Strongly nonlinear waves in capillary electrophoresis

In capillary electrophoresis, sample ions migrate along a micro-capillary filled with a background electrolyte under the influence of an applied electric field. If the sample concentration is sufficiently high, the electrical conductivity in the sample zone could differ significantly from the background.Under such conditions, the local migration velocity of sample ions becomes concentration dependent resulting in a nonlinear wave that exhibits shock like features. If the nonlinearity is weak, the sample concentration profile, under certain simplifying assumptions, can be shown to obey Burgers' equation (S. Ghosal and Z. Chen Bull. Math. Biol. 2010, 72(8), pg. 2047) which has an exact analytical solution for arbitrary initial condition.In this paper, we use a numerical method to study the problem in the more general case where the sample concentration is not small in comparison to the concentration of background ions. In the case of low concentrations, the numerical results agree with the weakly nonlinear theory presented earlier, but at high concentrations, the wave evolves in a way that is qualitatively different.Comment: 7 pages, 5 figures, 1 Appendix, 2 videos (supplementary material

On the distance of the poles of magnets

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Time dependence of the survival probability of an opinion in a closed community

The time dependence of the survival probability of an opinion in a closed community has been investigated in accordance with social temperature by using the Kawasaki-exchange dynamics based on previous study in Ref. [1]. It is shown that the survival probability of opinion decays with stretched exponential law consistent with previous static model. However, the crossover regime in the decay of the survival probability has been observed in this dynamic model unlike previous model. The decay characteristics of both two regimes obey to stretched exponential.Comment: Revised version of the paper (9 page, 5 Figures). Submitted to Int. J. Mod. Phys.

Non-exponential relaxation for anomalous diffusion

We study the relaxation process in normal and anomalous diffusion regimes for systems described by a generalized Langevin equation (GLE). We demonstrate the existence of a very general correlation function which describes the relaxation phenomena. Such function is even; therefore, it cannot be an exponential or a stretched exponential. However, for a proper choice of the parameters, those functions can be reproduced within certain intervals with good precision. We also show the passage from the non-Markovian to the Markovian behaviour in the normal diffusion regime. For times longer than the relaxation time, the correlation function for anomalous diffusion becomes a power law for broad-band noise.Comment: 6 pages, 2 figure

An Experimental and Theoretical Investigation of the Skeletal Frequencies of the Paraffin Hydrocarbons and the Far Infra‐Red Spectrum of Carbon Tetrachloride

The far infra‐red spectra of the paraffin hydrocarbons and of carbon tetrachloride have been investigated. The following bands were located: propane at 370.6 cm−1, n‐butane at 215 cm−1, and carbon tetrachloride at 315 cm−1, the latter showing isotope structure. The contours of the following near infra‐red bands for n‐butane were surveyed, and some fine structure was revealed: 1342.9 cm−1, 1295.6 cm−1, 1135.6 cm−1, 956.5 cm−1, and 740.0 cm−1. The assignment of the skeletal frequencies of vibration is made, and a theoretical analysis of the skeletal normal frequencies, assuming a valence potential for the molecules propane through pentane, is given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71089/2/JCPSA6-17-4-393-1.pd

Rotational Brownian motion on the sphere surface and rotational relaxation

The spatial components of the autocorrelation function of noninteracting dipoles are analytically obtained in terms of rotational Brownian motion on the surface of a unit sphere using multi-level jumping formalism based on Debye's rotational relaxation model, and the rotational relaxation functions are evaluated.Comment: RevTex, 4 pages, submitted to Chin. Phys. Let

Twist glass transition in regioregulated poly(3-alkylthiophenes)s

The molecular structure and dynamics of regioregulated poly(3-butylthiophene) (P3BT), poly(3-hexylthiophene)(P3HT), and poly(3-dodecylthiophene) (P3DDT) were investigated using Fourier transform infrared absorption (FTIR), solid state $^{13}$C nuclear magnetic resonance (NMR), and differential scanning calorimetry (DSC) measurements. In the DSC measurements, the endothermic peak was obtained around 340 K in P3BT, and assigned to enthalpy relaxation that originated from the glass transition of the thiophene ring twist in crystalline phase from results of FTIR, $^{13}$C cross-polarization and magic-angle spinning (CPMAS) NMR, $^{13}$C spin-lattice relaxation time measurements, and centerband-only detection of exchange (CODEX) measurements. We defined this transition as {\it twist-glass transition}, which is analogous to the plastic crystal - glassy crystal transition.Comment: 9 pages, 10 figures, 2 tables. Phys.Rev.B, in pres

The Infra‐Red Absorption Spectrum of Propane

Of the twenty‐seven internal degrees of freedom of propane, all nondegenerate, twenty‐two may appear as fundamental absorption bands. These bands fall into three symmetry classes, designated A1, B1 and B2, and distinguishable by their characteristic contours. Because of overlapping, however, it is impossible in many cases to determine their positions precisely. This is especially true in the regions of the C☒H valence and deformation frequencies. Some ten or twelve fundamental bands may be identified with confidence as well as a number of combinations. An A1 band at 870 cm—1 and a B2 band at 748 cm—1 have been partially resolved, the line spacing being about 1.47 cm—1 in agreement with predictions based upon electron diffraction measurements. The fine structure of the B1 bands has not been observed (the predicted spacing is 0.5 cm—1) but the interval between maxima of the P and R branches is approximately 26 cm—1 as expected. With 24 cm‐atmospheres of gas no bands were observed between 15μ and 35μ, although the symmetrical C☒C deformation might be expected to produce a band of appreciable intensity within these limits. This frequency has apparently been observed in Raman spectra at 375 cm—1.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70815/2/JCPSA6-9-7-487-1.pd

A Hybrid model for the origin of photoluminescence from Ge nanocrystals in SiO2_2 matrix

In spite of several articles, the origin of visible luminescence from germanium nanocrystals in SiO$_2$ matrix is controversial even today. Some authors attribute the luminescence to quantum confinement of charge carriers in these nanocrystals. On the other hand, surface or defect states formed during the growth process, have also been proposed as the source of luminescence in this system. We have addressed this long standing query by simultaneous photoluminescence and Raman measurements on germanium nanocrystals embedded in SiO$_2$ matrix, grown by two different techniques: (i) low energy ion-implantation and (ii) atom beam sputtering. Along with our own experimental observations, we have summarized relevant information available in the literature and proposed a \emph{Hybrid Model} to explain the visible photoluminescence from nanocrystalline germanium in SiO$_2$ matrix.Comment: 23 pages, 8 figure

Anomalous Rotational Relaxation: A Fractional Fokker-Planck Equation Approach

In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has a fractional form for complex disordered systems, which indicates relaxation has non-exponential character obeys to Kohlrausch-William-Watts law, following the Mittag-Leffler decay.Comment: Revtex4, 9 pages. Paper was revised. References adde