Intersoliton forces in weak-coupling quantum field theories

We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional φ4 theory. To do this, we construct analytically a static solution of the theory which can be interpreted as a kink and an antikink held a distance R apart. This leads to a definition of the potential energy U(R) for the pair, which is seen to have all the expected features. A corresponding evaluation is also done for U(R) between a soliton and an antisoliton of the sine-Gordon theory. When this U(R) is inserted into a nonrelativistic two-body problem for the pair, it yields a set of bound states and phase shifts. These are found to agree with exact results known for the sine-Gordon field theory in those regions where U(R) is expected to be significant, i.e., when R is large compared to the soliton size. We take this agreement as support that our procedure for defining U(R) yields the correct description of the dynamics of well-separated soliton pairs. An important feature of U(R) is that it seems to give strong intersoliton forces when the coupling constant is small, as distinct from the forces between the ordinary quanta of the theory. We suggest that this is a general feature of a class of theories, and emphasize the possible relevance of this feature to real strongly interacting hadrons.

Critical Exponent β and Rectilinear Diameter of the Binary-Liquid System Carbon Disulfide + Nitromethane

The system CS2 + CH3NO2 shows β=0.315±0.004 over 10-6<ε=|T-Tc| / Tc<2-10-1 with no indication of a classical value ½ even far away from Tc. The diameter shows a curvature and is of the form - c+b ε+fε7 / 8exp(-gεh).

Liquid-liquid critical phenomena. The coexistence curve of n-heptane-acetic anhydride

The coexistence curve of the binary liquid mixture n-heptane-acetic anhydride has been determined by the observation of the transition temperatures of 76 samples over the range of compositions. The functional form of the difference in order parameter, in terms of either the mole fraction or the volume fraction, is consistent with theoretical predictions invoking the concept of universality at critical points. The average value of the order parameter, the diameter of the coexistence curve, shows an anomaly which can be described by either an exponent 1 - a, as predicted by various theories (where a is the critical exponent of the specific heat), or by an exponent 20 (where P is the coexistence curve exponent), as expected when the order parameter used is not the one the diameter of which diverges asymptotically as 1 - a.

On-line Dynamic Security Assessment: Determination of Critical Transmission Lines

The main objective of on-line dynamic security assessment is to take preventive action if required or decide remedial action if a contingency actually occurs. Stability limits are obtained for different contingencies. The mode of instability is one of the outputs of dynamic security analysis. When a power system becomes unstable, it splits initially into two groups of generators, and there is a unique cutset in the transmission network known as critical cutset across which the angles become unbounded. The knowledge of critical cutset is additional information obtained from dynamic security assessment, which can be used for initiating preventive control actions, deciding emergency control actions, and adaptive out-of-step relaying. In this article, an analytical technique for the fast prediction of the critical cutset by system simulation for a short duration is presented. Case studies on the New England ten-generator system are presented. The article also suggests the applications of the identification of critical cutsets.

Critical test for Altshuler-Aronov theory: Evolution of the density of states singularity in double perovskite Sr2FeMoO6 with controlled disorder

With high-resolution photoemission spectroscopy measurements, the density of states (DOS) near the Fermi level (E-F) of double perovskite Sr2FeMoO6 having different degrees of Fe/Mo antisite disorder has been investigated with varying temperature. The DOS near E-F showed a systematic depletion with increasing degree of disorder, and recovered with increasing temperature. Altshuler-Aronov (AA) theory of disordered metals well explains the dependences of the experimental results. Scaling analysis of the spectra provides experimental indication for the functional form of the AA DOS singularity.

Critical lattice size limit for synchronized chaotic state in one- and two-dimensional diffusively coupled map lattices

We consider diffusively coupled map lattices with P neighbors (where P is arbitrary) and study the stability of the synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This generalizes earlier results for nearest neighbor coupling. We confirm the analytical results by performing numerical simulations on coupled map lattices with logistic map at each node. The above analysis is also extended to two-dimensional P-neighbor diffusively coupled map lattices.

Dynamics after a sweep through a quantum critical point

The coherent quantum evolution of a one-dimensional many-particle system after slowly sweeping the Hamiltonian through a critical point is studied using a generalized quantum Ising model containing both integrable and nonintegrable regimes. It is known from previous work that universal power laws of the sweep rate appear in such quantities as the mean number of excitations created by the sweep. Several other phenomena are found that are not reflected by such averages: there are two different scaling behaviors of the entanglement entropy and a relaxation that is power law in time rather than exponential. The final state of evolution after the quench is not characterized by any effective temperature, and the Loschmidt echo converges algebraically for long times, with cusplike singularities in the integrable case that are dynamically broadened by nonintegrable perturbations.

Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point

The critical behavior of osmotic susceptibility in an aqueous electrolyte mixture 1-propanol (1P)+water (W)+potassium chloride is reported. This mixture exhibits re-entrant phase transitions and has a nearly parabolic critical line with its apex representing a double critical point (DCP). The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths (by varying t) in the one-phase region. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in this mixture. For the TL far away from the DCP, the effective susceptibility exponent γeff as a function of t displays a nonmonotonic crossover from its single limit three-dimensional (3D)-Ising value ( ∼ 1.24) toward its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value toward its nearly doubled mean-field value with increase in t. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend toward shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover to the mean-field limit extends well beyond t>10−2 for the TL’s studied. The observed crossover behavior is attributed to the presence of strong ion-induced clustering in this mixture, as revealed by various structure probing techniques. As far as the critical behavior in complex or associating mixtures with special critical points (like the DCP) is concerned, our results indicate that the influence of the DCP on the critical behavior must be taken into account not only on the renormalization of the critical exponent but also on the range of the Ising regime, which can shrink with decrease in the influence of the DCP and with the extent of structuring in the system. The utility of the field variable tUL in analyzing re-entrant phase transitions is demonstrated. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value toward a value slightly lower than its nonasymptotic mean-field value of 1. This behavior in the nonasymptotic, high tUL region is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values, as foreseen earlier in micellar systems.

Vibrational phase relaxation of O–H stretch in bulk water: Role of large amplitude angular jumps and negative cross-correlations among the forces on the O–H bond

The ultrafast vibrational phase relaxation of O–H stretch in bulk water is investigated in molecular dynamics simulations. The dephasing time (T2) of the O–H stretch in bulk water calculated from the frequency fluctuation time correlation function (Cω(t)) is in the range of 70–80 femtosecond (fs), which is comparable to the characteristic timescale obtained from the vibrational echo peak shift measurements using infrared photon echo [W.P. de Boeij, M.S. Pshenichnikov, D.A. Wiersma, Ann. Rev. Phys. Chem. 49 (1998) 99]. The ultrafast decay of Cω(t) is found to be responsible for the ultrashort T2 in bulk water. Careful analysis reveals the following two interesting reasons for the ultrafast decay of Cω(t). (A) The large amplitude angular jumps of water molecules (within 30–40 fs time duration) provide a large scale contribution to the mean square vibrational frequency fluctuation and gives rise to the rapid spectral diffusion on 100 fs time scale. (B) The projected force, due to all the atoms of the solvent molecules on the oxygen (FO(t)) and hydrogen (FH(t)) atom of the O–H bond exhibit a large negative cross-correlation (NCC). We further find that this NCC is partly responsible for a weak, non-Arrhenius temperature dependence of the dephasing rate.

GMRT observations of the group Holmberg 124: Evolution by tidal forces and ram pressure?

We report new radio continuum and 21 cm HI observations using the Giant Metrewave Radio Telescope (GMRT) of the group Holmberg 124 ( Ho 124) comprising four late-type galaxies, namely NGC 2820, Mrk 108, NGC 2814 and NGC 2805. The three galaxies, NGC 2820, Mrk 108 and NGC 2814 which are closely located in the sky plane have clearly undergone tidal interactions as seen from the various morphological tidal signatures and debris. Moreover we note various features in the group members which we believe might be due to ram pressure. In this paper, we describe four interesting results emerging from our observations: a) detection of the tidal radio continuum bridge at 330 MHz connecting the galaxies NGC 2820+ Mrk 108 with NGC 2814. The radio bridge was discovered at 1465 MHz by van der Hulst & Hummel ( 1985, A& A, 150, 17). We find that the bridge has a fairly steep spectrum with a spectral index alpha(S proportional to nu(alpha)) of - 1.8(-0.2)(+0.3) which is much steeper than the - 0.8 quoted by van der Hulst & Hummel ( 1985); b) detection of other tidal features like the tilted HI and radio continuum disk of NGC 2814, a HI streamer and a radio continuum tail arising from the south of NGC 2814. We also report the detection of a possible tidal dwarf galaxy in HI; c) sharp truncation in the HI distribution in the south of NGC 2820 and in the HI and radio continuum distribution in the north of NGC 2814. The optical disks in both the cases look undisturbed. As pointed out by Davis et al. ( 1997, AJ, 114, 613), ram pressure affects different components of the interstellar medium to varying degrees. Simple estimates of pressure in different components of the interstellar medium ( radio continuum, Ha and HI) in NGC 2820 indicate that ram pressure will significantly influence HI; d) detection of a large one-sided HI loop to the north of NGC 2820. No radio continuum emission or Ha emission is associated with the HI loop. We discuss various scenarios for the origin of this loop including a central starburst, ram pressure stripping and tidal interaction. We do not support the central starburst scenario since the loop is not detected in ionized gas. Using the upper limit on X-ray luminosity of Ho 124 (Mulchaey et al. 2003, ApJS, 145, 39), we estimate an upper limit on the intragroup medium (IGrM) density of 8.8 x 10(-4) cm(-3). For half this electron density, we estimate the ram pressure force of the IGrM to be comparable to the gravitational pull of the disk of NGC 2820. Since tidal interaction has obviously influenced the group, we suggest that the loop could have formed by ram pressure stripping if tidal effects had reduced the surface density of HI in NGC 2820. From the complex observational picture of Ho 124 and the numerical estimates, we suggest that the evolution of the Ho 124 group may be governed by both tidal forces due to the interaction and the ram pressure due to motion of the member galaxies in the IGrM and that the IGrM densities should not be too low (i.e. >= 4 x 10(-4)). However this needs to be verified by further observations.

Critical phenomena in the coexistence curve of the binary liquid system

The coexistence curve of the carbondisulphide-acetic anhydride system has been measured. The shape of the curve in the critical region (Xc ≈ 70.89 mole % mole % CS2 and Tc ≈ 30.56° C) is determined by the equation |X′ - X″| = Bx (1 - T/Tc)β with the critical indices β = 0.34 ± 0.01 and Bx = 1.7 ± 0.1 over a range 10-6 < (Tc - T)/Tc < 10-2. The values of β and Bx agree with those of other systems and the theoretical predictions of the Ising model.

Estimation of the critical viscous sublayer in heat transfer problems

Imagining a disturbance made on a compressible boundary layer with the help of a heat source, the critical viscous sublayer, through which the skin friction at any point on a surface is connected with the heat transferred from a heated element embedded in it, has been estimated. Under similar conditions of external flow (Ray1)) the ratio of the critical viscous sublayer to the undisturbed boundary layer thickness is about one-tenth in the laminar case and one hundredth in the turbulent case. These results are similar to those (cf.1)) found in shock wave boundary layer interaction problems.

Contribution of different physical forces to the disjoining pressure of a thin water film being pressed by an oil droplet

With an objective to understand the nature of forces which contribute to the disjoining pressure of a thin water film on a steel substrate being pressed by an oil droplet, two independent sets of experiments were done. (i) A spherical silica probe approaches the three substrates; mica, PTFE and steel, in a 10 mM electrolyte solution at two different pHs (3 and 10). (ii) The silica probe with and without a smeared oil film approaches the same three substrates in water (pH = 6). The surface potential of the oil film/water was measured using a dynamic light scattering experiment. Assuming the capacity of a substrate for ion exchange the total interaction force for each experiment was estimated to include the Derjaguin-Landau-Verwey-Overbeek (DLVO) force, hydration repulsion, hydrophobic attraction and oil-capillary attraction. The best fit of these estimates to the force-displacement characteristics obtained from the two sets of experiment gives the appropriate surface potentials of the substrates. The procedure allows an assessment of the relevance of a specific physical interaction to an experimental configuration. Two of the principal observations of this work are: (i) The presence of a surface at constant charge, as in the presence of an oil film on the probe, significantly enhances the counterion density over what is achieved when both the surfaces allow ion exchange. This raises the corresponding repulsion barrier greatly. (ii) When the substrate surface is wettable by oil, oil-capillary attraction contributes substantially to the total interaction. If it is not wettable the oil film is deformed and squeezed out. (C) 2010 Elsevier Inc. All rights reserved.