Dynamic critical behavior in models of ferromagnetic gadolinium

A numerical technique combining Monte Carlo and molecular dynamics simulations is used for the first time to examine the complex critical dynamics of models of ferromagnetic gadolinium in which both strong exchange interactions and relativistic effects of several different types are taken into account. A finite-size scaling technique is used to calculate the corresponding dynamic critical exponents. The role played by isotropic dipole-dipole interaction in the critical behavior of gadolinium is evaluated. The results obtained provide an explanation for the anomalous dynamic critical behavior of gadolinium.     

Dynamic observation models

It is shown that radar and quantum mechanics may be modeled using the Kalman-Bucy state-equation observation approach. A method is given for realizing the optimal position filters.     

Oscillatory behavior in cosmological models

Oscillatory behavior in cosmological models is investigated, motivated, in part, by the apparent periodic distribution of galaxies in deep narrow-cone red-shift surveys. In particular, oscillatory behavior in two cosmological models is studied; a qualitative analysis is performed and approximate solutions are found for a soft inflationary model and for a Friedmann-Robertson-Walker model containing a perfect fluid and a scalar field source. These two models are conformally equivalent to particular models arising from a large class of scalar-tensor theories. It is then argued that such oscillatory behavior is a generic property of scalartensor theories of gravity.     

Rigorous results on mathematical models of catalytic surfaces

Two types of mathematical models of catalytic surfaces are considered. Conditions guaranteeing either convergence to traps with all sites occupied by a single reactant (poisoning) and or coexistence in equilibrium are established.     

Comparative analysis of mathematical models of the matrix photodetector used in digital holography

It is established, that in modern works on digital holography, three fundamentally different mathematical models of a matrix photodetector are used. Comparative analysis of these models, including analysis of the formula of each model and test calculations, has been conducted. The possibility of using these models to account for the influence of geometrical parameters of a matrix photodetector on the properties of recorded digital holograms is considered.     

Dynamic exponent in extremal models of pinning

The depinning transition of a front moving in a time-independent random potential is studied. The temporal development of the overall roughness w(L,t) of an initially flat front, , is the classical means to have access to the dynamic exponent. However, in the case of front propagation in quenched disorder via extremal dynamics, we show that the initial increase in front roughness implies an extra dependence over the system size which comes from the fact that the activity is essentially localized in a narrow region of space. We propose an analytic expression for the exponent and confirm this for different models (crack front propagation, Edwards-Wilkinson model in a quenched noise etc.). Received 27 August 1999     

Microscopic models of hydrodynamic behavior

We review recent developments in the rigorous derivation of hydrodynamic-type macroscopic equations from simple microscopic models: continuous time stochastic cellular automata. The deterministic evolution of hydrodynamic variables emerges as the law of large numbers, which holds with probability one in the limit in which the ratio of the microscopic to the macroscopic spatial and temporal scales go to zero. We also study fluctuations in the microscopic system about the solution of the macroscopic equations. These can lead, in cases where the latter exhibit instabilities, to complete divergence in behavior between the two at long macroscopic times. Examples include Burgers' equation with shocks and diffusion-reaction equations with traveling fronts.     

Chaos in the long-term behavior of some Bianchi-type VIII models

The long-term behavior of Bianchi-type VIII models with three different types of stress-energy tensors are examined and compared. The vacuum model, a matter-filled model, and a model with an electromagnetic field are considered. In each case the existence of chaotic behavior and transitions to chaotic behavior are discussed.     

Comparison of different mathematical models of diffusion-weighted prostate MR imaging

Purpose

To evaluate which mathematical model (monoexponential, biexponential, statistical, kurtosis) fits best to the diffusion-weighted signal in prostate magnetic resonance imaging (MRI).

Materials and Methods

24 prostate 3-T MRI examinations of young volunteers (YV, n= 8), patients with biopsy proven prostate cancer (PC, n= 8) and an aged matched control group (AC, n= 8) were included. Diffusion-weighted imaging was performed using 11 b-values ranging from 0 to 800 s/mm².

Results

Monoexponential apparent diffusion coefficient (ADC) values were significantly (P<.001) lower in the peripheral (PZ) zone (1.18±0.16 mm²/s) and the central (CZ) zone (0.73±0.13 mm²/s) of YV compared to AC (PZ 1.92±0.17 mm²/s; CZ 1.35±0.21 mm²/s). In PC ADC_mono values (0.61±0.06 mm²/s) were significantly (P<.001) lower than in the peripheral of central zone of AC. Using the statistical analysis (Akaike information criteria) in YV most pixels were best described by the biexponential model (82%), the statistical model, respectively kurtosis (93%) each compared to the monoexponential model. In PC the majority of pixels was best described by the monoexponential model (57%) compared to the biexponential model.

Conclusion

Although a more complex model might provide a better fitting when multiple b-values are used, the monoexponential analyses for ADC calculation in prostate MRI is sufficient to discriminate prostate cancer from normal tissue using b-values ranging from 0 to 800 s/mm².     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Classical behavior of deformed sine-Gordon models

In this work we deform the ?⁴ model with distinct deformation functions, to propose a diversity of sine-Gordon-like models. We investigate the proposed models and we obtain all the topological solutions that they engender. In particular, we introduce non-polynomial potentials which support some exotic two-kink solutions.     

Fast-ionic-conductor behavior of driven lattice-gas models

We discuss driven diffusive lattice-gas systems as a model for fast ionic conductors, derive associated hydrodynamic equations and expressions for transport coefficients, and compare mean-field theory, Monte Carlo results and experimental observations. The comparison between model and real behaviours helps to understand some properties of those materials which seem to be characterized by the occurrence of nonequilibrium steady states and phase transitions. In particular, our study suggests the existence in Nature of a novel (nonequilibrium) universality class.     

Dynamic behavior of nickel atoms in graphitic networks

The dynamic behavior of nickel atoms in graphitic carbon onions, observed by in situ atomic-resolution electron microscopy, shows the formation of stable new C-Ni phases. Nickel is observed to take substitutional in-plane positions in graphene layers, forming a planar graphitelike C-Ni lattice. Evidence is furthermore seen for the formation of a cubic C-Ni phase, suggesting a possible phase transformation in C-Ni from a graphitelike to a diamondlike structure. The stability of the planar phases is shown by first-principles calculations which also indicate that the C-Ni planes are metallic.