The stationary properties and the state transition of the tumor cell growth mode

We study the stationary properties and the state transition of the tumor cell growth model (the logistic model) in presence of correlated noises for the case of nonzero correlation time. We derived an approximative Fokker-Planck equation and the stationary probability distribution (SPD) of the model. Based the SPD, we investigated the effects of both correlation strength ( ) and correlation time ( ) of cross-correlated noises on the SPD, the mean of the tumor cell population and the normalized variance ( ) of the system, and calculated the state transition rate of the system between two stable states. Our results indicate that: (i) and play opposite roles in the stationary properties and the state transition of the system, i.e. increase of can produce a smaller mean value of the cell population and slow down the state transition, but increase of can produce a larger mean value of the cell population and enhance state transition; (ii) For large , there a peak structure on both - plot and - plot. For the small , increases with increasing , but increases with decreasing .Received: 26 June 2004, Published online: 30 September 2004PACS: 87.10. + e General theory and mathematical aspects - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 02.50.Ey Stochastic processes     

Scale dependent partitioning of one-dimensional aperiodic set diffraction

We give a multiresolution partition of pure point parts of diffraction patterns of one-dimensional aperiodic sets. When an aperiodic set is related to the Golden Ratio, denoted by , it is well known that the pure point part of its diffractive measure is supported by the extension ring of , denoted by . The partition we give is based on the formalism of the so called -integers, denoted by . The set of -integers is a selfsimilar set obeying , . The pure point spectrum is then partitioned with respect to this Russian doll like sequence of subsets . Thus we deduce the partition of the pure point part of the diffractive measure of aperiodic sets.Received: 24 March 2004, Published online: 12 July 2004PACS: 61.44.Br Quasicrystals - 61.10.Dp Theories of diffraction and scattering     

Scaling the $\alpha $-relaxation time of supercooled fragile organic liquids

It was shown recently [1] that the structural -relaxation time of supercooled o-terphenyl depends on a single control parameter , which is the product of a function of density , by the inverse temperature T ^-1. We extend this finding to other fragile glassforming liquids using light scattering data. Available experimental results do not allow to discriminate between several analytical forms of the function , the scaling arising from the separation of density and temperature in . We also propose a simple form for , which depends only on three material-dependent parameters, reproducing relaxation times over 12 orders of magnitude.Received: 16 July 2004, Published online: 23 December 2004PACS: 66.20. + d Viscosity of liquids; diffusive momentum transport - 78.35. + c Brillouin and Rayleigh scattering; other light scattering - 64.70.Pf Glass transitions     

Structural,electronic, and optical properties of beryllium monochalcogenides

The results of first-principles theoretical study of the structural, electronic and optical properties of beryllium monochalcogenides BeTe, BeSe and BeS, performed using the full potential linearized augmented plane wave (FP-LAPW) method are presented. The calculated structural parameters and band gaps compare very well with previous theoretical results. The trends of the band gap pressure coefficients and volume deformation potentials for these II-VI compounds are investigated. The linear pressure coefficients for the X and band gaps increase with decrease in anion atomic weight. The dependence of the direct and indirect band gaps on the relative change of lattice constant are found to follow almost the same type of trends in each of these compounds. The volume deformation potential ( ) for the direct ( ) and indirect ( ) gaps are positive, but negative for the indirect ( ) gap. Furthermore, , for transitions decreases with increase in anion atomic number whereas , increases. The optical properties have also been calculated. From the reflectivity spectra, the compounds will be useful for optical applications. The variation of the band gaps with respect to the application of pressure and the origin of some of the peaks in the optical spectra are discussed in terms the calculated electronic structure.Received: 26 September 2003, Published online: 18 June 2004PACS: 71.15.Ap Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.) - 71.15.Mb Density functional theory, local density approximation, gradient and other corrections - 71.20.Nr Semiconductor compounds     

The effect of mixture lengths of vehicles on the traffic flow behaviour in one-dimensional cellular automaton

The effect of mixture lengths of vehicles on the asymmetric exclusion model is studied using numerical simulations for both open and periodic boundaries in deterministic parallel dynamics. The vehicles are filed according to their length, the small cars type 1 occupy one cell whereas the big ones type 2 takes two. In the case of open boundaries two cases are presented. The first case corresponds to a chain with two entries where densities are calculated as a function of the injecting rates and of vehicles type 1 and type 2 respectively, and the phase diagram ( ) is presented for a fixed value of the extracting rate . In this situation the first order transition from low to high density phases occurs at and disappears for . The second case corresponds to a chain with one entry, where is the injecting rate of vehicles independent of their nature. Type 2 are injected with the conditional probability , where and n is the concentration of type 2. Densities are calculated as a function of the injecting rates , and the phase diagrams ( , ) are established for different values of n. In this situation the gap which is a characteristic of the first order transition vanishes with increasing for . However, the first order transition between high and low densities exhibit an end point above which the global density undergoes a continuous passage. The end point coordinate depends strongly on the value of n. In the periodic boundaries case, the presence of vehicles type 2 in the chain leads to a modification in the fundamental diagram (current, density). Indeed, the maximal current value decreases with increasing the concentration of vehicles type 2, and occurs at higher values of the global density.Received: 13 May 2004, Published online: 3 August 2004PACS: 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 82.20.Wt Computational modeling; simulation     

Packet transport along the shortest pathways in scale-free networks

We investigate a problem of data packet transport between a pair of vertices on scale-free networks without loops or with a small number of loops. By introducing load of a vertex as accumulated sum of a fraction of data packets traveling along the shortest pathways between every pair of vertices, it is found that the load distribution follows a power law with an exponent . It is found for the Barabási-Albert-type model that the exponent changes abruptly from for tree structure to as the number of loops increases. The load exponent seems to be insensitive to different values of the degree exponent as long as .Received: 4 February 2004, Published online: 14 May 2004PACS: 89.75.Fb Structures and organization in complex systems - 05.65. + b Self-organized systems - 02.10.Ox Combinatorics; graph theory     

Thermal conductivity of doped $\mathsf{La_2CuO_4}$ as an example for heat transport by optical phonons in complex materials

We investigate the phonon thermal conductivity of doped based on out-of-plane thermal conductivity measurements. When room temperature is approached the temperature dependence of strongly deviates from the T^-1-decrease which is usually expected for heat transport by acoustic phonons. Instead, decreases much weaker or even increases with rising temperature. Simple arguments suggest that such unusual temperature dependencies of are caused by heat transport via dispersive optical phonons.Received: 20 October 2003, Published online: 20 April 2004PACS: 66.70. + f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves - 74.72.Dn La-based cuprates - 44.10. + i Heat conduction     

$\mathsf{\sqrt{3}}$ linear structures in the Te/Ni(111) system

Surface structures in the Te/Ni(111) system are revealed by using reflection high-energy electron diffraction combined with X-ray and ultraviolet photoelectron spectroscopies. At a 0.33 mono-layer (ML)-Te/Ni(111) surface, a reversible structural phase transition is observed with a transition temperature T_c of 380 C. The diffraction pattern from the low temperature phase is accompanied by streaks. The high and low temperature phases are characterized by and rectangle, respectively. The mechanism of the phase transition is explained by the order-disorder transition with a rumpled chain model. Both 0.51 ML- and 0.44 ML-Te/Ni(111) surfaces exhibit the complex diffraction patterns accompanied by diffuse streaks. These surface structures are characterized by the rectangle and , respectively. All diffuse streaks obtained at the above surfaces are consistently interpreted in the view of the ill-ordered arrangements of the well-ordered linear chains. It is shown that the linear structure is the key in the Te/Ni(111) system.Received: 1 December 2003, Published online: 20 April 2004PACS: 61.14.Hg Low-energy electron diffraction (LEED) and reflection high-energy electron diffraction (RHEED) - 68.65.-k Low-dimensional, mesoscopic, and nanoscale systems: structure and nonelectronic properties - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems     

Surface critical behavior of fluids: Lennard-Jones fluid near a weakly attractive substrate

The phase behavior of fluids near weakly attractive substrates is studied by computer simulations of the coexistence curve of a Lennard-Jones (LJ) fluid confined in a slitlike pore. The temperature dependence of the density profiles of the LJ fluid was used to study the surface critical behavior. A universal critical behavior of the local order parameter, defined as the difference between the local densities of the coexisting liquid and vapor phases at some distance from the pore walls, , is observed in a wide temperature range and found to be consistent with the surface critical behavior of the Ising model. Near the surface the dependence of the order parameter on the reduced temperature obeys a scaling law ~1 with a critical exponent 1 of about 0.8, corresponding to the surface transition. A crossover from bulk-like to surface-like critical behavior occurs, when the distance to the surface is about twice the correlation length at the given temperature. Relations between the and transitions in Ising systems and the surface critical behavior of fluids are discussed.     

On the Meissner effect in a superconductor with 4-fermion attraction

A presence of a Meissner-Ochsenfeld effect in a gas of spin 1/2 fermions with an interaction , where is a volume of a region in real space which is taken by thesystem and with , satisfying Fermi anticommutation relations, is investigated. The effect proves to be weaker than in BCS by a factor 3/4 at T = 0, implying a greater penetration depth of external magnetic field. V ₄ is nonzero only within a thin layer of 1-fermion energies around the chemical potential .Received: 14 June 2004, Published online: 12 October 2004PACS: 74.20.-z Theories and models of superconducting state - 74.20.Fg BCS theory and its development     

Stability analysis of fronts in a tristable reaction-diffusion system

A stability analysis is performed analytically for the tristable reaction-diffusion equation, in which a quintic reaction term is approximated by a piecewise linear function. We obtain growth rate equations for two basic types of propagating fronts, monotonous and nonmonotonous ones. Their solutions show that the monotonous front is stable whereas the nonmonotonous one is unstable. It is found that there are two values of the growth rate for the most dangerous modes (corresponding to the longest possible wavelengths), and , for the monotonous front, so that at the perturbation eigenfunction is positive whereas when it changes sign. It is also noted that the eigenvalue becomes negative in an inhomogeneous system with a particular (stabilizing) inhomogeneity. Counting arguments for the number of eigenmodes of the linear stability operator are presented.Received: 9 August 2004, Published online: 23 December 2004PACS: 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 47.20.Ma Interfacial instability - 47.54. + r Pattern selection; pattern formation     

The $\beta$-function in duality-covariant non-commutative $\phi^4$-theory

We compute the one-loop -functions describing the renormalisation of the coupling constant and the frequency parameter for the real four-dimensional duality-covariant non-commutative -model, which is renormalisable to all orders. The contribution from the one-loop four-point function is reduced by the one-loop wavefunction renormalisation, but the -function remains non-negative. Both and vanish at the one-loop level for the duality-invariant model characterised by . Moreover, also vanishes in the limit , which defines the standard non-commutative -quantum field theory. Thus, the limit exists at least at the one-loop level.Received: 19 March 2004, Published online: 5 May 2004     

Structural and magnetic properties of \lbrackEr|Tb\rbrackmultilayers

We have investigated the structural and magnetic properties of Er|Tb multilayers by different scattering methods. Diffuse X-ray scattering under grazing incidence reveals the interface structure in Er|Tb bilayers and trilayers, indicating vertically correlated roughness between the Er and Tb interfaces. The magnetic properties of Er_nEr|Tb_nTb superlattices have been studied as a function of the superlattice composition (indices denote the number of atomic layers). Coupled ferromagnetic structures exist in all investigated samples. The phase transition temperature varies with the Tb layer thickness. Modulated magnetic order is short range for all samples beside the Er₂₀|Tb₅ superlattice, the sample with the smallest Tb layer thickness. We observe dipolar antiferromagnetic coupling between single ferromagnetic Tb layers in all samples, with the onset of this ordering depending on the Tb layer thickness. Due to competing interactions, exchange coupling is limited to the interface near region. Therefore long range modulated magnetic order is observed in the Er₂₀|Tb₅ superlattice only, where the interface regions overlap. The distinct differences to the magnetic structure of an Er_0.8Tb_0.2 alloy film are explained by a highly anisotropic arrangement of neighbouring atoms due to the correlated roughness.     

Influence of the growth method upon the phase transition of RbCdCl $\mathsf{_{3}}$

Structural properties of two RbCdCl₃ samples grown either from the melt or from aqueous solution are studied via X-ray diffraction over a closed temperature cycle between 20 C and 300 C. During cooling step (300 C), the crystal grown from the melt undergoes a phase transition at 110 C that drives it from the cubic structure into a tetragonal structure that still persists at 20 C. It undergoes exactly the reverse phase transition at the same temperature during the heating ( C) step that immediately follows. The other crystal grows from aqueous solution at 20 C in an orthorhombic structure (i.e. not tetragonal as that of the crystal grown from the melt and cooled down to this temperature). During the heating ( C) step, it undergoes a direct orthorhombic-cubic phase transition at 240 C (without passing through the tetragonal phase) whereas, during subsequent cooling (300 C), it does not exhibit the corresponding reverse phase transition but rather exhibits exactly the same cubic-tetragonal phase transition at 110 C as the crystal grown from the melt. However, for both crystals, this tetragonal phase observed at room temperature is unstable and slowly converts into an orthorhombic phase over the course of time. Complementary Differential Scanning Calorimetry (D.S.C.) and Thermo Gravimetric Analysis (T.G.A.) measurements have been carried out over the range ( ) C in order to interpret diffraction experiments.Received: 19 May 2004, Published online: 30 September 2004PACS: 61.10.Nz X-ray diffraction - 64.70.Kb Solid-solid transitions - 65.40.Ba Heat capacity     

\alpha-decay spectroscopy of light odd-odd Bi isotopes - II: 186Bi and the new nuclide 184Bi

Alpha-decay of the new nuclide ¹⁸⁴Bi has been studied in the complete-fusion reaction ⁹³Nb(⁹⁴Mo, 3n)¹⁸⁴Bi at the velocity filter SHIP. The evaporation residues were separated in-flight and subsequently identified on the basis of recoil- , recoil- - analysis and excitation functions measurements. Two -decaying isomeric states in ¹⁸⁴Bi with half-life values of 13(2) ms and 6.6(1.5) ms were identified. The -branching ratio of ¹⁸⁰Tl was deduced for the first time as . Improved data on the fine-structure -decay of ¹⁸⁶Bi were obtained in the ⁹³Nb(⁹⁵Mo, 2n)¹⁸⁶Bi reaction. A similarity of the decay energies and half-life values of ^184,186Bi is pointed out and a possible explanation for this effect is suggested.Received: 14 March 2003, Revised: 29 April 2003, Published online: 2 September 2003PACS: 23.60.+e decay - 27.70.+q - 27.80.+w K. Heyde: Present address: EP-ISOLDE, CERN, CH-1211, Geneva 23, Switzerland.     

Off equilibrium dynamics in the 3d-XY system

We investigate through Monte Carlo simulations the non-equilibrium behaviour of the three-dimensional XY-model quenched from a high temperature state to its ferromagnetic and critical phases. The two-times autocorrelation and response functions are determined in the asymptotic (scaling) regime, from which the nonequilibrium exponents and critical are extracted. The form of the scaling function is in agreement with the prediction of local scale-invariance. The so-called limit fluctuation-dissipation ratio is shown to vanish in the ordered phase and to reach a constant value around 0.43 for the critical quench.Received: 12 July 2004, Published online: 30 September 2004PACS: 75.40.Gb Dynamic properties - 05.70.Ln Non-equilibrium and irreversible thermodynamics     

Giant enhancement of optical nonlinearity in mixtures of graded particles with dielectric anisotropy

To investigate the effective linear dielectric constant and third-order nonlinear susceptibility of composite media, in which graded inclusions with radial dielectric anisotropy are randomly embedded in a linear isotropic matrix, we develop an nonlinear anisotropic differential effective dipole approximation (NADEDA). Alternatively, based on a first-principles approach, the exact expressions for and are also derived for the linear dielectric profiles with small slopes. Then, excellent agreement between the two methods is numerically demonstrated. As an application, we further apply the NADEDA to a nonlinear metal-dielectric composite, in which the metal particles possess spatially varying radial dielectric anisotropy, in an attempt to study the nonlinearity enhancement and the figure of merit of the composite. To this end, it is shown that the presence of gradation in the radial dielectric constant plays a crucial role in enhancing the optical nonlinearity as well as the figure of merit.Received: 16 August 2003, Published online: 30 January 2004PACS: 77.22.Ej Polarization and depolarization - 42.65.-k Nonlinear optics - 42.79.Ry Gradient-index (GRIN) devices - 77.84.Lf Composite materials     

Scaling behavior of jamming fluctuations upon random sequential adsorption

It is shown that the fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) ( ), decay with the lattice size according to the power-law , with ,where D is the dimension of the substrate and is the fractal dimension of the set of sites belonging to the substrate where the RSA process actually takes place. This result is in excellent agreement with the figure recently reported by Vandewalle et al. [Eur. Phys. J. B 14, 407 (2000)], namely for the RSA of needles with D = 2 and , that gives . Furthermore, our prediction is in excellent agreement with different previous numerical results. The derived relationships are also confirmed by means of extensive numerical simulations applied to the RSA of dimers on both stochastic and deterministic fractal substrates.Received: 17 October 2003, Published online: 8 December 2003PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 02.50.-r Probability theory, stochastic processes, and statistics     

An analysis of the time-dependent CP asymmetryin $B \to \pi \pi$ decays in the standard model

Measurements of the time-dependent CP-asymmetry in the decay and its charge conjugate by the BELLE and BABAR collaborations currently yield and , characterizing the direct and mixing-induced CP-asymmetries, respectively. We study the implication of these measurements on the CKM phenomenology taking into account the available information in the quark mixing sector. Our analysis leads to the results that the ratio |P _c /T _c | involving the QCD-penguin and tree amplitudes and the related strong phase difference in the decays are quite substantial. Using the isospin symmetry to constrain |P _c /T _c | and , where parameterizes the penguin-induced contribution, we present a fit of the current data including the measurements of and . Our best-fits yield , , , , and . At 68% C.L., the ranges are , , , and . Currently en vogue dynamical approaches to estimate the hadronic matrix elements in decays do not provide a good fit of the current data.Received: 5 April 2004, Published online: 14 July 2004A.Ya. Parkhomenko: On leave of absence from Department of Theoretical Physics, Yaroslavl State University, Sovietskaya 14, 150000 Yaroslavl, Russia.     

The optimal velocity traffic flow models with open boundaries

The effects of the open boundaries on the dynamical behavior of the optimal velocity traffic flow models with a delay time allowing the car to reach its optimal velocity is studied using numerical simulations. The particles could enter the chain with a given injecting rate probability , and could leave the system with a given extracting rate probability . In the absence of the variation of the delay time , it is found that the transition from unstable to metastable and from metastable to stable state occur under the effect of the probabilities rates and . However, for a fixed value of , there exist a critical value of the extraction rate above which the wave density disappears and the metastable state appears and a critical value above which the metastable state disappears while the stable state appears. and depend on the values of and the variation of the delay time . Indeed and increase when increasing and/or decreasing . The flow of vehicles is calculated as a function of , and for a fixed value of . Phase diagrams in the ( ) plane exhibits four different phases namely, unstable, metastable, stable. The transition line between stable phase and the unstable one is curved and it is of first order type. While the transition between stable (unstable) phase and the metastable phase are of second order type. The region of the metastable phase shrinks with increasing the variation of the delay time and disappears completely above a critical value .Received: 23 July 2003, Published online: 8 December 2003PACS: 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 82.20.Wt Computational modeling; simulation