Self-organised criticality in base-pair breathing in DNA with a defect

We analyse base-pair breathing in a DNA sequence of 12 base-pairs with a defective base at its centre. We use both all-atom molecular dynamics (MD) simulations and a system of stochastic differential equations (SDEs). In both cases, Fourier analysis of the trajectories reveals self-organised critical behaviour in the breathing of base-pairs. The Fourier Transforms (FTs) of the inter-base distances show power-law behaviour with gradients close to −1. The scale-invariant behaviour we have found provides evidence for the view that base-pair breathing corresponds to the nucleation stage of large-scale DNA opening (or ‘melting’) and that this process is a (second-order) phase transition. Although the random forces in our SDE system were introduced as white noise, FTs of the displacements exhibit pink noise, as do the displacements in the AMBER/MD simulations.     

The primary order parameter in antiferroelectric NaNbO3

X-ray scattering experiments on NaNbO₃ near the transition to antiferroelectric phase R indicate that the mode that softens — the primary mode or order parameter — is an octahedral rotational mode. It is argued that the antiferroelectric array of static Nb displacements present in phase R constitute the secondary order parameter; in other words non-zero values of the Nb displacements are induced through anharmonic coupling to the soft mode or primary mode. In current terminology, phase R is an improper antiferroelectric.     

Off-center displacements and hydrostatic pressure induced phase transition in perovskites

Pressure has a profound effect on the paraelectric and ferroelectric properties of perovskite crystals. In this paper we theoretically investigate the effect of pressure on the cubic-to-tetragonal phase transition and on the soft mode dynamics of some classical perovskite crystals: BaTiO(3), PbTiO(3), and KNbO(3). We use a model consisting of three subsystems: electrons, phonons, and off-center displacements treated as spins. Experiments show that pressure has a large effect on the tunneling and hopping of the off-center displacements, that in turn strongly affect the pressure dependence of the transition temperature and the soft mode frequency. This model, with a very small number of adjustable parameters, accounts quantitatively for the experimentally measured nonlinear pressure dependence of the cubic-to-tetragonal phase transition temperature, up to the critical pressure where the transition temperature is zero. It also accounts quantitatively for the pressure dependence of the soft mode frequency, which is finite at the phase transition in spite of the fact that the phase transition at elevated pressures is second order, and for the pressure dependence of the electronic gap energy.     

Investigation of specific features of the lattice dynamics and the ferroelectric transition in perovskite crystals

The specific features of diffuse X-ray scattering in BaTiO₃, KNbO₃, and PbTiP₃ perovskite crystals have been investigated. The former two perovskite compounds in cubic, tetragonal, and orthorhombic phases exhibit anomalous sheets due to diffuse X-ray scattering, whereas no similar sheets are observed in the case of diffuse X-ray scattering in PbTiO₃. For these compounds, the phonon spectra are calculated in the quasi-harmonic approximation within the polarizable-shell model, and the mechanism of stabilization of the soft mode above the temperature of the phase transition to the ferroelectric state is considered. It is demonstrated that, in the cubic phase of BaTiO₃ and KNbO₃ crystals, there exist quasi-one-dimensional “soft” modes of vibrations of ions in M-O-M-O- chains, where M = Ti or Nb. In PbTiO₃, this feature of the soft mode has not been revealed. The pair correlation functions of simultaneous atomic displacements in BaTiO₃, KNbO₃, and PbTiO₃ are determined and used to calculate the intensity of diffuse X-ray scattering. The results obtained are in good agreement with experimental data. This is a strong argument in support of the hypothesis that the specific features of diffuse scattering are associated with the existence of quasi-one-dimensional correlations of atomic displacements in the soft optical mode and that the ferroelectric transition in perovskites is a displacive ferroelectric phase transition. The possible influence of the specific features revealed in the phonon spectra of the perovskite crystals on the processes of nuclear magnetic resonance and X-ray absorption (extended X-ray absorption fine structure spectra) is briefly discussed.     

Pressure-induced amorphization of Gd2(MoO4)3: A high pressure Raman investigation

High pressure Raman spectroscopic studies on Gd₂(MoO₄)₃(GMO) have been carried out at ambient temperature in the diamond cell to 10 GPa hydrostatic pressure. These experiments have revealed pressure-induced phase transitions in GMO near 2 GPa and 6.0 GPa. The first transition is from Pba2(β′) phase to another undetermined crystalline phase, designated as phase II, and the second transition is to an amorphized state. On releasing pressure there is a partial reversion to the crystalline state. The Raman data indicate that the amorphization is due to disordering of the MoO₄ tetrahedral units. Further, it is inferred from the nature of the Raman bands in the amorphized material that the Mo-O bond lengths and bond angles have a range of values, instead of a few set values. The results of the present study as well as previous high pressure-high temperature quenching experiments strongly support that pressure-induced amorphization in GMO is a consequence of the kinetically impededβ toα phase transition. The system in frustration becomes disordered. The rare earth trimolybdates crystallizing in theβ′ structure are all expected to undergo similar pressure-induced amorphization.     

High pressure phase transition and elastic properties of thorium chalcogenides

The structural and elastic properties of thorium chalcogenides at high pressure, have been investigated using a suitable inter-ionic potential. The calculated equation of state, phase transition pressures for B1-B2 transition and bulk moduli for ThX (X=S,Se,Te) compounds agree well with the experimental results. ThTe, which crystallizes in the CsCl structure, does not show any structural transition up to 48 GPa. The present analysis does not show any anomalous features in elastic properties arising from ‘f’ electrons.     

Electron spectroscopy and density-functional study of ‘ferric wheel’ molecules

The Li-centered ‘ferric wheel’ molecules with six oxo-bridged iron atoms form molecular crystals. We probed their electronic structure by X-ray photoelectron and soft X-ray emission spectroscopy, having calculated in parallel the electronic structure of a single ‘ferric wheel’ molecule from first-principles by tools of the density-functional theory, using, specifically, the Siesta method. The Fe local moments were found to be 4μ_B, irrespective of their mutual orientation. Neighbouring atoms, primarily oxygen, exhibit a noticeable magnetic polarization, yielding effective spin S=5/2 per iron atom, that can get inverted as a ‘rigid’ one in magnetic transitions. Corresponding energy preferences can be mapped onto the Heisenberg model with effective exchange parameter J of about −80 K.     

High-resolution FTIR study of the para-terphenyl phase transition at high pressure

High-resolution infrared (IR) spectroscopy has been used to investigate the pressure-induced (0-11 kbar) polymorphic phase transition of crystalline para-terphenyl at low temperature (25 K). A number of doublet bands observed in low-pressure triclinic p-terphenyl were observed to coalesce in the high-pressure monoclinic phase. The coalescing of doublet bands was attributed to changes in factor group (Davydov) splittings associated with the transition from a low-pressure triclinic phase to a high-pressure monoclinic phase. The bands that ‘disappear’ also do not correlate with frequency changes associated with changes in molecular symmetry. Molecular dynamics (MD) simulations at low temperature (20 K) yield a non-planar average molecular structure for the high-pressure monoclinic phase, in contrast to the high-temperature monoclinic phase. The MD simulations also reveal a broadening of the distribution of ring torsion angles near the triclinic-monoclinic phase transition pressure.     

Thermodynamics of relation-based systems with applications in econophysics,sociophysics, and music

A methodology was developed to analyze relation-based systems evolving in time by using the fundamental concepts of thermodynamics. The behavior of such systems can be tracked from the scattering matrix which is actually a network of directed vectors (or pathways) connecting subsequent values, which characterize an event, such as the index values in stock markets. A system behaves in a rigid (elastic) way to an external effect and resists permanent deformation, or it behaves in a viscous (or soft) way and deforms in an irreversible way. It was shown in the past that a formula derived using the slope of paths gives a measure about the extent of viscoelastic behavior of relation-based systems Gündüz (2009) [5] Gündüz and Gündüz (2010) [6]. In this research the ‘work’ associated with ‘elastic’ component, and ‘heat’ associated with ‘viscous’ component were discussed and elaborated. In a simple two subsequent pathway system in a scattering diagram the first vector represents ‘the cause’ and the second ‘the effect’. By using work and heat energy relations that involve force and also storage and loss modulus terms, respectively, one can calculate the energy involved in relation-based systems. The modulus values can be found from the parallel and vertical components of the second vector with respect to the first vector. Once work-like and heat-like terms were determined the internal energy is also easily found from their summation. The parallel and vertical components can also be used to calculate the magnitude of torque and torque energy in the system. Three cases, (i) the behavior of the NASDAQ-100 index, (ii) a social revolt, and (iii) the structure of a melody were analyzed for their ‘work-like’, ‘heat-like’, and ‘torque-like’ energies in the course of their evolution. NASDAQ-100 exhibits highly dissipative behavior, and its work terms are very small but heat terms are of large magnitude. Its internal energy highly fluctuates in time. In the social revolt studied work and heat terms are of comparable magnitude. The melody depicts highly organized structure, and usually has larger work terms than heat terms, but at some intervals heat terms burst out and attain very large magnitudes. Torque terms reach high values when the system is recovering from a minimum value.     

Elastooptic effect and sources of the spontaneous birefringence in Gd2(MoO4)3

It is shown that a shear stress applied to support the spontaneous shear in improper ferroelectric Gd₂(MoO₄)₃(GMO) reduces the birefringence Δn'₁₂ measured when viewing along the c-axis. The elastooptic coefficient p₆₆^E in the paraelectric phase has been determined including sign. Using these and known electrooptical data, the soft mode, electrooptic and elastooptic contributions to Δn′₁₂ of GMO are evaluated. The two latter contributions have opposite sign to that of the soft mode which plays a prevailing role.     

Intrinsic paramagnetic defects probe superionic phase transition in Ag1−xCuxI (x=0, 0.05, 0.15 and 0.50) nanocrystals

EPR probed the zincblende (γ) to cubic (α) AgI structural phase transition in AgI at 423 K through two intrinsic paramagnetic centers: an Ag²⁺-based hole center (signal ‘A’) and an Ag⁰-based conduction electron center (signal ‘B’) associated with AgI nanocrystallites. Sudden drops in intensity (I_PP), <g>, and ΔH_PP observed at 423 K for pure AgI nanocrystals. Addition of Cu in AgI increases the thermal stability of the cation sublattice as seen from the increase in the transition temperature from 423 K (undoped AgI) to 453 K. Abrupt jumps in the number of spins (N) and reciprocal susceptibility (1/χ) observed at increased phase transition temperatures in Cu-substituted AgI relative to that in undoped AgI reflects progressively strengthened local bonding configuration of γ-AgI structure induced by Cu.     

Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in Rb2KInF6

The static and dynamic properties of cubic Rb₂KInF₆ crystals with elpasolite structure are calculated using a nonempirical method. Calculations are performed within a microscopic ionic-crystal model taking into account the deformation and polarization of ions. The deformation parameters of ions are determined by minimizing the total energy of the crystal. The calculated equilibrium lattice parameters agree satisfactorily with the experimental data. It is found that in the cubic phase there are vibrational modes that are unstable everywhere in the Brillouin zone. The eigenvectors of the unstablest mode at the center of the Brillouin zone of the cubic phase are associated with the displacements of F ions and correspond to rotations of InF₆ octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In order to describe the Fm3m → I4/m phase transition, an effective Hamiltonian is constructed under the assumption that the soft mode whose eigenvector corresponds to octahedron rotation is local and coupled with homogeneous elastic strains. The parameters of the effective Hamiltonian are determined using the calculated crystal energy for the distorted structures due to soft-mode condensation. The thermodynamic properties of the system with this model Hamiltonian are investigated using the Monte Carlo method. The phase transition temperature is calculated to be 550 K, which is twice its experimental value (283 K). The tetragonal phase remains stable down to T=0 K; the effective Hamiltonian used in this paper thus fails to describe the second phase transition (to the monoclinic phase). Thus, the transition to the tetragonal phase occurs for the most part through octahedron rotations; however, additional degrees of freedom, first of all, the displacements of Rb ions, should be included into the effective Hamiltonian in order to describe the transition to the monoclinic phase.     

Structure of the low-temperature phase of Rb3D(SeO4)2 by single-crystal neutron diffraction

Crystal structure of Rb₃D(SeO₄)₂ has been investigated at 25 K (below the transition temperature T_c=95.4 K) by single-crystal neutron diffraction. Accompanying the transition, the SeO₄ groups, which are all equivalent in the phase above the transition (space group A2/a), split into eight nonequivalent groups in a superlattice (a×2b×2c, space group A2) in the low-temperature phase. Based on the D atom positions obtained, each of the SeO₄ groups was identified to be in the state closer to a HSeO₄⁻ ion or to a SeO₄²⁻ ion and the dipole arrangement of SeO₄-D-SeO₄ dimer was revealed. This dipole arrangement has ‘ferri’ structure along the polar b-axis, but ‘antiferro’ structure in the plane perpendicular to the b-axis. These results are consistent with the characteristics found in the earlier dielectric measurements.     

Towards a novel simulation approach for the transport of atomic states through polarized photons

A novel approach for transferring logic states from one quantum node to other is proposed. Logic states ‘0’ and ‘1’ are represented by two subspaces of the hyperfine states space of rubidium atom (⁸⁷Rb). The atom, placed at the center of a two-mode cavity, is excited by simultaneous application of two laser beams, one for each subspace. Based on the logic state of the atom, it makes a transition to a higher energy level within the corresponding subspace. When the atom relaxes back to a lower state within the subspace, a left- or right-circularly polarized photon is emitted depending on whether the initial state was logic ‘0’ or logic ‘1’. The polarized photon leaks out of the cavity, reaches the receive node and gets detected therein. Simulation results show the efficacy of the approach.     

Ac behaviour and phase transition in PLZT 6/80/20 ferroelectric ceramics

The Ac behaviour of PLZT 6/80/20 ferroelectric ceramics was analyzed around and above the phase transition. Two relaxation processes are identified, showing that the so-called ‘universal relaxation law’ holds for the ceramics. A critical point in the values of the Ac conductivity, around the temperature corresponding to the maximum of the dielectric losses, is observed below the transition temperature due to the relaxor behaviour. The frequency dependence of the Ac conductivity at various temperatures and the hysteresis loops show classical relaxor behaviour with a diffuse phase transition.     

A Lagrangian description of transport associated with a front-eddy interaction: Application to data from the North-Western Mediterranean Sea

We discuss the Lagrangian transport in a time-dependent oceanic system involving a Lagrangian barrier associated with a salinity front which interacts intermittently with a set of Lagrangian eddies — ‘leaky’ coherent structures that entrain and detrain fluid as they move. A theoretical framework, rooted in the dynamical systems theory, is developed in order to describe and analyse this situation. We show that such an analysis can be successfully applied to a realistic ocean model. Here, we use the output of the numerical ocean model DieCAST from Dietrich et al. (2004) [17] and Fernández et al. (2005) [18] studied earlier in Mancho et al. (2008) [15] where a Lagrangian barrier associated with the North Balearic Front in the North-Western Mediterranean Sea was identified. The numerical model provides an Eulerian view of the flow and we employ the dynamical systems approach to identify relevant hyperbolic trajectories and their stable and unstable manifolds. These manifolds are used to understand the Lagrangian geometry of the evolving front-eddy system. Transport in this system is effected by the turnstile mechanism whose spatio-temporal geometry reveals intermittent pathways along which transport occurs. Particular attention is paid to the ‘Lagrangian’ interactions between the front and the eddies, and to transport implications associated with the transition between the one-eddy and two-eddy situation. The analysis of this ‘Lagrangian’ transition is aided by a local kinematic model that provides insight into the nature of the change in hyperbolic trajectories and their stable and unstable manifolds associated with the ‘birth’ and ‘death’ of leaky Lagrangian eddies.     

Switching an electrical current with atoms: the reproducible operation of a multi-atom relay

The demonstration of a multi-atom quantum point contact relay is reported, which can be reversibly switched between a quantized conducting ‘on-state’ and an insulating ‘off-state’ by applying an electrochemical control potential to a separate, third electrode, the control or gate electrode. The transition occurs directly from the conducting ‘on-state’ at 5 G₀ (G₀=2e²/h being the conductance quantum) to the insulating ‘off-state’. No stable intermediate levels are observed during the switching process, indicating a reproducible bistable reconfiguration of one single multi-atom contact rather than a deposition and dissolution of different parallel contacts. The results at the same time demonstrate the feasibility and reproducible operation of a configurable electronic device based on a multi-atom contact, which exhibits the functionality of an atomic relay or a transistor, opening intriguing perspectives for electronics and logics on the atomic scale.     

Collimation testing using wedge plate lateral shearing interferometry and Fourier fringe analysis

For checking the collimation of an optical beam Fourier fringe analysis has been incorporated into the wedge plate interferometric setup. Typical interferograms corresponding to ‘in-focus’, ‘at-focus’ and ‘out-of-focus’ positions of an optical beam have been recorded. As per the testing procedure, FFT of the recorded interferometer is computed digitally, and necessary processing for direct determination of phase is undertaken. Finally, the phase data is unwrapped and plotted as a function of pixel position along the direction perpendicular to the shear. The slope of the phase provides the information regarding collimation position of the collimator. As the collimation position is detected by the direct measurement of the phase over the whole area of the interferogram, high accuracy, reliability and precision are achieved.     

A quantitative criterion validating coupling power proportionality in statistical energy analysis

The response of two general spring-coupled elements is investigated to develop a unifying approach to the weak coupling criterion in Statistical Energy Analysis (SEA). First, the coupled deterministic equations of motion are expressed in the bases given by the uncoupled elements’ eigenmodes. Then, an iterative solution is expressed as a succession of exchanges between elements, where uncoupled motion provides the start approximation, converging if the ‘coupling eigenvalue’ is less than unity, in which case coupling is said to be weak. This definition is related to whether response is ‘local’ or ‘global’, encompassing a number of previously defined coupling strength definitions, applying for deterministically described structures. A stochastic ensemble is defined by that its members are equal to the investigated structure but the elements have random frequencies. It is required that the coupling eigenvalue be less than unity for all members of the ensemble. This requirement generates the title subject of the article: ‘the modal interaction strength’. It is similar to the previously defined coupling strength criterion characterising the ensemble average energy flow in uni-dimensional waveguides. Finally, SEA models are formulated in terms of the uncoupled elements’ modal data.