Vere-Jones' Self-Similar Branching Model

Motivated by its potential application to earthquake statistics, we study the exactly self-similar branching process introduced recently by Vere-Jones, which extends the ETAS class of conditional branching point-processes of triggered seismicity. One of the main ingredient of Vere-Jones' model is that the power law distribution of magnitudes m' of daughters of first-generation of a mother of magnitude m has two branches m'm with exponent beta+d, where beta and d are two positive parameters. We predict that the distribution of magnitudes of events triggered by a mother of magnitude $m$ over all generations has also two branches m'm with exponent beta+h, with h= d \sqrt{1-s}, where s is the fraction of triggered events. This corresponds to a renormalization of the exponent d into h by the hierarchy of successive generations of triggered events. The empirical absence of such two-branched distributions implies, if this model is seriously considered, that the earth is close to criticality (s close to 1) so that beta - h \approx \beta + h \approx \beta. We also find that, for a significant part of the parameter space, the distribution of magnitudes over a full catalog summed over an average steady flow of spontaneous sources (immigrants) reproduces the distribution of the spontaneous sources and is blind to the exponents beta, d of the distribution of triggered events.Comment: 13 page + 3 eps figure

Accuracy estimation of 3D machining surface of endoprosthesis knee-joint

Наведений аналіз сучасних методів оцінки точності складних поверхонь деталей машин щодо контролю 3D поверхні ендопротеза колінного суглобу людини. Представлена методика контролю точності виготовлення складної 3D поверхні ендопротеза та результати оцінки різними методами. Розроблено прикладну програму для оцінки та аналізу точності 3D поверхні виготовленого експериментального ендопротеза колінного суглоба людини. Прикладна програма дозволяє виконувати контроль робочої поверхні за полярним радіусом, по всім перетинам, що відповідає функціональному призначенню виробу. Доведено, що після операції шліфування на верстаті з ЧПК за розробленою управляючою програмою максимальне відхилення складає 0,05мм, що задовольняє технічним вимогам.The analysis of modern methods for accuracy estimation of complex surfaces of details of machines is resulted. The method of accuracy control of exactness for machining complex 3D surface of endoprosthesis genicular is presented to the joint of man and results of estimation by different methods. The application program is developed for an estimation and analysis of exactness of 3D surface of the machining experimental endoprosthesis of knee-joint of man. The application program allows to execute control of working surface on an polar radius, on all of sections, that corresponds the functional setting of good. It is well-proven that after the operation of grinding on a machine-tool with CNC on developed program control a maximal rejection makes 0,05мм, that satisfies with technical requirements. Purpose. To develop the method for accuracy estimation exactness of 3D shape of prosthetic appliance of knee-joint and application program for automation of control. Methodology. A method is based on the developed algorithm, allowing to compare the mathematical model of theoretical surface to the digital array, got as a result of measuring of detail on a CNC machine-tool. Comparison is executed on a radius the vector of surface in those points, what for a theoretical model. The developed application program executes visualization of results of control for the estimation of exactness on sections, and also allows to write down a control file in a text format. Conclusion. Approbation of the offered method and developed program approved their efficiency. It can draw on control results for the correction of control the program, that will promote exactness of machining on a CNC machine-tool.Приведен анализ современных методов оценки точности сложных поверхностей деталей машин применительно к контролю 3D поверхности эндопротеза коленного сустава человека. Представлена методика контроля точности изготовления сложной 3D поверхности эндопротеза и результаты оценки различными методами. Разработана прикладная программа для оценки и анализа точности 3D поверхности изготовленного экспериментального эндопротеза коленного сустава человека. Прикладная программа позволяет выполнять контроль рабочей поверхности по полярному радиусу, на всех сечениях, что соответствует функционированию изделия. Доказано, что после операции шлифования на станке с ЧПУ по разработанной управляющей программе максимальное отклонение составляет 0,05мм, что удовлетворяет техническим требованиям

Модуль CAD/САМ системы автоматизированного проектирования управляющих программ для обработки 3D поверхностей протезов коленного сустава человека

Представлений новий модуль САМ системи автоматизованої підготовки управляючих програм оброблення 3D робочих поверхонь протезів колінного суглоба людини на верстатах з ЧПК. Модуль забезпечує підготовку управляючих програм для трьох способів формоутворення: фрезерування сферичною і циліндричною фрезою, шліфування кругом у формі тора. Всі три способи можна реалізувати на верстатах з ЧПК при використанні всього трьох координат, що управляються. Модуль автоматично виконує проектування формоутворюючих траєкторій і на основі результатів моделювання процесу зрізування припуску розраховує управління подачею таким чином, щоб стабілізувати процес різання в циклі оброблення. При проектуванні управління за подачею по рядках застосовується підхід, що забезпечує однакову (задану) шорсткість всієї поверхні. При проектуванні управління для шліфування використовується граничний алгоритм зрізування припуску за проходами, а також оптимізується траєкторія холостих рухів за критерієм мінімуму динамічних навантажень на приводи верстата. Все це приводить до підвищення продуктивності оброблення при безумовному забезпеченні рівномірної якості 3D поверхні. Представлені результати практичної апробації функціонування модуля для виготовлення 3D поверхонь трьох типів протезів колінних суглобів.Purpose. Computer-aided design of the NC data for 3D surface manufacturing of prosthetic of human knee-joints on CNC machine with the management by the feed for stabilizing of process of cutting along of all shape-generating trajectory. Methodology. The new module of CAM system of preparation of the NC data for 3D surface of prosthetic of human knee-joints is created on CNC machine. The module provides preparation of the controls programs for three methods of shaping: milling by a spherical and cylindrical milling cutter, grinding wheel in the form of torus. All three methods can be realized on CNC machine at the use of only three axes. The module automatically executes planning of shape-generating trajectories and on the basis of results designing process of cutting allowance expects the management by the questioner serve so that to stabilize a cutting process in the manufacturing. At planning of management by the serve on lines approach which provides the identical (set) roughness of all surface is used. At planning of management for grinding the border algorithm of cutting allowance is used on passage-ways, and also the trajectory of lost motion is optimized on the criterion of minimum of the dynamic loadings on the drives of machine. All of it results in the increase of the productivity of manufacturing and providing regular quality of 3D surface both for roughness and on the structure of surface layer. Conclusion. The presented results of practical approbation of functioning of the module for 3D surfaces manufacturing of three types of prosthetic appliances of human knee-joints confirm efficiency of the created module of CAD/CAM system.Создан новый модуль САМ системы подготовки управляющей программы обработки 3D поверхности протезов коленных суставов человека на станках с ЧПУ. Модуль обеспечивает подготовку управляющих программ для трех способов формообразования: фрезерование сферической и цилиндрической фрезой, шлифование кругом в форме тора. Все три способа можно реализовать на станках с ЧПУ при использовании всего трех управляемых координат. Модуль автоматически выполняет проектирование формообразующих траекторий и на основе результатов моделирования процесса срезания припуска рассчитывает управление задающей подачей таким образом, чтобы стабилизировать процесс резания в цикле обработки. При проектировании управления подачей по строчкам применяется подход, который обеспечивает одинаковую (заданную) шероховатость всей поверхности. При проектировании управления для шлифования используется граничный алгоритм срезания припуска по проходам, а также оптимизируется траектория холостых ходов по критерию минимума динамических нагрузок на приводы станка. Все это приводит к повышению производительности обработки при безусловном обеспечении равномерного качества 3D поверхности, как по шероховатости, так и по структуре поверхностного слоя. Представленные результаты практической апробации функционирования модуля для изготовления 3D поверхностей трех типов протезов коленных суставов человека подтверждают эффективность созданного модуля CAD/CAM системы

Lithologic-paleogeographic characteristics of the Bobrikovskian sedimentation stage in the Orenburg region

Terrigenous beds of the Bobrikivskian horizon are among the principal production facilities in the Orenburg region. Diverse views on the formation environments of the deposits testify to the complex structure of the study object and emphasize the actuality of the current research. The paper deals with the structure, composition and formation environments of the Bobrikovskian horizon in the Orenburg region. Complex sedimentological examinations of the core material from the prospect-appraisal and exploratory wells have been made. Formation settings of the Bobrikovskian horizon have been reconstructed, a paleogeographic chart has been developed. Productive strata are peculiar for non-uniform structure, which is mostly controlled by the bed genesis. Aleurite-sandy and clayey rocks were formed either in the marine basin zones with active hydrodynamics of the sedimentation environment (coastal-marine, shallow-water marine facies of the near and the far zones), or in an accumulative alluvial-deltaic plain. At that, the principal sedimentation regulator consisted of the environment itself and the unstable sedimentation processes against the background of the basin general gradual subsidence in the Early Visean. Those fast-acting factors account for the frequent facies conversions of the aleurite-sandy rocks into clayey ones and for the lenticular- discontinuous structure of the strata, considerably complicating exploration and development of the hydrocarbon deposits. Peculiarities of the area tectonic structure and development, paleorelief of the bottom and the evolution character of the sedimentation basin have predestined development of a particular type of the Bobrikovskian horizon section within the specified facies-paleogeographic zones in the southeast of the Volga-Ural anteclise. Promising explorations are associated with the sections represented by alternating sandstones, aleurolites and argillites peculiar for higher contents of sandy material (up to 70%) and confined to the deltaic and coastalmarine facies-paleogeographic zones. Those may result in discoveries of hydrocarbon pools in non-structural and combined traps

Adiabaticity Conditions for Volatility Smile in Black-Scholes Pricing Model

Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Scholes (BS) expression with volatility in the form of a volatility smile. We show that this approach based on a volatility smile leads to relative minima for the distribution function ("bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring "adiabatic" conditions on the volatility smile

Turbulence and Multiscaling in the Randomly Forced Navier Stokes Equation

We present an extensive pseudospectral study of the randomly forced Navier-Stokes equation (RFNSE) stirred by a stochastic force with zero mean and a variance $\sim k^{4-d-y}$, where $k$ is the wavevector and the dimension $d = 3$. We present the first evidence for multiscaling of velocity structure functions in this model for $y \geq 4$. We extract the multiscaling exponent ratios $\zeta_p/\zeta_2$ by using extended self similarity (ESS), examine their dependence on $y$, and show that, if $y = 4$, they are in agreement with those obtained for the deterministically forced Navier-Stokes equation ($3d$NSE). We also show that well-defined vortex filaments, which appear clearly in studies of the $3d$NSE, are absent in the RFNSE.Comment: 4 pages (revtex), 6 figures (postscript

On two-dimensionalization of three-dimensional turbulence in shell models

Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell models we have obtained the following results: (i) progressive steepening of the energy spectrum with increased strength of the rotation, and, (ii) depletion in the energy flux of the forward forward cascade, sometimes leading to an inverse cascade. The presence of extended self-similarity and self-similar PDFs for longitudinal velocity differences are also presented for the rotating 3D turbulence case

Chaotic Cascades with Kolmogorov 1941 Scaling

We define a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure, thanks to the addition of infinitesimal noise. The zero-noise limit can be handled by Perron-Frobenius theory, just as the zero-diffusivity limit for the fast dynamo problem. Random multiplicative models do not possess Kolmogorov 1941 (K41) scaling because of a large-deviations effect. Our numerical studies indicate that deterministic multiplicative models can be chaotic and still have exact K41 scaling. A mechanism is suggested for avoiding large deviations, which is present in maps with a neutrally unstable fixed point.Comment: 14 pages, plain LaTex, 6 figures available upon request as hard copy (no local report #

Dragon-kings: mechanisms, statistical methods and empirical evidence

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.Comment: 20 page