Time Integration Procedure for the Finite Element Solution of Nonlinear, Time-Dependent Problems in the Mechanics of Deformable Bodies

A finite element procedure is discussed for the calculation of nonlinear structures subjected to external loads that vary arbitrarily with time. A technique utilizing the Runge–Kutta method is proposed for solving the differential equation of motion. This technique has the advantage that it eliminates a number of restrictions on the form of the differential equation and shortens the computing time.     

Fragmentation of polyatomic molecules by grazing incidence surface-induced dissociation (GI-SID).

The grazing incidence surface-induced dissociation (GI-SID) of n-hexadecylpyridinium and verapamil ions generated by fission fragment desorption was studied. These molecules show the effect of enhanced surface-induced dissociation at grazing incidence as it was observed in former experiments with metal organic ions. A liquid film of perfluorinated polyether is used as collision surface. Small hydrocarbon fragment ions predominate in the GI-SID spectra. Pyridine ions appear as specific fragment ions in the GI-SID spectrum of n-hexadecylpyridinium. The GI-SID conversion efficiency varies in the range 40-70%. The experimental results are discussed within the scope of a quantum mechanical model which is based on the accumulation of internal molecular energy by resonant excitation of collective vibrational states and energy transfer to a trap bond due to dipole-dipole interactions. In this context the GI-SID spectra of n-hexadecylpyridinium and verapamil ions are compared with the fragmentation occurring in regular (252)Cf plasma desorption mass spectrometry.     

Absorption of dilaton partial waves by D3-branes

We calculate the leading term in the low-energy absorption cross section for an arbitrary partial wave of the dilaton field by a stack of many coincident D3-branes. We find that it precisely reproduces the semiclassical absorption cross section of a 3-brane geometry, including all numerical factors. The crucial ingredient in making the correspondence is the identification of the precise operators on the D3-brane world-volume which couple to the dilaton field and all its derivatives. The needed operators are related through T-duality and the IIA/M-theory correspondence to the recently determined M(atrix) theory expressions for multiple moments of the 11D supercurrent. These operators have a characteristic symmetrized trace structure which plays a key combinatorial role in the analysis for the higher partial waves. The results presented here give new evidence for an infinite family of non-renormalization theorems which are believed to exist for two-point functions in N=4 gauge theory in four dimensions.     

Periodic problem for an evolution equation with a quadratic and a cubic nonlinearity

We study conditions for the existence of a solution of a periodic problem for a model nonlinear equation in the spatially multidimensional case and consider various types of large time asymptotics (exponential and oscillating) for such solutions. The generalized Kolmogorov-Petrovskii-Piskunov equation, the nonlinear Schrödinger equation, and some other partial differential equations are special cases of this equation. We analyze the solution smoothing phenomenon under certain conditions on the linear part of the equation and study the case of nonsmall initial data for a nonlinearity of special form. The leading asymptotic term is presented, and the remainder in the asymptotics of the solution is estimated in a spatially uniform metric.     

A criterion for the solvability of the multiple interpolation problem by simple partial fractions

Using reduction to polynomial interpolation, we study the multiple interpolation problem by simple partial fractions. Algebraic conditions are obtained for the solvability and the unique solvability of the problem. We introduce the notion of generalized multiple interpolation by simple partial fractions of order ≤ n. The incomplete interpolation problems (i.e., the interpolation problems with the total multiplicity of nodes strictly less than n) are considered; the unimprovable value of the total multiplicity of nodes is found for which the incomplete problem is surely solvable. We obtain an order n differential equation whose solution set coincides with the set of all simple partial fractions of order ≤ n.     

Atomic-force microscopy of bismuth films

The surface structure of bismuth films is investigated using atomic-force microscopy. The films are prepared through vacuum thermal evaporation on mica substrates, followed by annealing. It is established that the films have a block structure with the preferred orientation of the C ₃ axis perpendicular to the substrate plane. The C ₂ axes of the neighboring blocks predominantly have mutually opposite orientations. Upon annealing, the sizes of blocks with the C ₃ axis perpendicular to the substrate plane increase at the expense of a virtually complete disappearance of blocks with random orientations of the C ₃ axis and the coalescence of blocks with the same orientation. The size and configuration of the blocks are most clearly revealed upon preliminary treatment of the films in a diluted solution of the etchant. The results obtained are of interest for the interpretation of the data on the transport phenomena occurring in bismuth films.     

The mesoscopic modeling of the structure of a hydrated ionomeric membrane based on a sulfonated aromatic poly(ether-ether-ketone)

A proton conducting hydrated membrane on the basis of sulfonated aromatic poly(ether-ether-ketone) was modeled for the first time using dynamic density functional theory (the “mesoscopic dynamics” method). The model constructed was used to demonstrate the microphase separation of hydrophilic and hydrophobic polymer chain units in the selected region of parameters. A spatial network of water domains formed in the membrane volume. The domain walls consisted of polar (sulfonated) macromolecule units. A comparison with the well-studied Nafion-1100 membrane showed that the cross sections of water channels in the two systems had similar values. This must ensure approximately equal ionic conductivity characteristics.     

Adsorption inhibition of the growth of CaSO4 · 2H2O crystals in aqueous solutions

Crystallography Reports - The growth of gypsum CaSO4 · 2H2O crystals in aqueous solutions has been investigated, both on individual crystals and on crystals in a homogeneous suspension in the...     

Muon-spin-relaxation investigation of EuMn<Subscript>2</Subscript>O<Subscript>5</Subscript>

The magnetic properties of the EuMn₂O₅ multiferroic (samples consisting of single crystals and ceramic samples) have been investigated by the muon-spin-relaxation (μSR) method in the temperature range of 10–300 K. Below the magnetic ordering temperature T _N = 40 K, the loss of the polarization of muons and the effect of the external magnetic field have been observed. Both phenomena can be explained by an additional channel of the depolarization of muons owing to the appearance of muons in a medium with a low electron density due to the charge separation process (the redistribution of the electron density in the phase transition process). The “memory” phenomenon has been revealed in a sample in the external magnetic field; the memory relaxation time depends on the size of the structure units of the samples (single crystals or ceramic grains).