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.     

Can a single-wall carbon nanotube be modeled as a thin shell?

Single-wall carbon nanotubes (SWCNT) have been frequently modeled as thin shells, but the shell thickness and Young's modulus reported in literatures display large scattering. The order of error to approximate SWCNTs as thin shells is studied in this paper via an atomistic-based finite-deformation shell theory, which avoids the shell thickness and Young's modulus, but links the tension and bending rigidities directly to the interatomic potential. The ratio of atomic spacing (Δ≈0.14 nm) to the radius of SWCNT, Δ/R, which ranges from zero (for graphene) to 40% [for a small (5,5) armchair SWCNT (R=0.35 nm)], is used to estimate the order of error. For the order of error O[(Δ/R)³], SWCNTs cannot be represented by a conventional thin shell because their constitutive relation involves the coupling between tension and curvature and between bending and strain. For the order of error O[(Δ/R)²], the tension and bending (shear and torsion) rigidities of SWCNTs can be represented by an elastic orthotropic thin shell, but the thickness and elastic modulus cannot. Only for the order of error O(Δ/R), a universal constant shell thickness can be defined and SWCNTs can be modeled as an elastic isotropic thin shell.     

Who conceived the “complex viscosity”?

In small amplitude oscillatory shear flow, we now universally represent the response of a viscoelastic fluid as a complex quantity, which we call “complex viscosity.” This short piece deepens our understanding of the origins of the complex viscosity and of the man who coined this term, now widely used in rheology.     

Can Moderately Rarefied Gas Transport Through Round and Flat Tight Channels of Fractured Porous Media be Described Accurately?

We study the generation and flow of foam through rough-walled, fractured marble rocks that mimic natural fracture systems in carbonate reservoirs. Flow was isolated to the fracture network because of the very low rock permeability of the marble samples and foam generated in situ during co-injection of surfactant solution and gas. The foam apparent viscosities were calculated at steady pressure gradients for a range of gas fractions, and similar to foam flow in porous media, we identified two flow regimes for foam flow in fractures: a high-quality flow regime only dependent on liquid velocity and a low-quality flow regime determined by the gas and liquid velocities. Variations in local fluid saturation during co-injection were visualized and quantified using positron emission tomography combined with computed tomography.

     

Why monotonous and non-monotonous steady-flow curves can be obtained with the same non-Newtonian fluid? A single explanation

We show that a pronounced variation of the apparent viscosity with shear joined to the control shear mode of a rheometer can justify why monotonous and non-monotonous steady-flow curves can be obtained testing the same non-Newtonian fluid.     

Can We Hear the Echos of Cracks?

The detection of cracks in mechanical engineering is mainly based on ultrasonic testing and Foucault currents. But even if they are efficient tools, this technology requires an important handling and is limited to the detection of cracks which are close to the source. Recently, several searchers have discussed the possibility of using waves as Lamb waves, for thin plates and shells, but also Love waves for bimaterials. In both cases the structure works as a wave guide and enables a long range propagation which is a promising possibility for detecting a crack quite far from the source. In this paper, we discuss the observability property of a small crack inside an open set using Love waves (the goal is to detect the beginning of the growth). It is proved that an adapted selection of these waves is necessary in order to avoid a black out which can occur for particular frequencies. This phenomenon is due to the fact that the crack has two extremities which can cancel their influence in a detection criterion. The main contribution of this paper is to discuss this point from a mathematical point of view, using an energy criterion requiring measurements quite far from the defect which should be detected.     

Nonlinear stability analysis of the Bénard problem for fluids with a convex nonincreasing temperature depending viscosity

A nonlinear energy stability analysis of the onset of convection for fluids with viscosity convex nonincreasing function of temperature, is performed. It is shown that condition assuring linear stability, assures nonlinear (conditional) asymptotic stability too.     

Can one measure the temperature of a curve?

The entropy of a plane curve is defined in terms of the number of intersection points with a random line. The Gibbs distribution which maximizes the entropy enables one to define the temperature of the curve. At 0 temperature, the curve reduces to a straight segment. At high temperature, the curve is somewhat chaotic and behaves like a perfect gas. We attempt to show that thermodynamic formalism can be used for the study of plane curves. The curves we discuss have finite length, unlike Mandelbrot's fractal curves [1], yet we feel our approach to the mathematics is not far from his.     

Can dynamical mechanical measurements predict brittle fracture behaviour?

The uptake of water by low moisture cereal products can have detrimental effects on their texture, and cause loss of quality. Following the interest in developing techniques suitable for determining texture properties, there has also been a move towards identifying the origins of the observed changes. Although the origins of the hydration effects are not fully understood, dynamic rheology is believed to be a suitable technique for characterising mechanical properties, and for identifying the origins of the features observed after moisture pick-up. In a previous paper, the sensory crispness of white bread and of extruded flat bread were correlated with tan, through the increase in tan resulting from the increased hydration associated with loss of crispness. The present work shows that such a correlation does not exist with extruded starch-sugar samples. This means that tan data cannot be used to predict fracture properties like those covered by crispness. The information revealed by the results did, however, address various questions about the significance of tan. Indeed, the increase in tan with increasing hydration was shown to be particularly acute when the starch was mixed with sugar (sucrose or fructose). In order to interpret these results several hypotheses have been suggested, including increased heterogeneity of the systems, and sensitivity of tan to solute mobility or to localised motions of the matrix.     

Can Hamilton energy feedback suppress the chameleon chaotic flow?

Nonlinear Dynamics - The dynamical behaviors of nonlinear systems are much dependent on the parameter setting and nonlinear terms, and some controllable parameters can be adjusted to modulate the...     

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.     

Are waves with negative spatial damping unstable?

Conventional plane harmonic waves decay in direction of propagation, but unconventional harmonic waves grow in the direction of propagation. While a single unconventional wave cannot be a solution to a physically meaningful boundary value problem, these waves may have an essential contribution to the overall solution of a problem as long as this is a superposition of unconventional and conventional waves. A fourth order diffusion equation with proper thermodynamic structure, and the Burnett equations of rarefied gas dynamics exhibit conventional and unconventional waves. Steady state oscillating boundary value problems are considered to discuss the interplay of conventional and unconventional waves. Results show that as long as the second law of thermodynamics is valid, unconventional waves may contribute to the overall solution, which, however is dominated by conventional waves, and behaves as these.     

Statistical distributions and self-organizing phenomena: what conclusions should be drawn?

Some salient properties of the inverse power law distribution, the exponential distribution, catastrophe distributions, and the relationships among them were explored and compared. Self-organizing events may display any of these distributions. Catastrophe functions and their distributions do not display fractional (fractal) dimensions. Thus it is possible to have self-organization without the fractal. An empirical example from leadership emergence research illustrated a situation where a power law distribution provided a poor characterization of the data, but a swallowtail catastrophe model did so quite well. The results call into question some simplistic assumptions about the relationships among fractals, inverse power laws, self-organization and so-called pink noise.     

Adaptive bidirectionally coupled synchronization of?chaotic?systems with unknown parameters

This paper investigates the chaos synchronization of two bidirectionally coupled chaotic systems. In comparison with previous methods (identical bidirectionally coupled synchronization), the present control scheme is different bidirectionally coupled synchronization, which includes different complete bidirectionally coupled synchronization and different partial bidirectionally coupled synchronization. Based on the Lasalle invariance principle, adaptive schemes are designed to make two different bidirectionally coupled chaotic systems asymptotically synchronized, and unknown parameters are identified simultaneously in the process of synchronization. Theoretical analysis and numerical simulations are shown to verify the results.     

Controlling Hopf�CHopf interaction bifurcations of?a?two-degree-of-freedom self-excited system with?dry?friction

The feedback control problem of designing Hopf?CHopf interaction bifurcations into a dry friction system at a pre-specified parameter point is addressed. A new bifurcation criterion without using eigenvalues is established to preferably determine the control gains. Numerical simulation shows that the torus solution of Hopf?CHopf interaction bifurcation can be created in the friction system at a desired parameter location.     

Dynamics of three coupled limit cycle oscillators with?vastly?different frequencies

A system of three coupled limit cycle oscillators with vastly different frequencies is studied. The three oscillators, when uncoupled, have the frequencies ?? ₁=O(1), ?? ₂=O(1/??) and ?? ₃=O(1/?? ²), respectively, where ???1. The method of direct partition of motion (DPM) is extended to study the leading order dynamics of the considered autonomous system. It is shown that the limit cycles of oscillators 1 and 2, to leading order, take the form of a Jacobi elliptic function whose amplitude and frequency are modulated as the strength of coupling is varied. The dynamics of the fastest oscillator, to leading order, is unaffected by the coupling to the slower oscillator. It is also found that when the coupling strength between two of the oscillators is larger than a critical bifurcation value, the limit cycle of the slower oscillator disappears. The obtained analytical results are formal and are checked by comparison to solutions from numerical integration of the system.