Simulation and visualization of formation of vortex ring, its propagation and transportation of passive scalar

Рассматривается численное моделирование газодинамических процессов, сопровождающих формирование и распространение вихревых колец, получаемых при помощи поршневого генератора. Обсуждается влияние характеристик вихревого кольца на перенос пассивной примеси. Для численных расчетов применяются нестационарные уравнения Навье--Стокса, для дисукретизации которых применяется метод конечных объемов. Результаты численного моделирования позволяют получить геометрические и динамические характеристики вихревого кольца, которые соответствуют автомодельному теории вихревого кольца и экспериментальным данным. Помимо традиционных подходов к визуализации вихревых течений, основанных на построении линий уровня различных характеристик потока, для визуализации вихревых структур применяются инварианты тензора градиента скорости и метод показателей Ляпунова на конечном промежутке времени. Numerical simulation of gas-dynamic processes accompanying the formation and propagation of vortex rings obtained using a piston generator is considered. The influence of the characteristics of the vortex ring on the transfer of the passive particles is discussed. Unsteady Navier--Stokes equations are used for numerical calculations, and finite volume method is applied to their discretization. The results of numerical simulation make it possible to obtain the geometric and dynamic characteristics of the vortex ring, which correspond to the self-similar theory of the vortex ring and experimental data. In addition to traditional approaches to visualization of vortex flows based on the construction of contours of various flow quantities, invariants of the velocity gradient tensor and the method of Lyapunov exponents over a finite time interval are used to visualize vortex structures.

Plato on Democritean Films

Through close reading, I show that in Plato’s discussion of the lover (erastēs) and beloved (eromenos) at Phaedrus 250d-251c we can recognize an overlooked reference to the theories of the early atomist, Democritus. In particular, Plato borrows Democritus’ term for visual images/films, eidōla, while alluding to Empedocles’ similar theory of vision through effluences, aporroai. I also analyze the repeated stress on the adjective, enargēs, within the same context. Like eidōlon, the term enargēs would be picked up by later Hellenistic philosophers and become vital to their theories on criteria of truth and self-evidence, enargeia. By examining Plato’s usage of Democritus’ eidōla coupled with the adjective enargēs, first employed here in a philosophical context, we can not only better understand how Plato adapts contemporary scientific theories to suit his own philosophical principles, but also see how Democritus’ and Plato’s terminology would eventually influence Epicurus and the Stoa.

Experimental Comparison of Bohm-like Theories with Different Primary Ontologies

The de Broglie-Bohm theory is a hidden-variable interpretation of quantum mechanics which involves particles moving through space along deterministic trajectories. This theory singles out position as the primary ontological variable. Mathematically, it is possible to construct a similar theory where particles are moving through momentum-space, and momentum is singled out as the primary ontological variable. In this paper, we construct the putative particle trajectories for a two-slit experiment in both the position and momentum-space theories by simulating particle dynamics with coherent light. Using a method for constructing trajectories in the primary and non-primary spaces, we compare the phase-space dynamics offered by the two theories and show that they do not agree. This contradictory behaviour underscores the difficulty of selecting one picture of reality from the infinite number of possibilities offered by Bohm-like theories.

Confronting Vitruvius: a geometric framework and design methodology for Roman rectangular temples

Studies of design principles of Roman temples typically have been based on Vitruvius, which inspired a belief that the colonnade was at the core of the geometric framework of every temple and that the lower column diameter (D) was used as a module to plan all other aspects, both horizontally and vertically. Archaeological evidence, however, shows that most extant temples do not match the Vitruvian model.1 Scholars have tried to explain the discrepancies in different ways: for example, by claiming that Vitruvius did not describe the actual state of Roman architecture but “what it should be”,2 that architects had to make “adjustments” to the “Vitruvian ideal” to create a particular effect, or that they had to make on-site corrections.3 A few studies have shown that also other design principles must have been at play. P. Barresi, based on the geometric analyses of several temple-podia of the 5th to 1st c. B.C. in central Italy, argued that they were designed and built relative to a square grid.4 He derived the size of each grid-module from the proportions of the rectangles of the temples' bases. He later reached the same conclusion for the temples of the Capitolium at Sufetula,5 while J.-N. Bonneville presented a similar theory for temples at Baelo Claudia.6 M. Wilson Jones observed that the principal parts of the façades of the Temple of Portunus at Rome and the Maison Carrée at Nîmes formed square contours,7 which he considered a reason for the “irregularities” (relative to Vitruvian principles) in the intercolumniations. He also presented other examples of simple geometric shapes in the compositions of the façades of Roman buildings.

Abstraction reflective student in problem solving of Mathematics based cognitive style

The student's reflective abstraction ability in solving problems is necessary because the result of a person's reflective abstraction is a scheme used to understand something, finding solutions or solving problems. Besides, reflective abstractions are essential to higher mathematical, logical thinking as they occur in logical thinking in children. Therefore, to develop a reflective abstraction notion of high-level mathematical thinking, it is necessary to separate what is an essential feature of reflective abstraction, reflect its rules on higher mathematics, recognize and reconstruct it so that a similar theory of knowledge Mathematics and its instructions. While research that will researchers do is to know how the process of reflective abstraction of students in solving problems in terms of cognitive style. This is because the cognitive style is closely related to how to receive and process all information, especially in learning. The various trends in their learning can be identified and then classified whether the child belongs to an independent field cognitive style (thinking tends to have the independence of views) or field dependent.

The critical radius in sampling-based motion planning

We develop a new analysis of sampling-based motion planning in Euclidean space with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli and subsequent work. In particular, we prove the existence of a critical connection radius proportional to [Formula: see text] for n samples and d dimensions: below this value the planner is guaranteed to fail (similarly shown by Karaman and Frazzoli). More importantly, for larger radius values the planner is asymptotically (near-)optimal. Furthermore, our analysis yields an explicit lower bound of [Formula: see text] on the probability of success. A practical implication of our work is that asymptotic (near-)optimality is achieved when each sample is connected to only [Formula: see text] neighbors. This is in stark contrast to previous work that requires [Formula: see text] connections, which are induced by a radius of order [Formula: see text]. Our analysis applies to the probabilistic roadmap method (PRM), as well as a variety of “PRM-based” planners, including RRG, FMT*, and BTT. Continuum percolation plays an important role in our proofs. Lastly, we develop similar theory for all the aforementioned planners when constructed with deterministic samples, which are then sparsified in a randomized fashion. We believe that this new model, and its analysis, is interesting in its own right.

Chuckrow’s theory of the prenatal origin of music

In 1965, the second author, a graduate student in physics at New York University, drafted a paper entitled “Music: A synthesis of prenatal stimuli,” in which he proposed that structural elements of music such as rhythm and melody are analogs of fetal stimuli. In the 1980s, the first author independently published a similar theory. Both authors considered fetal perception of internal body sounds, correlations between those sounds and maternal states, the ability of the fetus to hear and remember sound patterns, biological and behavioral correlates of emotions shared by mother and fetus, transfer of hormones across the placenta, and effects of maternal psychopathology on infant behavior. Both argued that consideration of fetal consciousness is unnecessary because unconscious learning can influence later conscious behaviors and experiences. Chuckrow uniquely proposed that meter and polymeter, perceived as combinations of approximately isochronous pulses with one pulse in the foreground, might derive from the combined sound of maternal and fetal heartbeats as perceived by the fetus. We evaluate these theories in the context of more recent approaches to the origin of music. A systematic consideration of prenatal influences can parsimoniously explain communicative, emotional and structural aspects of music. Music may be a by-product of adaptations such as prenatal hearing and motherese that promoted infant survival in ancient hunter-gatherer settings.

HESS Opinions "Integration of groundwater and surface water research: an interdisciplinary problem?"

Today there is a great consensus that water resources research needs to become more holistic, integrating perspectives of a large variety of disciplines. Groundwater and surface water (hereafter: GW and SW) are typically identified as different compartments of the hydrological cycle and were traditionally often studied and managed separately. However, despite this separation, these respective fields of study are usually not considered to be different disciplines. They are often seen as different specialisations of hydrology with different focus, yet similar theory, concepts, methodology. The present article discusses how this notion may form a substantial obstacle in the further integration of GW and SW research and management. The article focusses on the regional scale (areas of approx. 103 to 106 km2), which is identified as the scale where integration is most greatly needed, but ironically the least amount of fully integrated research seems to be undertaken. The state of research on integrating GW and SW research is briefly reviewed and the most essential differences between GW hydrology (or hydrogeology, geohydrology) and SW hydrology are presented. Groundwater recharge and baseflow are used as examples to illustrate different perspectives on similar phenomena that can cause severe misunderstandings and errors in the conceptualisation of integration schemes. It is also discussed that integration of GW and SW research on the regional scale necessarily must move beyond the hydrological aspects, by collaborating with social sciences and increasing the interaction between science and the society in general. The typical elements of an ideal interdisciplinary workflow are presented and their relevance with respect to integration of GW and SW is discussed. The overall conclusions are that GW hydrology and SW hydrogeology study rather different objects of interest, using different types of observation, working on different problem settings. They have thus developed different theory, methodology and terminology. Yet, there seems to be a widespread lack of awareness of these differences which hinders the detection of the existing interdisciplinary aspects of GW and SW integration and consequently the development of truly unifying, interdisciplinary theory and methodology. Thus, despite having the ultimate goal of creating a more holistic approach, we should start integration by analysing potential disciplinary differences. Improved understanding among hydrologists of what interdisciplinary means and how it works is needed. Hydrologists, despite frequently being involved in multidisciplinary projects, are not sufficiently involved in developing interdisciplinary strategies and do usually not regard the process of integration as such as a research topic of its own. There seems to be a general reluctance to apply (truly) interdisciplinary methodology because this is tedious and few, immediate incentives are experienced.

Differential equations with general highly oscillatory forcing terms

The concern of this paper is in expanding and computing initial-value problems of the form y ′= f ( y )+ h ω ( t ), where the function h ω oscillates rapidly for ω ≫1. Asymptotic expansions for such equations are well understood in the case of modulated Fourier oscillators and they can be used as an organizing principle for very accurate and affordable numerical solvers. However, there is no similar theory for more general oscillators, and there are sound reasons to believe that approximations of this kind are unsuitable in that setting. We follow in this paper an alternative route, demonstrating that, for a much more general family of oscillators, e.g. linear combinations of functions of the form e i ωg k ( t ) , it is possible to expand y ( t ) in a different manner. Each r th term in the expansion is for some ς >0 and it can be represented as an r -dimensional highly oscillatory integral. Because computation of multivariate highly oscillatory integrals is fairly well understood, this provides a powerful method for an effective discretization of a numerical solution for a large family of highly oscillatory ordinary differential equations.