stability conditions are nothing but the positive definiteness of the macroscopic deformation energy, and can be expressed in the form of inequalities for the elastic constants. A new method is explained for calculating these as lattice sums, and this method is applied to the three monatomic lattice types assuming central forces. In this way one obtains a simple explanation of the fact that the face-centred lattice is stable, whereas the simple lattice is always unstable and the body-centred also except for small exponents of the attractive forces. It is indicated that this method might be used for an improvement of the, at present, rather unsatisfactory theory of strength.

Author(s):  
Rama Dhar Misra

On the assumption that the potential energy of the three cubic lattices of the Bravais type consists of two terms, an attractive one proportional to r−m and a repulsive one proportional to r−n, n > m, stability conditions are expressed in the form that two functions of the number n should be monotonically increasing. These functions have been calculated numerically for n = 4 to 15, and are represented as curves with the abscissa n. The result is that the face-centred lattice is completely stable, that the body-centred lattice is unstable for large exponents in the law of force, and that the simple lattice is always unstable,—in complete agreement with the results of Part I.


Author(s):  
H. W. Peng ◽  
S. C. Power

The main purpose of the paper is an investigation of the stability of a certain class of Bravais lattices, namely, those with a rhombohedral cell of arbitrary angle. The potential energy is assumed to consist of two terms, each proportional to a reciprocal power of the distance. In the continuous series of lattices obtained by changing the rhombohedral angle, there are included the three cubic Bravais lattices, the simple (s), the face-centred (f) and the body-centred (b) lattices. It is shown that (f) and (b) correspond to a minimum of the potential energy, and (s) to a maximum. A method for calculating the potential energy for the intermediate rhombohedral lattices is developed, and, with the help of a certain characteristic function, it is shown by numerical calculation that the (f) lattice corresponds to the absolute minimum of potential energy, and that no extrema, other than (f), (s) and (b), exist. In the last section, the case of a compound (non-Bravais lattice) is considered, and it is shown that the equilibrium and stability conditions for the law of force assumed can be divided into one set for change of volume, and an independent set for change of shape.We take this opportunity of expressing our sincere thanks to Prof. Born for his interest in our work, and for much valuable advice.


Author(s):  
M. Born

The theory of lattice deformations is presented in a new form, using the tensor calculus. The case of central forces is worked out in detail, and the results are applied to some simple hexagonal lattices. It is shown that the Bravais hexagonal lattice is unstable but the close-packed hexagonal lattice stable. The elastic constants of this lattice are calculated.


Author(s):  
M. Born ◽  
R. Fürth

The energy density of a cubic lattice, homogeneously deformed by a force acting in the direction of one axis, is calculated, and the equilibrium conditions and the stability conditions for any arbitrary small additional deformations are derived. A special assumption is made as to the law of force between the atoms, and the numerical calculations are performed for the face-centred lattice. In this way the strain as a function of the deformation is calculated and, from the stability conditions, the tensile strength is determined. The results are not in agreement with the experimental facts, and the possible reasons for this disagreement are discussed.


Author(s):  
Max Born ◽  
Rama Dhar Misra

In order to explain the phenomena of melting, tensile strength, etc., we have to investigate the stability of crystals for finite deformations, for which deviations from Hooke's law occur. Although these deviations are in most cases of an irreversible character, it is necessary, for a systematic study, to develop mathematical methods for treating the mechanical (reversible) case of a highly strained crystal lattice, where terms of higher order than the second in the deformation energy must be taken into account.


Author(s):  
S. C. Power

It is shown that the theorem stated in Born's paper, and proved for the case of a linear lattice of N equal particles under certain restrictions concerning the forces between the particles, that macroscopic stability (stability for long waves) implies microscopic stability, may be extended to three dimensions for the particular case of a face-centred cubic lattice, where the effects of all neighbours, other than the first twelve neighbours, are neglected.I take this opportunity of expressing my sincere thanks to Prof. Born for much valuable advice.


2020 ◽  
Vol 99 (4) ◽  
pp. 379-383
Author(s):  
Vasily N. Afonyushkin ◽  
N. A. Donchenko ◽  
Ju. N. Kozlova ◽  
N. A. Davidova ◽  
V. Yu. Koptev ◽  
...  

Pseudomonas aeruginosa is a widely represented species of bacteria possessing of a pathogenic potential. This infectious agent is causing wound infections, fibrotic cystitis, fibrosing pneumonia, bacterial sepsis, etc. The microorganism is highly resistant to antiseptics, disinfectants, immune system responses of the body. The responses of a quorum sense of this kind of bacteria ensure the inclusion of many pathogenicity factors. The analysis of the scientific literature made it possible to formulate four questions concerning the role of biofilms for the adaptation of P. aeruginosa to adverse environmental factors: Is another person appears to be predominantly of a source an etiological agent or the source of P. aeruginosa infection in the environment? Does the formation of biofilms influence on the antibiotic resistance? How the antagonistic activity of microorganisms is realized in biofilm form? What is the main function of biofilms in the functioning of bacteria? A hypothesis has been put forward the effect of biofilms on the increase of antibiotic resistance of bacteria and, in particular, P. aeruginosa to be secondary in charcter. It is more likely a biofilmboth to fulfill the function of storing nutrients and provide topical competition in the face of food scarcity. In connection with the incompatibility of the molecular radii of most antibiotics and pores in biofilm, biofilm is doubtful to be capable of performing a barrier function for protecting against antibiotics. However, with respect to antibodies and immunocompetent cells, the barrier function is beyond doubt. The biofilm is more likely to fulfill the function of storing nutrients and providing topical competition in conditions of scarcity of food resources.


2020 ◽  
Vol 2 (1) ◽  
pp. 32-55
Author(s):  
Natalia Christofoletti Barrenha
Keyword(s):  
The Face ◽  

This text seeks to explore the Argentine films Castro (Alejo Moguillansky, 2009) and El asaltante (Pablo Fendrik, 2007) from within the displacement of their characters through the city. This transit configures the organising element of the plots, determining the direction and rhythm of events. The escape motto will structure the film analyses, which are also twinned by the sensory apprehension that comes from the spaces they travel through. The notion of escape, as explored by Esteban Dipaola in Argentine cinema of the 1990s, continues to throb in mid-to-late 2000s production, and in these films represents the means by which the protagonists deploy critical attitudes—sometimes radical and explosive, sometimes silent—in the face of fixed notions, suggesting some scepticism about the “stability” and “order” that they (dis)encounter in normality. RESUMEN Este texto busca explorar los largometrajes argentinos Castro (Alejo Moguillansky, 2009) y El asaltante (Pablo Fendrik, 2007) a partir del desplazamiento de sus personajes por la ciudad. El transitar se configura como elemento organizador de las tramas, determinando la dirección y el ritmo de los acontecimientos. El tema de la fuga irá estructurando los análisis de las películas, las cuales también están relacionadas por la aprehensión sensorial que hacen de los espacios que recorren. La noción de fuga, tal y como fue explorada por Esteban Dipaola en el cine argentino de los años 90, continúa vigente en la producción de mediados/fines de la primera década del siglo XXI, y en estas películas es el recurso por medio del cual los protagonistas despliegan actitudes críticas – a veces radicales y explosivas, y a veces silenciosas – frente a nociones convencionales, lo cual hace pensar que existe un cierto escepticismo con relación a la “estabilidad” y al “orden” que ellos (des)encuentran en la normalidad. RESUMO Este texto busca explorar os longas-metragens argentinos Castro (Alejo Moguillansky, 2009) e El asaltante (Pablo Fendrik, 2007) a partir do deslocamento de seus personagens pela cidade. O transitar configura-se como elemento organizador das tramas, determinando a direção e o ritmo dos acontecimentos. O mote da fuga estruturará as análises dos filmes, os quais também se irmanam pela apreensão sensorial que fazem dos espaços que percorrem. A noção de fuga, conforme explorada por Esteban Dipaola no cinema argentino da década de 1990, continua a pulsar na produção de meados/fins dos anos 2000, e é, nestes filmes, o recurso através do qual os protagonistas desdobram atitudes críticas – às vezes radicais e explosivas, às vezes silenciosas – diante de noções fixas, sugerindo certo ceticismo em relação à “estabilidade” e à “ordem” que eles (des)encontram na normalidade.


Author(s):  
Natalia Prodiana Setiawati ◽  
Joko Santoso ◽  
Sri Purwaningsih

The utilization of local food commodities such as corn and cassava with seaweed addition as a dietary fiber source for producing artificial rice through extrusion technology is an  alternative for food diversification. The research was carried out to find out the best composition (rice, corn, cassava, and seaweed) and temperature of extrusion process on making artificial rice and the influence of dietary fibre on sensory properties and physicochemical. The composition of rice, corn, and cassava in proportion  of 1:3:1 with 20% seaweed, Eucheuma cottonii, addition and temperature extruder of 90 °C were selected as the best product for artificial rice. The  sensory evaluation was 8.02±0.21 (people’s preference). In physicochemical properties, dietary fiber significantly affected on low bulk density and starch digestibility. This condition is very good for health especially in maintaining the stability of blood glucose in the body. Keywords: artificial rice, composition, extrusion, seaweed, dietary fibre, temperature


Author(s):  
Fesenko, H.

Purpose. Increasing the uniformity of distribution of mineral fertilizers and other bulk materials due to the stability of their feed from the body to the spreading working bodies using the top feeder. Methods. The following methods are used to achieve this aim: the method of comparing the differences between individual groups of fertilizers, the method of analyzing the properties of a new technical system, the method of functional inventiveness, and the methods of theoretical and analytical mechanics. Results. The traction body of the conveyor of the upper feed of the body fat body machine for mineral fertilizers and other bulk materials was substantiated and the relationship between the height of its scrapers and the distance between them was established, as well as the nature of the mineral fertilizer pressure on the curvilinear wall of the body. In addition, the design of the advanced body fertilizer spreader is justified, which ensures a stable flow of fertilizers from the body due to the improvement of the top feeder. Conclusions. Because of the conducted researches, the advantages of machines equipped with top feeder are found. They create the conditions for the forced feeding mineral fertilizers and other loose materials from the container to the distribution bodies, which is a prerequisite for their evenness on the surface. With this, the imperfection of known machines with the top feeder constrains their introduction into agricultural production. On this account, a more thoroughly constructed solution of the body feeder of the top feed is substantiated, in which the conveyor provides a stable supply of fertilizers from the body with reduced energy consumption during operation. Keywords: analysis, feed, upper device, conveyor, stability, fertilizers, flow ability, body.


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