Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions

We study velocity statistics of electrostatically driven granular gases. For two different experiments: (i) non-magnetic particles in a viscous fluid and (ii) magnetic particles in air, the velocity distribution is non-Maxwellian, and its high-energy tail is exponential, P(v) ~ exp(-|v|). This behavior is consistent with kinetic theory of driven dissipative particles. For particles immersed in a fluid, viscous damping is responsible for the exponential tail, while for magnetic particles, long-range interactions cause the exponential tail. We conclude that velocity statistics of dissipative gases are sensitive to the fluid environment and to the form of the particle interaction.Comment: 4 pages, 3 figure

Kinetics of Heterogeneous Single-Species Annihilation

We investigate the kinetics of diffusion-controlled heterogeneous single-species annihilation, where the diffusivity of each particle may be different. The concentration of the species with the smallest diffusion coefficient has the same time dependence as in homogeneous single-species annihilation, A+A-->0. However, the concentrations of more mobile species decay as power laws in time, but with non-universal exponents that depend on the ratios of the corresponding diffusivities to that of the least mobile species. We determine these exponents both in a mean-field approximation, which should be valid for spatial dimension d>2, and in a phenomenological Smoluchowski theory which is applicable in d<2. Our theoretical predictions compare well with both Monte Carlo simulations and with time series expansions.Comment: TeX, 18 page

Symmetry effects and equivalences in lattice models of hydrophobic interaction

We establish the equivalence of a recently introduced discrete model of the hydrophobic interaction, as well as its extension to continuous state variables, with the Ising model in a magnetic field with temperature-dependent strength. In order to capture the effect of symmetries of the solvent particles we introduce a generalized multi-state model. We solve this model - which is not of the Ising type - exactly in one dimension. Our findings suggest that a small increase in symmetry decreases the amplitude of the solvent-mediated part of the potential of mean force between solute particles and enhances the solubility in a very simple fashion. High symmetry decreases also the range of the attractive potential. This weakening of the hydrophobic effect observed in the model is in agreement with the notion that the effect is entropic in origin.Comment: 19 pages, 2 figure

Random Geometric Series

Integer sequences where each element is determined by a previous randomly chosen element are investigated analytically. In particular, the random geometric series x_n=2x_p with 0<=p<=n-1 is studied. At large n, the moments grow algebraically, n^beta(s) with beta(s)=2^s-1, while the typical behavior is x_n n^ln 2. The probability distribution is obtained explicitly in terms of the Stirling numbers of the first kind and it approaches a log-normal distribution asymptotically.Comment: 6 pages, 2 figure

Discrete Analog of the Burgers Equation

We propose the set of coupled ordinary differential equations dn_j/dt=(n_{j-1})^2-(n_j)^2 as a discrete analog of the classic Burgers equation. We focus on traveling waves and triangular waves, and find that these special solutions of the discrete system capture major features of their continuous counterpart. In particular, the propagation velocity of a traveling wave and the shape of a triangular wave match the continuous behavior. However, there are some subtle differences. For traveling waves, the propagating front can be extremely sharp as it exhibits double exponential decay. For triangular waves, there is an unexpected logarithmic shift in the location of the front. We establish these results using asymptotic analysis, heuristic arguments, and direct numerical integration.Comment: 6 pages, 5 figure

Power-law velocity distributions in granular gases

We report a general class of steady and transient states of granular gases. We find that the kinetic theory of inelastic gases admits stationary solutions with a power-law velocity distribution, f(v) ~ v^(-sigma). The exponent sigma is found analytically and depends on the spatial dimension, the degree of inelasticity, and the homogeneity degree of the collision rate. Driven steady-states, with the same power-law tail and a cut-off can be maintained by injecting energy at a large velocity scale, which then cascades to smaller velocities where it is dissipated. Associated with these steady-states are freely cooling time-dependent states for which the cut-off decreases and the velocity distribution is self-similar.Comment: 11 pages, 9 figure

A simple electrostatic model applicable to biomolecular recognition

An exact, analytic solution for a simple electrostatic model applicable to biomolecular recognition is presented. In the model, a layer of high dielectric constant material (representative of the solvent, water) whose thickness may vary separates two regions of low dielectric constant material (representative of proteins, DNA, RNA, or similar materials), in each of which is embedded a point charge. For identical charges, the presence of the screening layer always lowers the energy compared to the case of point charges in an infinite medium of low dielectric constant. Somewhat surprisingly, the presence of a sufficiently thick screening layer also lowers the energy compared to the case of point charges in an infinite medium of high dielectric constant. For charges of opposite sign, the screening layer always lowers the energy compared to the case of point charges in an infinite medium of either high or low dielectric constant. The behavior of the energy leads to a substantially increased repulsive force between charges of the same sign. The repulsive force between charges of opposite signs is weaker than in an infinite medium of low dielectric constant material but stronger than in an infinite medium of high dielectric constant material. The presence of this behavior, which we name asymmetric screening, in the simple system presented here confirms the generality of the behavior that was established in a more complicated system of an arbitrary number of charged dielectric spheres in an infinite solvent.Comment: 15 pages, 6 figure

HERDING BEHAVIOR: MENGEKSPLORASI SISI ANALISIS BROKER SUMMARY

Our research focuses on herding behavior and broker summary analysis in the Covid-19 time frame in Indonesia. Herding behavior in the retail exchange community or the general public is considered detrimental due to the irrationality of analysis and promoting euphoria which results in very large losses. Answering the research gap, we offer a broad exploration concept to avoid and create positive returns by utilizing the herding behavior of the retail market community. We tested using multiple methods to ensure the existence of herding behavior in a regression setting of two and took advantage of positive opportunistic returns for exchange play. The first method shows that the research sample detected herding behavior during March 11, 2020 – March 11, 202 and we ensure the resilience of existence through two models. The second method, to get a positive return, we offer bandarmology analysis adopted from Dow theory for trading in a market maker style. Analyzing the movement and following market makers, we can conclude that it creates positive returns and prevents the stock exchange community from the impact of sustainable auto rejects. This study has limitations, for future research we expect the use of empirical models that are simpler and more efficient in revealing herding behavior. Furthermore, for the exploratory method, further research can be carried out in disclosing bandarmology analysis based on stock categorization (blue chip, second liner, and third liner), time horizon of market makers, and detailed analysis of camouflage behavior of market makers using retail securities. Penelitian kami berfokus pada perilaku herding dan analisis ringkasan broker dalam kerangka waktu Covid-19 di Indonesia. Perilaku menggiring di komunitas bursa ritel atau masyarakat umum dianggap merugikan karena irasionalitas analisis dan euforia yang menimbulkan kerugian yang sangat besar. Menjawab kesenjangan penelitian, kami menawarkan konsep eksplorasi yang luas untuk menghindari dan menciptakan pengembalian positif dengan memanfaatkan perilaku menggiring komunitas pasar ritel. Kami menguji menggunakan beberapa metode untuk memastikan keberadaan perilaku menggiring dalam pengaturan regresi dua dan memanfaatkan pengembalian oportunistik positif untuk permainan pertukaran. Metode pertama menunjukkan bahwa sampel penelitian mendeteksi perilaku penggembalaan selama 11 Maret 2020 – 11 Maret 202 dan kami memastikan ketahanan keberadaan melalui dua model. Metode kedua, untuk mendapatkan pengembalian positif, kami menawarkan analisis bandarmologi yang diadopsi dari teori Dow untuk perdagangan dalam gaya pembuat pasar. Menganalisis pergerakan dan mengikuti pembuat pasar, kita dapat menyimpulkan bahwa itu menciptakan pengembalian positif dan mencegah komunitas bursa dari dampak penolakan mobil berkelanjutan. Penelitian ini memiliki keterbatasan, untuk penelitian selanjutnya diharapkan penggunaan model empiris yang lebih sederhana dan efisien dalam mengungkap perilaku penggembalaan. Selanjutnya untuk metode eksplorasi dapat dilakukan penelitian lebih lanjut dalam mengungkap analisis bandarmologi berdasarkan kategorisasi saham (blue chip, second liner, dan third liner), time horizon market makers, dan analisis detail perilaku kamuflase market makers dengan menggunakan retail sekuritas

The resistance of randomly grown trees

Copyright @ 2011 IOP Publishing Ltd. This is a preprint version of the published article which can be accessed from the link below.An electrical network with the structure of a random tree is considered: starting from a root vertex, in one iteration each leaf (a vertex with zero or one adjacent edges) of the tree is extended by either a single edge with probability p or two edges with probability 1 − p. With each edge having a resistance equal to 1 omega, the total resistance Rn between the root vertex and a busbar connecting all the vertices at the nth level is considered. A dynamical system is presented which approximates Rn, it is shown that the mean value (Rn) for this system approaches (1 + p)/(1 − p) as n → ∞, the distribution of Rn at large n is also examined. Additionally, a random sequence construction akin to a random Fibonacci sequence is used to approximate Rn; this sequence is shown to be related to the Legendre polynomials and its mean is shown to converge with |(Rn) − (1 + p)/(1 − p)| ∼ n−1/2.Engineering and Physical Sciences Research Council (EPSRC

Stochastic Aggregation: Rate Equations Approach

We investigate a class of stochastic aggregation processes involving two types of clusters: active and passive. The mass distribution is obtained analytically for several aggregation rates. When the aggregation rate is constant, we find that the mass distribution of passive clusters decays algebraically. Furthermore, the entire range of acceptable decay exponents is possible. For aggregation rates proportional to the cluster masses, we find that gelation is suppressed. In this case, the tail of the mass distribution decays exponentially for large masses, and as a power law over an intermediate size range.Comment: 7 page