Computational Physics

A generalized form of the random walk algorithm to simulate diffusion processes is introduced. Unlike the usual approach, at a given time all the particles from a grid node are simultaneously scattered using the Bernoulli repartition. This procedure saves memory and computing time and no restrictions are imposed for the maximum number of particles to be used in simulations. We prove that for simple diffusion the method generalizes the finite difference scheme and gives the same precision for large enough number of particles. As an example, simulations of diffusion in random velocity field are performed and the main features of the stochastic mathematical model are numerically tested.

In this note we examine the implications of Cahn-Hilliard diffusion on mass conservation when using a phase-field model for simulating two-phase flows. Even though the phase-field variable φ is conserved globally, a drop shrinks spontaneously while φ shifts from its expected values in the bulk phases. Those changes are found to be proportional to the interfacial thickness, and we suggest guidelines for minimizing the loss of mass. Moreover, there exists a critical radius below which drops will eventually disappear. With a properly chosen mobility parameter, however, this process will be much slower than the physics of interest and thus has little ill effect on the simulation.

This paper describes a novel numerical algorithm for simulating interfacial dynamics of non-Newtonian fluids. The interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously. The property and evolution of the interfacial layer is governed by a phase-field variable / that obeys a Cahn-Hilliard type of convection-diffusion equation. This circumvents the task of directly tracking the interface, and produces the correct interfacial tension from the free energy stored in the mixing layer. Viscoelasticity and other types of constitutive equations can be incorporated easily into the variational phase-field framework. The greatest challenge of this approach is in resolving the sharp gradients at the interface. This is achieved by using an efficient adaptive meshing scheme governed by the phase-field variable. The finite-element scheme easily accommodates complex flow geometry and the adaptive meshing makes it possible to simulate large-scale two-phase systems of complex fluids. In two-dimensional and axisymmetric three-dimensional implementations, the numerical toolkit is applied here to drop deformation in shear and elongational flows, rise of drops and retraction of drops and torii. Some of these solutions serve as validation of the method and illustrate its key features, while others explore novel physics of viscoelasticity in the deformation and evolution of interfaces.

In this note we examine the implications of Cahn-Hilliard diffusion on mass conservation when using a phase-field model for simulating two-phase flows. Even though the phase-field variable φ is conserved globally, a drop shrinks spontaneously while φ shifts from its expected values in the bulk phases. Those changes are found to be proportional to the interfacial thickness, and we suggest guidelines for minimizing the loss of mass. Moreover, there exists a critical radius below which drops will eventually disappear. With a properly chosen mobility parameter, however, this process will be much slower than the physics of interest and thus has little ill effect on the simulation.

The coupled Navier-Stokes and Cahn-Hilliard equations, plus the constitutive equation for non-Newtonian fluids, are solved using second-order implicit time stepping. Within each time step, Newton iteration is used to handle the nonlinearity, and the linear algebraic system is solved by preconditioned Krylov methods. The phase-field model, with a physically diffuse interface, affords the method several advantages in computing interfacial dynamics. One is the ease in simulating topological changes such as interfacial rupture and coalescence. Another is the capability of computing contact line motion without invoking ad hoc slip conditions. As validation of the 3D numerical scheme, we have computed drop deformation in an elongational flow, relaxation of a deformed drop to the spherical shape, and drop spreading on a partially wetting substrate. The results are compared with numerical and experimental results in the literature as well as our own axisymmetric computations where appropriate. Excellent agreement is achieved provided that the 3D interface is adequately resolved by using a sufficiently thin diffuse interface and refined grid. Since our model involves several coupled partial differential equations and we use a fully implicit scheme, the matrix inversion requires a large memory. This puts a limit on the scale of problems that can be simulated in 3D, especially for viscoelastic fluids.

Electron emission from nanometric size emitters becomes of increasing interest due to its involvement to sharp electron sources, vacuum breakdown phenomena and various other vacuum nanoelectronics applications. The most commonly used theoretical tools for the calculation of electron emission are still nowadays the Fowler-Nordheim and the Richardson-Laue-Dushman equations although it has been shown since the 1990's that they are inadequate for nanometrically sharp emitters or in the intermediate thermal-field regime. In this paper we develop a computational method for the calculation of emission currents and Nottingham heat, which automatically distinguishes among different emission regimes, and implements the appropriate calculation method for each. Our method covers all electron emission regimes (thermal, field and intermediate), aiming to maximize the calculation accuracy while minimizing the computational time. As an example, we implemented it in atomistic simulations of the thermal evolution of Cu nanotips under strong electric fields and found that the predicted behaviour of such nanotips by the developed technique differs significantly from estimations obtained based on the Fowler-Nordheim equation. Finally, we show that our tool can be also successfully applied in the analysis of experimental I -V data.

Electron emission from nanometric size emitters becomes of increasing interest due to its involvement to sharp electron sources, vacuum breakdown phenomena and various other vacuum nanoelectronics applications. The most commonly used theoretical tools for the calculation of electron emission are still nowadays the Fowler-Nordheim and the Richardson-Laue-Dushman equations although it has been shown since the 1990's that they are inadequate for nanometrically sharp emitters or in the intermediate thermal-field regime. In this paper we develop a computational method for the calculation of emission currents and Nottingham heat, which automatically distinguishes among different emission regimes, and implements the appropriate calculation method for each. Our method covers all electron emission regimes (thermal, field and intermediate), aiming to maximize the calculation accuracy while minimizing the computational time. As an example, we implemented it in atomistic simulations of the thermal evolution of Cu nanotips under strong electric fields and found that the predicted behaviour of such nanotips by the developed technique differs significantly from estimations obtained based on the Fowler-Nordheim equation. Finally, we show that our tool can be also successfully applied in the analysis of experimental I -V data.

We compared systematically, for 20 radionuclides commonly emlpoyed in nuclear medicine, H p (0.07) in mSv/MBq for point-like and extended sources, either in contact or in presence of different thicknesses of interposed material (glass, plastic), as resulted from severeal releases of Varskin (mod2, 4, 5.3) with the output of Monte Carlo simulations in Geant4. Results indicate that the most recent version of Varskin gives the best agreement with Monte Carlo simulation, having implemented a more accurate treatment of both photons and electrons. A good agreement was found for all nuclides for a point source in contact with skin. When a material is interposed, however, the disagreement between analytical and Monte Carlo results increases with material thickness for some nuclides, particularly for pure beta emitters and low-energy electron emitters. These results can be explained by the deterministic approach in which electron energy deposition is treated in the analytical code and its influence in proximity of electron range, and to the neglection of bremsstrahlung emission. Another source of discrepancy, for some nuclides, is the difference in radionuclide emission spectra. When the accuracy of estimation of skin doses is critical, as after an anomalous exposition event with high activities in extended sources or with a thin layer of interposed material, Monte Carlo simulation is the most accurate calculation approach. References 1. Delacroix D. Radionuclide and radiation protection data handbook.

Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the presence of uncertainty in the conductivity field. Based on the relation between stochastic diffusion processes and PDEs, Monte Carlo (MC) methods are available to solve these PDEs. These methods are especially relevant for cases where we are interested in the solution in a small subset of the domain. The existing MC methods based on the stochastic formulation require restrictively small time steps for high variance conductivity fields. Moreover, in many applications the conductivity is piecewise constant and the existing methods are not readily applicable in these cases. Here we provide an algorithm to solve onedimensional elliptic problems that bypasses these two limitations. The methodology is demonstrated using problems governed by deterministic and stochastic PDEs. It is shown that the method provides an efficient alternative to compute the statistical moments of the solution to a stochastic PDE at any point in the domain. A variance reduction scheme is proposed for applying the method for efficient mean calculations.

Simulating hypersonic flow around a space vehicle is challenging because of the multiscale and nonequilibrium nature inherent in these flows. To effectively deal with such flows, a novel particle-particle hybrid scheme combining the stochastic particle Bhatnagar-Gross-Krook (BGK) method with Direct Simulation Monte Carlo (DSMC) was developed recently, but only for monatomic gases [Fei et. al., J. Comput. Phys. 2021]. Here this work is extended to the particleparticle hybrid method for polyatomic gases. In the near continuum regime, employing the Ellipsoidal-Statistical BGK model proposed by Y. Dauvois, et. al. [Eur. J. Mech. B Fluids, 2021] with discrete levels of vibrational energy, the stochastic particle BGK method is first established following the idea of the unified stochastic particle BGK (USP-BGK) scheme. In the fluid limit, it has been proven to be of second-order temporal and spatial accuracy. Then, the USP-BGK scheme with rotational and vibrational energies is combined with DSMC to construct a hybrid method for polyatomic gases. The present hybrid scheme is validated with numerical tests of homogenous relaxation, 1D shock structure and 2D hypersonic flows past a wedge and a cylinder. Compared to traditional stochastic particle methods, the proposed hybrid method can achieve higher accuracy at a much lower computational cost. Therefore, it is a more efficient tool to study multiscale hypersonic flows.

In this paper, an extension of the multi-scale finite-volume (MSFV) method is devised, which allows to simulate flow and transport in reservoirs with complex well configurations. The new framework fits nicely into the data structure of the original MSFV method and has the important property that large patches covering the whole well are not required. For each well, an additional degree of freedom is introduced. While the treatment of pressure-constraint wells is trivial (the well-bore reference pressure is explicitly specified), additional equations have to be solved to obtain the unknown well-bore pressure of rate-constraint wells. Numerical simulations of test cases with multiple complex wells demonstrate the ability of the new algorithm to capture the interference between the various wells and the reservoir accurately.

In this paper, an extension of the multi-scale finite-volume (MSFV) method is devised, which allows to simulate flow and transport in reservoirs with complex well configurations. The new framework fits nicely into the data structure of the original MSFV method and has the important property that large patches covering the whole well are not required. For each well, an additional degree of freedom is introduced. While the treatment of pressure-constraint wells is trivial (the well-bore reference pressure is explicitly specified), additional equations have to be solved to obtain the unknown well-bore pressure of rate-constraint wells. Numerical simulations of test cases with multiple complex wells demonstrate the ability of the new algorithm to capture the interference between the various wells and the reservoir accurately.

This paper addresses the convergence properties of implicit numerical solution algorithms for nonlinear hyperbolic transport problems. It is shown that the Newton-Raphson (NR) method converges for any time step size, if the flux function is convex, concave, or linear, which is, in general, the case for CFD problems. In some problems, e.g., multiphase flow in porous media, the nonlinear flux function is S-shaped (not uniformly convex or concave); as a result, a standard NR iteration can diverge for large time steps, even if an implicit discretization scheme is used to solve the nonlinear system of equations. In practice, when such convergence difficulties are encountered, the current time step is cut, previous iterations are discarded, a smaller time step size is tried, and the NR process is repeated. The criteria for time step cutting and selection are usually based on heuristics that limit the allowable change in the solution over a time step and/or NR iteration. Here, we propose a simple modification to the NR iteration scheme for conservation laws with S-shaped flux functions that converges for any time step size. The new scheme allows one to choose the time step size based on accuracy consideration only without worrying about the convergence behavior of the nonlinear solver. The proposed method can be implemented in an existing simulator, e.g., for CO 2 sequestration or reservoir flow modeling, quite easily. The numerical analysis is confirmed with simulation studies using various test cases of nonlinear multiphase transport in porous media. The analysis and numerical experiments demonstrate that the modified scheme allows for the use of arbitrarily large time steps for this class of problems.

A Fourier-Chebyshev collocation spectral method is employed in this work to compute the Lagrangian drift or mass transport due to periodic surface pressure loading in a thin layer of non-Newtonian fluid mud, which is modeled as a power-law fluid. Because of the non-Newtonian rheology, these problems are nonlinear and must be solved numerically. On assuming that the solutions are of the same permanent waveform as the pressure loading, the governing equations are made time-independent by referring to a horizontal axis that moves at the same speed as the wave. The solutions are periodic in the horizontal direction, but are non-periodic in the vertical direction, and the computational domain is therefore discretized according to the Fourier-Chebyshev spectral collocation scheme. In this study, the spatial derivatives are computed with a differentiation matrix. In order to incorporate the boundary conditions, the matrix diagonalization technique is used to solve the matrix equation, and all the definite integrals in the vertical direction based on the collocation points are performed by the modified Clenshaw-Curtis quadrature rule. The developed method is applied to compute the first-and second-order motion of the mud. The comparison between the numerical results and the analytical solution in the Newtonian limit shows the good accuracy of the spectral method.

Event-driven particle dynamics is a fast and precise method to simulate particulate systems of all scales. In this work it is demonstrated that, despite the high accuracy of the method, the finite machine precision leads to simulations entering invalid states where the dynamics are undefined. A general event-detection algorithm is proposed which handles these situations in a stable and efficient manner. This requires a definition of the dynamics of invalid states and leads to improved algorithms for event-detection in hard-sphere systems.

This chapter examines symmetries in the physical universe from the perspective of a geometry based on spheres of 4D space with a diameter equal to the Planck length. Through these spheres, a connection is proposed between the fundamental properties of particles and the fields they generate, highlighting that the properties of mass, energy, momentum and electric charge emerge as manifestations of the rotation and curvature of space.
The implications of these symmetries in the context of quantum mechanics and relativity are also reviewed, considering the possibility of unifying concepts in a deeper geometric framework. The exploration of these ideas could offer new perspectives on the nature of mass, energy and the fundamental interaction between particles.

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We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving formulation imposes a two-way coupling at the artificial interface boundaries through nonlinear penalty functions that vanish when the solutions coincide. The penalty functions are expressed in terms of entropy conserving fluxes originally introduced for finite volume schemes. In addition to the interface coupling, which is required, entropy dissipation and coupling can optionally be added through the use of linear penalties within the overlap region.

The theory of resonance interference factor (RIF) method is examined for thermal reactor problems, and the approximations and limitations are identified. To evaluate the interference effect between resonance isotopes, the RIF method establishes an approximate equivalent relationship between a heterogeneous system and a homogeneous system by introducing background cross sections, and the approximation is a source of deviation in self-shielding calculations. Furthermore, each resonance isotope is treated individually in the self-shielding procedure, which requires unnecessary calculation effort, especially for whole-core and burnup cases. Based on the analysis, a heterogeneous pseudo-resonant isotope method (HPRIM) is proposed to overcome these problems. The mixture of resonant nuclides is considered as a pseudo-resonant isotope, and the resonance integral is generated in a one-dimensional heterogeneous system. The numerical results show that HPRIM improves the accuracy of evaluating the resonance interference effect and improves the efficiency of the self-shielding procedure.

Next-generation exascale machines with extreme levels of parallelism will provide massive computing resources for large scale numerical simulations of complex physical systems at unprecedented parameter ranges. However, novel numerical methods, scalable algorithms and re-design of current state-of-the art numerical solvers are required for scaling to these machines with minimal overheads. One such approach for partial differential equations based solvers involves computation of spatial derivatives with possibly delayed or asynchronous data using high-order asynchrony-tolerant (AT) schemes to facilitate mitigation of communication and synchronization bottlenecks without affecting the numerical accuracy. In the present study, an effective methodology of implementing temporal discretization using a multi-stage Runge-Kutta method with AT schemes is presented. Together these schemes are used to perform asynchronous simulations of canonical reacting flow problems, demonstrated in one-dimension including auto-ignition of a premixture, premixed flame propagation and non-premixed autoignition. Simulation results show that the AT schemes incur very small numerical errors in all key quantities of interest including stiff intermediate species despite delayed data at processing element (PE) boundaries. For simulations of supersonic flows, the degraded numerical accuracy of well-known shock-resolving WENO (weighted essentially non-oscillatory) schemes when used with relaxed synchronization is also discussed. To overcome this loss of accuracy, high-order AT-WENO schemes are derived and tested on linear and non-linear equations. Finally the novel AT-WENO schemes are demonstrated in the propagation of a detonation wave with delays at PE boundaries.

• The four methods currently examined have all presented great precision on calculating the particle's trajectory. • The most efficient method among all studied cases was the Boris one. • The New Euler method has exhibited the best energy conservation properties. • The Boris method has presented for all studied cases no growth tendency in the particle's energy with simulation time.

Multiscale Hybrid-Mixed (MHM) finite element method have been recently developed for several operators, including hydro-dynamics and reaction-advection-diffussion models. The MHM method is a consequence of a hybridization procedure, and emerges as a method that naturally incorporates multiple scales while provides solutions with high-order precision. The computation of local problems is embedded in the upscaling procedure, which are completely independent and thus may be naturally obtained using parallel computation facilities. We conclude that the MHM method is naturally shaped to be used in parallel computing environments and appears to be a highly competitive option to handle realistic multiscale parabolic boundary value problems with precision on coarse meshes. Numerical experiments will also be shown in order to support the theoretical results.

In the present paper, using MPI-AMRVAC, we perform a 2.5-D numerical MHD simulation of the dynamics and associated thermodynamical evolution of an initially force-free Harris current sheet subjected to an external velocity perturbation under the condition of uniform resistivity. The amplitude of the magnetic field is taken to be 10 Gauss, typical of the solar corona. We impose a Gaussian velocity pulse across this current sheet mimicking the interaction of fast magnetoacoustic waves with a current sheet in corona. This leads to a variety of dynamics and plasma processes in the current sheet, which is initially quasi-static. The initial pulse interacts with the current sheet and splits into a pair of counter-propagating wavefronts, which forms a rarefied region and leads to inflow and a thinning of the current sheet. The thinning results in Petschek-type magnetic reconnection followed by tearing instability and plasmoid formation. The reconnection outflows containing outward-moving plasmoids have accelerated motions with velocities ranging from 105-303 km s -1 . The average temperature and density of the plasmoids are found to be 8 MK and twice the background density of the solar corona, respectively. These estimates of velocity, temperature and density of plasmoids are similar to values reported from various solar coronal observations. Therefore, we infer that the external triggering of a quasi-static current sheet by a single velocity pulse is capable of initiating magnetic reconnection and plasmoid formation in the absence of a localized enhancement of resistivity in the solar corona.

We present a method for computing incompressible viscous flows in three dimensions using block-structured local refinement in both space and time. This method uses a projection formulation based on a cell-centered approximate projection, combined with the systematic use of multilevel elliptic solvers to compute increments in the solution generated at boundaries between refinement levels due to refinement in time. We use an L 0 -stable second-order semi-implicit scheme to evaluate the viscous terms. Results are presented to demonstrate the accuracy and effectiveness of this approach.

We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the smallcell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L 1 for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.

The aim of this work is the development of an automatic, adaptive mesh refinement strategy for solving hyperbolic conservation laws in two dimensions. There are two main difficulties in doing this. The first problem is due to the presence of discontinuities in the solution and the effect on them of discontinuities in the mesh. The second problem is how to organize the algorithm to minimize memory and CPU overhead. This is an important consideration and will continue to be important as more sophisticated algorithms that use data structures other than arrays are developed for use on vector and parallel computers. b? 1989 Academic Press, Inc.

In this study, absorption of high frequency radio waves in the ionospheric plasma have been investigated. The wave equation was obtained in terms of ionospheric parameters. The numerical values of the absorption have been calculated for 4 MHz, 4.5 MHz and 5 MHz waves. The necessary parameters for calculation have been obtained using an International Reference Ionosphere (IRI) Model. The altitudinal, diurnal, seasonal and the variations of absorption with frequency have been examined. The calculations show that the highest absorption occurs in the D-region. The absorption is higher in summer than in other seasons and is maximum at daylight. In addition, absorption decreases with the increase of frequency.

In this paper, a simple approach for developing the model of a Si(Li) detector in Monte Carlo simulations is presented and validated. Experimental measurements using "point-like" standard radioactive sources including 133 Ba, 137 Cs, 152 Eu, 154 Eu, 241 Am were performed for both configurations with and without collimator, respectively. The MCNP6 code was used for Monte Carlo simulation of photon transport inside the models constructed similar to these configurations. Firstly, an initial model of the Si(Li) detector was constructed based on the manufacturer's specifications, but the simulated efficiency shows a very high discrepancy from the experiment. Then, the critical geometric parameters of the model of Si(Li) detector were improved step-by-step to achieve the optimized model. For the optimized model, a good agreement was obtained between the experimental and simulated results. The relative deviations of experimental and simulated efficiencies are less than 4% with energies in the range of 12-60 keV for both configurations.

The optical detection of auroral subarcs a few tens of m wide as well as the direct observation of shears several m/s per m over km to sub km scales by rocket instrumentation both indicate that violent and highly localized electrodynamics can occur at times in the auroral ionosphere over scales 100 m or less in width. These observations as well as the detection of unstable ion-acoustic waves observed by incoherent radars along the geomagnetic ®eld lines has motivated us to develop a detailed time-dependent two-dimensional model of short-scale auroral electrodynamics that uses current continuity, Ohm's law, and 8-moment transport equations for the ions and electrons in the presence of large ambient electric ®elds to describe wide auroral arcs with sharp edges in response to sharp cut-os in precipitation (even though it may be possible to describe thin arcs and ultra-thin arcs with our model, we have left such a study for future work). We present the essential elements of this new model and illustrate the model's usefulness with a sample run for which the ambient electric ®eld is 100 mV/m away from the arc and for which electron precipitation cuts o over a region 100 m wide. The sample run demonstrates that parallel current densities of the order of several hundred lA m À2 can be triggered in these circumstances, together with shears several m/s per m in magnitude and parallel electric ®elds of the order of 0.1 mV/m around 130 km altitude. It also illustrates that the local ionospheric properties like densities, temperature and composition can strongly be aected by the violent localized electrodynamics and vice-versa.

The present paper reports the combustion synthesis of LiMgBO3 and LiSrBO3 phosphor by various dopants Ce Cu, Eu, Dy and Mn and study their TL glow curve for TL dosimetry. During the combustion synthesis we have synthesized LiMgBO3 and LiSrBO3 phosphor by using various activators Ce, Cu, Eu, Dy and Mn so as to explore the possible compound for TL glow curve analysis and their application for TL dosimetry. The combustion synthesis method is very simple and time saving method. This work deals with detail procedure for synthesis LiMgBO3 and LiSrBO3 phosphor by various dopants Ce Cu, Eu, Dy and Mn and study of their TL glow curve analysis and luminescent characteristics for TL dosimetry.

In this work, three classes of numerical methods are investigated to evaluate the mean curvature, the unit normal vector and the surface tension on a front tracking interface encountered in the simulation of multiphase flows with separated phases. The Laplace-Beltrami Operator discretization, the Integral Formulation of the surface tension and the Surface Reconstruction technique are well-known methods used in the literature, but whose accuracy, robustness and convergence properties are seldom studied. In a first step, different variants of these methods are presented and compared against each other on a static analytical surface to measure their sensitivity to the size and regularity of the mesh. Then, to assess the influence of the surface advection scheme and the remeshing procedures, two original and time dependent analytical surfaces have been developed, leading to a ligament formation or the birth of a drop/bubble on a flat surface/liquid film. Comparisons to such dynamical surfaces are especially useful and significant, since they highlight the sensitivity of numerical methods for the interface property calculation to the errors produced by the Lagrangian transport of the front-tracking surface. Finally, the accuracy of the different approximations are correlated to their computation time, so that the user may choose the most appropriate method according to the desired accuracy and cost.

In this work, three classes of numerical methods are investigated to evaluate the mean curvature, the unit normal vector and the surface tension on a front tracking interface encountered in the simulation of multiphase flows with separated phases. The Laplace-Beltrami Operator discretization, the Integral Formulation of the surface tension and the Surface Reconstruction technique are well-known methods used in the literature, but whose accuracy, robustness and convergence properties are seldom studied. In a first step, different variants of these methods are presented and compared against each other on a static analytical surface to measure their sensitivity to the size and regularity of the mesh. Then, to assess the influence of the surface advection scheme and the remeshing procedures, two original and time dependent analytical surfaces have been developed, leading to a ligament formation or the birth of a drop/bubble on a flat surface/liquid film. Comparisons to such dynamical surfaces are especially useful and significant, since they highlight the sensitivity of numerical methods for the interface property calculation to the errors produced by the Lagrangian transport of the front-tracking surface. Finally, the accuracy of the different approximations are correlated to their computation time, so that the user may choose the most appropriate method according to the desired accuracy and cost.

In paper, mathematical bases of a creation method of difficult configuration area representation in finite-elements are developed. The algorithm of task solution allows to unite simple areas and to order numberings of knots. Thus the sequence of knots points are formed, where tape width of nonzero coefficients of the whole equations system will be locally minimums.

This paper presents the study on the feasibility of a differentiation of the individual materials using so called dual energy computed tomography. The individual pixels on tomogram are the results of X-ray attenuation penetrating through the sample from different angles of projections. Attenuation is caused by absorption and scattering of radiation. The contribution of these two main mechanisms is dependent on atomic number, electron density, and also the energy of the X-ray photons. The material characteristics may be quantitatively analyzed when the composition in to atomic number or density information is carried out. Therefore, two different X-ray spectra were used by application of filters. The principle of proposed method results in a numerical approach with the associated detector calibration. We tested first the method on the samples of known composition. From the results it was shown that we are able to obtain removal of "beam hardening" and the estimation of material composition. For further more precise determination of materials, the proposed method will be used with the respect to detector acquisition improvement.

Reference dosimetry by means of clinical linear accelerators in high-energy photon fields requires the determination of the beam quality specifier TPR 20,10 , which characterizes the relative particle flux density of the photon beam. The measurement of TPR 20,10 has to be performed in homogenous photon beams of size 10 × 10 cm 2 with a focus-detector distance of 100 cm. These requirements cannot be fulfilled by TomoTherapy treatment units from Accuray. The TomoTherapy unit provides a flatteningfilter-free photon fan beam with a maximum field width of 40 cm and field lengths of 1.0 cm, 2.5 cm and 5.0 cm at a focus-isocenter distance of 85 cm. For the determination of the beam quality specifier from measurements under nonstandard reference conditions Sauer and Palmans proposed experiment-based fit functions. Moreover, Sauer recommends considering the impact of the flattening-filter-free beam on the measured data. To verify these fit functions, in the present study a Monte Carlo based model of the treatment head of a TomoTher-apyHD unit was designed and commissioned with existing

BackgroundThe integration of magnetic resonance tomography into clinical linear accelerators provides high‐contrast, real‐time imaging during treatment and facilitates online‐adaptive workflows in radiation therapy treatments. The associated magnetic field also bends the trajectories of charged particles via the Lorentz force, which may alter the dose distribution in a patient or a phantom and affects the dose response of dosimetry detectors.PurposeTo perform an experimental and Monte Carlo‐based determination of correction factors , which correct the response of ion chambers in the presence of external magnetic fields in high‐energy photon fields.MethodsThe response variation of two different types of ion chambers (Sun Nuclear SNC125c and SNC600c) in strong external magnetic fields was investigated experimentally and by Monte Carlo simulations. The experimental data were acquired at the German National Metrology Institute, PTB, using a clinical linear accelerator with a nominal pho...

By using a model based on the second-order time-dependent perturbation theory, we show that the nonsequential two-photon double ionization of He can be understood in a virtual sequential picture: to excite the final double continuum state |k_{1},k_{2}⟩ by absorbing two photons from the ground state |1s^{2},^{1}S_{0}⟩, the single continuum states |1s,k_{1}⟩ and |1s,k_{2}⟩ serve as the dominant intermediate states. This virtual sequential picture is verified by the perfect agreement of the total ionization cross section, respectively, calculated by this model and by the sophisticated numerical solution to the full-dimensional time-dependent Schrödinger equation. This model, without the consideration of the electron correlation in the final double continuum state, works well for a wide range of laser parameters extending from the nonsequential to the sequential regime. The present Letter demonstrates that the electron correlation in the final double continuum state is not important in ...

We simulate the dynamics of H2+ and HD+ by direct solution of the time-dependent Schroedinger equation for the electronic and nuclear motion for the interaction of intense femtosecond pulses. On these timescales the rotational motion, even for such light molecules, is frozen. Therefore it is a reasonable assumption that the nuclear alignment is fixed during the pulse interaction and that rotation can be neglected. In terms of vibrational relaxation, and since the nuclei are light, vibration will be important over femtosecond timescales. Although homonuclear diatomics are IR-inactive, in an intense field one can create vibrational excitation through continuum coupling. To show the effect of vibration, consider a first approximation in which the nuclei are infinitely massive so they maintain their positions at a fixed bond length of R=2 a.u., throughout the process.

The dissociation spectrum of the hydrogen molecular ion by short intense pulses of infrared light is calculated. The time-dependent Schrödinger equation is discretized and integrated in position and momentum space. For few-cycle pulses one can resolve vibrational structure that commonly arises in the experimental preparation of the molecular ion from the neutral molecule. We calculate the corresponding energy spectrum and analyze the dependence on the pulse time-delay, pulse length, and intensity of the laser for λ ∼ 790nm. We conclude that the proton spectrum is a both a sensitive probe of the vibrational dynamics and the laser pulse. Finally we compare our results with recent measurements of the proton spectrum for 55 fs pulses using a Ti:Sapphire laser (λ ∼ 790nm). Integrating over the laser focal volume, for the intensity I ∼ 3 × 10 15 W cm -2 , we find our results are in excellent agreement with these experiments.

A higher order a.(:curat(' mnnerical t)roce(ture has been deveh)l)ed for solving incompressibh' Navier-Stokes equations for 2D or 3D fluid flow t)roblems. It is base(l on low-storage Runge-Kutta schemes for temporal discretization and fourth an(I sixth order corot)act finite-difference schemes for spatial discretization. Th(" particular difficulty of satisfying the divergence-free velocity field required in incompressit)le

We introduce solution dependent finite difference stencils whose coefficients adapt to the current numerical solution by minimizing the truncation error in the least squares sense. The resulting scheme has the resolution capacity of dispersion relation preserving difference stencils in under-resolved domains, together with the high order convergence rate of conventional central difference methods in well resolved regions. Numerical experiments reveal that the new stencils outperform their conventional counterparts on all grid resolutions from very coarse to very fine.

This paper presents a three-dimensional fully Lagrangian numerical model, based on the hybrid discrete element method (DEM) and moving particle semi-implicit (MPS) mesh-free techniques, for modelling the dynamics of river ice floes. The model considers the ice-water dynamics as a multiphase discrete-continuum system. The DEM uses a Hertzian contact dynamic model to simulate the ice floes interaction. It predicts the motion and collision of ice floes as well as their interaction with water, boundaries, and any obstacle in their way. Considering the mesh-free Lagrangian nature of the DEM and MPS, the developed model has an inherent ability to predict the highly dynamic movement of the ice floes (sliding, rolling, colliding, and piling-up) in violent free surface flow. The model is validated and evaluated with a small-scale experiment based on dam-break with floating block floes, which mimics the characteristics of a jam release. The results show the ability of the model to accurately reproduce the three-dimensional dynamic behavior of ice floes as well as the complex hydrodynamics, for example, the water surface motions in the horizontal and vertical directions. The model can be extended for simulations of more complex large-scale ice dynamic problems such as ice-jam formation and release and interaction of ice floes with hydraulic structures.

Solar flares (SFs) and intense radiation can generate additional ionization in the Earth’s atmosphere and affect its structure. These types of solar radiation and activity create sudden ionospheric disturbances (SIDs), affect electronic equipment on the ground along with signals from space, and potentially induce various natural disasters. Focus of this work is on the study of SIDs induced by X-ray SFs using very low frequency (VLF) radio signals in order to predict the impact of SFs on Earth and analyze ionosphere plasmas and its parameters. All data are recorded by VLF BEL stations and the model computation is used to obtain the daytime atmosphere parameters induced by this extreme radiation. The obtained ionospheric parameters are compared with results of other authors. For the first time we analyzed physics of the D-region—during consecutive huge SFs which continuously perturbed this layer for a few hours—in detail. We have developed an empirical model of the D-region plasma den...

Ion stopping in warm dense matter is a process of fundamental importance for the understanding of the properties of dense plasmas, the realization and the interpretation of experiments involving ion-beam-heated warm dense matter samples, and for inertial confinement fusion research. The theoretical description of the ion stopping power in warm dense matter is difficult notably due to electron coupling and degeneracy, and measurements are still largely missing. In particular, the low-velocity stopping range around the Bragg peak, that features the largest modeling uncertainties, remains virtually unexplored. Here, we report proton energy-loss measurements in warm dense plasma at unprecedented low projectile velocities, approaching significantly the Bragg-peak region. Our energy-loss data, combined with a precise target characterization based on plasma emission measurements using two independent spectroscopy diagnostics, demonstrate a significant deviation of the stopping power from c...

Chemical exchange saturation transfer (CEST) has recently evolved into a powerful approach for studying sparsely populated, "invisible" protein states in slow exchange with a major, visible conformer. Central to the technique is the use of a weak, highly selective radio-frequency field that is applied at different frequency offsets in successive experiments, "searching" for minor state resonances. The recording of CEST profiles with enough points to ensure coverage of the entire spectrum at sufficient resolution can be time-consuming, especially for applications that require high static magnetic-fields or when small chemical shift differences between exchanging states must be quantified. Here we show, with applications involving 15 N CEST, that the process can be significantly accelerated by using a multi-frequency irradiation scheme, leading in some applications to an order of magnitude savings in measurement time.

This chapter addresses the fields generated by mass and charge, along with other fundamental elements such as curvature and frequency, conceptualized as a single unified field. These elements, whether at rest or in motion, generate two types of interrelated fields, similar to what occurs in electromagnetism.
It analyzes how Planck units and the geometrical system of units simplify physical expressions, allowing wavelengths, energies and forces to be described by fundamental constants. In addition, the concept of "energy element" is introduced, defined as any physical magnitude capable of being expressed in terms of length or distance based on universal constants.
General expressions are presented for forces and fields generated by energy elements, both at rest and in motion. These expressions, derived from the proposed theoretical model, allow concepts such as gravity and electromagnetism to be extended to a more general framework that includes moving elements.
The chapter concludes with the generalization of Maxwell's equations and the formulation of gravitomagnetism, showing how the forces between elements of energy at rest and in motion can be unified into a consistent theoretical system. The potential of this approach to link classical and modern field theories is underlined.

I can sympathize with people's pains, but not with their pleasures. There is something curiously boring about somebody else's happiness. Aldous Huxley (1894Huxley ( -1963) ) Next to enjoying ourselves, the next greatest pleasure consists in preventing others from enjoying themselves, or, more generally, in the acquisition of power.