Projective deformations of hyperbolic 3-orbifolds with turnover ends

Our work is devoted to the elaboration of methods, algorithms and application package for reconstruction from a very limited number of projections with a strong noisy. Such problems exist, for example, in geophysics, by exploitation of oil and gas deposits, in optic, in reseach of plasma and of combustion processes in the internal-combustion engine. One of our problems is to restore tomogramms obtained by means of optical measurements. In this case the input data are the interferogramms which are representated by summary image of refrective index distribution in cross section of phase object. An essentional difference between this problem and the problems of traditional image reconstruction lies in the fact that initial data are not given by a set of projections which each taken separately but by means of summary image. We suggest new iterative algebraic algorithm SUM for solving this problem. In the bases of it there put the relaxation algorithm ART-3 obtained by Herman (1975) for solving the system of linear double-sided inequalities. The algorithm SUM was realised in the form of application programms for IBM PC/AT. It were conducted the computer simulations on a number of model 2-dimentional and 3-dimentional objects and was treated the interferogrammes obtained by research of concrete physical procedures. It was shown that this algorithm gives better results as compared with another wellknown algorithms, removes artifacts and permits a strong noisy of input data.KeywordsInput DataComputer SimulationOperation ResearchImage ReconstructionCombustion ProcessThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Capacitance transducers have been constructed that can operate at frequencies of up to 2 MHz in air, over a wide bandwidth, and with good efficiency. These have been used to propagate signals in air across regions containing variations in air flow and temperature. A source and receiver pair were scanned along a set of projections under computer control, allowing various ray paths across a chosen cross section to be selected. For each location, the received waveform was digitized and recorded, and the propagation time determined from cross-correlation techniques. The data were then used to form tomographic images, which corresponded to variations in either temperature or flow speed, both of which affect the local acoustic velocity. In one experiment, an air-jet was imaged at various distances from the nozzle. In another, the temperature variations in air above a hot metal tip were determined. Images will be shown for both sets of experiments, and the usefulness of the technique discussed.

A thrilling ROBLOX adventure called "Hide and Seek - Ultimate" invites players of all stripes to interact, form connections, and experience the excitement of the timeless Hide and Seek game. This project sets out to accomplish two goals: create a thriving gaming community and enthrall gamers with immersive gameplay. The unique aspects of the game constitute its core. Because each character has special abilities, the gameplay gains depth and a degree of strategy. The Hide and Seek experience is improved by the wide variety of characters that players can choose from, each of which has unique powers. The game's dynamic architectural structures, complex terrain, and eye-catching visuals are just a few of the innovative design features. Additionally, "Hide and Seek - Ultimate" includes a fascinating game economy. Participants

The ($\ensuremath{\alpha},p$) reaction for many angles between 0\ifmmode^\circ\else\textdegree\fi{} and 175\ifmmode^\circ\else\textdegree\fi{} has been used for fluctuation studies with target nuclei $^{19}\mathrm{F}$, $^{23}\mathrm{Na}$, and $^{31}\mathrm{P}$. Incident energies were 5.2 to 8.0 MeV, 5.9 to 7.9 MeV, and 13.0 to 15.7 MeV, and the measured coherence widths were 50, 35, and 33 keV, respectively. Cross-section peaks were unusually correlated between yields at different angles and between yields to different final states for 5.2- to 5.6-MeV alphaparticle energy on $^{19}\mathrm{F}$, and so only data above 5.6 MeV were analyzed for fluctuations for this target. The resulting sample sizes in the analyses were then 17, 20, and 27, respectively. Calculations of the effective number of sets of angular-momentum projections damping the fluctuations in the cross sections were used at all angles to determine the additional damping that results from the fraction of direct reactions. For the most forward angles, 0\ifmmode^\circ\else\textdegree\fi{} to 30\ifmmode^\circ\else\textdegree\fi{}, the fraction of direct reactions was generally found to be less than \textonehalf{} for the ground-state reactions and about 0.6 for the first-excited-state reactions. Even though the data were analyzed for the whole span of energies measured, the modest sample sizes available in these studies resulted in large uncertainties in determining these fractions of direct reactions. Nevertheless, the measured cross sections were in qualitative agreement with both distorted-wave Born-approximation calculations of the direct-reaction cross sections and Hauser-Feshbach calculations of the compound-nucleus cross sections.

We consider varieties of representations and characters of 2 and 3-dimensional orbifolds in semisimple Lie groups, and we focus on computing their dimension. For hyperbolic 3-orbifolds, we consider the component of the variety of characters that contains the holonomy composed with the principal representation, we show that its dimension equals half the dimension of the variety of characters of the boundary. We also show that this is a lower bound for the dimension of generic components. We furthermore provide tools for computing dimensions of varieties of characters of 2-orbifolds, including the Hitchin component. We apply this computation to the dimension growth of varieties of characters of some 3-dimensional manifolds in SL(n,C).

Exploring the influence of flexural rigidity variability of aquatic plants on stem deflection geometry and flow characteristics

A procedure is developed for determining the stoichiometry of a sample as function of depth from ion-beam analysis energy spectra. The approach is in principle equally applicable to back scattering experiments, experiments involving nuclear reactions with known cross sections and experiments combining these techniques. The procedure is especially suitable for routine computer evaluation of energy spectra. It is more straightforward and/or involves less rigid assumptions and approximations than alternative approaches. If all elemental signals are measured, an accurate beam dose is not needed. The limitations are basically those inherent to ion beam analysis in general.

This paper proposes a singularity-free beam element with Euler–Bernoulli assumption, i.e., the cross section remains rigid and perpendicular to the tangent of the centerline during deformation. Each node of this two-nodal beam element has eight nodal coordinates, including three global positions and one normal strain to describe the rigid translation and flexible deformation of the centerline, respectively, four Euler parameters or quaternion to represent the attitude of cross section. Adopting quaternion instead of Eulerian angles as nodal variables avoids the traditionally encountered singularity problem. The rigid cross section assumption is automatically satisfied. To guarantee the perpendicularity of cross section to the deformed neutral axes, the position and orientation coordinates are coupled interpolated by a special method developed here. The proposed beam element allows arbitrary spatial rigid motion, and large bending, extension, and torsion deformation. The resulting governing equations include normalization constraint equations for each quaternion of the beam nodes, and can be directly solved by the available differential algebraic equation (DAE) solvers. Finally, several numerical examples are presented to verify the large deformation, natural frequencies and dynamic behavior of the proposed beam element.

In this work, a geometrically exact, fully nonlinear Euler‐Bernoulli beam formulation is presented. Herewith a special case of Timoshenko rod models, discussed in various publications such as [2] or [4], is considered. Following the basic assumptions of transversal shear rigidity and plane cross sections, the formulation is based on displacements, their derivatives and a torsional rotation angle, in order to cover finite deformations and rotations. A straight reference configuration is considered, whereas the possibility for initially curved configurations is discussed in [1]. Within the Euler‐Bernoulli theory a cross section undergoes ridged body translation and rotation. While the translation is described by the motion of the beam axis only, the rotation is accounted within a rotational field, see e.g. [3]. In the present formulation, the rotational field is parametrized by the rotation tensor based on Rodrigues formula, which yields a simple update scheme as shown in [5], and is the first of its kind for Euler‐Bernoulli beam models. Using this parametrization an ansatz is presented, that allows for consistent connection of structural members, even in cases of physical discontinuities. On the element level C1 continuous Hermite polynomials are used to interpolate the displacements an their derivatives, while a Lagrangian interpolation scheme is chosen for the torsional rotation. A numerical Benchmark problems is presented to demonstrate the performance of the finite element formulation.

In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the outcome results have been compared to the results with those obtained from linear solution. The influence of the large deflections caused by a stretching effect due to the beam's fixed ends is captured. It was seen that existence of quadratic-cubic nonlinear terms in the nonlinear governing coupled PDEs of motion causes stiffening (hardening) behavior of the dynamic responses of the self-weight beam under the act of a traveling mass as well as equivalent concentrated moving force. Furthermore, in a case where the object leaves the beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption.

Three-dimensional flow calculations of the in-cylinder flow for a direct-injection Diesel engine have been carried out with different combustion chambers. In order to assess the decisive factors for the formation and evolution of the in-cylinder flow field, simplified piston bowls were used. A limited number of validation calculations of the compression stroke were performed. The results show that the geometries of the piston have a significant influence on the distribution of the cross section-averaged swirl ratio. The tangential velocity profiles at the cross sections are highly nonlinear, and the rigid body rotation assumption is less admissible. Furthermore, the turbulence in four combustion chambers is analyzed for an insight of the effects of bowl shape, initial swirl ratio and squish. It is found that the squish flow plays a significant role in the turbulence generation process near the top dead center (TDC) during compression. The coupling among the swirl, squish, bowl shape and turbulence is much more pronounced in the combustion chambers.

In this study, the nonlinear vibrations analysis of an inclined pinned-pinned self-weight Timoshenko beam made of linear, homogenous and isotropic material with a constant cross section and finite length subjected to a traveling mass/force with constant velocity is investigated. The nonlinear coupled partial differential equations of motion for the rotation of warped cross section, longitudinal and transverse displacements are derived using the Hamilton's principle. These nonlinear coupled PDEs are solved by applying the Galerkin's method to obtain dynamic responses of the beam. The dynamic magnification factor and normalized time histories of mid-point of the beam are obtained for various load velocity ratios and the outcome results have been compared to the results with those obtained from linear solution. The influence of the large deflections caused by a stretching effect due to the beam's fixed ends is captured. It was seen that existence of quadratic-cubic nonlinear terms in the nonlinear governing coupled PDEs of motion causes stiffening (hardening) behavior of the dynamic responses of the self-weight beam under the act of a traveling mass as well as equivalent concentrated moving force. Furthermore, in a case where the object leaves the beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption.

We study the problem of distance-based formation control in autonomous multi-agent systems in which only distance measurements are available. This means that the target formations as well as the sensed variables are both determined by distances. We propose a fully distributed distance-only control law, which requires neither a time synchronization of the agents nor storage of measured data. The approach is applicable to point agents in the Euclidean space of arbitrary dimension. Under the assumption of infinitesimal rigidity of the target formations, we show that the proposed control law induces local uniform asymptotic stability. Our approach involves sinusoidal perturbations in order to extract information about the negative gradient direction of each agent's local potential function. An averaging analysis reveals that the gradient information originates from an approximation of Lie brackets of certain vector fields. The method is based on a recently introduced approach to the problem of extremum seeking control. We discuss the relation in the paper.

In this study, we propose a THz computed tomography (CT) method based on phase contrast, which retrieves the phase shift information at each data point through a phase modulation technique using a Mach-Zehnder interferometer with a continuous wave (CW) source. The THz CT is based on first-generation CT, which acquires a set of projections by translational and rotational scans using a thin beam. From the phase-shift projections, we reconstruct a spatial distribution of refractive indices in a cross section of interest. We constructed a preliminary system using a highly coherent CW THz source with a frequency of 0.54 THz to prove the concept and performed an imaging experiment using phantoms to investigate its imaging features such as artifact-immune imaging, quantitative measurement, and selective detection.

During two last decades the ideas and methods of computerized tomography (CT) have found wide application in different fields of plasma physics1'2. Having in mind many other diagnostic tools and techniques applicable in studying of plasma processes one may conclude that the CT is especially efficient when the whole 2D image of the plasma cross—section (and sometimes even 3D image) can be derived from the set of projections measured simultaneously. Unique possibilities of that kind play the3 nost important role in the situations with magnetic reconnection . Magnetic reconnection in high-conductivity plasma is the fundamental physical process and the basis of various phenomena of plasma physics and astrophysics. Solar flares, magnetospheric , sub.storms, disruption processes in tokamaks, cardinal structural changes in the reversed-field pinches, plasma focus devices compact tori etc are the typical examples. As a result of reconnection the transfer of the excess magnetic energy into kinetic and thermal energies of plasma, into radiation and also into the energy of accelerated particles takes place. Physicists often distinguish two types of magnetic reconnection: spontaneous and forced. Laboratory plasmas and the natural processes in outer space are usually closer to a spontaneous reconnection. In that case a definite accumulation of magnetic energy precedes the reconnection and the process similar to tearing modes develops at that initial stage. The forced reconnection due to an external forces is more convenient for purposeful experimental observation of recon— ection phenomena, e.g. by creation of current sheets '8.It is also more suitable for theoretical description and numerical simulation. Some independent calculations and checks of the diagnostic CT results are possible in that case. We restrict the scope of this paper to the two examples of reconnection investigations by tomographic methods related firstly to spontaneous and secondly to forced reconnection. The Part I presents basic concepts and somewhat puzzling nowadays situation with the socalled saw tooth problem arising in tokamak devices. An advanced radial modulators CT algorithm of 2D image reconstruction from limited views chord—integrated plasma emission measurements is described. This algorithm can be recommended as an efficient diagnostic tool for the future study of magnetic reconnection in various laboratory plasmas.The novel version of Monte Carlo CT reconstruction suitable for spectrotomographic activity is also described. The Part II presents our own spectrotomographic experiment with the plane pinch current sheet in the nonlinear regime.