Arno Holz

Stability limit of supercooled liquids

Abstract We have calculated the lowest temperature to which liquid metals can be supercooled, using homogeneous nucleation theory. A new expression has been proposed for the change in volume free energy on solidification. The results obtained for maximum supercooling compare well with the latest experimental data.

Topological properties of static and dynamic defect configurations in ordered liquids

The topology of linked disclinations is studied in uniaxial nematic liquids and in anisotropic liquids with an order parameter space SO(3)/Pi(3). In these models {Pi(3)} are the finite point symmetry groups of 3-space with applications to helium 3 (Pi(3) = I), biaxial nematic liquid (Pi(3) = D2), and anisotropic super cooled liquids (Pi(3) = groups of Platonic solids). The topological properties are studied via Hopfs invariant of the O(3) σ model and its relation to the Wess-Zumino term of the SO(3)/Pi(3) σ model in an orthonormal drei-bein representation of SO(3). Dynamic processes are topology changing during intersection of disclinations and are studied via “magnetic” N-pole singularities and the instanton number η in an “electromagnetic” formalism. The connection with tunneling amplitudes in a SO(3) Yang-Mills theory is indicated. Applications of the theory to topological fluid dynamics is worked out for the uniaxial nematic liquid and indicated for the SO(3) spin liquid.

Crossover behavior of systems associated with extended-defect N-component systems in cubic anisotropic crystals

Extended-defect N-component systems in cubic anisotropic crystals have fixed points of the Gaussian [G], Ising [PI], isotropic N-component [PN] and cubic anisotropic N-component [PcN] systems as regular (pure) systems, and those of the Ising [DI], isotropic N-component [DN], cubic anisotropic XY [DcXY] and cubic anisotropic N-component [DcN] systems as extended-defect systems. Crossover behavior near these typical fixed point systems is studied by means of a renormalization-group (RG) approach and characteristic curve (CC) method. Crossover exponents of the systems and their behavior are calculated and illustrated to linear order in ϵ (≡ − d; d = dimension of space) and ≈ϵ (≡ϵ + ϵd; ϵd = dimension of space occupied by extended defects (impurities)).

Self-similarity law of particle size distribution and energy law in size reduction of solids

The concept of fractal dimension and scaling is used to determine the particle size distribution for ground powder and a generalized energy law for size reduction of solids. Based on the theory of stochastic processes, a master equation for the size distribution under a sieve is introduced. For the case that the functional forms of the transition probabilities are given, the solution is analutically obtained. Introducing a scaling concept and a characteristic size constant which measures the particle size distribution of the ground product, we present a power law for the distribution function. We, furthermore, present a generalized fractal energy law which has an intimate relation to the size distribution through a fractal specific surface area.

On the critical dynamics of extended-impurity systems in cubic anisotropic crystals

Critical dynamics is studied for N-component spin systems in cubic anisotropic crystals in the presence of extended impurities, namely ed-dimensionally connected impurities distributed randomly in d∼ (≡ d − ed) dimensions (d: dimensionality of the medium; d ≡ 4 - e). As extended impurities make the systems coordinate-anisotropic, new results are expected in the critical dynamics. By means of a field-theoretic renormalization-group (RG) approach, critical regions and dynamic critical exponents are evaluated, to the lowest order in a double e, ed expansion, for models corresponding to model A, model B and model C, proposed by Hohenberg and Halperin.

Static and dynamic properties of XY systems with extended defects in cubic anisotropic crystallines

Static and dynamic critical behavior ofXY systems in cubic anisotropic crystallines, with extended defects (or quenched nonmagnetic impurities) strongly correlated alongɛd-dimensional space and randomly distributed ind − ɛd dimensions, were studied. These extended defects make the systems coordinate anisotropic, resulting in unique critical behavior due to competition between the cubic anisotropy and the coordinate anisotropy. The systems were analyzed by anɛ1/2 (ɛ≡4 − d) type of expansion with double expansion parameters based on a renormalization-group (RG) approach. Critical exponents were calculated near the second-order phase transition point and the behavior of the first-order transition was evaluated near the tricritical point.

Melting transition in paraffins

Abstract The melting of paraffin layers is analysed in terms of the two dimensional dislocation theory of melting. Quantitative agreement is obtained between theory and experiment for the molecular weight dependence of the melting point.

Qualitative theory of the solid-liquid transition

Some qualitative attempts to the elucidation of the melting transition is solids are presented. The screening of the long range elastic interactions in the liquid phase is considered to originate from the presence of freely mobile infinitely extended dislocation loops. In contrast to other similar theories it is, however, assumed that cooperative diffusive motion (or “convective” motion) plays an equally important role in releasing any trapped in dislocation configurations which may lead to immobility of the system. The apparent universal nature of the discontinuity of the melting transition is studied on the basis of these concepts via possible nucleation mechanisms. The technical means used to treat dislocation configurations are combinatorics and the path integral formalism. The conclusion reached are that the universal nature of the discontinuity of the melting transition is a consequence of the strongly coupled dynamics of dislocations and cooperative diffusive motion.

Stability Analysis of Polymeric Liquid Crystal in Shearing Flow and Texture Formation

Nemato dynamics of polymeric liquid crystals in shearing flow is studied using the Ericksen-Leslie equations supplemented by suitable boundary conditions, for the viscosity regime |γ2/γ1| < 1, where a tumbling motion of the order parameter in a uniform system is predicted by Marrucci (1985). Taking account of boundary conditions it is shown that the tumbling motion at low shear rates γ˙ is replaced by formation of soliton-like patterns. The stability analysis of such order parameter configurations in a planar approximation shows that it becomes unstable with increasing |γ˙| as a consequence of shear thinning, leading into a nonuniform rotational state, where a dynamic array of disclinations prevents roll up effects of the order parameter. Texture formation upon arrest of flow is postulated to be a consequence of the relaxation of disclinations into a temporarily stable lattice associated with periodic twist deformations.

Gauge theory of two-dimensional spin-12 Heisenberg antiferromagnet

A gauge theory of the spin-12 Heisenberg antiferromagnet (HA) on a two-dimensional square lattice is developed, which is based on the diagonal GD of the group product SO(3)×SU(2). For classical gauge fields GD is homeomorphic to SO(3). The structure of the theory is such that the quantum spin-12 field propagates on the background gauge field. For special gauges the excitations of the spin-field are computed and compared to the excitations of the O(3) σ model for the same gauge. The significance of negative excitational modes with respect to a semiclassical actionГsc of the spin-12 HA is discussed. Some properties ofГsc represented as a chiral SO(3) model in a continuum representation are worked out.