STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

Dynamical collapse in a degenerate binary fermion mixture using a hydrodynamic model

We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion-fermion mixture ( DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances, there cannot be a collapse for repulsive interspecies fermion fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion-fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model, we study different aspects of collapse in such a DFFM initiated by a jump in the interspecies fermion-fermion interaction ( scattering length) to a large negative ( attractive) value using a Feshbach resonance. Suggestion for experiments of collapse in a DFFM of distinct atoms is made.

Survival probability of large rapidity gaps in a QCD model with a dynamical infrared mass scale

We compute the survival probability {vertical bar S vertical bar(2)} of large rapidity gaps (LRG) in a QCD based eikonal model with a dynamical gluon mass, where this dynamical infrared mass scale represents the onset of nonperturbative contributions to the diffractive hadron-hadron scattering. Since rapidity gaps can occur in the case of Higgs boson production via fusion of electroweak bosons, we focus on WW -> H fusion processes and show that the resulting {vertical bar S vertical bar(2)} decreases with the increase of the energy of the incoming hadrons; in line with the available experimental data for LRG. We obtain {vertical bar S vertical bar(2)} = 27.6 +/- 7.8% (18.2 +/- 17.0%) at Tevatron (CERN-LHC) energy for a dynamical gluon mass m(g) = 400 MeV. (c) 2006 Elsevier B.V. All rights reserved.

gamma p and gamma gamma scattering from (p)over-bar-p, pp forward amplitudes in a QCD eikonal model with a dynamical gluon mass

We examine the gamma p photoproduction and the hadronic gamma gamma total cross sections by means of a QCD eikonal model with a dynamical infrared mass scale. In this model, where the dynamical gluon mass is the natural regulator for the tree level gluon-gluon scattering, the gamma p and gamma gamma total cross sections are derived from the pp and (p) over barp forward scattering amplitudes assuming vector meson dominance and the additive quark model. We show that the validity of the cross section factorization relation sigma(pp)/sigma(gamma p)=sigma(gamma p)/sigma(gamma gamma) is fulfilled depending on the Monte Carlo model used to unfold the hadronic gamma gamma cross section data, and we discuss in detail the case of sigma(gamma gamma -> hadrons) data with W-gamma gamma> 10 GeV unfolded by the Monte Carlo generators PYTHIA and PHOJET. The data seems to favor a mild dependence with the energy of the probability (P-had) that the photon interacts as a hadron.

DYNAMICAL SYMMETRY BREAKING IN A MINIMAL 3-3-1 MODEL

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamical properties of a dissipative hybrid Fermi-Ulam-bouncer model

Some consequences of dissipation are studied for a classical particle suffering inelastic collisions in the hybrid Fermi-Ulam bouncer model. The dynamics of the model is described by a two-dimensional nonlinear area-contracting map. In the limit of weak and moderate dissipation we report the occurrence of crisis and in the limit of high dissipation the model presents doubling bifurcation cascades. Moreover, we show a phenomena of annihilation by pairs of fixed points as the dissipation varies. (c) 2007 American Institute of Physics.

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. © 2013 Elsevier B.V. All rights reserved.

Dynamical properties for a mixed Fermi accelerator model

The behavior of the decay of velocity in a semi-dissipative one-dimensional Fermi accelerator model is considered. Two different kinds of dissipative forces were considered: (i) F-v and; (ii) F-v2. We prove the decay of velocity is linear for (i) and exponential for (ii). During the decay, the particles move along specific corridors which are constructed by the borders of the stable manifolds of saddle points. These corridors organize themselves in a very complicated way in the phase space leading the basin of attraction of the sinks to be seemingly of fractal type. © 2013 Elsevier B.V. All rights reserved.

Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamical (super)symmetry vacuum properties of the supersymmetric Chern-Simons-matter model

By computing the two-loop effective potential of the D=3 N=1 supersymmetric Chern-Simons model minimally coupled to a massless self-interacting matter superfield, it is shown that supersymmetry is preserved, while the internal U(1) and the scale symmetries are broken at two-loop order, dynamically generating masses both for the gauge superfield and for the real component of the matter superfield.

Dynamical principles in biological processes: A model of charge migration in proteins and DNA

The generalized master equations (GMEs) that contain multiple time scales have been derived quantum mechanically. The GME method has then been applied to a model of charge migration in proteins that invokes the hole hopping between local amino acid sites driven by the torsional motions of the floppy backbones. This model is then applied to analyze the experimental results for sequence-dependent long-range hole transport in DNA reported by Meggers et al. [Meggers, E., Michel-Beyerle, M. E., & Giese, B. (1998) J. Am. Chem. Soc. 120, 12950–12955]. The model has also been applied to analyze the experimental results of femtosecond dynamics of DNA-mediated electron transfer reported by Zewail and co-workers [Wan, C., Fiebig, T., Kelley, S. O., Treadway, C. R., Barton, J. K. & Zewail, A. H. (1999) Proc. Natl. Acad. Sci. USA 96, 6014–6019]. The initial events in the dynamics of protein folding have begun to attract attention. The GME obtained in this paper will be applicable to this problem.

High-resolution dynamical downscaling products for the North Slope of Alaska and surrounding areas, links to model result files

Climatic changes are most pronounced in northern high latitude regions. Yet, there is a paucity of observational data, both spatially and temporally, such that regional-scale dynamics are not fully captured, limiting our ability to make reliable projections. In this study, a group of dynamical downscaling products were created for the period 1950 to 2100 to better understand climate change and its impacts on hydrology, permafrost, and ecosystems at a resolution suitable for northern Alaska. An ERA-interim reanalysis dataset and the Community Earth System Model (CESM) served as the forcing mechanisms in this dynamical downscaling framework, and the Weather Research & Forecast (WRF) model, embedded with an optimization for the Arctic (Polar WRF), served as the Regional Climate Model (RCM). This downscaled output consists of multiple climatic variables (precipitation, temperature, wind speed, dew point temperature, and surface air pressure) for a 10 km grid spacing at three-hour intervals. The modeling products were evaluated and calibrated using a bias-correction approach. The ERA-interim forced WRF (ERA-WRF) produced reasonable climatic variables as a result, yielding a more closely correlated temperature field than precipitation field when long-term monthly climatology was compared with its forcing and observational data. A linear scaling method then further corrected the bias, based on ERA-interim monthly climatology, and bias-corrected ERA-WRF fields were applied as a reference for calibration of both the historical and the projected CESM forced WRF (CESM-WRF) products. Biases, such as, a cold temperature bias during summer and a warm temperature bias during winter as well as a wet bias for annual precipitation that CESM holds over northern Alaska persisted in CESM-WRF runs. The linear scaling of CESM-WRF eventually produced high-resolution downscaling products for the Alaskan North Slope for hydrological and ecological research, together with the calibrated ERA-WRF run, and its capability extends far beyond that. Other climatic research has been proposed, including exploration of historical and projected climatic extreme events and their possible connections to low-frequency sea-atmospheric oscillations, as well as near-surface permafrost degradation and ice regime shifts of lakes. These dynamically downscaled, bias corrected climatic datasets provide improved spatial and temporal resolution data necessary for ongoing modeling efforts in northern Alaska focused on reconstructing and projecting hydrologic changes, ecosystem processes and responses, and permafrost thermal regimes. The dynamical downscaling methods presented in this study can also be used to create more suitable model input datasets for other sub-regions of the Arctic.

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached. We propose that inelastic x-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition.