Modelling collective opinion formation by means of active Brownian particles

The concept of active Brownian particles is used to model a collective opinion formation process. It is assumed that individuals in community create a two-component communication field that influences the change of opinions of other persons and/or can induce their migration. The communication field is described by a reaction-diffusion equation, the opinion change of the individuals is given by a master equation, while the migration is described by a set of Langevin equations, coupled by the communication field. In the mean-field limit holding for fast communication we derive a critical population size, above which the community separates into a majority and a minority with opposite opinions. The existence of external support (e.g. from mass media) changes the ratio between minority and majority, until above a critical external support the supported subpopulation exists always as a majority. Spatial effects lead to two critical “social” temperatures, between which the community exists in a metastable state, thus fluctuations below a certain critical wave number may result in a spatial opinion separation. The range of metastability is particularly determined by a parameter characterizing the individual response to the communication field. In our discussion, we draw analogies to phase transitions in physical systems. Received 26 November 1999     

(I) Theory of infrared vibrational frequency shifts: correlation with XPS shifts

A theory is developed to account for vibrational (stretching) or absorption frequency shifts in infrared spectroscopy. The correlation between these shifts and those observed for atomic core levels in X-ray photoelectron spectroscopy is derived, and applications are provided for the results obtained from copper and nickel dithiocarbamates and for nickel xanthates.     

Theory of collective dynamics of liquid polyvalent metal: Hg

Recently suggested microscopic theory of collective dynamics of a liquid has been used to successfully explain the detailed experimental dynamic structure factor of liquid mercury at room temperature, observed experimentally recently using high resolution inelastic X-ray scattering for various momentum transfers lying in the range 3 nm⁻¹–37.1 nm⁻¹.     

Theory of collective excitations in simple liquids

We present a parameter-free theory of the collective excitations in simple liquids such as liquid metals or rare gases. The theory is based on the mode-coupling theory (MCT), which has been previously applied successfully for explaining the liquid-to glass transition. The only input is the liquid structure factor. We achieve good agreement both for the liquid dispersion (maximum of the longitudinal current spectrum) and width (damping) with experimental findings. The time-dependent memory function predicted by MCT has a two-step exponential decay as previously found in computer simulations. Furthermore MCT predicts a scaling of the liquid dispersion with the effective hard-sphere diameter of the materials. This scaling is obeyed by the available experimental data.     

Theory of non-adiabatic cranking and nuclear collective motion

The cranking model is extended to the case of a general non-adiabatic motion. The time-dependent many-body Schrödinger equation is solved, where the time dependence of the collective motion is determined by the classical Lagrange equations of motion. The Lagrangian is obtained from the expectation value of the energy. In the case of one collective degree of freedom the condition that the expectation value of the energy is constant in time is sufficient to determine the collective motion. An iteration procedure is applied, of which the zeroth order is shown to be the common cranking formula. In an alternative approach the energy conservation is expressed in differential form. This leads in the case of one collective degree of freedom to a set of coupled, non-linear first-order differential equations in time for the expansion coefficients of the many-body wave function and for the collective variable. As an illustrative example we solve the case of two coupled linear harmonic oscillators.     

Theory of long wavelength collective motion in liquids

The theory of collective motion of liquids, recently suggested by the authors, has been found to explain successfully the three-peak structure for small momentum transfers, observed experimentally and confirmed by molecular dynamical calculations, in liquid rubidium. The theory happens to be the first microscopic theory of liquids which joins smoothly the zero-sound and hydrodynamical regions of density fluctuations in liquids.     

Theory of resonant Raman scattering from low-energy collective excitations of interacting electrons in quantum wires

The Raman spectra of quantum wires in the region of electronic intra-band excitations are investigated using one- and two-band models based on the Luttinger approximation with spin. Structures related to charge and spin density modes are identified, and analyzed with respect to their behavior with photon energy and temperature. It is found that the low-energy peaks in the polarized spectra, close to resonance that are commonly assigned to “single particle excitations”, can be interpreted as the signature of spin density excitations. A broad structure in the resonant depolarized spectrum is predicted above the frequency of the spin density excitations. This is due to simultaneous but independent propagation of spin and charge density modes. The results, when compared with experiment, show, that the electronic collective excitations of quantum wires at low energies are characteristic for a non-Fermi liquid. Received: 25 March 1998 / Accepted: 3 June 1998     

Transition from stick-slip to smooth sliding: an earthquakelike model

We present a detailed study of an earthquakelike model that exhibits a "transition" from stick-slip motion to smooth sliding at a velocity of the order of those observed in experiments. This contrasts with the many previous microscopic models in which the transition velocity is many orders of magnitude too large. The results show that experimentally observed smooth sliding at the macroscopic scale must correspond to microscopic-scale stick-slip motion.     

Observation of collective friction forces due to spatial self-organization of atoms: from Rayleigh to Bragg scattering

We demonstrate that emission-induced self-organization of two-level atoms can effect strong damping of the sample's center-of-mass motion. When illuminated by far-detuned light, cold cesium atoms assemble into a density grating that efficiently diffracts the incident light into an optical resonator. We observe random phase jumps of pi in the emitted light, confirming spontaneous symmetry breaking in the atomic self-organization. The Bragg diffraction results in a collective friction force with center-of-mass deceleration up to 1000 m/s(2) that is effective even for an open atomic transition.     

Theory of resonant inelastic x-ray scattering by collective magnetic excitations

I present a tractable theory for the resonant inelastic x-ray scattering (RIXS) of magnons. The low-energy transition operator is written as a product of local spin operators and fundamental x-ray absorption spectral functions. This leads to simple selection rules. The scattering cross section linear (quadratic) in spin operators is proportional to the fundamental magnetic circular (linear) dichroic spectral function. RIXS is a novel tool to measure magnetic quasiparticles (magnons) and the incoherent spectral weight, as well as multiple magnons up to very high energy losses, in small samples, thin films, and multilayers, complementary to neutron scattering.     

Theory of molecular collective excitation in the scattering of identical nuclei

The excitation of nuclear molecules, formed in the scattering of ¹²C on ¹²C, is treated by the collective two-center model (CTCM). The model is referred to a rotating coordinate system and describes the continuous transition from the collective states of the separated nuclei to the states of the compound system. The diagonalization of the interaction between the nuclei leads to a splitting of the excitation energies as function of parity and angular momentum projection. The theory is applied for the explanation of the molecular resonances observed in the ¹²C-¹²C scattering.     

Complex Networks: from Graph Theory to Biology

The aim of this text is to show the central role played by networks in complex system science. A remarkable feature of network studies is to lie at the crossroads of different disciplines, from mathematics (graph theory, combinatorics, probability theory) to physics (statistical physics of networks) to computer science (network generating algorithms, combinatorial optimization) to biological issues (regulatory networks). New paradigms recently appeared, like that of ‘scale-free networks’ providing an alternative to the random graph model introduced long ago by Erdös and Renyi. With the notion of statistical ensemble and methods originally introduced for percolation networks, statistical physics is of high relevance to get a deep account of topological and statistical properties of a network. Then their consequences on the dynamics taking place in the network should be investigated. Impact of network theory is huge in all natural sciences, especially in biology with gene networks, metabolic networks, neural networks or food webs. I illustrate this brief overview with a recent work on the influence of network topology on the dynamics of coupled excitable units, and the insights it provides about network emerging features, robustness of network behaviors, and the notion of static or dynamic motif.     

Reversible and irreversible denaturation processes in globular proteins: from collective to molecular spectroscopic analysis

Different spectroscopic techniques were applied for studying the structural properties of lysozyme in salt‐free aqueous solutions. The results of vibrational and Brillouin scattering measurements were compared to obtain both single‐molecule and collective properties of the solutions. The characterization of the protein system, from the conformation of the polypeptide chain to the exposure of side chains to the solvent and the arrangement of the solution network, was then achieved in the range 25–85 °C. Through the analysis of the indole breathing mode, a different environment for the six tryptophan residues of an unfolded lysozyme could be evidenced. Short and long exposures to high temperatures were used to modulate the competition between the thermally induced reversible and irreversible denaturation processes. These different thermal treatments were applied to distinguish between the effects of global unfolding of the single molecule from those of self‐aggregation and gel formation. It has been observed that clusterization occurs at melting temperatures with slow kinetics; also, aggregates evolve from the completely unfolded state of the protein and lead to a sensitive increase in viscosity. This effect probably hinders any further conformational rearrangement of the molecules in the aggregate; thus as a consequence, the disordered structure of clusters does not change to give the β‐sheet organization, characteristic of filaments or fibrils. Copyright © 2011 John Wiley & Sons, Ltd.     

Shape transition in artificial tumors: from smooth buckles to singular creases

Using swelling hydrogels, we study the evolution of a thin circular artificial tumor whose growth is confined at the periphery. When the volume of the outer proliferative ring increases, the tumor loses its initial symmetry and bifurcates towards an oscillatory shape. Depending on the geometrical and elastic parameters, we observe either a smooth large-wavelength undulation of the swelling layer or the formation of sharp creases at the free boundary. Our experimental results as well as previous observations from other studies are in very good agreement with a nonlinear poroelastic model.     

Integrable Models: from Dynamical Solutions to String Theory

We review the status of integrable models from the point of view of their dynamics and integrability conditions. A few integrable models are discussed in detail. We comment on the use it is made of them in string theory. We also discuss the SO(6) symmetric Hamiltonian with SO(6) boundary. This work is especially prepared for the 70th anniversaries of André Swieca (in memoriam) and Roland K?berle.