Yuri O. Popov

Evaporative deposition patterns: spatial dimensions of the deposit.

A model accounting for the finite spatial dimensions of the deposit patterns in evaporating sessile drops of a colloidal solution on a plane substrate is proposed. The model is based on the assumption that the solute particles occupy finite volume and hence these dimensions are of steric origin. Within this model, the geometrical characteristics of the deposition patterns are found as functions of the initial concentration of the solute, the initial geometry of the drop, and the time elapsed from the beginning of the drying process. The model is solved analytically for small initial concentrations of the solute and numerically for arbitrary initial concentrations of the solute. The agreement between our theoretical results and the experimental data is demonstrated, and it is shown that the observed dependence of the deposit dimensions on the experimental parameters can indeed be attributed to the finite dimensions of the solute particles. These results are universal and do not depend on any free or fitting parameters; they are important for understanding evaporative deposition and may be useful for creating controlled deposition patterns.

Field-Theoretic Simulations of Polyelectrolyte Complexation

We briefly discuss our recent field-theoretic study of polyelectrolyte complexation, which occurs in solutions of two oppositely charged polyelectrolytes. Charged systems require theoretical methods beyond the mean-field (or self-consistent field) approximation; indeed, mean-field theory is qualitatively incorrect for such polyelectrolyte solutions. Both analytical (one-loop) and numerical (complex Langevin) methods to account for charge correlations are discussed. In particular, the first application of field-theoretic simulations to polyelectrolyte systems is reported. The polyelectrolyte charge-charge correlation length and a phase diagram are provided; effects of charge redistribution are qualitatively explored.

Characteristic angles in the wetting of an angular region: deposit growth.

Solids dispersed in a drying drop migrate to the (pinned) contact line. This migration is caused by outward flows driven by the loss of the solvent due to evaporation and by geometrical constraint that the drop maintains an equilibrium surface shape with a fixed boundary. Here, in continuation of our earlier paper, we theoretically investigate the evaporation rate, the flow field, and the rate of growth of the deposit patterns in a drop over an angular sector on a plane substrate. Asymptotic power laws near the vertex (as distance to the vertex goes to zero) are obtained. A hydrodynamic model of fluid flow near the singularity of the vertex is developed and the velocity field is obtained. The rate of the deposit growth near the contact line is found in two time regimes. The deposited mass falls off as a weak power gamma of distance close to the vertex and as a stronger power beta of distance further from the vertex. The power gamma depends only slightly on the opening angle alpha and stays roughly between -1/3 and 0. The power beta varies from -1 to 0 as the opening angle increases from 0 degrees to 180 degrees. At a given distance from the vertex, the deposited mass grows faster and faster with time, with the greatest increase in the growth rate occurring at the early stages of the drying process.

Characteristic angles in the wetting of an angular region: Surface shape

Abstract:The shape of a liquid surface bounded by an acute or obtuse planar angular sector is considered by using classical analysis methods. For acute angular sectors the two principal curvatures are of the order of the (fixed) mean curvature. But for obtuse sectors, the principal curvatures both diverge as the vertex is approached. The power law divergence becomes stronger with increasing opening angle. Possible implications of this contrasting behavior are suggested.

Effects of sequence disorder on DNA looping and cyclization.

Effects of sequence disorder on looping and cyclization of the double-stranded DNA are studied theoretically. Both random intrinsic curvature and inhomogeneous bending rigidity are found to result in a remarkably wide distribution of cyclization probabilities. For short DNA segments, the range of the distribution reaches several orders of magnitude for even completely random sequences. The ensemble averaged values of the cyclization probability are also calculated, and the connection to the recent experiments is discussed.

Deposit growth in the wetting of an angular region with uniform evaporation.

Solvent loss due to evaporation in a drying drop can drive capillary flows and solute migration. The flow is controlled by the evaporation profile and the geometry of the drop. We predict the flow and solute migration near a sharp corner of the perimeter under the conditions of uniform evaporation. This extends the study of Popov and Witten [Phys. Rev. E 68, 036306 (2003)], which considered a singular evaporation profile, characteristic of a dry surrounding surface. We find the rate of the deposit growth along contact lines in early and intermediate time regimes. Compared to the dry-surface evaporation profile of Popov and Witten [Phys. Rev. E 68, 036306 (2003)], uniform evaporation yields more singular deposition in the early time regime, and nearly uniform deposition profile is obtained for a wide range of opening angles in the intermediate time regime. Uniform evaporation also shows a more pronounced contrast between acute opening angles and obtuse opening angles.

Strong field approximation within a Faddeev-like formalism for laser-matter interactions

Abstract We consider the interaction of atomic hydrogen with an intense laser field within the strong-field approximation. By using a Faddeev-like formalism, we introduce a new perturbative series in the binding potential of the atom. As a first test of this new approach, we calculate the electron energy spectrum in the very simple case of a photon energy higher than the ionisation potential. We show that by contrast to the standard perturbative series in the binding potential obtained within the strong field approximation, the first terms of the new series converge rapidly towards the results we get by solving the corresponding time-dependent Schrödinger equation. Graphical abstract

Discrete algorithms for symbolic computing of topological phases and observables in interferometric systems

Discrete algorithms for symbolic computation of topological phases and observables in optical interferometric systems are presented and illustrated using a set of test models. The calculation of the parameters of a birefringent plate that can be measured by means of Mach-Zehnder interferometer is implemented in terms of Maple and Mathematica. Near-field test models of the systems, that possess both geometrical and dynamical phases in the far-field region, are constructed beyond the the bounds of the ray approximation. These models imply a set of discrete sources with variable parameters and make use of the appropriate set of separable potentials.

Multiple ionization of atoms with xuv attosecond pulses: Two-photon double ionization of helium with 50 eV photons

We consider two-photon double ionization of helium by two xuv photons in the region around the sequential ionization threshold. We show that, on the attosecond timescale, the mechanism for double ionization is dominated by the absorption of one photon by each electron in the fundamental state He(1s2). We examine the dynamics of two-photon double ionization of helium for an averaged photon energy ω = 50 eV, with a pulse duration of two optical cycles. The double ionization rate, energy and angular distributions are calculated by solving the time-dependent Schrodinger equation. Results are discussed on the basis of a model.