Can a monkey with a computer create art?

A computer can be programmed to search through the solution of millions of equations to find a few hundred whose graphical display is aesthetically pleasing to humans. This paper describes some methods for performing such an exhaustive search, criteria for automatically judging aesthetic appeal, and examples of the results.     

Flow of a Viscoplastic Fluid on a Rotating Disk

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Flexural-wave-generation using a phononic crystal with a piezoelectric defect

This paper proposes a method to amplify the performance of a flexural-wave-generation system by utilizing the energy-localization characteristics of a phononic crystal(PnC) with a piezoelectric defect and an analytical approach that accelerates the predictions of such wave-generation performance. The proposed analytical model is based on the Euler-Bernoulli beam theory. The proposed analytical approach, inspired by the transfer matrix and S-parameter methods, is used to perform band-structure an...     

Stability and Self‐Oscillations of a Rotor Containing a Conducting Liquid in a Magnetic Field

This paper considers the problem of the stability in the small of the steadystate spinning of a rotor with a cylindrical cavity partly filled with a viscous, incompressible, conducting liquid in a magnetic field. The responses of the buttend boundary layers and the resultant force exerted by the liquid on the rotor performing circular precession of small radius are determined. The plane of the viscoelastic restraint parameters of the rotor axis was Dpartitioned into regions with different degrees of instability is constructed. Steadystate spinning near the boundary of the region of stability in the space of parameters is studied assuming nonlinear responses of the supports. It is shown that passage through the boundary of the region of stability leads to bifurcation of the steadystate spinning regime, resulting in periodic motion of the type of circular precession. The origin ofperiodic motion from steadystate spinning can be subcritical or supercritical.     

Oscillations of a?beam with a?time-varying mass

This paper analyzes dynamical behavior of a simply supported Euler?CBernoulli beam with a time-varying mass on its surface. Though the system under consideration is linear, it exhibits dynamics similar to a nonlinear system behavior including internal resonances. The asymptotical solutions for the beam displacement has been found by combining the classical Galerkin method with the averaging method for equations in Banach spaces. The resonance conditions have been derived. It has been proposed a method for finding a number of possible resonances.Effect of the beam parameters on its dynamical behavior is investigated as well.     

Nonlinear analysis of a structure loaded by a stochastic excitation

For a non-linear system excited by a stochastic load which is expressed as a time series,a recursive method based on the Z-transform is presented.To identify the obtained response time series,a discrete wavelet transform (DWT) technique is proposed.     

Shock Compression of a Plate on a Wedged–Shaped Target

Problems of compression of a plate on a wedge–shaped target by a strong shock wave and plate acceleration are studied using the equations of dissipationless hydrodynamics of compressible media. The state of an aluminum plate accelerated or compressed by an aluminum impactor with a velocity of 5—15 km/sec is studied numerically. For a compression regime in which a shaped–charge jet forms, critical values of the wedge angle are obtained beginning with which the shaped–charge jet is in the liquid or solid state and does not contain the boiling liquid. For the jetless regime of shock–wave compression, an approximate solution with an attached shock wave is constructed that takes into account the phase composition of the plate material in the rarefaction wave. The constructed solution is compared with the solution of the original problem. The temperature behind the front of the attached shock wave was found to be considerably (severalfold) higher than the temperature behind the front of the compression wave. The fundamental possibility of initiating a thermonuclear reaction is shown for jetless compression of a plate of deuterium ice by a strong shock wave.     

Entrance of a body with a lifting force and a heat‐conducting surface into the earth's atmosphere

The problem of gliding descent of a smooth blunted body possessing a lifting force and a heatconducting surface in the Earth's atmosphere is solved. The descent trajectory is represented not only by the altitude and velocity as functions of the flight time but also by angles of attack and sideslip varying with time. Threedimensional equations of a parabolized viscous shock layer for a multispecies mixture of gases are solved jointly with a threedimensional equation of unsteady heat conduction in the solid phase.     

Paradox of a particle’s trajectory moving on a string

This paper deals with the paradoxical properties of the solution of string vibration under a moving mass. The solutions published to date are not simple enough and cannot be applied to investigations in the entire range of mass speeds, including the overcritical range. We propose a formulation of the problem that allows us to reduce the problem to a second-order matrix differential equation. Its solution is characteristic of all features of the critical, subcritical, and overcritical motion. Results exhibit discontinuity of the mass trajectory at the end support point, which has not been previously reported in the literature. The closed solution in the case of a massless string is analyzed and the discontinuity is proved. Numerical results obtained for an inertial string demonstrate similar features. Small vibrations are analyzed, which is why the effect discussed in the paper is of purely mathematical interest. However, the phenomenon results in complexity in discrete solutions.     

Resonance Waves in a Model of a Two‐Layered Liquid

With allowance for surface interaction between phases, the behavior of longwave perturbations at the interface between two layers of dissimilar liquids, which form resonance triplets described by a pseudodifferential equation, is studied.     

Flow of a Weakly Conducting Fluid in a Channel Filled with a Darcy–Brinkman–Forchheimer Porous Medium

We investigate in this article, the fully developed flow in a fluid-saturated channel filled with a Darcy–Brinkman–Forchheimer porous medium, which is conducted with an electrically varying parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. With the homotopy analysis method (HAM), a particularly effective technique in solving nonlinear problems, analytical approximation series solutions with high accuracy are derived for fluid velocity and the results are illustrated in form of figures. All these flows are new and are presented for the first time in the literature.     

Relaxation of a Low‐Intensity Atomic Beam in a Quiescent Gas

Relaxation of a lowintensity atomic beam in a gas at rest is examined by means of numerical modeling with the method of test particles. Temperaturefield features in the mixing region are considered. A relation between the relaxation length and the initial velocity and mass of injected particles is obtained. Conditions are found under which the relaxation length is minimal.     

Viscosity of a Dilute Suspension in a High‐Frequency Electromagnetic Field

The action of a highfrequency electromagnetic field on a dilute suspension of spherical particles with a constant dipole moment is studied using statistical mechanics. An expression for effective viscosity is obtained. It is shown that the shear viscosity of the dilute suspension depends on the frequency, magnitude, and direction of the highfrequency electromagnetic field. Depending on the frequency of the highfrequency electromagnetic field, the rotation of the suspension particles is decelerated or accelerated, with the viscosity increasing or decreasing, respectively. It is shown that the acceleration of the suspension particles by a highfrequency electromagnetic field and, hence, the decrease in shear viscosity has a resonant nature.     

Mindlin??s Problem for a Halfspace Indented by a Flexible Plate

The paper deals with a contact problem for an isotropic elastic halfspace indented by a flexible circular plate and simultaneously subjected to a Mindlin-type axial force. The approach adopted is to solve the contact problem for the flexible circular plate and the elastic halfspace; this serves as the auxiliary solution to examine, via the Maxwell-Betti reciprocal theorem, the influence of the internal Mindlin force. The contact between the flexible plate and the elastic halfspace is solved using a variational approach. The net displacement of the flexible circular plate and the internal Mindlin force can be evaluated in analytical form. The result has applications to the in situ evaluation of the deformability characteristics of geologic media.     

Large-Eddy BreakUp Devices – a 40 Years Perspective from a Stockholm Horizon

In the beginning of the 1980’s Large Eddy BreakUp (LEBU) devices, thin plates or airfoils mounted in the outer part of turbulent boundary layers, were shown to be able to change the turbulent structure and intermittency as well as reduce turbulent skin friction. In some wind-tunnel studies it was also claimed that a net drag reduction was obtained, i.e. the reduction in skin-friction drag was larger than the drag on the devices. However, towing-tank experiments with a flat plate at high Reynolds numbers as well as with an axisymmetric body showed no net reduction, but instead an increase in total drag. Recent large-eddy simulations have explored the effect of LEBUs on the turbulent boundary layer and evaluations of the total drag show similar results as in the towing tank experiments. Despite these negative results in terms of net drag reduction, LEBUs manipulate the boundary layer in an interesting way which explains why they still attract some interest. The reason for the positive results in the wind-tunnel studies as compared to drag measurements are discussed here, although no definite answer for the differences can be given.     

Propagation of a mode-III interfacial crack in a piezoelectric–piezomagnetic bi-material

The transient response of a semi-infinite mode-III interfacial crack propagating between piezoelectric (PE) and piezomagnetic (PM) half spaces is investigated in this paper. The integral transform method together with the Wiener–Hopf and Cagniard–de Hoop techniques is used to solve the mixed boundary value problem under consideration. The existence of generalized Maerfeld–Tournois interfacial wave is discussed and the solutions of the coupled fields are derived for four different cases of bulk shear wave velocity. The dynamic intensity factors of stress, electric displacement and magnetic induction as well as energy release rate (ERR) are obtained in explicit forms. The numerical results of the universal functions and dimensionless ERR for several different material combinations are presented and discussed in details. It is found that the Bleustein–Gulyaev (generalized Maerfeld–Tournois) waves dominate the dynamic characteristics of the interfacial crack propagation in PE–PM bi-material.     

Bifurcations of a creeping air–water flow in a conical container

This numerical study describes the eddy emergence and transformations in a slow steady axisymmetric air–water flow, driven by a rotating top disk in a vertical conical container. As water height \(H_{\mathrm{w}}\) and cone half-angle \(\beta \) vary, numerous flow metamorphoses occur. They are investigated for \(\beta =30^{\circ }, 45^{\circ }\), and \(60^{\circ }\). For small \(H_{\mathrm{w}}\), the air flow is multi-cellular with clockwise meridional circulation near the disk. The air flow becomes one cellular as \(H_{\mathrm{w}}\) exceeds a threshold depending on \(\beta \). For all \(\beta \), the water flow has an unbounded number of eddies whose size and strength diminish as the cone apex is approached. As the water level becomes close to the disk, the outmost water eddy with clockwise meridional circulation expands, reaches the interface, and induces a thin layer with anticlockwise circulation in the air. Then this layer expands and occupies the entire air domain. The physical reasons for the flow transformations are provided. The results are of fundamental interest and can be relevant for aerial bioreactors.     

Simulation of Wind Flow Around a Building with a k–ε Model

The three-dimensional numerical simulation of airflow around a building using a k–ε two-equation turbulence model is presented in this paper. Several cases of numerical simulation of airflow around a building are carried out to estimate the influence of mesh spacing on simulated results. The accuracy of simulations is examined by comparing the predicted results with wind-tunnel experiments. It is confirmed that numerical simulations by means of the k–ε model reproduce the velocity fields well when using fine mesh resolution. In the latter part of the paper, the simulation method is applied to predict the flow field around a building with different width-to-height ratios, under light wind conditions. Received 16 June 1999 and accepted 20 July 2000     

On a Turbulent Mixing Layer Created Downstream of a “Λ” Notch Simulating One Wavelength of a Chevron Nozzle

Measurements were carried out in a turbulent mixing layer formed downstream of a splitter plate, that had a Λ-shaped trailing edge. The results revealed that the center of the mixing layer shifts toward the high-speed flow while its sides bend toward the low speed stream at larger distances from the splitter plate. This suggests the existence of a counter rotating streamwise eddies that dominate the flow and substantially increase its level of turbulence relative to the classical plane mixing layer. The change in the orientation of the vorticity, emanating from a chevron nozzle, decreases the susceptibility of the flow to spanwise uniform periodic excitation relative to a classical plane mixing layer.     

Generalization of Joukowski’s Solution for a Bubble in a Channel

Fluid Dynamics - A new exact solution for the problem of potential flow of a capillary fluid past a two-dimensional bubble in a rectilinear channel is derived; the solution generalizes the known...