Search

In a few previous papers, we introduced a so-called fluctuation model accounting for inelastic effects in molecular energy transfers induced by collisions. This model resulted in «symmetrisation rules» to be applied to the classical expressions for energy transfer probabilities, so that the detailed balance principle is satisfied. In this paper, we show that these symmetrisation procedures can also be successfully applied to various nuclear and molecular model processes. The resulting expressions for the probabilities, penetrabilities or cross-sections here obtained are shown to display correct behaviours and are worthy to be compared with the corresponding exact QM results. The comparison demonstrates interesting conceptual improvement of the classical equations and confirms that the symmetrisation procedures—as well as the underlying fluctuation model—are of a somewhat general applicability in physics, ranging from inelastic processes to tunnelling phenomena.

In a few previous papers, we introduced a so-called fluctuation model accounting for inelastic effects in molecular energy transfers induced by collisions. This model resulted in «symmetrisation rules» to be applied to the classical expressions for energy transfer probabilities, in order to insure detailed balancing. In this paper, we show that the symmetrisation procedures can also be applied successfully to the classical equations for energy loss and radiative transitions induced by Coulomb collisions of charged particles in stopping media. The resulting expressions display correct threshold behaviours and are worthwhile to be compared with the exact QM results. The comparison demonstrates interesting conceptual improvement of the classical equations and confirms that the symmetrisation procedures—as well as the underlying fluctuation model—are of a somewhat general applicability to inelastic processes in physics.

In a previous paper, we developed a so-called fluctuation model for the inelastic collisional interactions governing molecular energy transfers. The model results in a procedure to be applied to the classical equations for energy transfer probabilities in order to obtain «symmetrized» expressions respecting the detailed balance principle. Since the procedure reveals some generality, we revisit in this paper the classical radiation problem,i.e.the interaction between the classical electromagnetic field and the black body. We propose a «classical alternative» to Planck’s procedures. Based on the «continuum» physics assisted by appropriate probabilistic postulates, our method seems able to take into account energy «fluctuations» δE and to result in the correct Bose-Einstein or Planck energy distributions for the radiation and the mechanical oscillator in thermodynamical equilibrium, inclusive of a zero-point energy term. We propose the procedures for consideration in this paper.

In this paper, which is the third part of a work devoted to modelling high-power CO2lasers, the kinetic and fluid-dynamic model of the investigated device is presented. The kinetic model takes into account intermode vibrational exchange and vibrational-energy transfer among different molecular species (CO2, N2and CO). The fluid-dynamic equations have been reduced to a single equation coupled to kinetic and discharge equations via gas flow velocity in the discharge chamber. Effects of temperature, density and velocity variations in the flowing mixture on laser small signal gain have been investigated by using a numerical code based on the above theoretical model. Profiles of sustainer current, small signal gain and fluid-dynamic parameters in the discharge chamber have been obtained. The output power has been calculated by using a simplified model for the optical cavity. Finally, numerical and experimental results are compared.

Part I of the paper—devoted to modelling high-power CW lasers—gives a brief description of the investigated device and uses an analytical approximation to Bethe’s formula to calculate the following quantities: the space profiles in the discharge chamber of the electron beam energy, the stopping power and the source term under operating conditions for four-component mixtures of practical interest. The energy loss of the primary beam in travelling through a thin Al foil is calculated. Parts II and III will be published promptly. Part II will be devoted to the plasma characteristics in the discharge chamber and to the kinetic and fluid-dynamic model of the laser. Part III will be devoted to an assessment of the numerical results obtained from the model and their comparison with experimental data. La parte I del présente lavoro (che tratta della modellistica dei laser di alta potenza continua) descrive dapprima brevemente il tipo di sorgente laser a cui si fa riferimento e tratta poi il problema del calcolo, mediante un’approssimazione analitica della formula di Bethe, dell’andamento spaziale dell’energia del fascio di elettroni nella regione della scarica elettrica, del potere di arresto nel gas e del termine sorgente, considerando condizioni di lavoro con le miscele gassose a quattro componenti più usate nella pratica. Si calcola anche la perdita di energia del fascio primario di elettroni quando attraversa un sottile foglio di Al. Le parti II e III, che saranno pubblicate successivamente, trattano a) le caratteristiche del plasma nella regione della scarica ed il modello cineticofluidodinamico del laser (parte II), b) il complesso dei risultati numerici forniti dal modello ed il confronto di questi con. dati sperimentali (parte III). В первой части работы, посвященной высокоинтенсивным СW лазерам, приводится к раткое описание иссл едуемого прибора и ис пользуетс описание исследуемо го прибора и использу ется аналитическое п риближение формулы Б ете для вычисления сл едующих величин: аналитическое прибл ижение формулы Бете д ля вычисления следую щих величин: вычисления следующи х величин: пространственных пр офилей энергии элект ронов пучка в разрядной камере, тор мозной способности и члена, описывающего и сточник при условиях для четырехкомпон описывающего источн ик при условиях для че тырехкомпонентных с месей, имеющих практи ческий интерес. Вычис ляются энергетическ ие потери первичн четырехкомпонентны х смесей, имеющих прак тический интерес. Выч исляются энергетиче ские потери первично го пучка, проходящего через тонкую пленку а люминия. Части II и III этой работы будут вскоре о пу интерес. Вычисляются энергетические поте ри первичного пучка, п роходящего через тон кую пленку алюминия. Ч асти II и III этой работы бу дут вскоре опубликов аны. Часть II будет посв ящена характеристик ам плазмы в разрядной камере и кинетическо й и г первичного пучка, про ходящего через тонку ю пленку алюминия. Час ти II и III этой работы буду т вскоре опубликован ы. Часть II будет посвящ ена характеристикам плазмы в разрядной ка мере и кинетической и гидродинамической м одели лазера. Часть III б удет посвящена оценк е численных результа тов, получен алюминия. Части II и III это й работы будут вскоре опубликованы. Часть II б удет посвящена харак теристикам плазмы в р азрядной камере и кин етической и гидродин амической модели лаз ера. Часть III будет посв ящена оценке численн ых результатов, получ енных из предложенно й модели, и их сравнени ю с экспериментальны ми результатами. опубликованы. Часть II б удет посвящена харак теристикам плазмы в р азрядной камере и кин етической и гидродин амической модели лаз ера. Часть III будет посв ящена оценке численн ых результатов, получ енных из предложенно й модели, и их сравнени ю с экспериментальны ми результатами. плазмы в разрядной ка мере и кинетической и гидродинамической м одели лазера. Часть III б удет посвящена оценк е численных результа тов, полученных из пре дложенной модели, и их сравнению с эксперим ентальными результа тами. гидродинамической м одели лазера. Часть III б удет посвящена оценк е численных результа тов, полученных из пре дложенной модели, и их сравнению с эксперим ентальными результа тами. посвящена оценке чис ленных результатов, п олученных из предлож енной модели, и их срав нению с эксперимента льными результатами. из предложенной моде ли, и их сравнению с экс периментальными рез ультатами. экспериментальными результатами.

Using an analogy with statistical thermodynamics and the Einstein equation for fluctuation probabilities, «fluctuation» model for the inelastic collisional interaction governing molecular energy transfers is introduced. «Symmetrized» expressions respecting the detailed balance principle are obtained for the classical and semi-classical transition probabilities. These expressions are shown to be equal—within standard approximations (saddle point for perturbation integrals)—to the corresponding quantum-mechanical WKB equations. Although here introduced for the case of vibration-translation molecular energy transfers, the model equations reveal some generality and can be applied to a number of inelastic processes in physics. A few possible applications and developments are discussed. Usando un‚analogia con la ter probabilità di fluttuazione si sviluppa un modello di «fluttuazione” per l'interazione collisionale inelastica che governa i trasferimenti di energia molecolari. Si ottengono espressioni «simmetrizzate» delle probabilità di transizione classiche e semiclassiche che rispettano il principio del bilancio dettagliato e risultano equivalenti—nei limiti di approssimazioni standard (metodo del punto sella per gli integrali di perturbazione)—alle corrispondenti equazioni quantistiche valide nel limite quasiclassico (WKB). Sebbene qui introdotto per il caso dei trasferimenti di energia molecolari vibrazione-traslazione, il modello risulta alquanto generale e può essere applicato ad altri tipi di processi inelastici in fisica. Se ne discutono alcuni dei possibili sviluppi e applicazioni. Используя аналогию со статистической термодинамикой и уравнение Эйнштейна для вероятностей флуктуаций, предлагается модель «флуктуаций» для неупругого взаимодействия, определяющего обмен энергиями при соударении молекул. Получаются «симметризованные» выражения для классических и полуклассических вероятностей переходов, которые соответствуют принципу детального равновесия. Показывается, что эти выражения в рамках стандартного приближения (метод седловой точки для пертурбационных интегралов) эквивалентны соотвествующим квантовомеханическим ВКБ-уравнениям. Предложенные модельные уравнения обладают некоторой общностью и могут быть применены к ряду неупрутих процессов. Обсуждаются возможные приложения и усовершенствования теории.

In order to investigate the relationships between three-dimensional and colinear molecular-collision models with particular emphasis on the role of repulsive and attractive forces in vibrational-energy transfers in gases, a theoretical analysis is developed in this paper. A few known results—mainly the Cottrell and Ream equation, the Takayanagi and the Shin expressions of the transfer probability—relevant to repulsive-force-dominated processes are obtained and/or discussed in the proposed frame. Light is also given on long-range, attractive-forces-dominated processes. The main result of this investigation is that, when a suitable hypothesis is done on the transfer probability, centrifugal effects on the intermolecular trajectories due to standard potentials are negligible in the low-temperature range. A quasi-colinear collision model, which is found to be correlated to the Cottrell and Ream expression for the transfer probability, is regained from a three-dimensional geometry in these conditions. Nel presente lavoro si svolge un’analisi teorica rivolta allo studio delle relazioni fra modelli di collisione molecolare tridimensionali e collineari con particolare riguardo al ruolo delle forze repulsive e attrattive nel corso di trasferimenti di energia vibrazionale in fase gassosa. Alcuni risultati già noti—principalmente l’equazione di Cottrell e Ream e le espressioni di Takayanagi e di Shin per la probabilità di trasferimento—riguardanti processi dominati da forze di tipo repulsivo sono ottenuti e/o discussi nello schema proposto. Si discutono anche alcuni aspetti dei processi dominati da forze attrattive a lungo raggio. Il risultato principale di questo studio è che, quando è verificata un’opportuna ipotesi sulla probabilità di trasferimento, gli effetti centrifughi sulle traiettorie intermolecolari governate da potenziali standard sono trascurabili a bassa temperatura. In queste condizioni a partire da una geometria di collisione tridimensionale si ritrova un modello di collisione quasi-collineare, che è correlato alla espressione di Cottrell e Ream per la probabilità di trasferimento. В этой статье развивается теоретический анализ с целью исследовать связь между моделями соударений трехмерных и колинеарных молекул. Особое внимание уделяется анализу сил отталкивания и притяжения при передаче вибрационной энергии в газах. Получаются и обсуждаются некоторыено вые результаты, в основном, уравнение Котрела и Рима, выражения Такаянаги и Шина для вероятности пепедачи, относящиеся к силам отталкивания. Также обсуждаются длиннодействующие силы притяжения. Основной результат проведенного исследования состоит в том, что при соответствующем предположении о вероятности передачи центробежные эффекты в межмолекулярных траекториях, определяемых стандартными потенциалами, являются пренебрежимо малыми в области низких температур. При этих условиях из трехмерной геометрии снова получается модель квазиколинеарных соударений, которая связана с выражением Котрела и Рима для вероятности передачи.

We studied some kinetic, fluid-dynamic and electrical problems arising in the numerical modelling of a c.w. TE high power CO 2 laser operating with N 2 , He and CO additives. We adapted a five-temperature pulsed laser model to the c.w. case by coupling a set of fluid-dynamic equations to the kinetic set. We added the rate equation for the secondary electron density. We calculated in some detail the ionization term and fitted experimental results to determine attachment and recombination coefficients in the discharge chamber. In order to solve our equations a numerical code has been developed. By this means we investigated the effects of temperature, density and velocity variations in the flowing mixture on the small signal gain of the device. We obtained profiles in the laser chamber of the sustainer current, small signal gain and fluid-dynamic parameters. A simple (Fabry-Perot) optical cavity model has been used to calculate output power and electrical efficiency of the device. A comparison of numerical code predictions and experimental results is presented.

A Fortran computer algorithm has been used to analyze the nucleotide sequence of several structural genes. The analysis performed on both coding and complementary DNA strands shows that whereas open reading frames shorter than 100 codons are randomly distributed on both DNA strands, open reading frames longer than 100 codons (“virtual genes”) are significantly more frequent on the complementary DNA strand than on the coding one. These “virtual genes” were further investigated by looking at intron sequences, splicing points, signal sequences and by analyzing gene mutations. On the basis of this analysis coding and complementary DNA strands of several eukaryotic structural genes cannot be distinguished. In particular we suggest that the complementary DNA strand of the human ɛ-globin gene might indeed code for a protein.

Computer programs, implemented on an Univac II00/80 computer system, for the identification and characterization of protein coding genes and for the analysis of nucleic acid sequences, are described.