Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes.

Measurement of contact voltage drop and resistance in organic solar cells

Bulk heterojunction organic solar cells based on poly[4,7-bis(3- dodecylthiophene-2-yl) benzothiadiazole-co-benzothiadiazole] and [6,6]-phenyl C71-butyric acid methyl ester are investigated. A prominent kink is observed in the fourth quadrant of the current density-voltage (J-V) response. Annealing the active layer prior to cathode deposition eliminates the kink. The kink is attributed to an extraction barrier. The J-V response in these devices is well described by a power law. This behavior is attributed to an imbalance in charge carrier mobility. An expected photocurrent for the device displaying a kink in the J-V response is determined by fitting to a power law. The difference between the expected and measured photocurrent allows for the determination of a voltage drop within the device. Under simulated 1 sun irradiance, the peak voltage drop and contact resistance at short circuit are 0.14 V and 90 Ω, respectively. © 2012 American Institute of Physics.

Free vibration of a kinked cantilever with attached masses

In this paper free vibration characteristics of a centrally kinked cantilever beam of unit mass carrying masses at the kink (m(k)) and at the tip (m(t)) are analyzed. Frequency factors are presented for the first two modes for different combinations of m(k),m(t) and the kink angle delta. A relationship of the form f(m(k),m(t), delta) = m(k) + m(t)(4 + 10/3 cos delta+ 2/3 cos(2) delta)=const appears to give the same fundamental frequency for a given delta and different combinations of [m(k), m(t)]. Mode shapes as well as bending moments at the support and at the kink are also discussed. The utility of a discrete beam model in understanding the free vibration characteristics is also highlighted.

Conformational Dynamics in Alkyl Chains of an Anchored Bilayer: A Molecular Dynamics Study

Molecular dynamics (MD) simulations are reported for an anchored bilayer formed by the intercalation of cetyl trimethyl ammonium (CTA) and CH3(CH2)15N+(CH3) ions in a layered solid, CdPS3. The intercalated CTA ions are organized with the cationic headgroups tethered to the inorganic sheet and the hydrocarbon tails arranged as bilayers. Simulations were performed at three temperatures, 65, 180, and 298 K, using an isothermal−isobaric ensemble that was subsequently switched once macroscopic parameters had converged to a canonical isothermal−isochoric ensemble. The simulations are able to reproduce the experimental features of this system, including the formation of the bilayer and layer-to-layer separation distance. An analysis of the conformation of the chains showed that at all three temperatures a fraction of the alkyl chains retained a planar all-trans conformation, and that gauche bonds occurred as part of a “kink” (gauche+−trans−gauche−) sequence and not as isolated gauche bonds. Trans−gauche isomerization rates for the alkyl chains in the anchored bilayer are slower than those in lipid bilayers at the same temperature and show a progressive increase as the torsion numbers approach the tail. A two-dimensional periodic Voronoi tessellation analysis was performed to obtain the single-molecular area of an alkyl chain in the bilayer. The single-molecular area relaxation times are an order of magnitude longer than the trans−gauche isomerization times. The results indicate that the trans−gauche isomerization is associated with the creation and annihilation of a kink defect sequence. The results of the present MD simulation explain the apparent conflicting estimates of the gauche disorder in this system as obtained from infrared and 13C nuclear magnetic resonance measurements.

Impurity states in Sb-doped amorphous semiconductors

A systematic investigation of the effects of antimony dopant on the electronic transport properties of amorphous (GeSe3.5)100−xSbx under high pressure (up to 120 kbar) has been carried out down to liquid-nitrogen temperature for the first time. Differential thermal analysis and x-ray diffraction methods were used for the characterization of freshly prepared and pressure-quenched materials which indicated the presence of structural phase transition in both GeSe3.5 and (GeSe3.5)100−xSbx around 105 kbar pressure. Electrical transport data revealed the strong compositional dependence of the electronic conduction process. A distinct kink in the conductivity temperature plot at pressures>15 kbar was observed in the Sb-doped compositions indicating the presence of different conduction processes. An attempt has been made to interpret the pressure-induced effect in the transport properties of these glasses considering the possible presence of both thermally activated conduction in the extended states and hopping process in the localized tail states. However, the interpretation of the transport data is not straightforward and the pressure dependence of the thermoelectric power will be needed to complete the picture. Journal of Applied Physics is copyrighted by The American Institute of Physics.

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.

The incongruous observation of magnetic phase separation in La0.85Sr0.15CoO3 spin glass system

Phase separation (PS) in hole-doped cobaltites (La1-xSrxCoxO3) is drawing renewed interest recently. In particular, the magnetic behavior of La0.85Sr0.15CoO3 has been subjected to a controversial debate for the past several years; while some groups show evidence for magnetic PS, others show spin glass (SG) behavior. Here, an attempt is made to resolve the controversy related to ``PS versus SG'' behavior in this compound. We present the results of a comprehensive investigation of the dc magnetization, ac susceptibility, and the magnetotransport properties of La0.85Sr0.15CoO3 samples. We contemplate that the magnetic PS in La0.85Sr0.15CoO3 is neither intrinsic nor inherent, but it is a consequence of the preparation conditions. It is realized that a low temperature annealed (LTA) sample shows PS whereas the high temperature annealed (HTA) sample shows SG behavior. The Brillouin-like behavior of field cooled dc magnetization and apparently no frequency dependent peak shift in ac susceptibility for the LTA sample characterize it to be of ferromagneticlike whereas a kink in field cooled dc magnetization and a considerable amount (similar to 3 K) of frequency dependent peak shift in the ac susceptibility for the HTA sample characterize it to be of SG state. The magnetotransport properties show that the HTA sample is more semiconducting as compared to the LTA sample. This is interpreted in terms of the presence of isolated as well as coalescing metallic ferromagnetic clusters in the case of LTA sample. The magnetoresistance (MR) at 10 K for the HTA sample exhibits a huge value (similar to 65%) as compared to the LTA sample, and it monotonically decreases with the rise in temperature. Such a high value of MR in the case of HTA sample is strongly believed to be due to the spin dependent part of random potential distribution. Further, the slow decay of remnant magnetization with progress of time and the existence of hysteresis at higher temperatures (up to 200 K) in the case of LTA sample as compared to the HTA sample clearly unveil different magnetic states associated with them.

A numerical study of crack tip constraint in ductile single crystals

In this work, the effect of crack tip constraint on near-tip stress and deformation fields in a ductile FCC single crystal is studied under mode I, plane strain conditions. To this end, modified boundary layer simulations within crystal plasticity framework are performed, neglecting elastic anisotropy. The first and second terms of the isotropic elastic crack tip field, which are governed by the stress intensity factor K and T-stress, are prescribed as remote boundary conditions and solutions pertaining to different levels of T-stress are generated. It is found that the near-tip deformation field, especially, the development of kink or slip shear bands, is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the crack tip are also strongly influenced by the level of T-stress, with progressive loss of crack tip constraint occurring as T-stress becomes more negative. A family of near-tip fields is obtained which are characterized by two terms (such as K and T or J and a constraint parameter Q) as in isotropic plastic solids.

Crack Tip Fields in a Single Edge Notched Aluminum Single Crystal Specimen

We report a combined experimental and computational study of a low constraint aluminum single crystal fracture geometry and investigate the near-tip stress and strain fields. To this end, a single edge notched tensile (SENT) specimen is considered. A notch, with a radius of 50 µm, is taken to lie in the (010) plane and its front is aligned along the [101] direction. Experiments are conducted by subjecting the specimen to tensile loading using a special fixture inside a scanning electron microscope chamber. Both SEM micrographs and electron back-scattered diffraction (EBSD) maps are obtained from the near-tip region. The experiments are complemented by performing 3D and 2D plane strain finite element simulations within a continuum crystal plasticity framework assuming an isotropic hardening response characterized by the Pierce–Asaro–Needleman model. The simulations show a distinct slip band forming at about 55 deg with respect to the notch line corresponding to slip on (11-bar 1)[011] system, which corroborates well with experimental data. Furthermore, two kink bands occur at about 45 deg and 90 deg with respect to the notch line within which large rotations in the crystal orientation take place. These predictions are in good agreement with the EBSD observations. Finally, the near-tip angular variations of the 3D stress and plastic strain fields in the low constraint SENT fracture geometry are examined in detail.

An evaluation of rate-controlling obstacles for low-temperature deformation of zirconium

The low-temperature plastic flow of alpha-zirconium was studied by employing constantrate tensile tests and differential-stress creep experiments. The activation parameters, enthalpy and area, have been obtained as a function of stress for pure, as well as commercial zirconium. The activation area is independent of grain size and purity and falls to about 9b2 at high stresses. The deformation mechanism below about 700° K is found to be controlled by a single thermally activated process, and not a two-stage activation mechanism. Several dislocation mechanisms are examined and it is concluded that overcoming the Peierls energy humps by the formation of kink pairs in a length of dislocation is the rate-controlling mechanism. The total energy needed to nucleate a double kink is about 0.8 eV in pure zirconium and 1 eV in commercial zirconium

A critical re-examination and a revised phase diagram of La1-xSrxCoO3

We report the results of a comprehensive study on dc magnetization, ac susceptibility, and the magnetotransport properties of the La1-xSrxCoO3(0 <= x <= 0.5) system. At higher Sr doping (x >= 0.18), the system exhibits Brillouin-like field cooled magnetization (M-FC). However, for x < 0.18, the system exhibits a kink in the M-FC, a peak at the intermediate field in the thermoremnant magnetization and a non-saturating tendency in the M-H plot that all point towards the characteristic of spin glass behavior. More interestingly, dc magnetization studies for x < 0.18 do not suggest the existence of ferromagnetic correlation that can give rise to an irreversible line in the spin glass regime. The ac susceptibility study for x > 0.2 exhibits apparently no frequency dependent peak shift around the ferromagnetic transition region. However, a feeble signature of glassiness is verified by studying the frequency dependent shoulder position in chi `' (T) and the memory effect below the Curie temperature. But, for x < 0.18, the ac susceptibility study exhibits a considerable frequency dependent peak shift, time dependent memory effect, and the characteristic spin relaxation time scale tau(0) similar to 10(-13) s. The reciprocal susceptibility versus temperature plot adheres to Curie-Weiss behavior and does not provide any signature of preformed ferromagnetic clusters well above the Curie temperature. The magnetotransport study reveals a cross over from metallic to semiconducting-like behavior for x <= 0.18. On the semiconducting side, the system exhibits a large value of magnetoresistance (upto 75%) towards low temperature and it is strongly connected to the spin dependent part of the random potential distribution in the spin glass phase. Based on the above observations, we have reconstructed a new magnetic phase diagram and characterized each phase with associated properties.

CA/TG sequence at the 5' end of oligo(A)-tracts strongly modulates DNA curvature

An analysis of the base pair doublet geometries in available crystal structures indicates that the often reported intrinsic curvature of DNA containing oligo-(d(A).d(T)) tracts may also depend on the nature of the flanking sequences. The presence of CA/TG doublet in particular at the 5' end of these tracts is expected to enhance their intrinsic bending property. To test this proposition, three oligonucleotides, d(GAAAAACCCCCC), d(CCCCCCAAAAAG), d(GAAAAATTTTTC), and their complementary sequences were synthesized to study the effect of various flanking sequences, at the 5' and 3' ends of the A-tracts, on the curvature of DNA in solution. An analysis of the polyacrylamide gel electrophoretic mobilities of these sequences under different conditions of salts and temperatures (below their melting points) clearly showed that the oligomer with CA/TG sequence in the center was always more retarded than the oligomer with AC/GT sequence, as well as the oligomer with AT/AT sequence. Hydroxyl radical probing of the sequences with AC/GT and CA/TG doublet junctions gives a similar cutting pattern in the A-tracts, which is quite different from that in the C-tracts, indicating that the oligo(A)-tracts have similar structures in the two oligomers. KMnO4 probing shows that the oligomer with a CA/TG doublet junction forms a kink that is responsible for its inherent curvature and unusual electrophoretic mobility. UV melting shows a reduced thermal stability of the duplex with CA/TG doublet junction, and circular dichroism (CD) studies indicate that a premelting transition occurs in the oligomer with CA/TG doublet step before global melting but not in the oligomer with AC/GT doublet step, which may correspond to thermally induced unbending of the oligomer. These observations indicate that the CA/TG doublet junction at the 5' end of the oligo(A)-tract has a crucial role in modulating the overall curvature in DNA.

Implications of rapid footpoint motions of photospheric flux tubes for coronal heating

Some recent observations at Pic-du-Midi (Mulleret al., 1992a) suggest that the photospheric footpoints of coronal magnetic field lines occasionally move rapidly with typical velocities of the order 3 km s–1 for about 3 or 4 min. We argue that such occasional rapid footpoint motions could have a profound impact on the heating of the quiet corona. Qualitative estimates indicate that these occasional rapid motions can account for the entire energy flux needed to heat the quiet corona. We therefore carry out a mathematical analysis to study in detail the response of a vertical thin flux tube to photospheric footpoint motions in terms of a superposition of linear kink modes for an isothermal atmosphere. We find the resulting total energy that is asymptotically injected into an isothermal atmosphere (i.e., an atmosphere without any back reflection). By using typical parameter values for fast and slow footpoint motions, we show that, even if the footpoints spend only 2.5% of the time undergoing rapid motions, still these rapid motions could be more efficient in transporting energy to the corona than the slow motions that take place most of the time.

CA\TG Sequence at the 5'end of Oligo(A)-tracts Strongly Modulates DNA Curvature

An analysis of the base pair doublet geometries in available crystal structures indicates that the often reported intrinsic curvature of DNA containing oligo-(d(A).d(T)) tracts may also depend on the nature of the flanking sequences. The presence of CA/TG doublet in particular at the 5' end of these tracts is expected to enhance their intrinsic bending property. To test this proposition, three oligonucleotides, d(GAAAAACCCCCC), d(CCCCCCAAAAAG), d(GAAAAATTTTTC), and their complementary sequences were synthesized to study the effect of various flanking sequences, at the 5' and 3' ends of the A-tracts, on the curvature of DNA in solution. An analysis of the polyacrylamide gel electrophoretic mobilities of these sequences under different conditions of salts and temperatures (below their melting points) clearly showed that the oligomer with CA/TG sequence in the center was always more retarded than the oligomer with AC/GT sequence, as well as the oligomer with AT/AT sequence. Hydroxyl radical probing of the sequences with AC/GT and CA/TG doublet junctions gives a similar cutting pattern in the A-tracts, which is quite different from that in the C-tracts, indicating that the oligo(A)-tracts have similar structures in the two oligomers. KMnO4 probing shows that the oligomer with a CA/TG doublet junction forms a kink that is responsible for its inherent curvature and unusual electrophoretic mobility. UV melting shows a reduced thermal stability of the duplex with CA/TG doublet junction, and circular dichroism (CD) studies indicate that a premelting transition occurs in the oligomer with CA/TG doublet step before global melting but not in the oligomer with AC/GT doublet step, which may correspond to thermally induced unbending of the oligomer. These observations indicate that the CA/TG doublet junction at the 5' end of the oligo(A)-tract has a crucial role in modulating the overall curvature in DNA.