scholarly journals Binding of muonated hydrogen molecules and Born–Oppenheimer approximation revisited

2020 ◽  
Vol 98 (4) ◽  
pp. 379-384 ◽  
Author(s):  
A.J.C. Varandas ◽  
J. da Providência ◽  
J.P. da Providência
Keyword(s):  
Hydrogen Molecules ◽  
Unit Charge ◽  
90Th Anniversary ◽  
Oppenheimer Approximation ◽  
The Stability ◽  
The Masses ◽  
Gaussian Orbital

The stability of four fermionic particles with unit charge, of which two are positively and two negatively charged, is discussed. Except for using the simplest approximation of a single Gaussian orbital per particle, the problem is exactly solved variationally by varying the masses to simulate molecular di-hydrogen, mono-muonated di-hydrogen, and di-muonated di-hydrogen. We illustrate the celebrated Born–Oppenheimer approximation 2 years after the occasion of its 90th anniversary. It is suggested that this method is valid only for di-hydrogen.

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

scholarly journals THE QUESTION OF BOOM LIFTING EQUIPMENT OPERATION STABILITY ON A WHEELED CHASSIS

2021 ◽  
pp. 100-108
Author(s):  
В.И. Токарев ◽  
Н.В. Бабоченко
Keyword(s):  
Longitudinal Direction ◽  
Equipment Operation ◽  
Mathematical Expressions ◽  
Maximum Stability ◽  
Operation Stability ◽  
Quality Of Movement ◽  
The Stability ◽  
The Masses ◽  
Constituent Elements ◽  
Lifting Equipment

В статье представлены на рассмотрение характеристики стабильности работы стреловых грузоподъемных средств на колесном шасси в форме математических выражений. Математические выражения представлены в виде не громоздких зависимостей от конкретно заданных параметров. Качество движения зависит от возрастания линейных размеров, масс, моментов инерции, а также скоростей и других механических параметров грузоподъемных средств. Достижение стабильности работы выносных стреловых грузоподъемных средств достигается путем распределения нагрузки между утлегарью (выносной стрелой грузоподъемного средства) и опорными колесами колесного шасси. Считаем, что при существовании ряда концепцией со своими теориями. возможно определение стабильности работы стрелового грузоподъемного средства на колесном шасси. Нами установлено, что возможно обеспечить стабильность работы путем выбора целесообразных значений механических составляющих всех звеньев рабочего механизма для спланировано составленных рабочих ситуаций. В зависимости от возможного размещения грузоподъемного устройства показатели стабильности работы меняются и это подтверждают составленные нами математические выражения, которые приводятся в статье. Установлено, что путем варьирования различными вариантами положений и массой составляющих элементов конструкции грузоподъемного средства, а также графически определяя возможные варианты перемещения груза в зависимости от заданной длины утлегарьи, имеет место выражение, позволяющее определить ряд значений масс, безопасно поднимаемых грузоподъемным средством. Нами получены значения необходимых для графических построений грузовых характеристик грузоподъемного средства, выражающие зависимость между массой груза и вылетом утлегарьи с весом ее элементов. Реакции в шарнирах утлегарьи и усилия в ее составляющих звеньях возможно установить из данных грузовой характеристики. Стремление обеспечить максимальную стабильность работы грузоподъемного средства накладывает ограничения на контроль за несколькими подвижными операциями одновременно, что неблагоприятно сказывается на эффективности рабочего процесса. Установили, что обеспечение стабильности работы в поперечной и продольной плоскостях грузоподъемного средства является необходимым компонентом безопасной эксплуатации. По зависимостям для определения показателя грузового равновесия возможно определение предварительного места установки выносных опор грузоподъемного средства. Как подтверждают полученные результаты, стабильность работы грузоподъемного средства в продольном направлении определяется аналогично стабильности работы в поперечном направлении и для номинальной массы груза при наибольшем вылете утлегарьи и выставленных выносных опорах. В итоге отметим, что показателем грузового равновесия служит отношение удерживающего момента относительно ребра опрокидывания, создаваемого весом грузоподъемного средства на колесном шасси с учетом уменьшающих его дополнительных внешних нагрузок и влияния уклона площадки к опрокидывающему моменту, создаваемому рабочим грузом. The article presents for consideration the characteristics of the stability of the boom lifting equipment on a wheeled chassis in the form of mathematical expressions. Mathematical expressions are presented in the form of not cumbersome dependencies on specified parameters. The quality of movement depends on the increase in linear dimensions, masses, moments of inertia, as well as speeds, and other mechanical parameters of the lifting equipment. Achievement of the stability of the outboard boom lifting device is achieved by distributing the load between the jib boom (outboard boom of the lifting device) and the support wheels of the wheeled chassis. We believe that with the existence of a number of concepts with their theories, it is possible to determine the stability of the boom lifting device on a wheeled chassis. It has been found that it is possible to ensure the stability of work by choosing the appropriate values of the mechanical components of all links of the working mechanism for planned working situations. Depending on the possible placement of the lifting device, the stability indicators are changed, and this is confirmed by the mathematical expressions we compiled, which are given in the article. It has been established that by varying the positions and the mass of the constituent elements of the structure of the lifting device, as well as graphically defining the possible options of the load moving, depending on the given length of the jib boom, an expression takes place that makes it possible to determine a number of values of the masses safely lifted by the lifting device. There have been obtained the values of the cargo characteristics of the lifting device necessary for graphic constructions, expressing the relationship between the weight of the cargo and the overhanging of the jib boom with the weight of its elements. The reactions in the joints of the jig boom and the forces in its constituent links can be established from the data of the load characteristics. The desire to ensure maximum stability in the operation of the lifting device imposes restrictions on the control of several mobile operations at the same time, which adversely affects the efficiency of the work process. It has been established that ensuring the stability of operation in the transverse and longitudinal planes of the lifting device is a necessary component of safe operation. According to the dependencies for determining the indicator of cargo balance, it is possible to determine the preliminary installation site of the outriggers of the lifting device. As the results obtained confirm, the stability of the operation of the lifting device in the longitudinal direction is determined similarly to the stability of the operation in the transverse direction and for the nominal weight of the load with the greatest overhanging of the jib boom and the set outriggers. As a result, we note that the ratio of the holding moment relative to the overturning rib created by the weight of the lifting device on the wheeled chassis, taking into account the additional external loads that reduce it and the influence of the platform slope to the overturning moment created by the working load, serves as an indicator of the cargo balance.

NON-PERTURBATIVE RESTORATION OF DECOUPLING

1991 ◽  
Vol 06 (16) ◽  
pp. 1459-1463 ◽  
Author(s):  
D. C. KENNEDY
Keyword(s):  
Gauge Theories ◽  
Radiative Corrections ◽  
Radiative Effects ◽  
Heavy Particles ◽  
The Stability ◽  
The Masses

Radiative corrections due to heavy particles can be large in broken gauge theories, growing with their masses. However, simple arguments show that this is only a perturbative effect: the masses of such particles and thus their radiative effects are bounded by the stability and non-linearity of the theory.

scholarly journals Histori Filantropi: Tinjauan Teori Postmodern

2018 ◽  
Vol 5 (1) ◽  
pp. 149
Author(s):  
Aris Puji Purwatiningsih ◽  
Hendri Hermawan Adinugraha
Keyword(s):  
Social Institutions ◽  
Public Security ◽  
Body Parts ◽  
Font Size ◽  
Postmodern Theory ◽  
Non Profit ◽  
History Of ◽  
The Stability ◽  
The Masses ◽  
The Needy

<p><em><span lang="IN"><span style="font-size: medium;">Postmodern is a breeding effort, epistemological innovation, so anthropology becomes more adaptive and productive. This can be demonstrated through the application of his theory in practice and philanthropy models. This paper aims to describe the history of philanthropy in terms of the perspective of postmodern theory. The results of the literature review indicate that at first the emergence of the philanthropy movement was the way of the rulers of the time to maintain the stability of public security by providing assistance to the community, but in the postmodern period turned into non-profit social institutions or institutions that serve as mediators of donors to the needy. Philanthropy, initially only in the form of goods aimed at relieving and meeting the needs of a deficient society, in the postmodern era can develop into donor body parts, smiles and even empathy can be referred to as philanthropy. Alms that were originally human goods, the postmodern expanded that spread the science, moving the masses can also be called philanthropy.</span></span></em></p>

scholarly journals Singularities in Structural Optimization of the Ziegler Pendulum

10.14311/1400 ◽  
2011 ◽  
Vol 51 (4) ◽  
Author(s):  
O. N. Kirillov
Keyword(s):  
Structural Optimization ◽  
Degrees Of Freedom ◽  
Optimization Problems ◽  
Stability Boundary ◽  
Research Area ◽  
Stability Domain ◽  
Conservative Systems ◽  
The Stability ◽  
Flutter Load ◽  
The Masses

Structural optimization of non-conservative systems with respect to stability criteria is a research area with important applications in fluid-structure interactions, friction-induced instabilities, and civil engineering. In contrast to optimization of conservative systems where rigorously proven optimal solutions in buckling problems have been found, for nonconservative optimization problems only numerically optimized designs have been reported. The proof of optimality in non-conservative optimization problems is a mathematical challenge related to multiple eigenvalues, singularities in the stability domain, and non-convexity of the merit functional. We present here a study of optimal mass distribution in a classical Ziegler pendulum where local and global extrema can be found explicitly. In particular, for the undamped case, the two maxima of the critical flutter load correspond to a vanishing mass either in a joint or at the free end of the pendulum; in the minimum, the ratio of the masses is equal to the ratio of the stiffness coefficients. The role of the singularities on the stability boundary in the optimization is highlighted, and an extension to the damped case as well as to the case of higher degrees of freedom is discussed.

scholarly journals DESIGNING THE SOVIET IDENTITY (THROUGH THE EXAMPLE OF ELYOR ISHMUKHAMEDOV’S FILMS TENDERNESS AND LOVERS)

2020 ◽  
Vol 16 (4) ◽  
pp. 33-62
Author(s):  
SVETLANA Ya. SHCHEBROVA ◽  
Keyword(s):  
Cultural Identity ◽  
Everyday Life ◽  
Cultural Transformation ◽  
Semiotic System ◽  
Main Research ◽  
The People ◽  
Life Model ◽  
The 1960S ◽  
The Stability ◽  
The Masses

The article studies the Soviet identity, which fell into a crisis in the context of globalization and ethnic localization, gradually intensifying after the collapse of the USSR. In response to the decay of the Soviet mentality, it is necessary to understand how to overcome the split in society and make the process of cultural transformation under modernization conditions less painful for people. One of the mechanisms of forming the cultural identity of peoples is an appeal to the positive experience in common history. Simply copying the previous forms and means of forming cultural identity is impossible, since socio-economic foundations change; therefore, the problem needs a different solution. Exploring the Soviet past, one can understand which ideological values contributed to the consolidation of society in order to use this experience in construction of Russian civilizational identity. The purpose of the article is to study the films by Elyor Ishmukhamedov Tenderness (1966) and Lovers (1969) as “texts” that construct Soviet identity by dint of the recognition and acceptance of the ideal life model by the society. Since humans transform themselves and the world around them through an imitation, the main research questions are as follows: what social interaction features can be identified in these films? What is the appeal of the Soviet discourse and how is it transmitted in such seemingly “non-ideological” films? Ishmukhamedov’s films were studied as a semiotic system, in which the main myths and archetypes were revealed that had a manipulative and mobilizing influence on the viewer, thereby creating an image of a Soviet person which is attractive to the masses. The everyday life captured in these films symbolizes the stability and reliability of living in the USSR and Central Asia in the 1960s. After analyzing the figurative system of the Soviet-time everyday life in Ishmukhamedov’s films, the author finds out that identity is a system consisting of ethnic, cultural, age, natural, social, professional, mental, artifact identities, as well as the identity of the genus and small groups, which set the models and patterns of behavior for a Soviet person, which patterns were accepted and copied by the people.

scholarly journals The orbital stability of the Sun-Jupiter-Saturn system

1996 ◽  
Vol 172 ◽  
pp. 53-56
Author(s):  
J. R. Donnison ◽  
D. F. Mikulskis
Keyword(s):  
Solar System ◽  
Orbital Stability ◽  
The Sun ◽  
Numerical Investigations ◽  
The Stability ◽  
The Masses ◽  
Mass Enhancement

Kuiper(1973) suggested that the stability of the Solar System may be meaningfully investigated by studying the stability of the Sun-Jupiter-Saturn system. Numerical investigations by Nacozy(1976) showed that mass enhancement of the two planets beyond a factor of 29.25 led to instabilities in the system. In this new investigation similar mass enhancements were studied in detail numerically and compared with the analytical values derived from the c2H method. In addition, the eccentricities of the two planets were varied as well as their masses. It was found that the system soon showed signs of instability for the increased eccentricities when the masses of the planets were enhanced by fairly small factors.

Lithium Decorated Borane Clusters (BnHnLi6, n=5-7) as Promising Materials for Hydrogen Storage: A Computational Study

2021 ◽  
Author(s):  
Shakti S Ray ◽  
Sridhar Sahu
Keyword(s):  
Hydrogen Storage ◽  
Density Functional ◽  
Hydrogen Adsorption ◽  
Computational Study ◽  
Density Functional Theory Calculations ◽  
Md Simulations ◽  
Department Of Energy ◽  
Hydrogen Molecules ◽  
The Stability ◽  
Almost All

Abstract In this study, we have investigated the hydrogen adsorption potential of lithium decorated borane clusters (BnHnLi6, n = 5–7) using density functional theory calculations. The principle of maximum hardness and minimum electrophilicity confirmed the stability of the hydrogen adsorbed complexes. The outcomes of the study reveals that, the hydrogen molecules are adsorbed in a quasi-molecular fashion via Niu-Rao-Jena type of interaction with average adsorption energy falling in the range of 0.10-0.11eV/H2and average Li-H2 bond length is in the range of 2.436–2.550Å. It was found that the hydrogen molecules are physiosorbed at the host clusters at low temperature range 0K- 77K with gravimetric density up to 26.4 wt% which was well above target set by U.S. Department of Energy (US-DOE). ADMP-MD simulations showed that almost all the H2 molecules are desorbed at higher temperature form 373K-473K without distorting the host clusters which indicates the studied clusters can be promoted as promising reversible hydrogen storage

scholarly journals A MATHEMATICAL THEORY FOR VIBRATIONAL LEVELS ASSOCIATED WITH HYDROGEN BONDS II: THE NON-SYMMETRIC CASE

2009 ◽  
Vol 21 (02) ◽  
pp. 279-313 ◽  
Author(s):  
GEORGE A. HAGEDORN ◽  
ALAIN JOYE
Keyword(s):  
Hydrogen Bonds ◽  
Arbitrary Order ◽  
Symmetric Case ◽  
Vibrational Modes ◽  
Electron Energy Level ◽  
Vibrational Levels ◽  
Oppenheimer Approximation ◽  
Electronic Motion ◽  
Specialized Form ◽  
The Masses

We propose an alternative to the usual time-independent Born–Oppenheimer approximation that is specifically designed to describe molecules with non-symmetrical hydrogen bonds. In our approach, the masses of the hydrogen nuclei are scaled differently from those of the heavier nuclei, and we employ a specialized form for the electron energy level surface. As a result, the different vibrational modes appear at different orders of approximation. Although we develop a general theory, our analysis is motivated by an examination of the FHCl- ion. We describe our results for it in detail. We prove the existence of quasimodes and quasienergies for the nuclear vibrational and rotational motion to arbitrary order in the Born–Oppenheimer parameter ∊. When the electronic motion is also included, we provide simple formulas for the quasienergies up to order ∊3 that compare well with experiment and numerical results.

Sign in / Sign up

Export Citation Format

Share Document