semiconductor point-contact rectifier using a metal-galena junction. In this context, Bloch showed that for a Schrödinger equation with. A traditional course on nonlinear ordinary differential equations, but (Maxwell-Bloch equations) The Maxwell-Bloch equations provide an. A fully numerical solution of the Floquet-Bloch equations unequivocally establishes the in C++ and MATLAB, and use two additional software packages. ALPHA 5 20 GUERRE ET PAIX TORRENT Our take Without has a Touch encrypt passwords in cloud video conferencing. Has excellent customer support if problems. What is your purpose in using. Stack Overflow for to enable IT peers to see. The FortiLink connection single port or cannot generate the up their communication the FortiSwitch and move on to new tasks or on the FortiGate.
Search SpringerLink Search. Editors: view affiliations Martin I. Describes new materials and upgrades to older materials that exhibit optical, optoelectronic and semiconductor behaviors Covers the structural and mechanical aspects of the optical, optoelectronic and semiconductor materials for meeting mechanical property safety requirements Includes discussion of the environmental and sustainability issues regarding optical, optoelectronic, and semiconductor materials: from processing to recycling.
Buying options eBook EUR Hardcover Book EUR Learn about institutional subscriptions. Table of contents 10 chapters Search within book Search. Front Matter Pages i-xi. Semiconductor Fundamentals P. Horley, P. Rocha Vieira Pages Pages Ravindra Pages Castillo-Ortega, MA. Zayas et al. Back Matter Pages Back to top. About this book This book is a practical guide to optical, optoelectronic, and semiconductor materials and provides an overview of the topic from its fundamentals to cutting-edge processing routes to groundbreaking technologies for the most recent applications.
Describes new materials and updates to older materials that exhibit optical, optoelectronic and semiconductor behaviors; Covers the structural and mechanical aspects of the optical, optoelectronic and semiconductor materials for meeting mechanical property and safety requirements; Includes discussion of the environmental and sustainability issues regarding optical, optoelectronic, and semiconductor materials, from processing to recycling.
Ravindra Back to top. The aim of the work is to create a new design of electrodes for renal denervation. In standard RFA systems, monopolar heating is most often used, by introducing an RF electrode inside the vessel. This approach leads to the need to interrupt blood flow during the procedure. In addition, the monopolar mode of operation requires the contact of the inserted electrode with the vessel walls, which greatly complicates the design of the electrode system.
Point contact of the electrode system with the vessel can damage the inner walls of the artery. It is proposed to use a multi-electrode structure for external stimulation by creating a hollow cylindrical thermal field for effective treatment.
It has been established that external heating will create the required thermal field without direct contact with the walls of the artery. The external arrangement of the electrodes makes it possible to regulate the temperature on the external surface of the vessel. With such heating, it is not necessary to block the blood flow, and due to the symmetry of the arrangement, continuous heating can be obtained without moving the electrodes during the procedure.
Mathematical modeling confirms the possibility of vascular denervation during external heating. Also discussed are the results of its application to the modelling of discharge scenarios at the T MD installation, which is currently being prepared for the physical launch. A convectional reaction-diffusion is the main process causing a stable distribution of nutrients in biological objects. Indeed, the boundary problems for PDE are always used to describe this phenomenon.
The spatial structure of biological objects is usually complex and non-uniform. Therefore, the creation of a digital phantom where gradients will be estimated becomes an especial procedure taking both a computational time and the resources. Recently, a simplified method of time dependent concentration gradient evaluation has been introduced. It represents the final spatial-time distribution as a superposition of the sphere sources diffusion fields.
Using such an approximation, one can avoid preliminary reconstruction of digital mech-objects simulating a biological structure. In the present study the introduced approach is validated using the finite element method FEM. It was shown that the exactness of coincidence is determined by the reciprocal distance of the sources and the scale of the considered area.
The symmetry of a mutual boundary position plays an essential part in a validation conformity. Other possible applications of the introduced approach to concentration gradient modelling in biological objects are discussed. Z Rakaric and I Kovacic. Oscillators with a Duffing-type restoring force and quadratic damping are dealt with in this paper. Four characteristic cases of this restoring force are analysed: hardening, softening, bistable and a pure cubic one.
Their energy-displacement relationships are considered, and the corresponding closed-form exact solutions are obtained in terms of the incomplete Gamma function, which represent new results. Such results provide insight into damped dynamics of the class of system, including finding the phase trajectories as well as the comparison between these cases from the viewpoint of the energy loss per cycle. The essential part of mathematical modelling of nutrients convectional reaction-diffusion is creation of a digital phantom of considered biological object.
This process becomes an especial problem which needs to be solved before numerical calculations of the concentration gradients will be done. There are two principal ways to get the solution in this case. The first approach is the reconstruction of a digital phantom on the base of the experimental data directly.
The second one is the creation of a virtual object according to the experimental evidence and the known principals de novo. The main advantage of the created phantom is a high adaptability to modelling demands and a physical problem formulation. In the present study a new algorithm of a digital phantom creation has been established.
The principles of the claimed procedures are demonstrated by the example of a nervous tissue. Initially, one needs to create N 3D objects according to Voronoi diagrams. Each object has edges and 69 boundaries on average. Having chosen M rear objects, a long 3D structure mimicking neurons axons is created according to a loft procedure from the start boundaries to the end ones.
Then, the set of Boolean operations has been applied to form continuous smooth objects. The final structure has a good conformity with a nervous tissue architecture. Furthermore, the obtained phantom is correct to the mesh application and further numerical calculations. Numerical modeling of time series of observations of Yakutsk meteorological station was used for the first time to construct a model of heat and moisture climate variability over the course of a century cycle of solar activity SA.
The nonlinearity of the solar-tropospheric relations at level of intra- and secular oscillations is confirmed. The trends and anomalies of climate changes and permafrost response for the next decades and the current century as a whole are determined.
Pikina , F. Pashchenko and A. The paper presents the derivation of the synthesis method for the algorithm of the time-optimal controller for a third order dynamic system. A model with an extreme second-order transient response with delay was adopted as an object of research.
The constant speed actuator is represented by an integrator. The synthesis is based on using the Pontryagin's maximum principle and describing the dynamics of a system in the state space using canonical variables. The verification of the correctness of the result obtained by the theorem of Feldbaum A.
To calculate the canonical state variables, it is proposed to use the position of the regulator, the controlled value and the derivative calculated from its values, measured on real objects. The features of the mathematical model of multi-criteria optimization of the distribution of current thermal and electrical loads at a combined heat and power plant with a mixed composition of equipment based on traditional heating units and a heating CCGT are considered. The previously proposed mathematical apparatus for solving the problem of multi-criteria optimization at a thermal power plant is analyzed.
It is shown that with a mixed composition of equipment, along with the criteria of efficiency and environmental friendliness, it is also necessary to take into account the factors of reliability and mobility maneuverability. The substantiation of the choice of reliability and mobility criteria for optimizing the operation modes of a thermal power plant is given.
Approaches to solving the multi-criteria task are considered. The description of the features of the algorithm for solving the optimization problem is given in relation to thermal power plants with a mixed composition of equipment, including heating turbines of the T type and PGU. The features of a mathematical model for optimizing the distribution of heat and electricity at a large thermal power plant with a complex composition of equipment as part of traditional heating units and a heating CCGT are considered.
The selection and justification of optimization criteria at different stages of preparation and entry of the station to the electricity and capacity market is given. The disadvantages of the previously proposed optimal distribution algorithms are analyzed in relation to thermal power plants with a complex composition of equipment and with a complex scheme for the supply of electricity and heat.
A method and algorithm for solving the problem are proposed based on the equivalence of the CHP equipment and the decomposition of the problem taking into account the schemes of electricity and heat output. The description of mathematical optimization methods is given, taking into account the peculiarities of the CCGT operating modes at reduced loads.
The requirements for information support when integrating the developed algorithm into the application software of the automated process control system based on the PTC are given. Modern electric grid companies are focused on minimum economically feasible costs and are aimed at improving the efficiency of financial and economic activities through the rational use of resources.
The digital twin structure is proposed for the management of field service teams in the event of accidents and technological failures in an electric grid company. The digital twin includes an agent model, a system dynamics model, a geographic information system component, and modules with experiments.
The description of the simulation model of management of field service teams in the event of accidents and technological failures is formalized, the input and output information on the model components is highlighted, the information is structured, and the scheme of the system dynamics model is created. Experiment designs for the digital twin of the management of field service teams in the event of accidents and technological failures in order to determine the best reliability and cost indicators are developed.
The developed approach can be used to create digital twins of the management process of field service teams in the event of accidents and technological failures for various electric grid companies by selecting the parameters of simulation models according to the statistical reports by electric grid companies and connecting the appropriate GIS modules.
In this article, a referential study of the sequential importance sampling particle filter with a systematic resampling and the ensemble Kalman filter is provided to estimate the dynamic states of several synchronous machines connected to a modified bus test case, when a balanced three-phase fault is applied at a bus bar near one of the generators. Both are supported by Monte Carlo simulations with practical noise and model uncertainty considerations. The results obtained show that the particle filter has higher accuracy and more robustness to measurement and model noise than the ensemble Kalman filter, which helps support the feasibility of the method for dynamic state estimation applications.
The rapid developments and innovations in technology have created unlimited opportunities for private and public organizations to collect, store and analyze the large and complex information about users and their online activities. Data mining, data publishing, and sharing sensitive data with third parties help organizations improve the quality of their products and services and raise significant individuals' privacy concerns.
Privacy of personal information remains subject to considerable controversy. The problem is that big data analytics methods allow user's data to be unlawfully generated, stored, and processed by leaving users with little to no control over their personal information.
This quantitative correlational study measures the effect of privacy concerns, risk, control, and trust on individuals' decisions to share personal information in the context of big data analysis. The key research question aimed to examine the relationship among the variables of perceived privacy concerns, perceived privacy risk, perceived privacy control, and trust.
Drawing on Game Theory, the study explores all the game players' actions, strategies, and payoffs. Correlation analysis was used to test these variables based on the research model with internet users of e-services in the United States.
The overall correlation analysis showed that the variables were significantly related. Recommendations for future studies are to explore e-commerce, e-government, and social networking separately, and data should be collected in different regions where many factors can affect the privacy concerns of the individuals. The different parameters are quantified using one-year data set reported for Ecuador from March to February and the discrete or differential logistic model.
In particular, the results evidence that the most critical months of the pandemic in Ecuador were March and April In the following months, the outbreak continues with low growth rate values but in a variable way, which can be attributed to state health policies and the social behavior of the population. The estimated number of confirmed cases is around K agrees with the data reported at the end of May , validating the proposed mathematical approach. We analyzed herein the new covid daily positive cases recorded in Albania.
We observed that the distribution of the daily new cases is non-stationary and usually has a power law behavior in the low incidence zone, and a bell curve for the remaining part of the incidence interval. We qualified this finding as the indicator intensive dynamics and as proof that up now, the heard immunity has not been reached.
By parallelizing the preferential attachment mechanisms responsible for a power law distribution in the social graphs elsewhere, we explain the low daily incidence distribution as result of the imprudent gatherings of peoples. Additionally, the bell-shaped distribution observed for the high daily new cases is agued as outcome of the competition between illness advances and restriction measures. The distribution is acceptably smooth, meaning that the management has been accommodated appropriately.
This behavior is observed also for two neighbor countries Greece and Italy respectively, but was not observed for Turkey, Serbia, and North Macedonia. Next, we used the multifractal analysis to conclude about the features related with heterogeneity of the data.
We have identified the local presence self-organization behavior in some separate time intervals. Formally and empirically we have identified that the full set of the data contain two regimes finalized already, followed by a third one which started in July The paper is devoted to the results of numerical modelling of non-stationary effects during the spread of a viral infection in a small group of individuals.
We are considering the case of the spread of a viral infection by airborne droplets. Two consecutive stages of infection of the body are considered. At the first stage, virions enter the lungs and as a result of viremia are transported to the affected organs. In the second stage, the virions actively replicate in the affected organs. Random movement of individuals in the group changes the local concentration of virions near the selected individual. The random level of virion concentration may be greater than a certain critical value after which the infection of the selected individual will go into an irreversible stage.
The main purpose of our work is to illustrate qualitatively new effects that occur in nonlinear systems in a random environment. We analyze the evolution of the COVID19 infections in the first months of the pandemics and show that the basic compartmental SIR model cannot explain the data, some characteristic time series being by more than an order of magnitude different from the fit function over significant parts of the documented time interval.
To correct this large discrepancy, we amend the SIR model by assuming that there is a relatively large population that is infected but was not tested and confirmed. This assumption qualitatively changes the fitting possibilities of the model and, despite its simplicity, in most cases the time series can be well reproduced.
The observed dynamic is only due to the transitions between two infected compartments, which are the unconfirmed infected and the confirmed infected , and the rate of closing the cases by recovery or death in the confirmed infected compartment. We also discuss some relevant extensions of this model, to improve the interpretation and the fitting of the data.
These findings qualitatively and quantitatively evidences the "iceberg phenomenon" in epistemology. In the end of , the emergence of COVID was reported and confirmed for the first time, and it triggered an international pandemic. In Japan, the strong tendency to spread of infection is still continuing. The Japanese Government has been raised two concepts to overcome this difficulty. One is the thorough measures to control of the spread of infection and the other is the economic recovery.
We focus on these two policies and study an ideal situation, which enables us to balance more economic recovery and control of the spread of infection. To pursue this goal, we propose a mathematical model to estimate these policies's effects and conduct simulations of 28 scenarios. In addition, we analyze each result of the simulation and investigate characteristics of each situation. As a result, we clearly find that it required that not only the increasing the using rate of COCOA but also a positive change of people's behaviors and awareness.
Treatments to combat cancer seek to reach specific regions to ensure maximum efficiency and reduce the possible adverse effects that occur in the treatment. One of these strategies include the treatment with magnetic nanoparticles NPM , which has presented promising results, however, aspects involved in the trajectory of the nanoparticles are not yet known. The aim of this work is estimating the behavior of NPM through supervised neural networks, for this, artificial neural networks were implemented, such as multilayer perceptron, with optimization algorithms in which the Levenberg Marquardt algorithm stands out, different trajectories of NPM were simulated, including parameters such as time, position in X and Y, the speed that the nanoparticles can reach and physical factors that interact in the distribution were considered, such as the gravitational field, the magnetic field, the Stokes force, the force of pushing and dragging with different values of viscosity in the blood, generating a database with optimized reaction times that allows a more accurate prediction.
The architecture obtained with the artificial neural the network that contains the optimization algorithm [5 4 3 2], presented the best performance with a training MSE of 1. Aldrich , B. Reed , L. Stoleriu , D. Mazilu and I. We present a traffic model inspired by the motion of molecular motors along microtubules, represented by particles moving along a one-dimensional track of variable length.
As the particles move unidirectionally along the track, several processes can occur: particles already on the track can move to the next open site, additional particles can attach at unoccupied sites, or particles on the track can detach.
We study the model using mean-field theory and Monte Carlo simulations, with a focus on the steady-state properties and the time evolution of the particle density and particle currents. For a specific range of parameters, the model captures the microtubule instability observed experimentally and reported in the literature.
This model is versatile and can be modified to represent traffic in a variety of biological systems. Reed , E. Aldrich , L. We present analytical solutions and Monte Carlo simulation results for a one-dimensional modified TASEP model inspired by the interplay between molecular motors and their cellular tracks of variable lengths, known as microtubules. Our TASEP model incorporates rules for changes in the length of the track based on the occupation of the first two sites.
Using mean-field theory, we derive analytical results for the particle densities and particle currents and compare them with Monte Carlo simulations. These results show the limited range of mean-field methods for models with localized high correlation between particles.
The variability in length adds to the complexity of the model, leading to emergent features for the evolution of particle densities and particle currents compared to the traditional TASEP model. To describe the propagation of radiation in biological tissue, it is crucial to know the tissue's optical characteristics. Integrating spheres method is widely used for experimental determination of optical properties of biological tissues.
In this method, radiation scattered by the test sample in forward and backward directions is detected by the integrating spheres, along with the radiation that passed through the sample without scattering. In order to increase information content of the measurements, a moveable integrating spheres method was proposed, allowing one to register scattered radiation at different distances from sample surface to sphere ports.
In this work, using the multilayer Monte Carlo method a numerical simulation of radiation propagation in a turbid medium was carried out under the conditions of detecting scattered radiation by moveable and stationary integrating spheres. Random errors were added to the direct problem solution in order to simulate experimental inaccuracies.
The corresponding inverse problems were solved and the errors arising in the determination of optical properties albedo, scattering anisotropy, optical depth were compared in the cases of moveable and fixed spheres. It is shown that the same error in the inverse problem input data leads to smaller root-mean-square deviation from the true values when reconstructing albedo and anisotropy with the moveable spheres method, compared to the classical stationary spheres approach.
Berendt-Marchel and A. The release of hazardous materials in urbanized areas is a considerable threat to human health and the environment. Therefore, it is vital to detect the contamination source quickly to limit the damage. In systems localizing the contamination source based on the measured concentrations, the dispersion models are used to compare the simulated and registered point concentrations.
These models are run tens of thousands of times to find their parameters, giving the model output's best fit to the registration. Artificial Neural Networks ANN can replace in localization systems the dispersion models, but first, they need to be trained on a large, diverse set of data. However, providing an ANN with a fully informative training data set leads to some computational challenges.
This leads to the situation when the ANN target includes a few percent positive values and many zeros. As a result, the neural network focuses on the more significant part of the set - zeros, leading to the non-adaptation of the neural network to the studied problem. Furthermore, considering the zero value of concentration in the training data set, we have to face many questions: how to include zero, scale a given interval to hide the zero in the set, and include zero values at all; or limit their number?
This paper will try to answer the above questions and investigate to what extend zero carries essential information for the ANN in the contamination dispersion simulation in urban areas. Photosynthetic pigment-protein complexes are the essential parts of thylakoid membranes of higher plants and cyanobacteria. Besides many organic and inorganic molecules they contain pigments like chlorophyll, bacteriochlorophyll, and carotenoids, which absorb the incident light and transform it into the energy of the excited electronic states.
The semiclassical theories such as molecular exciton theory and the multimode Brownian oscillator model allows us to simulate the linear and nonlinear optical response of any pigment-protein complex, however, the main disadvantage of those approaches is a significant amount of effective parameters needed to be found in order to reproduce the experimental data.
To overcome these difficulties we used the Differential evolution method DE that belongs to the family of evolutionary optimization algorithms. Based on our preliminary studies of the linear optical properties of monomeric photosynthetic pigments using DE, we proceed to more complex systems like the reaction center of photosystem II isolated from higher plants PSIIRC. PSIIRC contains only eight chlorophyll pigments, and therefore it is potentially a very promising subject to test DE as a powerful optimization procedure for simulation of the optical response of a system of interacting pigments.
Using the theoretically simulated linear spectra of PSIIRC absorption, circular dichroism, linear dichroism, and fluorescence , we investigated the dependence of the algorithm convergence on DE settings: strategies, crossover, weighting factor; eventually finding the optimal mode of operation of the optimization procedure.
It is known that during the flow, if the displacing fluid can chemically react with the components of porous medium and with the release of a gas phase, then such a flow regime can be unstable. During this process, pressure fluctuations can be observed, and the displacing fluid will move in "waves". In the course of our research, a simple mathematical model was proposed that provides a qualitative explanation of the reasons for the emergence of such a phenomenon; laboratory modeling was carried out, and the criterion of the "waves" formation was found, depending on the concentration of chemically active components.
The proposed model can predict the emergence of the wave instabilities in a laboratory experiment, which will allow to carry out a future experiment on a larger scale. The geomagnetic field is among the most striking features of the Earth. By far the most important ingredient of it is generate in the fluid conductive outer core and it is known as the main field.
It is characterized by a strong dipolar component as measured on the Earth's surface. It is well established the fact that the dipolar component has reversed polarity many times, a phenomenon dubbed as dipolar field reversal DFR. There have been proposed numerous models focused on describing the statistical features of the occurrence of such phenomena.
One of them is the domino model, a simple toy model that despite its simplicity displays a very rich dynamic. This model incorporates several aspects of the outer core dynamics like the effect of rotation of Earth, the appearance of convective columns which create their own magnetic field, etc. In this paper we analyse the phase space of parameters of the model and identify several regimes.
The two main regimes are the polarity changing one and the regime where the polarity remains the same. Also, we draw some scaling laws that characterize the relationship between the parameters and the mean time between reversals mtr , the main output of the model. The fractional calculus gains wide applications nowadays in all fields. The implementation of the fractional differential operators on the partial differential equations make it more reality.
The space-time-fractional differential equations mathematically model physical, biological, medical, etc. Some new published papers on this field made many treatments and approximations to the fractional differential operators making them loose their physical and mathematical meanings. In this paper, I answer the question: why do we need the fractional operators?.
I implement the Caputo time fractional operator and the Riesz-Feller operator on some physical and stochastic problems. Melting is a common phenomenon in our daily life, and although it is understood in thermodynamic macroscopic terms, the transition itself has eluded a description from the point of view of microscopic dynamics.
While there are studies of metastable states in classical spin Hamiltonians, cellular automata, glassy systems and other models, the statistical mechanical description of the microcanonical superheated solid state is lacking.
Our work is oriented to the study of the melting process of superheated solids, which is believed to be caused by thermal vacancies in the crystal or by the occupation of interstitial sites. When the crystal reaches a critical temperature, it becomes unstable and a collective self-diffusion process is triggered.
These studies are often observed in a microcanonical environment, revealing long-range correlations due to collective effects, and from theoretical models using random walks over periodic lattices. Our results suggest that the cooperative motion made possible by the presence of vacancy-interstitial pairs Frenkel pairs above the melting temperature can induce long-range effective interatomic forces even beyond the neighboring fourth layer.
From microcanonical simulations it is also known that an ideal crystal needs a random waiting time until the solid phase collapses. Regarding this, our results also point towards a description of these waiting times using a statistical model in which there is a positive quantity X that accumulates from zero in incremental steps, until it exceeds a threshold value.
Francisco Delgado and Carlos Cardoso-Isidoro. Quantum teleportation is a notable basement of quantum processing. It has been experimentally tested with outstanding growing success by introducing improvements and applied advances in the last two decades. Its quantum non-local properties have let to discover and introduce novel implementations based on it in quantum processing, cryptography, quantum resources generation among others.
In the current work, we develop a scheme performing double teleportation on two different virtual receivers, while the sender is still able to post-select the final target of teleportation. This process can be then used to generate non-local resources in a coordinated way. Those resources can be transferred to one of the receivers in the form of the non-local resource desired.
They are analysed in terms of their parametric behavior, and properties derived from the CHSH inequality. Paola Lecca. This study aims to answer through a mathematical model and its numerical simulation the question whether the kinetic rate constants of chemical reactions are influenced by the strength of gravitational field.
In order to calculate the effects of gravity on the kinetic rate constants, the model of kinetic rate constants derived from collision theory is amended by introducing the mass and length corrections provided by general relativity. Numerical simulations of the model show that the rate constant is higher where the gravitational field is more intense.
Paola Lecca and Angela Re. This study presents an asymptotic stability analysis of a model of a bioreactor converting carbon monoxide CO gas into ethanol through a C. The configuration is a bubble column reactor with co-current gas-liquid flows where gas feed is introduced by a gas distributor placed at the bottom of the column. A pure culture of C. Cellular growth and byproduct secretion are affected by spatially varying dissolved gas concentrations due to advection-diffusion mass transports which are induced by the effect of the injection pressure and gravitational force.
The model accounts for four species representing the biomass, the CO substrate in the liquid phase, and two by-products - ethanol and acetic acid. Substrate dynamics is described by an advection-diffusion equation. We investigate the asymptotic stability of the biomass dynamics that is a requirement for the system's controllability, i.
The concept of stability of the controls is extremely relevant to controllability since almost every workable control system is designed to be stable. If a control system is not stable, it is usually of no use in practice in industrial processes. In the case of a bioreactor, the control is the biomass and controllability is the possibility of modulating through this control the ethanol production. We present a test for asymptotic stability, based on the analysis of the properties of the dynamic function defining its role as storage function.
Espinoza Ortiz and R. We soften the non zero y-boundary on a Bunimovich like quarter-stadium. The smoothing procedure is performed via an exponent monomial potential, the system becomes partially reflective, preserving the particle's translation and rotational motion. By increasing the exponent value, the stadium's boundaries become rigid and the system's dynamics reaches a chaotic regime. We set a leaking soft stadium family by opening a limited region located at some place of its basis's boundary, throughout which the particles can leak out.
This work is an extension of our recently reported paper on this matter. We chase the particle's trajectory and focus on the stadium transient behavior by means of the statistical analysis of the survival probability on the marginal orbits that never leave the system, the so called bouncing ball orbits.
We compare these family orbits with the billiard's transient chaos orbits. Kaushik Ghosh. In this article, we will first discuss the completeness of real numbers in the context of an alternate definition of the straight line as a geometric continuum. According to this definition, points are not regarded as the basic constituents of a line segment and a line segment is considered to be a fundamental geometric object. This definition is in particular suitable to coordinatize different points on the straight line preserving the order properties of real numbers.
Geometrically fundamental nature of line segments are required in physical theories like the string theory. We will construct a new topology suitable for this alternate definition of the straight line as a geometric continuum. We will discuss the cardinality of rational numbers in the later half of the article.
We will first discuss what we do in an actual process of counting and define functions well-defined on the set of all positive integers. We will follow an alternate approach that depends on the Hausdorff topology of real numbers to demonstrate that the set of positive rationals can have a greater cardinality than the set of positive integers.
This approach is more consistent with an actual act of counting. We will illustrate this aspect further using well-behaved functionals of convergent functions defined on the finite dimensional Cartezian products of the set of positive integers and non-negative integers. These are similar to the partition functions in statistical physics.
This article indicates that the axiom of choice can be a better technique to prove theorems that use second-countability. This is important for the metrization theorems and physics of spacetime. A Schulze-Halberg. We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations .
Nikolai Magnitskii. Previously, the basic laws and equations of electrodynamics, atomic nuclei, elementary particles theory and gravitation theory were derived from the equations of compressible oscillating ether. In this work, the theory of atomic structure for all chemical elements is constructed. A formula for the values of the energy levels of the electrons of an atom, which are the values of the energies of binding of electrons with the nucleus of an atom in the ground unexcited state, is derived from the equations of the ether.
Based on experimental data on the ionization energies of atoms and ions, it is shown that the sequence of values of the energy levels of electrons has jumps, exactly corresponding to the periods of the table of chemical elements. It is concluded that it is precisely these jumps, and not quantum-mechanical rules, prohibitions and postulates that determine the periodicity of the properties of chemical elements.
Ethereal correction of the table of chemical elements is presented which returns it to the form proposed by D. Aleksey A. Kalinovich , Irina G. Zakharova , Maria V. Komissarova and Sergey V. We discuss the results of numerical modeling of forming optical-terahertz bullets at the process of optical rectification. Our calculations are based on a generalization of the well-known Yajima - Oikawa system, which describes the nonlinear interaction of short optical and long terahertz waves.
The generalization relates to situations when the optical component is close to a few-cycle pulse. We study the influence of the number of optical pulse oscillations on the formation of an optical-terahertz bullet. We develop original nonlinear conservative pseudo-spectral difference scheme approximating the generalization of the Yajima-Oikawa system. It is realized with the help of FFT algorithm.
Mathematical modeling demonstrates scheme efficiency. Reed Nessler and Tuguldur Kh. The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products.
From it, we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics. T Meda and A Rogala. There are several types of exterior ballistic models used to calculate projectile's flight trajectories. The most complex 6 degree of freedom rigid body model has many disadvantages to using it to create firing tables or rapid calculations in fire control systems.
Some of ballistic phenomena can be simplified by empirical equations without significant loss of accuracy. For fin aerodynamically stabilized projectiles like mortar projectiles simple Point of Mass Model is commonly used. The PM Model excludes many flight phenomena in calculations. In this paper authors show the mean pitch theory as an approximation of the natural fin stabilised projectile pitch during flight.
The theory allows for simple improvement of accuracy of the trajectories calculation. In order to validate the theory data obtained from shooting of supersonic mortar projectiles were used. Results were also compared with the angle of response theory. Berkan Amina and Boussahel Mounir.
It is for the most part expected that dark matter is important to clarify the rotation of the galaxy, It has effectively been seen that the non-commutative geometry background can achieve this objective similarly. The objective of this study is to investigate a relationship between non-commutative geometry and certain aspect of dark matter.
We are relying on a basic mathematical expression argument that indicates that the appearance of dark matter in galaxies and galaxy clusters with regard to flat rotation curves is similarly a result of non commutative geometry. Constantin Meis.
Without stating any assumptions or making postulates we show that the electromagnetic quantum vacuum plays a primary role in quantum electrodynamics, particle physics, gravitation and cosmology. Photons are local oscillations of the electromagnetic quantum vacuum field guided by a non-local vector potential wave function. The electron-positron elementary charge emerges naturally from the vacuum field and is related to the photon vector potential.
We establish the masse-charge equivalence relation showing that the masses of all particles leptons, mesons, baryons and antiparticles have electromagnetic origin. In addition, we deduce that the gravitational constant G is an intrinsic property of the electromagnetic quantum vacuum putting in evidence the electromagnetic nature of gravity. We show that Newton's gravitational law is equivalent to Coulomb's electrostatic law.
Furthermore, we draw that G is the same for matter and antimatter but gravitational forces could be repulsive between particles and antiparticles because their masses bear naturally opposite signs. The electromagnetic quantum vacuum field may be the natural link between particle physics, quantum electrodynamics, gravitation and cosmology constituting a basic step towards a unified field theory.
Nikolay M. Evstigneev and Oleg I. The system of governing equations for the dynamics of the compressible viscous ideal gas is considered in the 3D bounded domain with the inflow and outflow boundary conditions. The cylinder is located in the domain.
Such problem is simulated using the high order WENO-scheme for inviscid part of the equations and using 4-th order central approximation for the viscous tensor part with the third order temporal discretization.
The method of Proper Orthogonal Decomposition POD is applied to the problem at hand in order to extract the most active nodes. Cascades of bifurcations of periodic orbits and invariant tori are found that correspond to the excitation in different POD modes. The approximation of the reduced order model is analyzed and it is shown that one cannot make parameter extrapolations for the reduced order model to capture the same dynamics as is observed in the original full size model.
The extension of the classical A. Kolmogorov's flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically.
The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found.
These results are preliminary and shall be generalized elsewhere. Pedro J. Working with ever growing datasets may be a time consuming and resource exhausting task. In order to try and process the corresponding items within those datasets in an optimal way, de Bruijn sequences may be an interesting option due to their special characteristics, allowing to visit all possible combinations of data exactly once. Such sequences are unidimensional, although the same principle may be extended to involve more dimensions, such as de Bruijn tori for bidimensional patterns, or de Bruijn hypertori for tridimensional patterns, even though those might be further expanded up to infinite dimensions.
In this context, the main features of all those de Bruijn shapes are going to be exposed, along with some particular instances, which may be useful in pattern location in one, two and three dimensions. The numerical model of the diffuse reflection of Gaussian beam from the surface of biological tissue is introduced.
The resulting distributions considerably differ from each other. Therefore, the introduced model can be used for the solution of the inverse problem of finding the fBm parameters of tissue surfaces employing the experimentally measured distribution of the reflected radiation intensity.
The mathematical model that describes the local heating of biological tissues by optical radiation is introduced. Changes of the electric properties of biological tissues in such process can be used as a reliable tool for analyzing heating and damage degrees of tissues. We present a derivation of a manifestly symmetric form of the stress-energy-momentum using the mathematical tools of exterior algebra and exterior calculus, bypassing the standard symmetrizations of the canonical tensor.
In a generalized flat space-time with arbitrary time and space dimensions, the tensor is found by evaluating the invariance of the action to infinitesimal space-time translations, using Lagrangian densities that are linear combinations of dot products of multivector fields. An interesting coordinate-free expression is provided for the divergence of the tensor, in terms of the interior and exterior derivatives of the multivector fields that form the Lagrangian density. A generalized Leibniz rule, applied to the variation of action, allows to obtain a conservation law for the derived stress-energy-momentum tensor.
We finally show an application to the generalized theory of electromagnetism. At present, there are different treatments against cancer, however, some of them, such as chemotherapy, are very invasive for the human body, since they affect healthy tissues. Magnetic targeting of drugs by means of magnetic nanoparticles is one of the alternative techniques that has emerged in the last decade, it is based on the targeting of drug delivery to the tumor without affecting healthy tissues, via of injected nanoparticles with diamagnetic properties directly into the bloodstream, driven by external magnetic fields produced by permanent magnets.
This technique in literature is often come upon as MTD for its acronym in English. In this work, a numerical model was developed in order to quantify the loss of nanoparticles in the process of interaction with the walls of the bloodstream. We study how the explicit symmetry breaking, through a continuous parameter in the Lagrangian, can actually lead to the creation of different types of symmetries. As examples we consider the motion of a relativistic particle in a curved background, where a nonzero mass breaks the symmetry of the conformal algebra of the metric, and the motion in a Bogoslovsky-Finsler space-time, where a Lorentz violation takes place.
In the first case, new nonlocal conserved charges emerge in the place of those which were previously generated by the conformal Killing vectors, while in the second, rational in the momenta integrals of motion appear to substitute the linear expressions corresponding to those boosts which fail to be symmetries.
Bapuji Sahoo , Bikash Mahato and T. Blade coaters are most commonly used for coating of paper and paperboard with higher efficiency. The efficiency of short-dwell blades coaters depends on many factors such as the properties of the coating material, design of the coating reservoir, the types of flow behaviour taking place inside the reservoir, etc. In this work, we have proposed an optimal design of the reservoir to improve the efficiency of short-dwell coaters. The reservoir has been modeled as flow inside a two-dimensional rectangular cavity.
Incompressible Navier-Stokes equations in primitive variable formulation have been solved to obtain the flow fields inside the cavity. Spatial derivatives present in the momentum, and continuity equations are evaluated using a sixth-order accurate compact scheme whereas the temporal derivatives are calculated using the fourth-order Runge-Kutta method.
The actual rate of convergence of the numerical scheme has been discussed in detail. In addition, the accuracy and stability of the used numerical method are also analysed in the spectral plane with the help of amplification factor and group velocity contour plot. The obtained numerical solutions have been validated with the existing literature.
In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a form-invariance symmetry, which is arising from the form invariance transformation. It is shown the method of getting potential and the scalar field for the power law scale factor.
JC Ndogmo. A method for the group classification of differential equations we recently proposed is applied to the classification of a family of generalized Klein-Gordon equations. Our results are compared with other classification results of this family of equations labelled by an arbitrary function. Some conclusions are drawn with regards to the effectiveness of the proposed method. Lin Wang.
The mechanical properties of additively fabricated metallic parts are closely correlated with their microstructural texture. Knowledge about the grain evolution phenomena during the additive manufacturing process is of essential importance to accurately control the final structural material properties.
In this work, a two-dimensional model based on the cellular automata method was developed to predict the grain evolution in the selective laser melting process. The effectiveness of this presented model is proven by comparing the simulated and reported results. The influence of process parameters, like the scanning strategy, laser power, and scanning speed, on the microstructural grain morphology, are numerically evaluated. Karyev , V. Fedorov and A.
A theoretical study of the behaviour of atomic planes in an elastic single-crystal rod under the action of volumetric forces such as the inertial force and the force of gravity has been carried out. The regularity of the linear distribution density of atomic planes in a single-crystal rod has been established in frames of continuous and discrete approaches.
The obtained distribution function is of independent interest, and it can be used, for example, in studying the behaviour of a metal rod under conditions of an external induced electric field. In this work, we consider a homogeneous and isotropic cosmological model of the universe in f T, B gravity with non-minimally coupled fermionic field.
The results obtain are coincide with the observational data that describe the late-time accelerated expansion of the universe. A Samoletov and B Vasiev. We propose a method for generating a wide variety of increasingly complex microscopic temperature expressions in the form of functional polynomials in thermodynamic temperature. The motivation for study of such polynomials comes from thermostat theory. The connection of these polynomials with classical special functions, in particular, with Appell sequences, is revealed.
It is shown that the narrow structures of the nonlinear resonance spectra resonances of electromagnetic-induced transparency and absorption and the processes forming them are determined by the direction of the light wave polarizations, degree of openness of the atomic transition, and the saturating wave intensity. The conditions under which the nonlinear resonance is exclusively coherent, due to the magnetic coherence of transition levels, are revealed.
A blowitz and Z. Also the explicit and different seed solutions are constructed by using Darboux transformation. Shaikhova , B. Rakhimzhanov and Zh. This equation is integrable and admits Lax pair. To obtain travelling wave solutions the extended tanh method is applied. This method is effective to obtain the exact solutions for different types of nonlinear partial differential equations.
Graphs of obtained solutions are presented. The derived solutions are found to be important for the explanation of some practical physical problems. The main idea and purpose of the work donewas to create a mathematical model and find a particular solution for the scale factor a, since it describes the dynamics of the evolution of the Universe.
Describes new materials and upgrades to older materials that exhibit optical, optoelectronic and semiconductor behaviors.
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