Multi-stable cylindrical lattices

We present a cylindrical lattice structure that mimics the behaviour of the virus bacteriophage T4 in having two (or more) stable states which differ in their radii and length. While the virus achieves bistability through molecular mechanisms we use composite materials to exploit the interplay between pre-stress, material properties and structural geometry. We demonstrate (computationally) that multi-stability is a robust phenomenon. We also show (analytically) that it is possible to choose the design variables so that the energy is independent of the radius, thus resulting in every state of the structure being stable.     

Laser marked shadowgraphy: a novel optical planar technique for the study of microbubbles and droplets

A novel combination of backlighting and glare point velocimetry and sizing (GPVS) is proposed to measure the size distribution of microbubbles (or microdroplets). This new technique, which we will call laser marked shadowgraphy, avoids sizing out-of-focus bubbles (or droplets) and the associated bias error. Compared to backlighting, this combination also improves the precision of the diameter measurement and allows void fraction measurements. Compared with GPVS, a more robust image processing is obtained. The applicability of the developed technique is demonstrated on a cloud of electrochemically generated hydrogen bubbles.     

Cosserat elastic lattices

Meccanica - Lattices composed of cubic and triangular prismatic unit cells with polymeric Sarrus linkage rib elements are designed, fabricated via 3D printing and studied experimentally. Size...     

Weak martensitic transformations in bravais lattices

Dedicated to B. D. Coleman, on the Occasion of His Sixtieth Birthday     

Localized transition waves in bistable-bond lattices

Discrete two-dimensional square- and triangular-cell lattices consisting of point particles connected by bistable bonds are considered. The bonds follow a trimeric piecewise linear force-elongation diagram. Initially, Hooke's law is valid as the first branch of the diagram; then, when the elongation reaches the critical value, the tensile force drops to the other. The latter branch can be parallel with the former (mathematically this case is simpler) or have a different inclination. For a prestressed lattice the dynamic transition is found analytically as a wave localized between two neighboring lines of the lattice particles. The transition wave itself and dissipation waves carrying energy away from the transition front are described. The conditions are determined which allow the transition wave to exist. The transition wave speed as a function of the prestress is found. It is also found that, for the case of the transition leading to an increased tangent modulus of the bond, there exists nondivergent tail waves exponentially localized in a vicinity of the transition line behind the transition front. The previously obtained solutions for crack dynamics in lattices appear now as a partial case corresponding to the second branch having zero resistance. At the same time, the lattice-with-a-moving-crack fundamental solutions are essentially used here in obtaining those for the localized transition waves in the bistable-bond lattices. Steady-state dynamic regimes in infinite elastic and viscoelastic lattices are studied analytically, while numerical simulations are used for the related transient regimes in the square-cell lattice. The numerical simulations confirm the existence of the single-line transition waves and reveal multiple-line waves. The analytical results are compared to the ones obtained for a continuous elastic model and for a related version of one-dimensional Frenkel-Kontorova model.     

Self-propelling,coalescing droplets

This work proposes and explores a new propulsion mechanism for sessile droplets which could be of interest for microfluidic applications. This mechanism relies on the Marangoni stresses resulting from the surface tension gradient arising when two droplets of different surface tensions coalesce. We argue that the tendency of the fluid to flow towards regions of higher surface tension is sufficient to displace the droplet. The coalescence of two miscible, partially wetting droplets with different surface tensions is investigated theoretically in this paper and modeled in the lubrication approximation framework. The problem is described by a set of three highly non-linear, coupled partial differential equations which is solved with a commercial finite element code. The analysis reveals two important dimensionless numbers which govern the flow characteristics, one related to the strength of the surface tension gradient and the other to the diffusion time scale. The numerical results confirm the occurrence of the self-propulsion behavior and a parametric study is performed to explore the role of the two dimensionless numbers on the propulsion speed and the total displacement. Unsurprisingly, self-propulsion is enhanced for larger values of the surface tension contrast between the two droplets and smaller values of the diffusion time scale which results in more time for the surface tension gradient to act.     

On the number of droplets in aerosols

The number of droplets which may be formed with a supersaturated vapor in presence of a gas cannot exceed a number proportional to (p_v−p_v0)⁴ where p_v and p_v0 denote at the same temperature the pressure of the supersaturated vapor–gas mixture and the pressure of the saturated vapor–gas mixture. The energy necessary to the droplet formation is also bounded by a number proportional to (p_v−p_v0)².     

Hysteresis in multi-stable lattices with non-local interactions

We study a model for martensitic phase transitions represented by a lattice of mass points connected by bi-stable nearest neighbor (NN) springs and harmonic next to nearest neighbor (NNN) springs. Our main assumption of weak NNN interactions allows us to obtain a fully analytical representation of the quasistatic evolution of the overdamped system, including both the ‘non-local’ interaction with the external load and the presence of imperfections.This simple model reproduces the experimental observation of different evolution strategies, with internal or boundary nucleation and with the possibility of one or more coherently propagating phase fronts. The model describes also the observation of a Peierls stress higher or lower than the nucleation stress. We show that all these properties are also preserved in the ‘continuum’ limit.     

Periodic solutions in one-dimensional coupled map lattices

IntroductionDynamicsofcoupledmaplattices (CML )haverecentlyattractedconsiderableattention[1- 4].IthasbeenfoundthatCMLsexhibitavarietyofspace_timepatterns:space_timeintermittency ,spatiotemporalchaos,frontsandinterfaces,nonlinearperiodicsolutions.Inthispaper,anone_dimensionalinfinitechainofnonlinearcoupledmapsisconsideredandtheexistenceofperiodicsolutionsisprovedwhenthecouplingstrengthαissmallenough .Ourapproachistheanti_integrablelimitintroducedinRefs.[5-7] .Intheanti_integrablelimit(coup…     

Initial tension in randomly disordered periodic lattices

This paper is concerned with probabilistic analysis of initial member stress in geometrically imperfect regular lattice structures with periodic boundary conditions. Spatial invariance of the corresponding statistical parameters is shown to arise on the Born-von Kármán domains. This allows analytical treatment of the problem, where the parameters of stress distribution are obtained in a closed form. Several benchmark problems with beam- and plate-like lattices are considered, and the results are verified by the direct Monte–Carlo simulations. Behaviour of the standard deviation as a function of lattice repetitive cell number is investigated, and dependence on the lattice structural redundancy is pointed out.     

Bifurcation and Martensitic transformations in Bravais lattices

Behavior of crystalline solids exhibiting shape memory effects seems to be associated with special kinds of Martensitic transformations, near which some linear elastic moduli are small compared to others. This work explores the possibility of interpreting this in terms of special kinds of bifurcations.This work was supported by AFOSR/XOP and NSF, under NSF grant DMS-8842048.     

Adhesion of oriented nematic droplets

We propose and analyze a two-dimensional model for the equilibrium of oriented droplets of nematic liquid crystals that may adhere to a rigid substrate, while surrounded by an isotropic environment. We obtain the contact condition at the edge where the liquid crystal, the substrate, and the environment come together. We further develop a fairly general method to arrive at the equilibrium shapes of a drop, which is then applied to the case where the surface tension at the liquid crystal interface is given by Rapini and Papoular's expression. In this case, we also predict the existence of concave equilibrium shapes. Here is indeed the main difference between this method and Wulff's construction, which always yields convex equilibrium shapes for a drop free from adhesion. Received February 22, 2000     

Mechanics of hexagonal atomic lattices

A theoretical framework for describing the kinematics and energetics of hexagonal atomic lattices, including planar carbon graphene sheets and cylindrical nanotubes, is proposed. By analogy with the membrane theory of thin shells, the deformation of the particulate lattice in the neighborhood of each atom is described in terms of a uniquely defined deformation gradient and companion local inner displacement. Expressions for the pointwise tensions developing in the plane of the lattice are developed, and a rational procedure for deriving discrete equilibrium equations is discussed. An alternative formulation involving the second-order deformation gradient that parallels the strain gradient theory of bulk media is proposed, and a tentative analogy with a the theory of micropolar elastic media is outlined.     

Stability of moving soliton lattices

A quasistationary dynamic state of such systems as a long Josephson junction, a superconducting film of periodically modulated thickness and some others is known to be a sequence of regularly spaced solitons moving with a constant velocity. Corresponding self-similar solutions of the nonconservative sine-Gordon equation are investigated. Their stability and a small oscillation spectrum are analyzed. Current-voltage characteristics are obtained for the case of coherent oscillations.     

Modeling of strongly nonlinear effects in diatomic lattices

A previously developed strongly nonlinear continuum model for diatomic crystals is examined using continuum limit of a discrete diatomic model. It suggested suitable expression for the forces in the discrete model; however, its continuum limit not only explains the nonlinear terms continuum model but also gives rise to some additional terms. It turns out that one of them supports bell-shaped localized variations in the diatomic material but suppresses kink-shaped variations.     

Synchronization in delayed map lattices with scale-free interactions

In this paper, we study synchronization of delayed map lattices with scale-free interactions. By numerical simulations and theoretical analysis, we find that time delays influence the network synchronization but the heterogeneity seems to have little effect on network synchronization, yet no synchronization happens with the homogeneously topological structures.     

Binary collision dynamics of fuel droplets

An experimental study has been carried out in which the collision dynamics of two n-haxane fuel droplets are studied. The experiments are performed on the collision of two burning droplets, as well as two nonburning droplets, to assess the influence of the high temperature combustion environment on the dynamics of the collision.The results indicate that as the Weber number is increased, the collision type moves toward higher energy collision, and for the same Weber number, different types of collisions, depending on the local value of the collision impact parameter, may occur. In the range of the Weber numbers studied, the results show that for the nonburning droplets, the collision type can be bouncing, grazing, temporary coalescence-satellite generating, or permanent coalescence, depending on the local value of the impact parameter. For the burning droplets in the same initial Weber number range, only temporary coalescence and permanent coalescence are observed.