Physical adsorption and surface plasmons

The quantum mechanical formulation of the screening of a point charge by surface plasmons is extended to describe the coupling of a fluctuating atomic dipole with a metallic surface of planar, spherical or cylindrical shape. This allows for the calculation of the nonretarded Van der Waals attraction of an atom by a solid surface in the three different geometries. Applications of the theoretical formulae are made to obtain numerical values of the dispersion energy by a spherical particle, a spherical pore, a thin film, a slot-like prore, a cylindrical fiber or a cylindrical pore.     

A generalized Beraha conjecture for non-planar graphs

We study the partition function _ZG(nk,k)(Q,v)$Z_{G(nk,k)}(Q,v)$ of the Q  -state Potts model on the family of (non-planar) generalized Petersen graphs G(nk,k)$G(nk,k)$. We study its zeros in the plane (Q,v)$(Q,v)$ for 1?k?7$1?k?7$. We also consider two specializations of _ZG(nk,k)$Z_{G(nk,k)}$, namely the chromatic polynomial _PG(nk,k)(Q)$P_{G(nk,k)}(Q)$ (corresponding to v=−1$v=-1$), and the flow polynomial _ΦG(nk,k)(Q)${\Phi }_{G(nk,k)}(Q)$ (corresponding to v=−Q$v=-Q$). In these two cases, we study their zeros in the complex Q  -plane for 1?k?7$1?k?7$. We pay special attention to the accumulation loci of the corresponding zeros when n→∞$n\to \infty$. We observe that the Berker–Kadanoff phase that is present in two-dimensional Potts models, also exists for non-planar recursive graphs. Their qualitative features are the same; but the main difference is that the role played by the Beraha numbers for planar graphs is now played by the non-negative integers for non-planar graphs. At these integer values of Q, there are massive eigenvalue cancellations, in the same way as the eigenvalue cancellations that happen at the Beraha numbers for planar graphs.     

Determination of preferential rare earth adatom adsorption geometries on Si(001)

The adsorption patterns of rare earth atoms on Si(001) were investigated using scanning tunneling microscopy measurements and density functional calculations. Stable configurations were systematically determined via calculation of binding energies of various adatom coverage and adsorption geometry. Competition between inter-adatom hybridization and Coulomb repulsion is the mechanism contributing to binding energy minima associated with commonly observed rare earth adsorption geometries. Comparison of stable configurations with experimental scanning tunneling microscopy images demonstrated accuracy of the theoretical models. This paves a way for the understanding of self-assembly of rare earth disilicide nanowires on vicinal Si(001) substrates.     

Physical adsorption of gases at high pressure

The adsorption of a (modified) Lennard-Jones gas on a plane, rigid solid surface is studied using the grand canonical ensemble Monte Carlo method for a wide range of physical conditions. The shapes of the adsorption isotherms are in good qualitative agreement with those observed experimentally. Multilayers adsorption is observed at temperatures from just below to well above the critical temperature, T_c . As the pressure is increased for T?T_c the adsorbed film tends to become thick in the sense that the outer adsorbed layer becomes highly deloealized and asymmetric.     

Flexible piezoelectric transducer for ultrasonic inspection of non-planar components

This paper presents the fabrication and characterisation of a flexible ultrasonic transducer using commercially available PZT-5A piezoelectric fibers which are lapped to form rectangular piezoelectric elements. The key feature in the device construction is the inclusion of gaps between the piezoelectric fibers to ensure good flexibility in the plane normal to the fiber direction. The spatial response of the transducer ultrasonic output was assessed using acoustographic imaging. The flexibility of the transducer and its applicability in pulse-echo mode on curved sections was demonstrated by testing on a 38 mm diameter steel rod. The transducer response was found to be broad band and highly non uniform but good pulse-echo performance was achieved at 5 MHz.     

Renormalizability conditions for almost-commutative geometries

We formulate conditions for almost-commutative (spacetime) manifolds under which the asymptotically expanded spectral action is renormalizable. These conditions are of a graph-theoretical nature, involving the Krajewski diagrams that classify such geometries. This applies in particular to the Standard Model of particle physics, giving a graph-theoretical argument for its renormalizability. A promising potential application is in the selection of physical (renormalizable) field theories described by almost-commutative geometries, thereby going beyond the Standard Model.     

Physical adsorption of nitric oxide on metal oxides

Adsorption isotherms have been measured at 77.5 K for nitric oxide and nitrogen on Al₂O₃, MgO, ZnO and NiO, and at 90.2 K. for nitric oxide on A1₂O₃ and NiO. Three isotherm measurements at 77.5 K were made on the Al₂O₃ sample for each adsorbate to examine the effect of different degrees of surface dehydroxylation. The latter was assessed by means of infrared absorption studies on an Al₂O₃ disc. Isosteric heats for NO adsorption on Al₂O₃ and NiO increase from ca. 8 kJ mol^?1 and 6 kJ mol^?1 (respectively) at half monolayer coverage to near the value of the enthalpy of sublimation (16.6 kJ mol^?1) at monolayer completion. These results are discussed in terms of adsorbate dimerisation. Anomalous adsorption-desorption behaviour for the NONiO system is discussed. Effective adsorbate molecular cross-sectional areas and results for N2 adsorption on preadsorbed NO do not support the existence of either localisation or micro-porosity.     

Distortion correction for imaging on non-planar surface using freeform lens

The method of designing a freeform lens which can image on a formula describable non-planar surface with low distortion was proposed aimed on distortion correction. In this method, the Snell's law and the correspondence between the coordinates of object and the distortion free image are used to establish the partial differential equation which characterizes the freeform surface, and the partial differential equation can be solved to form the freeform surface. Take projection on spherical surface for example, a freeform lens is designed. After adding this lens to the ordinary projection lens at a certain position, the system (ordinary projection lens and freeform lens) can project an image on sphere with absolute distortion about 2 mm for an observer at half of the projection distance, and the MTF on sphere is analyzed in detail after.     

Peierls-Nabarro model of non-planar screw dislocation cores

The Peierls-Nabarro model originally developed for dislocations with planar cores is modified to describe the cores of screw dislocations extended along two or three intersecting slip planes, under the action of external stress. This concept generalizes the simplified concept of sessile splitting of screw dislocations into singular partials and enables an instructive interpretation of fully atomistic models of screw dislocation cores developed recently for b.c.c. metals. As an example, a numerical solution of the modified Peierls-Nabarro equation is given for the equilibrium configuration of a 1/2 [111] screw dislocation core in -Fe extended along three {110} planes.     

Planar and non-planar Wilson loops in QCD

A general QCD sum rule calculation of vacuum expectation values of Wilson loops is presented and particularized to several specific planar and non-planar contours. The string tension obtained is √σ = 0.50(5) GeV. Within the errors of the approach, this result is shape-independent. We comment on the possibility that corrections to the area and perimeter laws could be parametrized by a geodesic curvature term.     

Tailored nearfield Green's functions for arbitrary geometries

An iterative technique, taken from the field of optics, is used to obtain tailored Green's functions suitable for the evaluation, in the nearfield, of pressure fluctuations generated by turbulent flow in the vicinity of solid boundaries. Comparisons are made with the analytical solution for the solid sphere, and with results obtained using conventional boundary element method (BEM) for the case of a thick semi-infinite plate. A divergence issue in the case of the solid sphere is resolved by the introduction of a relaxation factor. The performance of the iterative approach is found to be comparable to that of conventional BEM, except at irregular frequencies, where the bandwidth of the error is slightly larger than that of the conventional BEM. The main advantage of the iterative approach is a significantly reduced computational cost, which allows for higher surface mesh densities and a broader useful frequency range.     

Counting non-planar diagrams: an exact formula

We present an explicit solution of a simply stated, yet unsolved, combinatorial problem, of interest both in quantum field theory (Feynman diagrams enumeration, beyond the planar approximation) and in statistical mechanics (high temperature loop expansion of some frustrated lattice spin model).     

Star product geometries

We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows us to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. Principles of symmetry can be implemented in this way. Two examples are considered: (a) the general covariance in noncommutative spacetime, which leads to a noncommutative theory of gravity, and b) symplectomorphims of the algebra of observables associated with noncommutative configuration spaces, which leads to a geometric formulation of quantization on noncommutative spacetime (i.e., we establish a noncommutative correspondence principle from ⋆-Poisson brackets to ⋆-commutators).     

Graded non-commutative geometries

We present a short exposition of graded finite non-commutative geometries. The theory that serves as an example is based on the algebra of matrices M_n . This non-commutative algebra replaces the algebra of functions on a manifold. Consequently, vector fields (differentiations), forms and connections are constructed. The gauge theory can be introduced without the notion of internal manifold. We discuss some physical application, the similarities with the standard model, and the graded version of this geometry.