DNA nanomachines

We are learning to build synthetic molecular machinery from DNA. This research is inspired by biological systems in which individual molecules act, singly and in concert, as specialized machines: our ambition is to create new technologies to perform tasks that are currently beyond our reach. DNA nanomachines are made by self-assembly, using techniques that rely on the sequence-specific interactions that bind complementary oligonucleotides together in a double helix. They can be activated by interactions with specific signalling molecules or by changes in their environment. Devices that change state in response to an external trigger might be used for molecular sensing, intelligent drug delivery or programmable chemical synthesis. Biological molecular motors that carry cargoes within cells have inspired the construction of rudimentary DNA walkers that run along self-assembled tracks. It has even proved possible to create DNA motors that move autonomously, obtaining energy by catalysing the reaction of DNA or RNA fuels.     

Molecular motors: nature's nanomachines

Molecular motors are protein-based machines that convert chemical potential energy into mechanical work. This paper aims to introduce the non-specialist reader to molecular motors, in particular, acto-myosin, the prototype system for motor protein studies. These motors produce their driving force from changes in chemical potential arising directly from chemical reactions and are responsible for muscle contraction and a variety of other cell motilities.     

Computational engineering of metallic nanostructures and nanomachines

Small structures with dimensions in the nanometer regime play an important role within a lot of modern technological branches like, for example, genetics, chip fabrication, material science, medicine, or chemistry. While highly sophisticated characterization methods would be necessary to study such nanostructures, computational methods and models have made their entrance into the field of nanotechnology. The present work gives an overview of the problems connected with quantum mechanics, many-particle systems, and nanophysical models. Further, the application of molecular dynamics (MD)--a typical computational method suitable for modelling at the nanolevel--is introduced and outlined. The setup and use of specific MD models, advanced computation techniques, and efficient algorithms are discussed, while the focus is laid on the subjects nanodesign and nanoengineering which are demonstrated for the example of metallic nanostructures. Finally, the introduced techniques and methods are applied to stability studies of theoretical nanomachines.     

Cationic comb-type copolymers for boosting DNA-fueled nanomachines

For the better applications and developments of DNA nanomachines, their responding kinetics, output, and sequence-selectivity need to be improved. Furthermore, the DNA nanomachines currently have several limitations in operating conditions. Here we show that a simple addition of a cationic comb-type copolymer, poly(l-lysine)-graft-dextran, produces the robust and quick responses of DNA nanomachines under moderate conditions including physiologically relevant conditions even at very low strand concentrations (nanomoles per liter range) through hybrid stabilization and DNA strand exchange acceleration.     

Atomic-scale STM experiments on semiconductor surfaces: towards molecular nanomachines

The electronic or quantum control of individual molecules with the scanning tunnelling microscope offers exciting perspectives on operating molecular nanomachines. This implies the use of semiconductor surfaces rather than metallic surfaces which would rapidly quench the electronic excitations. We review recent results illustrating the state of the art and the main problems which need to be solved: the choice, design and properties of functionalized organic molecules on semiconductor surfaces; the control of the inelastic electronic channels through a single molecule; and the search for well-controlled atomic-scale wide-band-gap semiconductor surfaces.     

Acceleration of DEM algorithm for quasistatic processes

The discrete element method (particle dynamics) is an invaluable tool for studying the complex behavior of granular matter. Its main shortcoming is its computational intensity, arising from the vast difference between the integration time scale and the observation time scale (similar to molecular dynamics). This problem is particularly acute for macroscopically quasistatic deformation processes. We first provide the proper definition of macroscopically quasistatic processes, on the basis of dimensional analysis, which reveals that the quasistatic nature of a process is size‐dependent. This result sets bounds for application of commonly used method for computational acceleration, based on superficially increased mass of particles. Next, the dimensional analysis of the governing equations motivates the separation of time scales for the numerical integration of rotations and translations. We take advantage of the existence of fast and slow variables (rotations and translations) to develop a two‐timescales algorithm based on the concept of inertial manifolds suggested by Gear and Kevrekidis. The algorithm is tested on a 2D problem with axial strain imposed by rigid plates and pressure on lateral boundaries. The benchmarking against the accurate short‐time step results confirms the accuracy of the new algorithm for the optimal arrangement of short‐ and long‐time steps. The algorithm provides moderate computational acceleration. Copyright © 2010 John Wiley & Sons, Ltd.     

Cohesive models for quasistatic cracking in inelastic solids

In has been shown that slow stable cracking process can be sustained by strain-softening materials such as cementitious composites, e.g., rock, concrete, mortars, ceramics and others. A mathematical model is proposed based on the theory of quasi-static crack extension governed by Wnuk's criterion of final stretch (equivalent to the CTOA condition). Requirement of self-similarity of the crack opening profile, maintained during the quasistatic growth phase, leads to a differential equation defining the material resistance to sustained crack extension, as a function of crack growth increment, material properties such as tearing modulus, strain-softening parameter, and the size of the process zone.The equations derived on the basis of the step-like distribution of the restraining stress which operates within a structured end zone associated with a moving crack, are compared against the Wnuk-Rice-Sorensen equation to ran R-curve in an ideal elasto-plastic material, and with the more recent results of Wnuk and Hunsacharoonroj [1] pertaining to strain-hardening materials which obey the Ramberg-Osgood power law.Present results suggest that the nature of constitutive equations substantially influence composite fracture resistance as measured by the R-curve. Ability to absorb energy and the ensuing resistance to crack growth can be significantly enhanced when the mechanisms of energy dissipation within the matrix are properly understood. This work establishes a bridge between the continuum mechanics and micromechanics of deformation and meture processes by providing a relation between material fracture toughness and its constitutive equations supplemented by certain microstructural characteristics.     

Numerical analysis of a quasistatic thermoviscoelastic frictional contact problem

We study a quasistatic frictional contact problem between a viscoelastic body and a deformable obstacle. A thin lubricant layer is assumed on the contact surface and, then, a normal damped response contact condition considered. Thermal and frictional effects are also taken into account. A fully discrete scheme is proposed, using the finite element method for the spatial approximation and the Euler scheme for discretizing the time derivatives. Error estimates on the solutions are derived and the linear convergence, under suitable regularity hypotheses, is obtained. The scheme was implemented and some numerical examples are included to show the performance of the method.Acknowledgments This work was partially supported by MCYT-Spain (Project BFM2003-05357) and it is also part of the project New Materials, Adaptive systems and their Nonlinearities: Modelling, Control and Numerical Simulation carried out in the framework of the european community program Improving the Human Research Potential and the Socio-Economic Knowledge Base (Contract n° HPRN-CT-2002-00284).     

Detachment size of bubbles during quasistatic growth on heater

The critical bubble dimensions for detachment from a smooth surface and from the edge of a recess are calculated. The boundary of the quasistatic regime is estimated on the basis of the pressure.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 5, pp. 841–847, May, 1976.     

Unified nonlinear quasistatic and dynamic analysis of RF-MEMS switches

In this paper, the modified couple stress-based strain gradient theory is used to provide a unified nonlinear model of the quasistatic and dynamic behavior of an electrostatic microelectromechanical systems microbeam capacitive switch of the Euler–Bernoulli type. Our model not only accounts for the contact between the microbeam and the dielectric substrate using nonlinear springs and dampers, but also accounts for the system size by introducing an internal material length scale parameter. In view of the size of the microbeam and electrostatic gaps involved, Casimir and Van der Waals forces, damping force due to the squeeze membrane effect and electrostatic force with first-order fringing field effects were accounted for in our model. The resulting nonlinear system of PDEs was expanded into a coupled system using series expansion and integrated into ODEs using weighted residuals of the Galerkin type. To overcome the difficulties associated with the determination of the contact length, the Heaviside function for deflection was replaced with a Heaviside function for the contact length, and an iterative procedure was adopted to determine the contact length. To obtain the time variation of the microbeam, the dynamic system of equations was solved using Newmark’s integration scheme. The outcome of our work shows the dependence of the pull-in voltage upon the inertia force, slenderness ratios of the microbeam, the electrostatic gap and the initial boundary conditions of the switch. In addition, we were also able to provide the full history of the microbeam past the pull-in threshold.     

ALE stress update for transient and quasistatic processes

A key issue in Arbitrary Lagrangian–Eulerian (ALE) non-linear solid mechanics is the correct treatment of the convection terms in the constitutive equation. These convection terms, which reflect the relative motion between the finite element mesh and the material, are found for both transient and quasistatic ALE analyses. It is shown in this paper that the same explicit algorithms can be employed to handle the convection terms of the constitutive equation for both types of analyses. The most attractive consequence of this fact is that a quasistatic simulation can be upgraded from Updated Lagrangian (UL) to ALE without significant extra computational cost. These ideas are illustrated by means of two numerical examples. © 1998 John Wiley & Sons, Ltd.     

CQM-based BEM formulation for uncoupled transient quasistatic thermoelasticity analysis

A boundary element method based on the convolution quadrature method for the numerical solution of uncoupled transient thermoelasticity problems is presented. In the proposed formulation, the time-domain integral equation is numerically approximated by a quadrature formula whose weight factors are computed by means of integral expressions involving the Laplace transform of the fundamental solution. Compared with other numerical methods that operate directly in the Laplace transformed domain, the proposed formulation requires only the definition of the time-step used by the procedure of integration, and does not need special techniques of inversion from the Laplace-domain to the time-domain. Numerical examples of transient thermoelasticity problems are presented to show the versatility and accuracy of the method.     

Centrally symmetric quasistatic problem of thermoelasticity for a temperature sensitive body

The perturbation method is used to construct the general solution of a centrally symmetric quasistatic problem of elasticity under the assumption that all thermomechanical characteristics of a body are functions of temperature. As special cases, we obtain the solutions of the corresponding problems of thermoelasticity for hollow and continuous balls and a space containing a spherical cavity. We also perform the numerical analysis of the temperature field and the stress-strain state induced by this field in the space with spherical cavity free of external loads. Note that the process of convective heat exchange with an ambient medium of constant temperature is realized through this cavity.Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 40, No. 3, pp. 62–68, May–June, 2004.     

Computation of thermal stresses in quasistatic non-stationary thermoelasticity using boundary elements

In this paper we present the boundary integral formulation for the solution of quasi-static problems of two-dimensional uncoupled thermoelasticity. A detailed scheme for the numerical solution of the boundary integral equations and computation of internal stresses by regularized integral representation is developed in time formulation. The method is tested in a numerical example.     

A variational discrete element method for quasistatic and dynamic elastoplasticity

We propose a new discrete element method supporting general polyhedral meshes. The method can be understood as a lowest-order discontinuous Galerkin method parametrized by the continuous mechanical parameters (Young's modulus and Poisson's ratio). We consider quasistatic and dynamic elastoplasticity, and in the latter situation, a pseudoenergy conserving time-integration method is employed. The computational cost of the time-stepping method is moderate since it is explicit and used with a naturally diagonal mass matrix. Numerical examples are presented to illustrate the robustness and versatility of the method for quasistatic and dynamic elastoplastic evolutions.     

New developments in the inelastic analysis of quasistatic and dynamic problems

The computational aspects are examined for the numerical analysis of inelastic structures and continua. In this context, the tracing of quasistatic and dynamic motions is considered with particular emphasis on the interaction of nonlinear and transient problems. In the first part, explicit and implicit solution schemes are developed for the numerical integration of inelastic first-order rte processes governing creep, viscoelasticity and viscoplasticity. In the second part, the exposition is extended to second-order inertial problems and in particular to the field of dynamic plasticity, devoting special attention to the kinematics of finite deformation problems.