A Five Dimensional Perspective on Many Particles in the Snyder basis of Double Special Relativity

After a brief summary of Double Special Relativity (DSR), we concentrate on a five dimensional procedure, which consistently introduce coordinates and momenta in the corresponding four-dimensional phase space, via a Hamiltonian approach. For the one particle case, the starting point is a de Sitter momentum space in five dimensions, with an additional constraint selected to recover the mass shell condition in four dimensions. Different basis of DSR can be recovered by selecting specific gauges to define the reduced four dimensional degrees of freedom. This is shown for the Snyder basis in the one particle case. We generalize the method to the many particles case and apply it again to this basis. We show that the energy and momentum of the system, given by the dynamical variables that are generators of translations in space and time and which close the Poincar\'e algebra, are additive magnitudes. From this it results that the rest energy (mass) of a composite object does not have an upper limit, as opposed to a single component particle which does.Comment: 12 pages, no figures, AIP Conf. Pro

Деякі аспекти дослідження стародавніх українських цитр

The article is dedicated to some aspects of origin of vertical medieval Ukrainian zithers. Later they became one of the prototypes of modern bandura (Ukrainian musical instrument)

From a discrete model of chemotaxis with volume-filling to a generalized Patlak–Keller–Segel model

We present a discrete model of chemotaxis whereby cells responding to a chemoattractant are seen as individual agents whose movement is described through a set of rules that result in a biased random walk. In order to take into account possible alterations in cellular motility observed at high cell densities (i.e. volume-filling), we let the probabilities of cell movement be modulated by a decaying function of the cell density. We formally show that a general form of the celebrated Patlak–Keller–Segel (PKS) model of chemotaxis can be formally derived as the appropriate continuum limit of this discrete model. The family of steady-state solutions of such a generalized PKS model are characterized and the conditions for the emergence of spatial patterns are studied via linear stability analysis. Moreover, we carry out a systematic quantitative comparison between numerical simulations of the discrete model and numerical solutions of the corresponding PKS model, both in one and in two spatial dimensions. The results obtained indicate that there is excellent quantitative agreement between the spatial patterns produced by the two models. Finally, we numerically show that the outcomes of the two models faithfully replicate those of the classical PKS model in a suitable asymptotic regime

Multiple jumps and vacancy diffusion in a face-centered cubic metal

The diffusion of monovacancies in gold has been studied by computer simulation. Multiple jumps have been found to play a central role in the atomic dynamics at high temperature, and have been shown to be responsible for an upward curvature in the Arrhenius plot of the diffusion coefficient. Appropriate saddle points on the potential energy surface have been found, supporting the interpretation of vacancy multiple jumps as distinct migration mechanisms.Comment: 16 page

Analysis of the Operational and Safety Features of the In-Core Bubbling System of the Molten Salt Fast Reactor

A foreseen feature of the Molten Salt Fast Reactor is the adoption of a bubbling system for the removal of gaseous and metallic fission products (FPs). This mechanism injects helium bubbles into the core to remove FPs from the salt through floating and mass transfer mechanisms for metallic and gaseous FPs, respectively. The present work is aimed at analyzing this helium bubbling system, focusing on gaseous FPs. We investigate both operational and safety-related features in order to get information useful for the design and to assess the convenience of its adoption. Accordingly, our investigations split into two strands: (1) analyzing the characteristics of the bubbling system itself and (2) assessing the safety features of the reactor in its presence. In order to perform the above analyses, we add the capability to simulate production, transport, and mass transfer of an arbitrary number of gaseous FPs to a preexisting multiphysics solver, built with the OpenFOAM suite. In terms of operational characterization, our analyses quantify the removal efficiency through a characteristic removal time and estimate the poisoning effect of gaseous FPs. In addition, we evaluate the activity and decay heat of the removed gas, which is an aspect crucial for the design of the off-gas unit, and the effect of the bubbling system on the power versus the fuel mass flow rate curve, which is a possible control mechanism. Among our safety-related studies, we first evaluate the void coefficient, determining upper bounds on the helium flow rate in order to avoid prompt supercriticality in case of prompt loss of helium injection. The latter accidental scenario is also analyzed considering the thermal-hydraulic dynamics of the system. We also discuss another accident: complete loss of helium removal

A COMPOSITE MODEL FOR THE SIMULATION OF SKIING TECHNIQUES

INTRODUCTION In this work we present a model for skiing technique analysis and simulation: it consists of a man model, an equipment model and a contact (ski-snow) model. Such a model is the basis for a deeper understanding of the interaction between skier and equipment and its use will be profitable in various applications such as: equipment optimisation and technique improvement. Moreover this simulation technique can be profitably used for teaching the basic principles of skiing. MATERIAL AND METHODS To build our model we combined the methods used for multibody systems dynamic analysis (man model with finite element techniques (ski model). The human body model consists of 3D chains of rigid bodies: according to the "sophistication" of the simulation we use 16 segments, with 39'internal d.0.f (full man model), or 7 segments, with 6 internal d.0.f . To describe rigid body dynamics and kinematics (man model) we adopt a method based on homogeneous matrices (Casolo 1995): both the absolute and the relative position, velocity and acceleration are described by 4x4 matrices, as well as the inertial properties and the external loads. This approach allows to embed both the linear and angular terms in the same formalism. To derive the equation of motion a Lagrangian approach was adopted, leading to this expression: Mq+C(cf.q.t) = Fl(q.q,t) +Ft(q,q) where M is the mass matrix, C contain the weight, the centrifugal and Coriolis effect, Ft contains joint torques, F2 represent the action exchanged with ski through the bindings and the vector q contains joints laws of motion. The model can be used to perform direct and inverse dynamics analysis of skiing, since it allows the input of joint torques and/or joint relative movements, that can be experimental data or can be generated by scratch, by a law of motion preprocessor. Skis are modelled with Finite Element techniques. The internal structure of a ski is quite complex: different material, with complex arrangement, are employed giving rise to properties (stiffness, damping and mass) which can be determined by experimental measures or by complex FE analysis. These properties can be quite well reproduced by means of a simplified model consisting of 3D beam elements . Some geometrical features, such as camber and sidecut, can be easily reproduced. Ski equations of motion, in matrix form, are: M9+ q v r e l + Kq&f = F,,I +Fnlon-ski f F.+.ki - cn,,wn where M, C, K are, respectively, the ski mass, damping and stiffness matrices. The ski load consists of three terms: weight, action exerted by the skier through the bindings and the contact action exerted by the snow. A simple contact model has been also developed, based on the assumption that the snow reacts both to ski deepening, sliding and skidding. This simple model can take into account, for example, the effect of ski vibration on the ski-snow interaction. RESULTS Some simulations have been performed to test model capabilities: we analysed the effect of ski torsional stiffness, as well as the amount of sidecut, on skier trajectory during traverse and turns. The model is also used to simulate the aerial phase of a free-style jump and the following landing phase. In all of these cases simulation can be an useful tool for predicting the effect of changing joint movements (i.e varying skiing technique) and equipment characteristics. A sensitivity analysis can be a first step toward a technique and equipment optimisation. References Casolo F., Legnani G., Righettini P., Zappa B. "A homogeneous matrix approach to 3D kinematics and dynamics", TMM (in press)

model of reversible breakdown in hfo2 based on fractal patterns

We propose a model of the kinetics of reversible breakdown in metal-insulator-metal structures with afnia based on the growth of fractal patterns of defects when the insulator is subject to an external voltage. The probability that a defect is (or is not) generated and the position where it is generated depend on the electric field distribution. The new defect moves accordingly to fractal rules and attach to another defect in a tree branch. When the two electrodes sandwiching the insulating film are connected a conductive filament is formed and the breakdown takes place. The model is calibrated with experiments inducing metastable soft breakdown events in Pt/HfO2/Pt capacitors

Bridging the gap between individual-based and continuum models of growing cell populations

Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations that describe the evolution of cellular densities in response to pressure gradients generated by population growth. Little prior work has explored the relation between such continuum models and related single-cell-based models. We present here a simple stochastic individual-based model for the spatial dynamics of multicellular systems whereby cells undergo pressure-driven movement and pressure-dependent proliferation. We show that nonlinear partial differential equations commonly used to model the spatial dynamics of growing cell populations can be formally derived from the branching random walk that underlies our discrete model. Moreover, we carry out a systematic comparison between the individual-based model and its continuum counterparts, both in the case of one single cell population and in the case of multiple cell populations with different biophysical properties. The outcomes of our comparative study demonstrate that the results of computational simulations of the individual-based model faithfully mirror the qualitative and quantitative properties of the solutions to the corresponding nonlinear partial differential equations. Ultimately, these results illustrate how the simple rules governing the dynamics of single cells in our individual-based model can lead to the emergence of complex spatial patterns of population growth observed in continuum models

FIRMS’INVOLVEMENT IN OPEN SOURCE PROJECTS: A CONTROVERSIAL ROLE

In this paper, we focus on Community OS projects with the goal of understanding whether the involvement of firms through their professional developers has an impact on the quality of the software product and on its overall success. We distinguish between two main typologies of firms’ involvement: Development firms contributions and Non-development firms contributions. The paper posits that a higher percentage of code contributed by paid developers has a positive impact of project success and size. However, it also puts forward a negative impact of non-development firms contribution on software design quality. Hypotheses are tested on a sample of 643 applications from the SourceForge.net repository, corresponding to 5,335 versions. Data were collected by means of an online questionnaire and a tool developed ad hoc to calculate software design quality metrics. Empirical findings support our hypotheses. Overall, our data confirm that firms are significantly investing in OS projects and that they can play a crucial role in determining projects’ success when they also take active part in code development. However, most of them are taking a short-term perspective that does not focus on quality. This may lead to higher costs and a lower user satisfaction in the long term