Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice

Using infinite projected entangled-pair states, exact diagonalization, and flavor-wave theory, we show that the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, in contrast with its SU(2) and SU(3) counterparts, which develop Néel and three-sublattice stripelike long-range order. Since the ground state of a dimer is not a singlet for SU(4) but a 6-dimensional irreducible representation, this leaves the door open for further symmetry breaking. We provide evidence that, unlike in SU(4) ladders, where dimers pair up to form singlet plaquettes, here the SU(4) symmetry is additionally broken, leading to a gapless spectrum in spite of the broken translational symmetry.     

Development of peptide-based patterns by laser transfer

Peptide-based arrays and patterns have provided a powerful tool in the study of protein recognition and function. A variety of applications have been identified, including the interactions between peptides-enzymes, peptides-proteins, peptides-DNA, peptides-small molecules and peptides-cells. One of the main and most critical unresolved issues is the generation of high-density arrays which maintain the biological function of the peptides. In this study, we employ nanosecond laser-induced forward transfer for the generation of high-density peptide arrays and patterns on modified glass surfaces. We show that peptide-based microarrays can be fabricated on solid surfaces and specifically recognized by appropriate fluorescent tags, with the transfer not affecting the ability of the peptides to form fibrils. These initial results are poised to the construction of larger peptide patterns as scaffolds for the incorporation and display of ligands critical for cell attachment and growth, or for the templating of inorganic materials.     

Measurements of energy transport patterns in solid density laser plasma interactions at intensities of 5x10(20) W cm-2

Kalpha x-ray emission, extreme ultraviolet emission, and plasma imaging techniques have been used to diagnose energy transport patterns in copper foils ranging in thickness from 5 to 75 microm for intensities up to 5x10(20) W cm-2. The Kalpha emission and shadowgrams both indicate a larger divergence angle than that reported in the literature at lower intensities [R. Stephens, Phys. Rev. E 69, 066414 (2004)]. Foils 5 microm thick show triple-humped plasma expansion patterns at the back and front surfaces. Hybrid code modeling shows that this can be attributed to an increase in the mean energy of the fast electrons emitted at large radii, which only have sufficient energy to form a plasma in such thin targets.     

A variational theory of hyperbolic Lagrangian Coherent Structures

We develop a mathematical theory that clarifies the relationship between observable Lagrangian Coherent Structures (LCSs) and invariants of the Cauchy-Green strain tensor field. Motivated by physical observations of trajectory patterns, we define hyperbolic LCSs as material surfaces (i.e., codimension-one invariant manifolds in the extended phase space) that extremize an appropriate finite-time normal repulsion or attraction measure over all nearby material surfaces. We also define weak LCSs (WLCSs) as stationary solutions of the above variational problem. Solving these variational problems, we obtain computable sufficient and necessary criteria for WLCSs and LCSs that link them rigorously to the Cauchy-Green strain tensor field. We also prove a condition for the robustness of an LCS under perturbations such as numerical errors or data imperfection. On several examples, we show how these results resolve earlier inconsistencies in the theory of LCS. Finally, we introduce the notion of a Constrained LCS (CLCS) that extremizes normal repulsion or attraction under constraints. This construct allows for the extraction of a unique observed LCS from linear systems, and for the identification of the most influential weak unstable manifold of an unstable node.     

Self-assembly of block copolymers grafted onto a flat substrate:Recent progress in theory and simulations

Block copolymers are a class of soft matter that self-assemble to form ordered morphologies on the scale of nanometers, making them ideal materials for various applications. These applications directly depend on the shape and size of the self-assembled morphologies, and hence, a high degree of control over the self-assembly is desired. Grafting block copolymer chains onto a substrate to form copolymer brushes is a versatile method to fabricate functional surfaces. Such surfaces demonstrate a response to their environment, i.e., they change their surface topography in response to different external conditions. Furthermore, such surfaces may possess nanoscale patterns, which are important for some applications; however, such patterns may not form with spun-cast films under the same condition. In this review, we summarize the recent progress of the self-assembly of block copolymers grafted onto a flat substrate. We mainly concentrate on the self-assembled morphologies of end-grafted AB diblock copolymers, junction point-grafted AB diblock copolymers(i.e.,Y-shaped brushes), and end-grafted ABA triblock copolymers. Special emphasis is placed on theoretical and simulation progress.     

Model for the extreme wetting hysteresis of liquid helium on cesium

Although the liquid- 4He-cesium system is a nearly ideal one for studying wetting phenomena, it can show extreme hysteresis which is profoundly nonideal in behavior. It is suggested that this is due to the roughness of these Cs surfaces. We show that stable micropuddles of liquid 4He can form in shallow cavities on a Cs surface. It is the potential to form micropuddles, as the liquid tries to recede, which pins the contact line due to the large energy needed to create the surface of a micropuddle. This model also accounts for the memory that these surfaces have of being in contact with liquid 4He.     

On Lipschitz solutions of the constant astigmatism equation

We show that the solutions of the constant astigmatism equation that correspond to a class of surfaces found by Lipschitz in 1887, exactly match the Lie symmetry invariant solutions and constitute a four-dimensional manifold. The two-dimensional orbit space with respect to the Lie symmetry group is described. Our approach relies on the link between constant astigmatism surfaces and orthogonal equiareal patterns. The counterpart sine–Gordon solutions are shown to be Lie symmetry invariant as well.     

Coxeter’s frieze patterns and discretization of the Virasoro orbit

We show that the space of classical Coxeter’s frieze patterns can be viewed as a discrete version of a coadjoint orbit of the Virasoro algebra. The canonical (cluster) (pre)symplectic form on the space of frieze patterns is a discretization of Kirillov’s symplectic form. We relate a continuous version of frieze patterns to conformal metrics of constant curvature in dimension 2.     

Effect of the point spread function on the average contrast of image speckle patterns

The effect of the point spread function on the average contrast of image speckle patterns is studied by varying its form depending on the optical imaging system. This effect is actually evaluated on the basis of a computer simulation of various rough surfaces by investigating the average contrast variation of image speckle patterns as a function of the point spread of the optical system. It becomes clear that the form of the point spread function, i.e. the type of the optical imaging system producing image speckle patterns, does not largely affect the average contrast of image speckle patterns.     

Dimer-anticorrelation-induced stabilization of adsorbate clustering on the Si100-(2 x 1) surface

It is well established that absorbate-absorbate interactions play a key role in determining the distribution of adsorbates on surfaces. In cases where these interactions are repulsive adsorbates frequently arrange so as to minimize these unfavorable interactions. This simple picture, however, neglects the influence of adsorption on the properties on the underlying substrate. Here, using STM, we show that on Si(100) many intrinsically repulsive adsorbates cluster to form surface patches even at low surface coverages. With the aid of density functional theory calculations and Monte Carlo simulations, we show that patch formation is an intrinsic property of the Si(100) surface that is driven by the energy lowering associated with the formation of extended regions of bare dimers. The enhanced attraction between anticorrelated tilted bare dimers is sufficient to offset the repulsions between adsorbates.     

Method for detecting superconducting stripes in high-temperature superconductors based on nonlinear resistivity measurements

We theoretically study the effect that stripelike superconducting inclusions would have on the nonlinear resistivity in single crystals. Even if the stripe orientation varies throughout the sample between two orthogonal directions due to twinning, we predict that there should be a universal dependence of the nonlinear resistivity on the angle between the applied current and the crystal axes. This prediction can be used to test the existence of superconducting stripes at and above the superconducting transition temperature in cuprate superconductors.     

Ferroelectric phase transitions in ultrathin films of BaTiO3

We present molecular dynamics simulations of a realistic model of an ultrathin film of BaTiO3 sandwiched between short-circuited electrodes to determine and understand effects of film thickness, epitaxial strain, and the nature of electrodes on its ferroelectric phase transitions as a function of temperature. We determine a full epitaxial strain-temperature phase diagram in the presence of perfect electrodes. Even with the vanishing depolarization field, we find that ferroelectric phase transitions to states with in-plane and out-of-plane components of polarization exhibit dependence on thickness; it arises from the interactions of local dipoles with their electrostatic images in the presence of electrodes. Secondly, in the presence of relatively bad metal electrodes which only partly compensate the surface charges and depolarization field, a qualitatively different phase with stripelike domains is stabilized at low temperature.     

Fractal structure of digital speckle patterns produced by rough surfaces

We report on the fractal analysis of digital speckle patterns experimentally generated using an optical setup to record the light scattered from metallic rough surfaces in the normal direction. Using the differential box counting technique, we have calculated the fractal dimension of digital speckle patterns for six samples with different roughness. Our results show a quadratic dependence between the surface roughness and the fractal dimension of the corresponding digital speckle pattern. As an application a method to determine the surface roughness of metallic surfaces is proposed.     

Phyllotactic patterns on plants

We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the deformation configurations seen on plant surfaces may be understood as the energy-minimizing buckling pattern of a compressed shell (the plant's tunica) on an elastic foundation. The key new idea is that the strain energy is minimized by configurations consisting of special triads of almost periodic deformations. We reproduce a wide spectrum of plant patterns, all with the divergence angles observed in nature, and show how the occurrences of Fibonacci-like sequences and the golden angle are natural consequences.     

Edge states in doped antiferromagnetic nanostructures

We study competition between different phases in a strongly correlated nanostructure with an edge. Making use of the self-consistent Green's function and density matrix renormalization group methods, we study a system described by the t-J(z) and t-J models on a strip of a square lattice with a linear hole density n(||). At intermediate interaction strength J/t we find edge stripelike states, reminiscent of the bulk stripes that occur at smaller J/t. We find that stripes attach to edges more readily than hole pairs, and that the edge stripes can exhibit a peculiar phase separation.     

Self assembly modulated by interactions of two heterogeneously charged surfaces

Recent experiments have measured attractive interactions between two surfaces that each bear two molecular species with opposite charge. Such surfaces form charged domains of finite size. We present a theoretical model that predicts the dependence of the domain size, phase behavior and the interlayer forces as a function of spacing and salt concentration for two such interacting surfaces. A strong correlation between two length scales, the screening length and the surface separation, at the spinodal is shown. Remarkably, the first-order phase transition to infinite sized domains depends logarithmically on the ratio of the domain size to the molecular size. Finally, we fit the predicted pressure with experiments.     

Quantum scattering of fast atoms and molecules on surfaces

We present evidence for the diffraction of light keV atoms and molecules grazingly scattered on LiF(001) and NaCl(001) surfaces. At such energies, the de Broglie wavelength is 2 orders of magnitude smaller that the mean thermal atomic displacement in the crystal. Thus, no coherent scattering was expected and interaction of keV atoms with surfaces is routinely treated with classical mechanics. We show here that well-defined diffraction patterns can be observed indicating that, for grazing scattering, the pertinent wavelength is that associated with the slow motion perpendicular to the surface. The experimental data are well reproduced by an ab initio calculation.     

In-plane and out-of-plane diffraction of H(2) from metal surfaces

We have measured in-plane and out-of-plane diffraction of H2 and D2 molecular beams scattered by reactive Pd(111) and nonreactive NiAl(110) surfaces at 140-150 meV. A comparison with six-dimensional quantum dynamics and classical trajectory calculations shows for the first time that accurate diffraction patterns can be obtained from state-of-the-art potential energy surfaces based on density functional theory. Our measurements show that, at general incidence conditions, out-of-plane diffraction is much more important than was assumed in previous experiments.     

Atomic force microscopy investigation of growth process of organic TCNQ aggregates on SiO2 and mica substrates

<正>Deposition patterns of tetracyanoquinodimethane(TCNQ) molecules on different surfaces are investigated by atomic force microscopy.A homemade physical vapour deposition system allows the better control of molecule deposition. Taking advantage of this system,we investigate TCNQ thin film growth on both SiO_2 and mica surfaces.It is found that dense island patterns form at a high deposition rate,and a unique seahorse-like pattern forms at a low deposition rate.Growth patterns on different substrates suggest that the fractal pattern formation is dominated by molecule-molecule interaction.Finally,a phenomenal "two-branch" model is proposed to simulate the growth process of the seahorse pattern.