Front Propagation and Diffusion in the A <--> A + A Hard-core Reaction on a Chain

We study front propagation and diffusion in the reaction-diffusion system A $\leftrightharpoons$ A + A on a lattice. On each lattice site at most one A particle is allowed at any time. In this paper, we analyze the problem in the full range of parameter space, keeping the discrete nature of the lattice and the particles intact. Our analysis of the stochastic dynamics of the foremost occupied lattice site yields simple expressions for the front speed and the front diffusion coefficient which are in excellent agreement with simulation results.Comment: 5 pages, 5 figures, to appear in Phys. Rev.

Asymptotic Scaling of the Diffusion Coefficient of Fluctuating "Pulled" Fronts

We present a (heuristic) theoretical derivation for the scaling of the diffusion coefficient $D_f$ for fluctuating ``pulled'' fronts. In agreement with earlier numerical simulations, we find that as $N\to\infty$, $D_f$ approaches zero as $1/\ln^3N$, where $N$ is the average number of particles per correlation volume in the stable phase of the front. This behaviour of $D_f$ stems from the shape fluctuations at the very tip of the front, and is independent of the microscopic model.Comment: Some minor algebra corrected, to appear in Rapid Comm., Phys. Rev.

Fronts with a Growth Cutoff but Speed Higher than v∗v^*

Fronts, propagating into an unstable state $\phi=0$, whose asymptotic speed $v_{\text{as}}$ is equal to the linear spreading speed $v^*$ of infinitesimal perturbations about that state (so-called pulled fronts) are very sensitive to changes in the growth rate $f(\phi)$ for $\phi \ll 1$. It was recently found that with a small cutoff, $f(\phi)=0$ for $\phi < \epsilon$, $v_{\text{as}}$ converges to $v^*$ very slowly from below, as $\ln^{-2} \epsilon$. Here we show that with such a cutoff {\em and} a small enhancement of the growth rate for small $\phi$ behind it, one can have $v_{\text{as}} > v^*$, {\em even} in the limit $\epsilon \to 0$. The effect is confirmed in a stochastic lattice model simulation where the growth rules for a few particles per site are accordingly modified.Comment: 4 pages, 4 figures, to appear in Rapid Comm., Phys. Rev.

Fluctuating "Pulled" Fronts: the Origin and the Effects of a Finite Particle Cutoff

Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed $v^*$ for $N \to \infty$ is extremely slow -- going only as $\ln^{-2}N$. In this paper, we study the front propagation in a simple stochastic lattice model. A detailed analysis of the microscopic picture of the front dynamics shows that for the description of the far tip of the front, one has to abandon the idea of a uniformly translating front solution. The lattice and finite particle effects lead to a ``stop-and-go'' type dynamics at the far tip of the front, while the average front behind it ``crosses over'' to a uniformly translating solution. In this formulation, the effect of stochasticity on the asymptotic front speed is coded in the probability distribution of the times required for the advancement of the ``foremost bin''. We derive expressions of these probability distributions by matching the solution of the far tip with the uniformly translating solution behind. This matching includes various correlation effects in a mean-field type approximation. Our results for the probability distributions compare well to the results of stochastic numerical simulations. This approach also allows us to deal with much smaller values of $N$ than it is required to have the $\ln^{-2}N$ asymptotics to be valid.Comment: 26 pages, 11 figures, to appear in Phys. rev.

Near-infrared photoabsorption by C(60) dianions in a storage ring

We present a detailed study of the electronic structure and the stability of C(60) dianions in the gas phase. Monoanions were extracted from a plasma source and converted to dianions by electron transfer in a Na vapor cell. The dianions were then stored in an electrostatic ring, and their near-infrared absorption spectrum was measured by observation of laser induced electron detachment. From the time dependence of the detachment after photon absorption, we conclude that the reaction has contributions from both direct electron tunneling to the continuum and vibrationally assisted tunneling after internal conversion. This implies that the height of the Coulomb barrier confining the attached electrons is at least similar to 1.5 eV. For C(60)(2-) ions in solution electron spin resonance measurements have indicated a singlet ground state, and from the similarity of the absorption spectra we conclude that also the ground state of isolated C(60)(2-) ions is singlet. The observed spectrum corresponds to an electronic transition from a t(1u) lowest unoccupied molecular orbital (LUMO) of C(60) to the t(1g) LUMO+1 level. The electronic levels of the dianion are split due to Jahn-Teller coupling to quadrupole deformations of the molecule, and a main absorption band at 10723 cm(-1) corresponds to a transition between the Jahn-Teller ground states. Also transitions from pseudorotational states with 200 cm(-1) and (probably) 420 cm(-1) excitation are observed. We argue that a very broad absorption band from about 11 500 cm(-1) to 13 500 cm(-1) consists of transitions to so-called cone states, which are Jahn-Teller states on a higher potential-energy surface, stabilized by a pseudorotational angular momentum barrier. A previously observed, high-lying absorption band for C(60)(-) may also be a transition to a cone state

Amplitude and Frequency Spectrum of Thermal Fluctuations of A Translocating RNA Molecule

Using a combination of theory and computer simulations, we study the translocation of an RNA molecule, pulled through a solid-state nanopore by an optical tweezer, as a method to determine its secondary structure. The resolution with which the elements of the secondary structure can be determined is limited by thermal fluctuations. We present a detailed study of these thermal fluctuations, including the frequency spectrum, and show that these rule out single-nucleotide resolution under the experimental conditions which we simulated. Two possible ways to improve this resolution are strong stretching of the RNA with a back-pulling voltage across the membrane, and stiffening of the translocated part of the RNA by biochemical means.Comment: Significantly expanded compared to previous version, 13 pages, 4 figures, to appear in J. Phys.: Condens. Matte

The Weakly Pushed Nature of "Pulled" Fronts with a Cutoff

The concept of pulled fronts with a cutoff $\epsilon$ has been introduced to model the effects of discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (Pulled fronts are the fronts which propagate into an unstable state, and have an asymptotic front speed equal to the linear spreading speed $v^*$ of small linear perturbations around the unstable state). In this paper, we demonstrate that the introduction of a cutoff actually makes such pulled fronts weakly pushed. For the nonlinear diffusion equation with a cutoff, we show that the longest relaxation times $\tau_m$ that govern the convergence to the asymptotic front speed and profile, are given by $\tau_m^{-1} \simeq [(m+1)^2-1] \pi^2 / \ln^2 \epsilon$, for $m=1,2,...$.Comment: 4 pages, 2 figures, submitted to Brief Reports, Phys. Rev.

Emergence of pulled fronts in fermionic microscopic particle models

We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process A + A A$ on the lattice when only a particle is allowed per site. To this end we identify the parameter that controls the strength of internal fluctuations in this model, namely, the number of particles per correlated volume. When internal fluctuations are suppressed, we explictly see the matching between the deterministic FKPP description and the microscopic particle model.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. E as a Rapid Communicatio

Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems

The master equation approach to Lyapunov spectra for many-particle systems is applied to non-equilibrium thermostatted systems to discuss the conjugate pairing rule. We consider iso-kinetic thermostatted systems with a shear flow sustained by an external restriction, in which particle interactions are expressed as a Gaussian white randomness. Positive Lyapunov exponents are calculated by using the Fokker-Planck equation to describe the tangent vector dynamics. We introduce another Fokker-Planck equation to describe the time-reversed tangent vector dynamics, which allows us to calculate the negative Lyapunov exponents. Using the Lyapunov exponents provided by these two Fokker-Planck equations we show the conjugate pairing rule is satisfied for thermostatted systems with a shear flow in the thermodynamic limit. We also give an explicit form to connect the Lyapunov exponents with the time-correlation of the interaction matrix in a thermostatted system with a color field.Comment: 10 page

Newly established tumourigenic primary human colon cancer cell lines are sensitive to TRAIL-induced apoptosis in vitro and in vivo

Most data on the therapeutic potential of tumour necrosis factor-related apoptosis-inducing ligand (TRAIL) as well as resistance to FAS ligand (FASL) in colorectal cancer have come from in vitro studies using cell lines. To gain a clearer understanding about the susceptibility of patient tumours to TRAIL and FASL, we derived primary human cancer epithelial cells from colon cancer patients. Characterisation of primary cultures PAP60 and MIH55 determined their highly proliferating advantage, transforming capability and tumorigenicity in vitro and in vivo. Although FASL treatment appeared to cause little apoptosis only in the PAP60 primary culture, increased apoptosis independent of p53 was observed in both primary PAP60 and MIH55 and control cell lines Caco-2, HT29 and DLD-1 after treatment with SuperKiller TRAIL. Expression analysis of death receptors (DR) in the original parental tumours, the primary cultures before and after engraftment as well as the mouse xenografts, revealed a significant upregulation of both DR4 and DR5, which correlated to differences in sensitivity of the cells to TRAIL-induced apoptosis. Treating patient tumour xenograft/SCID mouse models with Killer TRAIL in vivo suppressed tumour growth. This is the first demonstration of TRAIL-induced apoptosis in characterised tumorigenic primary human cultures (in vitro) and antitumour activity in xenograft models (in vivo)