On the Oval Shapes of Beach Stones

This article introduces a new stochastic non-isotropic frictional abrasion model, in the form of a single short partial integro-differential equation, to show how frictional abrasion alone of a stone on a planar beach might lead to the oval shapes observed empirically. The underlying idea in this theory is the intuitive observation that the rate of ablation at a point on the surface of the stone is proportional to the product of the curvature of the stone at that point and the likelihood the stone is in contact with the beach at that point. Specifically, key roles in this new model are played by both the random wave process and the global (non-local) shape of the stone, i.e., its shape away from the point of contact with the beach. The underlying physical mechanism for this process is the conversion of energy from the wave process into the potential energy of the stone. No closed-form or even asymptotic solution is known for the basic equation, which is both non-linear and non-local. On the other hand, preliminary numerical experiments are presented in both the deterministic continuous-time setting using standard curve-shortening algorithms and a stochastic discrete-time polyhedral-slicing setting using Monte Carlo simulation.

Determination of Parameters of Electronic Devices by the Method of Passive Radio-Sensor Technical Diagnostics

Introduction. Technical diagnostics (TD) as a nascent discipline is rapidly developing in the field of both software and hardware. Modern TD methods, such as vibrometry, thermal control, JTAG testing and optical control, either exhibit high inertia, consume processor time, require suspension of the electronic device, or demand a galvanic contact with the study object, which is often unacceptable. These disadvantages can be eliminated by passive radio-sensor TD. To date, little information has been published on the parameters of electronic devices provided by this method.Aim. Determination of the parameters of electronic devices, the assessment of which can be provided by passive radio-sensor TD.Materials and methods. Signal radio profiles were obtained experimentally using metrological equipment and software-numerical methods for modeling radio wave processes. The parameters of the signal radio profile were calculated by a mathematical method for solving differential equations.Results. The main principles and results of radio-sensor TD, as well as the simplest toolkit, are shown. An equation is obtained for the signal radio profile emitted by the electronic unit of the device, as well as an expression for its free components. An approach for assessing the TD correctness based on the number of free components of the received signal radio profile and the reference is described. The possibility of obtaining information about temperature, voltage drop, speed of emitting nodes, as well as the state of its components and modes of operation of p–njunctions is demonstrated. It is shown that this information is carried by the parameters of the basic equation for the signal radio profile.Conclusion. The derived basic equation allows a non-contact, remote passive radio-sensor TD to be conducted by correlation analysis of the received signal, providing a detailed examination of malfunctions in each electronic unit. The described TD method based on the presented parameters is promising for assessing the technical state of electronic devices.

FUNCTIONAL DAMAGE OF RADIO ELECTRONIC SYSTEMS

Purpose: The most important problem of any state is protection of the control and management systems used for the country, national armed forces, high-risk facilities (nuclear power plants, large chemical plants, airports, etc.). Here, the fact that the means of attack can be deployed on ballistic and cruise missiles, aircraft, and drones should be accounted for. The flight altitude of these vehicles varies from ≈300 km to ≈ 10 m. Any attack vehicle is equipped with complex avionics consisting of circuit elements sensitive to electromagnetic fields. Since the 1980s, a new scientific and engineering direction has been developing, being termed as a “functional damage to avionics”. It is based on the creation of powerful means of electromagnetic radiation possessing the energetic capabilities of incapacitating avionics at significant distances (from ~ 100 m to ~ 1000 km). The purpose of this work is to analyze the possible functional damage to avionics with account for the tendencies in avionics technologies. Design/methodology/approach: The analysis is made on the capability of inflicting functional damage to avionics accounting for the modern trends in developing the powerful means of electromagnetic energy generation in the microwave and shorter wavelength ranges, miniaturization and integration of avionics circuit elements. The regression is constructed for the critical energy time dependence. It has been determined that for decades the critical energy required to damage the circuit elements shows a tendency to decrease. This is due to the further miniaturization and integration of microcircuits according to the Moore’s law, which is still valid for now. For a number of circuit elements, the critical energy is found to be in the range of 10-11–10-10 J. At the same time, a reverse tendency arises to protect avionics from being functionally damaged. In this case, the critical energy makes 10-7–10-6 J and greater. From the derived version of the basic equation of functional damage to avionics, the maximum distance at which the damage is possible with the energetics of the existing radio systems is estimated. For the ground-based facilities, this distance can attain hundreds of kilometers. For mobile vehicles, it can reach 10–100 km. Combining target detection, identification and avionics damage capabilities in one radio system has been validated and advised. The transition from the first mode of operation to the second one occurs at shorter distances with an increase of 2–3 orders of magnitude in the pulse energy. Findings: The regression equation has been obtained for the time dependence of the critical energy required for inflicting functional damage to avionics. Its constant decrease has been confirmed. Such a behavior is closely related to the Moore’s law, which characterizes the degree of miniaturization and integration of avionics circuit elements. It has been predicted that for a number of instruments the critical energy can be smaller than 10-11–10-10 J. A version of the basic equation of functional damage to avionics has been obtained. The maximum distance for a modern radio system to damage the avionics has been shown to attain many hundreds of kilometers. For the radio systems installed on mobile vehicles, this distance makes 10–100 km. Target detection, tracking and identification, as well as avionics damage capabilities, have been proved to be rationally combined in one radio system. To cause damage at a corresponding range, the pulse energy needs to be increased by a factor of 102–103. Conclusions: There are all science and technology prerequisites for developing effective radio systems inflicting functional damage to avionics and for the state defense and protection, armed forces, and high-risk facility controlling systems. Key words: functional damage; avionics; critical energy; Moore’s law; functional damage equation; radiolocation equation; detection and destruction range

Singularly Perturbed Solutions for a Class of Thermoelastic Weakly Coupled Problems

Based on the basic equation of Green Lindsay (G-L) theory, the thermoelastic weak coupling problem under the basic equation is discussed, that is, two thermal relaxation parameters are added to the constitutive equation, the influence of the coupling term on the temperature field and elastic field is considered, and the asymptotic solution of the governing equation is constructed. Firstly, in order to obtain the asymptotic solution, the singularly perturbed expansion method is used.Then,combined with the corresponding boundary conditions, the partial differential equation method is used to solve the external solution and the boundary layer correction term. Secondly, in the case of weak coupling, the uniformly efficient estimation of the remainder of the asymptotic solution is obtained by using Gronwall inequality, so as to obtain the uniformly efficient of the formal asymptotic solution. Finally, the first term of the asymptotic solution is numerically analyzed by using the singularly perturbed numerical method. The present work will be conducive to the analysis of thermoelastic processes and numerical simulation of different materials in the case of weak coupling.

Hydrodynamic Analysis of 3D Hydrofoil Using Nonuniform Rational B-Spline and Boundary Element Method

In this paper, two different 3D hydrofoils with profiles NACA0012 are simulated in the potential flow. Boundary element method (BEM) and nonuniform rational B-spline (NURBS) are coupled to reduce error and increase accuracy. The computer code is developed in different submergence depths (d), flow velocities (U), and various angles of attack (AoA), and the pressure is obtained by NURBS formulation. The pressure on a 3D hydrofoil with NACA412 profile iscompared with other existing methods. The validity of result is revealed. The accuracy of the results is acceptable. The competition of the two models’ results indicates that the increasing chord length leads to increase in C p min , and the decrease in depth and angle of attack leads to the growing value of C p min . Moreover, when the flow velocity is changed, the changes of potential and pressure coefficient distribution do not follow the specific trend. NURBS is a basic equation in different CAD packages because it is able to mesh surfaces. This study demonstrates that this algorithm does mesh surface of high quality, so it can be developed to generate mesh on the submerged three-dimensional bodies .

A collocation method for the Williams equation with Chebyshev polynomials

The linearized problem of gas flow in plane channel with infinite walls has been solved in the kinetic approximation. The flow in the channel is caused by a constant pressure gradient parallel to the walls of the channel. The Williams equation has been used as a basic equation, and the boundary condition has been set in terms of the diffuse reflection model. The collocation method for Chebyshev polynomials has been applied to construct the solution of the equation of Williams with the given boundary conditions. The mass flux of the gas in the channel has been calculated.

Kinetic Modeling and Algorithm of Three-Component Reaction Network

The definite solutions of the differential equations from a three-component triangle reaction network have been obtained by utilizing the concept of virtual component concentration and some mathematical techniques. The kinetic model forming from the above definite solutions reveals that the overall reaction rate will be affected by the distribution entropy of the rate coefficients. The improved eigenvector method including a basic equation, algorithm, and criterion has been proposed for calculating the rate coefficients from experimental concentration curves.

Appearance of Thermal Time

In this paper a viewpoint that time is an informational and thermal entity is presented. We consider a model for a simple relaxation process for which a relationship among event, time and temperature is mathematically formulated. It is then explicitly illustrated that temperature and time are statistically inferred through measurement of events. The probability distribution of the events thus provides an intrinsic correlation between temperature and time, which can relevantly be expressed in terms of the Fisher information metric. The two-dimensional differential geometry of temperature and time then leads us to a finding of a simple equation for the scalar curvature, $$R = -1$$ R = - 1 , in this case of relaxation process. This basic equation, in turn, may be regarded as characterizing a nonequilibrium dynamical process and having a solution given by the Fisher information metric. The time can then be interpreted so as to appear in a thermal way.

Basic Equation for the Different Coupled Equations between the First and Second Laws of Thermodynamics at Strong Coupling

For some physical processes, the first and second laws of thermodynamics can be at strong coupling. Also, it is possible that the familiar inequalities of macroscopic thermodynamics cannot be used in the analysis of the system, and it is needed that the inequalities rewrote as equalities. In these cases, the work, internal energy, dissipated energy, and entropy production must be considered and identified together. In this paper, the basic equation for the different coupled equations between the first and second laws of thermodynamics at strong coupling is extracted. Also, inspired by the first and second laws of thermodynamics and different approaches to the second law, a thermophysical equation for thermodynamics is extracted. This equation can be used instead of the first and second laws of thermodynamics as to the analysis of the performed process these laws must be established together. It is tried that effective internal energy, directly to be related to the entropy or vice versa, in one general equation. Also, the presented equation is in the same line with the different approaches to the second law and energy structure theory.