Elasticity Theory Connection Rules for Epitaxial Interfaces

Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt heterojunctions and interfaces. The conventional interface boundary conditions, or connection rules, require that the displacement field and its associated stress field be continuous through the interface. We argue, however, that these boundary conditions are generally incorrect for epitaxial interfaces, and we give the general procedure for deriving the correct conditions, which depend essentially on the detailed microscopic structure of the interface. As a simple application of our theory we analyze in detail a one-dimensional model of an inhomogeneous crystal, a chain of harmonic oscillators with an abrupt change in mass and spring stiffness parameters. Our results have implications for phonon dynamics in nanostructures such as superlattices and nanoparticles, as well as for the thermal boundary resistance at epitaxial interfaces.Comment: 7 pages, Revte

Deposited footprints let cells switch between confined, oscillatory, and exploratory migration

For eukaryotic cells to heal wounds, respond to immune signals, or metastasize, they must migrate, often by adhering to extracellular matrix (ECM). Cells may also deposit ECM components, leaving behind a footprint that influences their crawling. Recent experiments showed that some epithelial cell lines on micropatterned adhesive stripes move persistently in regions they have previously crawled over, where footprints have been formed, but barely advance into unexplored regions, creating an oscillatory migration of increasing amplitude. Here, we explore through mathematical modeling how footprint deposition and cell responses to footprint combine to allow cells to develop oscillation and other complex migratory motions. We simulate cell crawling with a phase field model coupled to a biochemical model of cell polarity, assuming local contact with the deposited footprint activates Rac1, a protein that establishes the cell's front. Depending on footprint deposition rate and response to the footprint, cells on micropatterned lines can display many types of motility, including confined, oscillatory, and persistent motion. On two-dimensional (2D) substrates, we predict a transition between cells undergoing circular motion and cells developing an exploratory phenotype. Small quantitative changes in a cell's interaction with its footprint can completely alter exploration, allowing cells to tightly regulate their motion, leading to different motility phenotypes (confined vs. exploratory) in different cells when deposition or sensing is variable from cell to cell. Consistent with our computational predictions, we find in earlier experimental data evidence of cells undergoing both circular and exploratory motion

The onset of magnetic order in fcc-Fe films on Cu(100)

On the basis of a first-principles electronic structure theory of finite temperature metallic magnetism in layered materials, we investigate the onset of magnetic order in thin (2-8 layers) fcc-Fe films on Cu(100) substrates. The nature of this ordering is altered when the systems are capped with copper. Indeed we find an oscillatory dependence of the Curie temperatures as a function of Cu-cap thickness, in excellent agreement with experimental data. The thermally induced spin-fluctuations are treated within a mean-field disordered local moment (DLM) picture and give rise to layer-dependent `local exchange splittings' in the electronic structure even in the paramagnetic phase. These features determine the magnetic intra- and interlayer interactions which are strongly influenced by the presence and extent of the Cu cap.Comment: 13 pages, 3 figure

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

Impurity Scattering from δ\delta-layers in Giant Magnetoresistance Systems

The properties of the archetypal Co/Cu giant magnetoresistance (GMR) spin-valve structure have been modified by the insertion of very thin (sub-monolayer) $\delta$-layers of various elements at different points within the Co layers, and at the Co/Cu interface. Different effects are observed depending on the nature of the impurity, its position within the periodic table, and its location within the spin-valve. The GMR can be strongly enhanced or suppressed for various specific combinations of these parameters, giving insight into the microscopic mechanisms giving rise to the GMR.Comment: 5 pages, 2 figure

Induced four fold anisotropy and bias in compensated NiFe/FeMn double layers

A vector spin model is used to show how frustrations within a multisublattice antiferromagnet such as FeMn can lead to four-fold magnetic anisotropies acting on an exchange coupled ferromagnetic film. Possibilities for the existence of exchange bias are examined and shown to exist for the case of weak chemical disorder at the interface in an otherwise perfect structure. A sensitive dependence on interlayer exchange is found for anisotropies acting on the ferromagnet through the exchange coupling, and we show that a wide range of anisotropies can appear even for a perfect crystalline structure with an ideally flat interface.Comment: 7 pages, 7 figure

Tenfold Magnetoconductance in a Non-Magnetic Metal Film

We present magnetoconductance (MC) measurements of homogeneously disordered Be films whose zero field sheet conductance (G) is described by the Efros-Shklovskii hopping law $G(T)=(2e^2/h)\exp{-(T_o/T)^{1/2}}$. The low field MC of the films is negative with G decreasing 200% below 1 T. In contrast the MC above 1 T is strongly positive. At 8 T, G increases 1000% in perpendicular field and 500% in parallel field. In the simpler parallel case, we observe {\em field enhanced} variable range hopping characterized by an attenuation of $T_o$ via the Zeeman interaction.Comment: 9 pages including 5 figure

Curvature correction to the mobility of fluid membrane inclusions

For the first time, using rigorous low-Reynolds-number hydrodynamic theory on curved surfaces via a Stokeslet-type approach, we provide a general and concise expression for the leading-order curvature correction to the canonical, planar, Saffman-Delbrück value of the diffusion constant for a small inclusion embedded in an arbitrarily (albeit weakly) curved fluid membrane. In order to demonstrate the efficacy and utility of this wholly general result, we apply our theory to the specific case of calculating the diffusion coefficient of a locally curvature inducing membrane inclusion. By including both the effects of inclusion and membrane elasticity, as well as their respective thermal shape fluctuations, excellent agreement is found with recently published experimental data on the surface tension dependent mobility of membrane bound inclusions

Emergent dynamic chirality in a thermally driven artificial spin ratchet

Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice1, 2 can lead to specific collective behaviour3, including emergent magnetic monopoles4, 5, charge screening6, 7 and transport8, 9, as well as magnonic response10, 11, 12. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet13, 14, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells

Dissipative Chaos in Semiconductor Superlattices

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.Comment: 33 pages, 8 figure