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Phonons in solid-state quantum emitters play a crucial role in their performance as photon sources in quantum technology. For resonant driving, phonons dampen the Rabi oscillations resulting in reduced preparation fidelities. The phonon spectral density, which quantifies the strength of the carrier-phonon interaction, is non-monotonous as a function of energy. As one of the most prominent consequences, this leads to the reappearance of Rabi rotations for increasing pulse power, which was theoretically predicted in Phys. Rev. Lett. 98, 227403 (2007). In this paper we present the experimental demonstration of the reappearance of Rabi rotations.

We define the $Q$-factor in the percolation problem as the quotient of the size of the largest cluster and the average size of all clusters. As the occupation probability $p$ is increased, the $Q$-factor for the system size $L$ grows systematically to its maximum value $Q_{max}(L)$ at a specific value $p_{max}(L)$ and then gradually decays. Our numerical study of site percolation problems on the square, triangular and the simple cubic lattices exhibits that the asymptotic values of $p_{max}$ though close, are distinctly different from the corresponding percolation thresholds of these lattices. We have also shown using the scaling analysis that at $p_{max}$ the value of $Q_{max}(L)$ diverges as $L^d$ ($d$ denoting the dimension of the lattice) as the system size approaches to their asymptotic limit. We have further extended this idea to the non-equilibrium systems such as the sandpile model of self-organized criticality. Here, the $Q(\rho,L)$-factor is the quotient of the size of the largest avalanche and the cumulative average of the sizes of all the avalanches; $\rho$ being the drop density of the driving mechanism. This study has been prompted by some observations in Sociophysics., Comment: 9 pages, 13 figures

The radiative decay of the Hoyle state is the doorway to the production of heavier elements in stellar environment. Here we report, an exclusive measurement of electric quadruple (E$_2$) transitions of the Hoyle state to the ground state of $^{12}$C through the $^{12}$C(p, p$^\prime$$\gamma$$\gamma$)$^{12}$C reaction. Triple coincidence measurement yields a value of radiative branching ratio $\Gamma_{rad}$/$\Gamma$ = 4.01 (30) $\times$ 10$^{-4}$. The result has been corroborated by an independent experiment based on the complete kinematical measurement $via.$ $^{12}$C(p, p$^\prime$)$^{12}$C reaction ($\Gamma_{rad}$/$\Gamma$ = 4.04 (30) $\times$ 10$^{-4}$). Using our results together with the currently adopted values of $\Gamma_{\pi}$(E$_0$)/$\Gamma$ and $\Gamma_{\pi}$($E_0$), the radiative width of the Hoyle state is found to be 3.75 (40) $\times$ 10$^{-3}$ eV. We emphasize here that our result is not in agreement with 34 $\%$ increase in the radiative decay width of the Hoyle state measured recently but consistent with the currently adopted value., Comment: 7 pages, 5 figures

The notion of Self-organized criticality (SOC) had been conceived to interpret the spontaneous emergence of long range correlations in nature. Since then many different models had been introduced to study SOC. All of them have few common features: externally driven dynamical systems self-organize themselves to non-equilibrium stationary states exhibiting fluctuations of all length scales as the signatures of criticality. In contrast, we have studied here in the framework of the sandpile model a system that has mass inflow but no outflow. There is no boundary, and particles cannot escape from the system by any means. Therefore, there is no current balance, and consequently it is not expected that the system would arrive at a stationary state. In spite of that, it is observed that the bulk of the system self-organizes to a quasi-steady state where the grain density is maintained at a nearly constant value. Power law distributed fluctuations of all length and time scales have been observed which are the signatures of criticality. Our detailed computer simulation study gives the set of critical exponents whose values are very close to their counter parts in the original sandpile model. This study indicates that (i) a physical boundary and (ii) the stationary state though sufficient but may not be the necessary criteria for achieving SOC., Comment: 7 pages, 10 figures

The well-known problem of gradient percolation has been revisited to study the probability distribution of island sizes. It is observed that as the ordinary percolation, this distribution is also described by a power-law decaying function but the associated critical exponents are found to be different. Because of the underlying gradient for the occupation probability, the average value of the island sizes also has a gradient. The variation of the average island size with the probability of occupation along the gradient has been studied together with its scaling analysis. Further, we have introduced and studied the gradient bond percolation and by studying the island size distribution statistics, we have obtained very similar results. We have also studied the characteristics of the diffusion profile of the particle system on a lattice that is initially half filled and half empty. Here also we observe the same value for the island size probability distribution exponent. Finally, the same study has been repeated for the nonlinear gradient percolation and the value of the island size distribution exponent is found to be a function of the strength of the nonlinear parameter., Comment: 9 pages, 13 figures

We have studied few social inequality measures associated with the sub-critical dynamical features (measured in terms of the avalanche size distributions) of four self-organized critical models while the corresponding systems approach their respective stationary critical states. It has been observed that these inequality measures (specifically the Gini and Kolkata indices) exhibit nearly universal values though the models studied here are widely different, namely the Bak-Tang-Wiesenfeld sandpile, the Manna sandpile and the quenched Edwards-Wilkinson interface, and the fiber bundle interface. These observations suggest that the self-organized critical systems have broad similarity in terms of these inequality measures. A comparison with similar earlier observations in the data of socio-economic systems with unrestricted competitions suggest the emergent inequality as a result of the possible proximity to the self-organized critical states., Comment: 12 pages, 9 figures (Accepted for publication in Physica A)

The isospin dependence of nuclear level density has been investigated by analyzing the spectra of evaporated neutrons from excited $^{116}$Sn and $^{116}$Te nuclei. These nuclei are populated via $p$ + $^{115}$In and $^{4}$He + $^{112}$Sn reactions in the excitation energy range of 18 - 26 MeV. Because of low excitation energy, the neutron spectra are predominantly contributed by the first-chance decay leading to the $\beta$-stable $^{115}$Sn and neutron-deficient $^{115}$Te as residues for the two cases. Theoretical analysis of the experimental spectra have been performed within the Hauser-Feshbach formalism by employing different models of the level density parameter. It is observed that the data could only be explained by the level density parameter that decreases monotonically when the proton number deviates from the $\beta$-stable value. This is also confirmed by performing a microscopic shell-model calculation with the Wood-Saxon mean field. The results have strong implication on the estimation of the level density of unstable nuclei, and calculation of astrophysical reaction rates relevant to $r$- and $rp$-processes.

The nuclear level density of $^{115}$Sn has been measured in an excitation energy range of $\sim $2 - 9 MeV using the experimental neutron evaporation spectra from the $^{115}$In($p,n$)$^{115}$Sn reaction. The experimental level densities were compared with the microscopic Hartree-Fock BCS (HFBCS), Hartree-Fock-Bogoliubov plus combinatorial (HFB+C), and an exact pairing plus independent particle model (EP+IPM) calculations. It is observed that the EP+IPM provides the most accurate description of the experimental data. The thermal properties (entropy and temperature) of $^{115}$Sn have been investigated from the measured level densities. The experimental temperature profile as well as the calculated heat capacity show distinct signatures of a transition from the strongly-paired nucleonic phase to the weakly paired one in this nucleus., Comment: This article has been submitted to European Journal of Physics A for publication

Neutron kinetic energy spectra in coincidence with low-energy $\gamma $-ray multiplicities have been measured around $A\approx $ 110 in the $^{16}$O, $^{20}$Ne + $^{93}$Nb reactions in a compound nuclear excitation energy range of $\approx $ 90 - 140 MeV. The excitation energy (temperature) and angular momentum (spin) dependence of the inverse level density parameter $k$ has been investigated by comparing the experimental data with statistical Hauser-Feshbach calculation. In contrast to the available systematic in this mass region, the inverse level density parameter showed an appreciable increase as a function of the excitation energy. The extracted $k$-values at different angular momentum regions, corresponding to different $\gamma $-multiplicities also showed an overall increase with the average nuclear spins. The experimental results have been compared with a microscopic statistical-model calculation and found to be in reasonable agreement with the data. The results provide useful information to understand the variation of nuclear level density at high temperature and spins.

Resistive heating and mechanical rolling methods have been employed to prepare isotopically enriched thin target foils of 116Sn (~380 \mu g/cm2), 124Sn(~400 \mu g/cm2) and thicker foils of 112Sn (1.7 mg/cm2),120Sn (1.6 mg/cm2),respectively. Preparation of enriched targets with small amount of material, selection of releasing agent for thin targets and separation of deposited material insolvent were among the several challenges while fabrication of the thin targets. Uniformity of the targets has been measured using 241Am {\alpha}-source. NaCl has been used as releasing agent in preparation of the thin targets. These targets have been successfully used in nuclear physics experiments at VECC.

We consider a percolation process in which $k$ points separated by a distance proportional to system size $L$ simultaneously connect together ($k>1$), or a single point at the center of a system connects to the boundary ($k=1$), through adjacent connected points of a single cluster. These processes yield new thresholds $\overline p_{ck}$ defined as the average value of $p$ at which the desired connections first occur. These thresholds are not sharp as the distribution of values of $p_{ck}$ for individual samples remains broad in the limit of $L \to \infty$. We study $\overline p_{ck}$ for bond percolation on the square lattice, and find that $\overline p_{ck}$ are above the normal percolation threshold $p_c = 1/2$ and represent specific supercritical states. The $\overline p_{ck}$ can be related to integrals over powers of the function $P_\infty(p)$ equal to the probability a point is connected to the infinite cluster; we find numerically from both direct simulations and from measurements of $P_\infty(p)$ on $L\times L$ systems that, for $L \to \infty$, $\overline p_{c1} = 0.51755(5)$, $\overline p_{c2} = 0.53219(5)$, $\overline p_{c3} = 0.54456(5)$, and $\overline p_{c4} = 0.55527(5).$ The percolation thresholds $\overline p_{ck}$ remain the same, even when the $k$ points are randomly selected within the lattice. We show that the finite-size corrections scale as $L^{-1/\nu_k}$ where $\nu_k = \nu/(k \beta +1)$, with $\beta=5/36$ and $\nu=4/3$ being the ordinary percolation critical exponents, so that $\nu_1= 48/41$, $\nu_2 = 24/23$, $\nu_3 = 16/17$, $\nu_4 = 6/7$, etc. We also study three-point correlations in the system, and show how for $p>p_c$, the correlation ratio goes to 1 (no net correlation) as $L \to \infty$, while at $p_c$ it reaches the known value of 1.022., Comment: 9 pages, 11 figures

The 12C(20Ne,16O)16O {\alpha}-transfer reaction at Elab=150 MeV is first time used to determine the ANC of the 6.92 MeV and 7.12 MeV states of 16O. The 20Ne+ 12C potential parameters are also obtained from elastic scattering. The direct reaction code FRESCO is used to determine the {\alpha}-spectroscopy factor (S{\alpha} ) of the three states of 16O (6.92 MeV, 7.12 MeV and 11.52 MeV) and ANC of the two states (6.92 MeV and 7.12 MeV) of 16O. The extracted ANC and S{\alpha} are compareable to previous measurements., Comment: 8 pages and 18 figures

The brittle to quasibrittle transition has been studied for a compound of two different kinds of fibrous materials, having distinct difference in their breaking strengths under the framework of the fiber bundle model. A random fiber bundle model has been devised with a bimodal distribution of the breaking strengths of the individual fibers. The bimodal distribution is assumed to be consisting of two symmetrically placed rectangular probability distributions of strengths $p$ and $1 - p$, each of width $d$, and separated by a gap $2s$. Different properties of the transition have been studied varying these three parameters and using the well known equal load sharing dynamics. Our study exhibits a brittle to quasibrittle transition at the critical width $d_c(s,p) = p(1/2 - s)/(1 + p)$ confirmed by our numerical results.

A variant of the well known Vicsek model of the collective motion of a group of agents has been studied where the range of interactions are spatially quenched and non-overlapping. To define such interactions, the underlying two dimensional space is discretized and is divided into the primitive cells of an imaginary square lattice. At any arbitrary time instant, all agents within one cell mutually interact with one another. Therefore, when an agent crosses the boundary of a cell, and moves to a neighboring cell, only then its influence is spread to the adjacent cell. Tuning the strength of the scalar noise $\eta$ it has been observed that the system makes a discontinuous transition from a random diffusive phase to an ordered phase through a critical noise strength $\eta_c$ where directed bands with high agent densities appear. Unlike the original Vicsek model here a host of different types of bands has been observed with different angles of orientation and different wrapping numbers. More interestingly, two mutually crossed independent sets of simultaneously moving bands are also observed. A prescription for the detailed characterization of different types of bands have been formulated., Comment: 13 figures

The random sequential adsorption (RSA) model is a classical model in Statistical Physics for adsorption on two-dimensional surfaces. Objects are deposited sequentially at random and adsorb irreversibly on the landing site, provided that they do not overlap any previously adsorbed object. The kinetics of adsorption ceases when no more objects can be adsorbed (jamming state). Here, we investigate the role of post-relaxation on the jamming state and percolation properties of RSA of dimers on a two-dimensional lattice. We consider that, if the deposited dimer partially overlaps with a previously adsorbed one, a sequence of dimer displacements may occur to accommodate the new dimer. The introduction of this simple relaxation dynamics leads to a more dense jamming state than the one obtained with RSA without relaxation. We also consider the anisotropic case, where one dimer orientation is favored over the other, finding a non-monotonic dependence of the jamming coverage on the strength of anisotropy. We find that the density of adsorbed dimers at which percolation occurs is reduced with relaxation, but the value depends on the strength of anisotropy.

Molybdenum carbide (Mo2C) nanoparticles and thin films are particularly suitable catalysts for catalytic fast pyrolysis (CFP) as they are effective for deoxygenation and can catalyze certain reactions that typically occur on noble metals. Oxygen deposited during deoxygenation reactions may alter the carbide structure leading to the formation of oxycarbides, which can determine changes in catalytic activity or selectivity. Despite emerging spectroscopic evidence of bulk oxycarbides, so far there have been no reports of their precise atomic structure or their relative stability with respect to orthorhombic Mo2C. This knowledge is essential for assessing the catalytic properties of molybdenum (oxy)carbides for CFP. In this article, we use density functional theory (DFT) calculations to (a) describe the thermodynamic stability of surface and subsurface configurations of oxygen and carbon atoms for a commonly studied Mo-terminated surface of orthorhombic Mo2C, and (b) determine atomic structures for oxycarbides with a Mo:C ratio of 2:1. The surface calculations suggest that oxygen atoms are not stable under the top Mo layer of the Mo2C(100) surface. Coupling DFT calculations with a polymorph sampling method, we determine (Mo2C)xOy oxycarbide structures for a wide range of oxygen compositions. Oxycarbides with lower oxygen content (y/x <=2) adopt layered structures reminiscent of the parent carbide phase, with flat Mo layers separated by layers of oxygen and carbon; for higher oxygen content, our results suggest the formation of amorphous phases, as the atomic layers lose their planarity with increasing oxygen content.

Background: The influence of shell effect on the dynamics of the fusion fission process and it's evolution with excitation energy in the pre-actinide Hg-Pb region in general is a matter of intense research in recent years. In particular, a strong ambiguity remains for the neutron shell closed $^{210}$Po nucleus regarding the role of shell effect in fission around $\approx$ 30 - 40 MeV of excitation energy. Purpose: We have measured the fission fragment mass distribution of $^{210}$Po populated using fusion of $^{4}$He + $^{206}$Pb at different excitation energies and compare the result with recent theoretical predictions as well as with our previous measurement for the same nucleus populated through a different entrance channel. Mass distribution in the fission of the neighbouring nuclei $^{213}$At is also studied for comparison. Methods: Two large area Multi-wire Proportional Counters (MWPC) were used for complete kinematical measurement of the coincident fission fragments. The time of flight differences of the coincident fission fragments were used to directly extract the fission fragment mass distributions. Results: The measured fragment mass distribution for the reactions $^{4}$He + $^{206}$Pb and $^{4}$He + $^{209}$Bi were symmetric and the width of the mass distributions were found to increase monotonically with excitation energy above 36.7 MeV and 32.9 MeV, respectively, indicating the absence of shell effects at the saddle. However, in the fission of $^{210}$Po, we find minor deviation from symmetric mass distributions at the lowest excitation energy (30.8 MeV). Conclusion: Persistence of shell effect in fission fragment mass distribution of $^{210}$Po was observed at the excitation energy $\approx$ 31 MeV as predicted by the theory; at higher excitation energy, however, the present study reaffirms the absence of any shell correction in the fission of $^{210}$Po.

A model named `Colored Percolation' has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability $p$ and are then colored by one of the $n$ distinct colors using uniform probability $q = 1/n$. Denoting different colors by the letters of the Roman alphabet, we have studied different versions of the model like $AB, ABC, ABCD, ABCDE, ...$ etc. Here, only those lattice bonds having two different colored atoms at the ends are defined as connected. The percolation thresholds $p_c(n)$ asymptotically converges to its limiting value of $p_c$ as $1/n$. The model has been generalized by introducing a preference towards a subset of colors when $m$ out of $n$ colors are selected with probability $q/m$ each and rest of the colors are selected with probability $(1 - q)/(n - m)$. It has been observed that $p_c(q,m)$ depends non-trivially on $q$ and has a minimum at $q_{min} = m/n$. In another generalization the fractions of bonds between similar and dissimilar colored atoms have been treated as independent parameters. Phase diagrams in this parameter space have been drawn exhibiting percolating and non-percolating phases.

Two distinct transition points have been observed in a problem of lattice percolation studied using a system of pulsating discs. Sites on a regular lattice are occupied by circular discs whose radii vary sinusoidally within $[0,R_0]$ starting from a random distribution of phase angles. A lattice bond is said to be connected when its two end discs overlap with each other. Depending on the difference of the phase angles of these discs a bond may be termed as dead or live. While a dead bond can never be connected, a live bond is connected at least once in a complete time period. Two different time scales can be associated with such a system, leading to two transition points. Namely, a percolation transition occurs at $R_{0c} =0.908$ when a spanning cluster of connected bonds emerges in the system. Here, information propagates across the system instantly, i.e., with infinite speed. Secondly, there exists another transition point $R_0^* = 0.5907$ where the giant cluster of live bonds spans the lattice. In this case the information takes finite time to propagate across the system through the dynamical evolution of finite size clusters. This passage time diverges as $R_0 \to R_0^*$ from above. Both the transitions exhibit the critical behavior of ordinary percolation transition. The entire scenario is robust with respect to the distribution of frequencies of the individual discs. This study may be relevant in the context of wireless sensor networks.

The fission fragment mass distributions have been measured in the reactions 16O + 184W and 19F+ 181Ta populating the same compound nucleus 200Pb? at similar excitation energies. It is found that the widths of the mass distribution increases monotonically with excitation energy, indicating the absence of quasi-fission for both reactions. This is contrary to two recent claims of the presence of quasi-fission in the above mentioned reactions., Comment: Accepted for publication as a regular article in Physical Review C

The ranges of transmission of the mobiles in a Mobile Ad-hoc Network are not uniform in reality. They are affected by the temperature fluctuation in air, obstruction due to the solid objects, even the humidity difference in the environment, etc. How the varying range of transmission of the individual active elements affects the global connectivity in the network may be an important practical question to ask. Here a new model of percolation phenomena, with an additional source of disorder, has been introduced for a theoretical understanding of this problem. As in ordinary percolation, sites of a square lattice are occupied randomly with the probability $p$. Each occupied site is then assigned a circular disc of random value $R$ for its radius. A bond is defined to be occupied if and only if the radii $R_1$ and $R_2$ of the discs centered at the ends satisfy certain pre-defined condition. In a very general formulation, one divides the $R_1 - R_2$ plane into two regions by an arbitrary closed curve. One defines that a point within one region represents an occupied bond, otherwise it is a vacant bond. Study of three different rules under this general formulation, indicates that the percolation threshold is always larger and varies continuously. This threshold has two limiting values, one is $p_c$(sq), the percolation threshold for the ordinary site percolation on the square lattice and the other being unity. The variation of the thresholds are characterized by exponents, which are not known in the literature. In a special case, all lattice sites are occupied by discs of random radii $R \in \{0,R_0\}$ and a percolation transition is observed with $R_0$ as the control variable, similar to the site occupation probability.

The even-even nucleus $^{26}$Mg has been studied through the reaction $^{27}$Al(d,$^{3}$He) at 25 MeV beam energy. The spectroscopic factors have been extracted upto 7.50 MeV excitation energy using local, zero range distorted wave Born approximation. The comparison of the spectroscopic factors have been done with previously reported values using the same reaction probe. The extracted spectroscopic factors for different excited states were found to be in good agreement with the previously reported values for the same. The present results were also compared with the predictions from shell model as well as rotational model. The analog states of $^{26}$Al and $^{26}$Mg were found to be in good agreement.

Mass distributions of the fragments in the fission of $^{206}$Po and the N=126 neutron shell closed nucleus $^{210}$Po have been measured. No significant deviation of mass distributions has been found between $^{206}$Po and $^{210}$Po, indicating the absence of shell correction at the saddle point in both the nuclei, contrary to the reported angular anisotropy and pre-scission neutron multiplicity results. This new result provides benchmark data to test the new fission dynamical models to study the effect of shell correction on the potential energy surface at saddle point., Comment: Accepted for publication as Rapid Communications in Phys. Rev. C

We present a study of the fiber bundle model using equal load sharing dynamics where the breaking thresholds of the fibers are drawn randomly from a power law distribution of the form $p(b)\sim b^{-1}$ in the range $10^{-\beta}$ to $10^{\beta}$. Tuning the value of $\beta$ continuously over a wide range, the critical behavior of the fiber bundle has been studied both analytically as well as numerically. Our results are: (i) The critical load $\sigma_c(\beta,N)$ for the bundle of size $N$ approaches its asymptotic value $\sigma_c(\beta)$ as $\sigma_c(\beta,N) = \sigma_c(\beta)+AN^{-1/\nu(\beta)}$ where $\sigma_c(\beta)$ has been obtained analytically as $\sigma_c(\beta) = 10^\beta/(2\beta e\ln10)$ for $\beta \geq \beta_u = 1/(2\ln10)$, and for $\beta<\beta_u$ the weakest fiber failure leads to the catastrophic breakdown of the entire fiber bundle, similar to brittle materials, leading to $\sigma_c(\beta) = 10^{-\beta}$; (ii) the fraction of broken fibers right before the complete breakdown of the bundle has the form $1-1/(2\beta \ln10)$; (iii) the distribution $D(\Delta)$ of the avalanches of size $\Delta$ follows a power law $D(\Delta)\sim \Delta^{-\xi}$ with $\xi = 5/2$ for $\Delta \gg \Delta_c(\beta)$ and $\xi = 3/2$ for $\Delta \ll \Delta_c(\beta)$, where the crossover avalanche size $\Delta_c(\beta) = 2/(1-e10^{-2\beta})^2$., Comment: 7 pages, 7 figures

We study a system of interacting particles in a periodically moving external potential, within the simplest possible description of paradigmatic symmetric exclusion process on a ring. The model describes diffusion of hardcore particles where the diffusion dynamics is locally modified at a uniformly moving defect site, mimicking the effect of the periodically moving external potential. The model, though simple, exhibits remarkably rich features in particle transport, such as polarity reversal and double peaks in particle current upon variation of defect velocity and particle density. By tuning these variables, the most efficient transport can be achieved in either direction along the ring. These features can be understood in terms of a traveling density wave propagating in the system. Our results could be experimentally tested, e.g., in a system of colloidal particles driven by a moving optical tweezer.

A region of two-dimensional space has been filled randomly with large number of growing circular discs allowing only a `slight' overlapping among them just before their growth stop. More specifically, each disc grows from a nucleation center that is selected at a random location within the uncovered region. The growth rate $\delta$ is a continuously tunable parameter of the problem which assumes a specific value while a particular pattern of discs is generated. When a growing disc overlaps for the first time with at least another disc, it's growth is stopped and is said to be `frozen'. In this paper we study the percolation properties of the set of frozen discs. Using numerical simulations we present evidence for the following: (i) The Order Parameter appears to jump discontinuously at a certain critical value of the area coverage; (ii) the width of the window of the area coverage needed to observe a macroscopic jump in the Order Parameter tends to vanish as $\delta \to 0$ and on the contrary (iii) the cluster size distribution has a power law decaying functional form. While the first two results are the signatures of a discontinuous transition, the third result is indicative of a continuous transition. Therefore we refer this transition as a sharp but continuous transition similar to what has been observed in the recently introduced Achlioptas process of Explosive Percolation. It is also observed that in the limit of $\delta \to 0$, the critical area coverage at the transition point tends to unity, implying the limiting pattern is space-filling. In this limit, the fractal dimension of the pore space at the percolation point has been estimated to be $1.42(10)$ and the contact network of the disc assembly is found to be a scale-free network., Comment: 8 pages, 10 figures

A simple model of the two dimensional collective motion of a group of mobile agents have been studied. Like birds, these agents travel in open free space where each of them interacts with the first $n$ neighbors determined by the topological distance with a free boundary condition. Using the same prescription for interactions used in the Vicsek model with scalar noise it has been observed that the flock, in absence of the noise, arrives at a number of interesting stationary states. In the `single sink state' the entire flock maintains perfect cohesion and coherence. In the `cyclic state' every agent executes a uniform circular motion, and the entire flock executes a pulsating dynamics i.e., expands and contracts periodically between a minimum and a maximum size of the flock. When refreshing rate of the interaction zone is the fastest, the entire flock gets fragmented into smaller clusters of different sizes. On introduction of scalar noise a crossover is observed when the agents cross over from a ballistic motion to a diffusive motion. Expectedly the crossover time is dependent on the strength of the noise $\eta$ and diverges as $\eta \to 0$. In simpler version the translational degrees of freedom of the agents are suppressed but their angular motion are retained. Here agents are the spins, placed at the sites of a square lattice with periodic boundary condition. Every spin interacts with its $n$ = 2, 3 or 4 nearest neighbors. In the stationary state the entire spin pattern moves as a whole when interactions are anisotropic with $n$ = 2 and 3; but it is completely frozen when the interaction is isotropic with $n=4$. These spin configurations have vortex-antivortex pairs whose density increases as the noise $\eta$ increases and follows an excellent finite-size scaling analysis., Comment: 15 pages, 18 figures

Using extensive numerical analysis of the Fiber Bundle Model with Equal Load Sharing dynamics we studied the finite-size scaling forms of the relaxation times against the deviations of applied load per fiber from the critical point. Our most crucial result is we have not found any $\ln (N)$ dependence of the average relaxation time $\langle T(\sigma,N) \rangle$ in the precritical state. The other results are: (i) The critical load $\sigma_c(N)$ for the bundle of size $N$ approaches its asymptotic value $\sigma_c(\infty)$ as $\sigma_c(N) = \sigma_c(\infty) + AN^{-1/\nu}$. (ii) Right at the critical point the average relaxation time $\langle T(\sigma_c(N),N) \rangle$ scales with the bundle size $N$ as: $\langle T(\sigma_c(N),N) \rangle \sim N^{\eta}$ and this behavior remains valid within a small window of size $|\Delta \sigma| \sim N^{-\zeta}$ around the critical point. (iii) When $1/N < |\Delta \sigma| < 100N^{-\zeta}$ the finite-size scaling takes the form: $\langle T(\sigma,N) \rangle / N^{\eta} \sim {\cal G}[\{\sigma_c(N)-\sigma\}N^{\zeta}]$ so that in the limit of $N \to \infty$ one has $\langle T(\sigma) \rangle \sim (\sigma - \sigma_c)^{-\tau}$. The high precision of our numerical estimates led us to verify that $\nu = 3/2$, conjecture that $\eta = 1/3$, $\zeta = 2/3$ and therefore $\tau = 1/2$., Comment: 8 pages, 11 figures