The Dilute Potts Model on Random Surfaces

We present a new solution of the asymmetric two-matrix model in the large-N limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with the topology of the sphere (resp. the disk) for closed (resp. open) surfaces; we elaborate on the resulting phase diagram. The method can be equally well applied to a more general (Q+1)-matrix model which represents the dilute Potts model on random dynamical lattices. We discuss in particular duality of boundary conditions for open random surfaces.     

Thermal and non-thermal fluctuations in active polar gels

We discuss general features of noise and fluctuations in active polar gels close to and away from equilibrium. We use the single-component hydrodynamic theory of active polar gels built by Kruse and coworkers to describe the cytoskeleton in cells. Close to equilibrium, we calculate the response function of the gel to external fields and introduce Langevin forces in the constitutive equations with correlation functions respecting the fluctuation-dissipation theorem. We then discuss the breakage of the fluctuation-dissipation theorem due to an external field such as the activity of the motors. Active gels away from equilibrium are considered at the scaling level. As an example of application of the theory, we calculate the density correlation function (the dynamic structure factor) of a compressible active polar gel and discuss possible instabilities.     

Designing N-halamine based antibacterial surface on polymers: Fabrication, characterization, and biocidal functions

We demonstrate a valuable method to generate reactive groups on inert polymer surfaces and bond antibacterial agents for biocidal ability. Polystyrene (PS) surfaces were functionalized by spin coating of sub-monolayer and monolayer films of poly(styrene-b-tert-butyl acrylate) (PS-PtBA) block copolymer from solutions in toluene. PS-PtBA self-assembled to a bilayer structure on PS that contains a surface layer of the PtBA blocks ordering at the air-polymer interface and a bottom layer of the PS blocks entangling with the PS substrate. The thickness of PtBA layer could be linearly controlled by the concentration of the spin coating solution and a 2.5 nm saturated monolayer coverage of PtBA was achieved at 0.35% (w/w). Carboxyl groups were generated by exposing the tert-butyl ester groups of PtBA on saturated surface to trifluoroacetic acid (TFA) to bond tert-butylamine via amide bonds that were further chlorinated to N-halamine with NaOCl solution. The density of N-halamine on the chlorinated surface was calculated to be 1.05 × 10⁻⁵ mol/m² by iodimetric/thiosulfate titration. Presented data showed the N-halamine surface provided powerful antibacterial activities against Staphylococcus aureus and Escherichia coli. Over 50% of the chlorine lost after UVA irradiation could be regained upon rechlorination. This design concept can be virtually applied to any inert polymer by choosing appropriate block copolymers and antibacterial agents to attain desirable biocidal activity.     

Stability and electronic properties of the O-terminated Cu2O(111) surfaces: First-principles investigation

The effect of different vacancies on the morphology of the O-terminated Cu₂O(111) surface has been studied through the first-principles calculations. Our results show that Cu and O vacancies trigger large relaxations and formation of two different facets. Our emulated STM images are in consistent with the experimental STM patterns. A sizeable magnetic moment (∼1.0 μ_B) was found for surfaces with either Cu or O vacancies. The calculated formation energies of surface vacancies indicate that the deficient surfaces are more stable than the stoichiometric O-terminated (1×1) surface, which is also in line with our results obtained from ab initio atomistic thermodynamics studies.     

Atomic structure of the Si(5 5 12)-2 × 1 surface

Based on the results of scanning tunneling microscopy studies of the reconstructed Si(5 5 12)-2 × 1 surface, its atomic structure has been found. It turns out that Si(5 5 12)-2 × 1 consists of four one-dimensional structures: honeycomb (H) chain, π-bonded H′ (π) chain, dimer-adatom (D/A) row, and tetramer (T) row. Its period is composed of three subunits, i.e., (i) (3 3 7) unit with a D/A row [D(3 3 7)], (ii) (3 3 7) unit with a T row [T(3 3 7)], and (iii) (2 2 5) unit with both a D/A and a T row. Two kinds of adjacent subunits, T(3 3 7)/D(3 3 7) and D(3 3 7)/(2 2 5), are divided by H chains with 2× periodicity due to buckling, while one kind of adjacent subunits, T(3 3 7)/(2 2 5), is divided by a π chain with 1× periodicity. Two chain structures, H and π chains, commute with each other depending upon the external stresses perpendicular to the chain, which is the same for two row structures, D/A and T rows. It can be concluded that the wide and planar reconstruction of Si(5 5 12)-2 × 1 is originates from the stress balance among two commutable chains and two commutable rows.     

Anomalous lateral beam shift and total absorption due to excitation of surface waves in materials with negative refraction

We studied electromagnetic beam reflection from layered structures that include materials with negative refraction. Excitation of leaky surface waves leads to the formation of anomalous lateral shifts in the reflected beams with single or double peak structures. The presence of reasonable losses within material with negative refraction, besides significant influence on manifestation of the giant lateral shifts, can lead to their total suppression and anomalously high absorption of the incident radiation. If, in addition to the resonant excitation of leaky surface waves, radiation inflow exactly compensates their irreversible damping, total absorption of the incoming radiation can be achieved for moderately wide beams.     

Density functional theory investigation of the structure of SO2 and SO3 on Cu(1 1 1) and Ni(1 1 1)

Density functional theory (DFT) slab calculations, mainly using the generalised gradient approximation, have been used to investigate the minimum energy structures of molecular SO₂ and SO₃ on Cu(1 1 1) and Ni(1 1 1) surfaces. On Ni(1 1 1) the optimal local adsorption structures are in close agreement with experimental results for both molecular species obtained using the X-ray standing wavefield technique, although for adsorbed SO₂ the energetic difference between two alternative lateral positions of the lying-down molecule on the surface is marginally significant. On Cu(1 1 1) the results for adsorbed SO₂, in particular, were sensitive to the DFT functional used in the calculations, but in all cases failed to reproduce the experimentally-established preference for adsorption with the molecular plane perpendicular to the surface. This result is discussed in the context of previously published DFT results for these species adsorbed on Cu(1 0 0). The optimal geometry found for SO₃ on Cu(1 1 1) is similar to that on Ni(1 1 1), providing agreement with experiment regarding the molecular orientation but not the adsorption site.     

Ab initio simulation of the BaZrO3 (0 0 1) surface structure

Electronic and atomic structures of different terminations of the (0 0 1) non-polar orientation of BaZrO₃ surfaces have been studied using first-principles calculations. We found that surface energies at both possible surface terminations, BaO and ZrO₂, were very close. The (0 0 1)-BaO and (0 0 1)-ZrO₂ terminated surfaces have bandgap values smaller than that of a bulk BaZrO₃ crystal. In addition, the relative surface stability has been analyzed as a function of chemical environment.     

Analysis of polymer adsorption onto colloidal particles

The structure of the layer formed after polymer adsorption onto a spherical particle is numerically studied by means of the application of the Single-Chain Mean-Field theory. We have determined several overall layer properties including the monomer volume fraction profiles, the layer thickness, adsorbances related to loops and to tails, as well as the variation of the crossover distance between loops and tails for different particle radii and fixed polymer length. When the radius of the sphere is small enough to affect the loop layer, one enters a single-adsorbed-chain regime, characterized by a critical sphere radius. In this regime, structural changes in the adsorbed layer arise. For such small sphere, the loop layer is confined to a region whose thickness is of the order of the radius of the adsorbing sphere, and two long tails dominate the outer layer and the adsorbance due to tails dominates that due to loops. An analysis of the structure of the outer tail layer for this small sphere case is also presented.     

Spherical gravitational collapse with photon emission and a generalized Schwarzchild interior solution

The general dynamical equations for perfect fluid filled spheres with an outward flux of photons are derived. The vital role played by the energy density of the free gravitational field in accelerating photon production has been emphasized. It is pointed out that even when the material energy density is finite, the energy density of the free gravitational field can take infinitely large values resulting in vanishing surface area of the star. A generalized Schwarzschild interior solution with conformally flat geometry but with photon emission has been obtained. It is pointed out that the interior conformal coordinate system bears a strong resemblance to the exterior Krushkal coordinates. It is shown that for spherical star the invariant velocity of the fluid particles, falling towards the centre, is proportional to its radius suggesting that the outer envelopes collapse at a faster rate than the core part. It is shown that the interior radiating solution can be matched with generalized Schwarzchild exterior solution.