Nonlinear response and discrete breather excitation in driven micro-mechanical cantilever arrays

We explain the origin of the generation of discrete breathers (DBs) in experiments on damped and driven micromechanical cantilever arrays (M.Sato et al. Phys. Rev. Lett. {\bf 90}, 044102, 2003). Using the concept of the nonlinear response manifold (NLRM) we provide a systematic way to find the optimal parameter regime in damped and driven lattices where DBs exist. Our results show that DBs appear via a new instability of the NLRM different from the anticipated modulational instability (MI) known for conservative systems. We present several ways of exciting DBs, and compare also to experimental studies of exciting and destroying DBs in antiferromagnetic layered systems.Comment: 4 pages, 5 figure

A Computer Model for Laser Photopolymerization

A computer model for a laser induced photopolymerization process has been established which simulates stereolithography. The model couples irradiation, chemical reaction, and heat transfer equations to provide insights into rate processes occurring in the volume element contacted by the laser beam. Quantities predicted include the spatial variation in conversion of monomer to polymer, depletion of photoinitiator, and local variations in temperature in and around the spot contacted by the laser. This allows predictions to be made about the laser dwell time, depth penetration and uniformity of the photopolymer formed in the process.Mechanical Engineerin

Fermionic bound states on a one-dimensional lattice

We study bound states of two fermions with opposite spins in an extended Hubbard chain. The particles interact when located both on a site or on adjacent sites. We find three different types of bound states. Type U is predominantly formed of basis states with both fermions on the same site, while two states of type V originate from both fermions occupying neighbouring sites. Type U, and one of the states from type V, are symmetric with respect to spin flips. The remaining one from type V is antisymmetric. V-states are characterized by a diverging localization length below some critical wave number. All bound states become compact for wave numbers at the edge of the Brilloin zone.Comment: 4 pages, 3 figure

Material and Process Parameters that Affect Accuracy in Stereolithography

Experimental real time linear shrinkage rate measurements simulating stereolithography are used in an analysis of shrinkage during line drawing in stereolithography. While the amount of shrinkage depends on the polymerization kinetics, shrinkage kinetics and overall degree of cure, it also depends on the length of time to draw a line of plastic. A line drawn slowly will exhibit less apparent shrinkage than one drawn very quickly because much of the shrinkage is compensated for as the line is drawn. The data also indicates that a typical stereolithography resin in the green state may shrink to only 65% of its maximum, thus retaining considerable potential for shrinkage during post-cure. This infonnation can be used to predict the amount of shrinkage to be expected under certain exposure conditions and to fonnulate overall strategies to reduce shrinkage and subsequent warpage that causes shape distortion.Mechanical Engineerin

Slow Relaxation and Phase Space Properties of a Conservative System with Many Degrees of Freedom

We study the one-dimensional discrete $\Phi^4$ model. We compare two equilibrium properties by use of molecular dynamics simulations: the Lyapunov spectrum and the time dependence of local correlation functions. Both properties imply the existence of a dynamical crossover of the system at the same temperature. This correlation holds for two rather different regimes of the system - the displacive and intermediate coupling regimes. Our results imply a deep connection between slowing down of relaxations and phase space properties of complex systems.Comment: 14 pages, LaTeX, 10 Figures available upon request (SF), Phys. Rev. E, accepted for publicatio

Anderson localization in generalized discrete time quantum walks

We study Anderson localization in a generalized discrete time quantum walk - a unitary map related to a Floquet driven quantum lattice. It is controlled by a quantum coin matrix which depends on four angles with the meaning of potential and kinetic energy, and external and internal synthetic flux. Such quantum coins can be engineered with microwave pulses in qubit chains. The ordered case yields a two-band eigenvalue structure on the unit circle which becomes completely flat in the limit of vanishing kinetic energy. Disorder in the external magnetic field does not impact localization. Disorder in all the remaining angles yields Anderson localization. In particular, kinetic energy disorder leads to logarithmic divergence of the localization length at spectral symmetry points. Strong disorder in potential and internal magnetic field energies allows to obtain analytical expressions for spectrally independent localization length which is highly useful for various applications.Comment: 11 pages, 14 figure

Magnetic field induced control of breather dynamics in a single plaquette of Josephson junctions

We present a theoretical study of inhomogeneous dynamic (resistive) states in a single plaquette consisting of three Josephson junctions. Resonant interactions of such a breather state with electromagnetic oscillations manifest themselves by resonant current steps and voltage jumps in the current-voltage characteristics. An externally applied magnetic field leads to a variation of the relative shift between the Josephson current oscillations of two resistive junctions. By making use of the rotation wave approximation analysis and direct numerical simulations we show that this effect allows to effectively control the breather instabilities, e. g. to increase (decrease) the height of the resonant steps and to suppress the voltage jumps in the current-voltage characteristics.Comment: 4 pages, 3 figure

Simulation of Laminated Object Manufacturing (LOM) with Variation of Process Parameters

A previously developed and verified thermal model for Laminated Object Manufacturing (LOM) was used to investigate the effects of various processing parameters on the temperature profile in a LOM part during the build cycle. The mathematical model, based on 3-dimensional transient heat conduction in a rectangular geometry LOM part, allows calculation ofthe transient temperature distribution within the part during the application of a new layer as well as during other periods ofthe LOM build cycle. The parameters roller temperature, roller speed, chamber air temperature, base plate temperature, and laser cutting time were independently varied, and the LOM process response simulated. The results were analyzed in order to gain insight into potential strategies for intelligent process control.Mechanical Engineerin