Modern high-performance SAW filters utilize thin-film technology to optimize losses, temperate stability, filter bandwidth, and manufacturing sensitivity. Fast design of these complicated structures calls for accurate and more general simulation tools. The versatility of the finite element method (FEM) makes it attractive for this purpose. However, the application of FEM in the SAW field has been hampered by the associated very large memory requirements and excessive computation times. Here, we describe frequency-domain FEM simulation of SAW devices with the hierarchical cascading algorithm, including thermal effects. The method utilizes the periodic block structure, which is typical to SAW devices, to eliminate redundant calculations from FEM. The approach has all the advantages of FEM, with-for structures with high degree of periodicity-drastically reduced memory consumption and computation time.

Application of finite element methods (FEM) to the simulation of SAW devices has been constrained by the large number of degrees-of-freedom required, resulting in large memory usage and long computation times. Here, we propose a hierarchical cascading approach which takes advantage of the periodic structure typical of SAW devices. In this approach, each unique electrode period is modeled and simulated only once. Smaller blocks are cascaded to describe larger blocks until the whole device is modeled. This is equivalent to full simulation of the device with FEM, however - for structures with high degree of periodicity - with drastically reduced memory consumption and simulation time.

We study the self-assembly of a diblock copolymer melt confined within a porous medium with a prescribed regular two-dimensional geometry using self-consistent field theory. We find that the morphology of the polymer sensitively depends on the characteristic length scales of the porous material and the polymer radius of gyration (Rg). When the pore size is much larger than Rg, the polymer self-assembly is affected only locally close to the contact with the pore surface. However, when the size of the pores and the distance between them is comparable to the diblock characteristic length, novel morphologies appear and the polymer structure changes according to the constraints imposed by the porous material. We develop an interaction potential for the solid particle and copolymer, and show how this provides an understanding of the qualitative feature of the morphologies.

In classical mechanics, discrete breathers (DBs) - a spatial time-periodic localization of energy - are predicted in a large variety of nonlinear systems. Motivated by a conceptual bridging of the DB phenomena in classical and quantum mechanical representations, we study their signatures in the dynamics of a quantum equivalent of a classical mechanical point in phase space - a coherent state. In contrast to the classical point that exhibits either delocalized or localized motion, the coherent state shows signatures of both localized and delocalized behavior. The transition from normal to local modes have different characteristics in quantum and classical perspectives. Here, we get an insight into the connection between classical and quantum perspectives by analyzing the decomposition of the coherent state into system's eigenstates, and analyzing the spacial distribution of the wave-function density within these eigenstates. We find that the delocalized and localized eigenvalue components of the coherent state are separated by a mixed region, where both kinds of behavior can be observed. Further analysis leads to the following observations. Considered as a function of coupling, energy eigenstates go through avoided crossings between tunneling and non-tunneling modes. The dominance of tunneling modes in the high nonlinearity region is compromised by the appearance of new types of modes - high order tunneling modes - that are similar to the tunneling modes but have attributes of non-tunneling modes. Certain types of excitations preferentially excite higher order tunneling modes, allowing one to study their properties. Since auto-correlation functions decrease quickly in highly nonlinear systems, short-time dynamics are sufficient for modeling quantum DBs. This work provides a foundation for implementing modern semi-classical methods to model quantum DBs, bridging classical and quantum mechanical signatures of DBs, and understanding spectroscopic experiments that involve a coherent state.

The arrangement of the electronic levels in an interface between organic semiconductors is crucial for the operation of devices such as solar cells and light emitting diodes. With the addition of designed macromolecules, we show that it is possible to control the relative position of the highest occupied molecular orbital and lowest unoccupied molecular orbital levels, and consequently improve the performance. The designed macromolecules consist of two end segments, each compatible with one of the interface components, and a central segment which adds functionality to the interface. The tails control the position and the orientation of the functional units. When the central functional unit is an electric dipole, an electrostatic field is created due to the orientation of the dipoles, which shifts the electronic levels in a controlled way. We develop a theoretical framework, based on self-consistent field theory, to study the concentration and the orientation of the central functional units. We find that the levels can shift by as much as several tenths of an eV.

We demonstrate that period-doubled discrete breathers appear from the anticontinuum limit of the driven Peyrard-Bishop-Dauxois model of DNA. These novel breathers result from a stability overlap between subharmonic solutions of the driven Morse oscillator. Subharmonic breathers exist whenever a stability overlap is present within the Feigenbaum cascade to chaos and therefore an entire cascade of such breathers exists. This phenomenon is present in any driven lattice where the on-site potential admits subharmonic solutions. In DNA these breathers may have ramifications for cellular gene expression.

We investigate a model of elasticity-driven polaron pattern formation on a two-dimensional lattice at finite temperatures. We show that, at high densities, polaron stripes (glass-like) form when the gas is cooled. These stripes melt to a polaron gas upon heating. We attribute the emergent behavior to the role of the long-range, directional elastic interactions that favor a minimum in energy for polaron stripe formation.

We investigate in the framework of Landau theory the distortion of the strain fields at the interface of two dissimilar ferroelastic oxides that undergo a structural cubic-to-tetragonal phase transition. Simple analytical solutions are derived for the dilatational and the deviatoric strains that are valid over the entire heterostructure. The solutions reveal that the dilatational strain exhibits compression close to the interface, which may in turn affect the electronic properties in that region.

Block copolymers remain one of the most extensively investigated classes of polymers due to their abilities to self-organize into various nanostructures and modify polymer/polymer interfaces. Despite fundamental and technological interest in these materials, only a handful of experimental phase diagrams exist due to the laborious task of preparing such diagrams. In this work, two copolymer series are each synthesized from a single macromolecule via sequential living anionic polymerization to yield molecularly asymmetric diblock and triblock copolymers systematically varying in composition. The phase behavior and morphology of these copolymers are experimentally interrogated and quantitatively compared with predictions from mean-field theories, which probe copolymer phase behavior beyond current experimental conditions.

We use the hybrid particle-Self Consistent Field calculation (hybrid particle-SCF) to study the distribution of particles in a multi-block copolymer nano-composite. Using the static approach, we first find the effective interaction potential between the nano-particles and the polymer. The interaction has an entropic and an enthalpic component. The dynamical simulation confirms that the distribution of particles has a maximum at the minima of the interaction potential. We also study the situation where the nano-particles are distributed in a blend of AB diblock and A homopolymer. In this case, for large homopolymer concentration (larger than 20%), an interface is created between components that are identical, but they come from different types of polymer chains (i.e. the AB diblock or the A homopolymer). We find that the interaction potential has a minimum in this A/A interface which is of pure entropic origin. Furthermore the dynamical simulation reveals that the distribution of nano-particles has a maximum in the area around this interface.

Self-consistent field theory is used to study the self-assembly of a triblock copolymer melt. Two different external factors (temperature and solvent) are shown to affect the self-assembly. Either one or two-step self-assembly can be found as a function of temperature in the case of a neat triblock melt, or as a function of increasing solvent content (for non-selective solvents) in the case of a triblock-solvent mixture. For selective solvents, it is shown that increasing the solvent content leads to more complicated self-assembly mechanisms, including a reversed transition where order is found to increase instead of decreasing as expected, and re-entrant behavior where order is found to increase at first, and then decrease to a previous state of disorder.

We use a strain description to couple long-range elastic fields adiabatically to electronic density to describe the behavior of a quantum particle in an elastic medium. We show that in this generalization of the Holstein polaron problem, a bound polaronic state results with strong long-range angular dependence in the elastic fields, but a localized electronic core. The deformation of the elastic fields creates an anisotropic, indirect interaction between polarons extending to large distances. For a given density of polarons, this interaction favors the formation of strings of polarons in preferred directions.

The self-assembly of a diblock copolymer melt in a confined regular geometry with a given pore size is studied using self-consistent field theory. For a particle in a polymer domain, we obtain the interaction potential as a function of the distance from the polymer interface. For a given concentration of particles of a certain size and separation, we find that microphase segregation is sensitive to the characteristic length scales of the geometry. In particular, novel polymer morphologies arise when the size of the pores and the distance between them are comparable to the diblock polymer radius of gyration Rg. Confinement can result in morphologies not allowed in the bulk. However, if the pore size is much larger than Rg, the effects are then limited to the vicinity of the pore surface.

We study quantum mechanical evolution in an optical lattice under the influence of combined external constant and time dependent fields [1]. It is known that in the purely linear case of a tight binding Hamiltonian, the presence of a constant field induces localization of the particles due to the energy mismatch between adjacent lattices sites introduced by the field. On the other hand, when a pure ac electric field is present in the lattice, generally the particles become delocalized except in some special cases. When both dc and ac fields are present the Stark localization is generally winning except in the special case of resonant tunneling. The latter occurs when the multiphonon ac-terms match the site energy non-degeneracy introduced by the constant field. We analyze the linear case and obtain exact solutions for the modified tunneling rates as well as the mean square displacement of the initially localized Bose gas population. We compare the exact results with simulations and find perfect agreement. Subsequently we introduce nonlinearity in the form of the Bose-Hubbard Hamiltonian that leads to the Discrete Nonlinear Schrodinger (DNLS) equation driven by combined dc and ac fields. We search numerically for the modification of the resonant tunneling condition and calculate numerically the modified tunneling rate. We compare our numerical results with approximate expressions for the tunneling rates and explore the regimes where there is agreement [2]. We also address the problem from the point of view of the integrable Ablowitz-Ladik equation where nonlinearity modifies the transfer rates directly rather than the on-site Hubbard term[3]. We compare our theoretical and numerical analysis with recent experimental findings on resonant tunneling [4] and also comment on multiband extensions of this problem [5].

We demonstrate how a generalized self-consistent field theory for polymer melts that includes elastic stress and strain fields can be applied to the study of AB diblock copolymers melts. By obtaining the stress distributions for volume conserving strain loadings where lamellar and hexagonal morphologies are stable, we show that the local stress is reduced at the domain interface but slightly enhanced in the immediate vicinity of the interface. The overall stress profile is the result of the combined effects of chain connectivity across the interface, which yields a positive contribution, and the immiscible nature of the monomers, which leads to a stress reduction because of interfacial tension.

We study a one-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DB's) can be explicitly constructed by an exact separation of their time and space dependence. Introducing parametric periodic driving, we first show how a variety of such DB's can be obtained by selecting spatial profiles from the homoclinic orbits of an invertible map and combining them with initial conditions chosen from the Poincaré surface of section of a simple Duffing's equation. Placing then our initial conditions at the center of the islands of a major resonance, we demonstrate how the corresponding DB can be stabilized by varying the amplitude of the driving. We thus discover around elliptic points a large region of quasiperiodic breathers, which are stable for very long times. Starting with initial conditions close to the elliptic point at the origin, we find that as we approach the main chaotic layer, a quasiperiodic breather either destabilizes by delocalization or turns into a chaotic breather, with an evidently broadbanded Fourier spectrum before it collapses. For some breather profiles stable quasiperiodic breathers exist all the way to the separatrix of the Duffing equation, indicating the presence of large regions of tori around the DB solution in the multidimensional phase space. We argue that these strong localization phenomena are due to the absence of phonon resonances, as there are no linear dispersion terms in our lattices. We also show, however, that these phenomena persist in more realistic physical models, in which weak linear dispersion is included in the equations of motion, with a sufficiently small coefficient.