Dynamics of forest fire under rotational constraint

A rotationally constrained forest fire model is studied on square and triangular lattices of size 400×400. The critical probabilityp _c for onset of fire propagation is determined. The scaling relationsMt ^d _r, R_gt^v andMR _g ^d _f are analysed at fire propagation probabilityp=p _c whereM is the number of burnt trees,R _g the radius of gyration andd _f the fractal dimension of the cluster of burnt trees at timet. Numerical estimates ofd _t, v andd _f have been obtained.     

Deep bandtail states picosecond intensity-dependent carrier dynamics of GaN epilayer under high excitation

Picosecond carrier dynamics of deep bandtail states (3.1 eV) in an unintentionally n-doped GaN epilayer at room temperature under high excitation densities (i.e., N ₀ = 1.0× 10¹⁹– 1.1× 10²⁰ cm^–3) have been investigated with nondegenerate femtosecond pump–probe (267/400 nm) reflectance ( R/R ₀). All R/R ₀ traces possess a 2 ps buildup time that represents an overall time for the initial non-thermal carrier population to relax towards the continuum extremes and then into the probed tail states. We observe a saturation of R/R ₀ initial (first 10 ps) recovery rate _i at a density of 5– 6×10¹⁹ cm^–3 close to the Mott transition threshold obtained from time-integrated PL measurements. Such a saturation phenomenon has been identified as the trap-bottleneck due to the bandtail states and deep traps. As N ₀ is further increased, _i accelerates due to the onset of Auger recombination as the trap-bottleneck becomes effective. The best fit by the Auger model for N ₀ in the range of the mid-10¹⁹–10²⁰ cm^–3 yields an Auger coefficient of C _a 5.0× 10^–30 cm⁶ s^–1.     

Self-consistent calculation of statics and dynamics of the roughening transition

Statics and dynamics of the modified kinetic discrete Gaussian model are treated selfconsistently using a Gaussian probability assumption. A non-trivial roughening temperatureT _R is found in exactly two dimensions only. The free energyF, the correlation length and the interface roughness h ² are found to behave—lnFlnh ²(T _R –T)^–1 for temperaturesT approachingT _R from below. The linear relaxation rate of the order parameter is found to be proportional to ^–2. As a model for crystal growth, the growth rate depends linearly upon the chemical potential difference aboveT _R , shows a metastable regime belowT _R with a spinodal limit of metastability _c , beyond which oscillatory growth starts. The critical behavior of _c is found to be ln _c –(T _R –T)^–1+O(ln (T _R –T)).     

The Split of the Dirac Hamiltonian into Precisely Predictable Energy Components

We are dealing with the Dirac Hamiltonian H = H₀ + V with no magnetic field and radially symmetric electrostatic potential V = V(r), preferably the Coulomb potential. While the observable H is precisely predictable, its components H₀ (relativistic mass) and V (potential energy) are not. However they both possess precisely predictable approximations H₀ and V which approximate accurately if the particle is not near its nucleus. On the other hand, near 0, H₀ and V are practically unpredictable, perhaps in agreement with the fact, that a neutrino also should be in the game. [We have not yet studied the corresponding observables for the ( 12-dimensional) problem of electro-weak interaction.] Mathematically we are focusing on the spectral theory of the unbounded self-adjoint operators H₀ and V . We can prove that V is unitarily equivalent to V(r) again, by a unitary map given as Wiener-Hopf-type singular integral operator in the standard separation of variables for radially symmetric Dirac Hamiltonians. [This is, as far as the continuous spectrum is concerned.] Very similar unitary equivalence holds for H ₀ and H ₀. We are tempted to regard this as a form of renormalization.     

Resonant generation of even-order harmonics in metal vapors

Generation of the second- and fourth-order harmonics of laser radiation is reported in Mg vapor at the forbidden 3s ²¹ S _o–4s ¹ S _o transition. The conversion efficiency for the second-order harmonics has been measured to be 10^–2% and for the fourth one 10^–8%.     

Temperature dependence of the spinS=1/2 fluctuation rate and the low-spin versus high-spin transition in native chloroperoxidase

We analyzed two preparations of native, low-spin ferric chloroperoxides as a function of temperature with the following results. (i) The spin lattice transition rateW(T) is relative slow, following a power lawW=0.035 (T/K)^4.98 (rad/s) for one of the samples. (ii) The quadrupole splitting is strongly temperature dependent, dropping from ¦E _Q¦ 2.94 mm/s at 100 K to 2 mm/s at 250 K. (iii) Starting at 190 K, the low-spin heme iron in frozen adqueous solution converts reversibly to a high-spin form, reaching 40% high-spin at 250 K. The two forms appear to be in thermal equilibrium, (iv) Optical data indicate that in a 70% glycerol glass, the conversion starts at lower temperature and reaches 50% highspin at 190 K.Supported in part by GM 49513 and GM 16406.     

Wetting and Phase Separation in Polymer Blend Films: Identification of Four Thickness Regimes with Distinct Morphological Pathways

Using forward recoil spectrometry and atomic force microscopy, the phase evolution of a critical blend thin film of deuterated poly(methyl methacrylate) (dPMMA) and poly(styrene-ran-acrylonitrile) (SAN) is found to depend on film thickness. Four regimes are identified as film thickness l ₀ decreases from semi-infinite to below the radius of gyration, R _g. In the semi-infinite limit or regime IV (l ₀ R _g), surface directed spinodal decomposition is observed and found to agree with cell dynamic simulations. In regime III (10 R _g < l ₀ < 150 R _g), three stages of evolution are observed. During the early stage, wetting dominates and produces a dPMMA-rich/SAN-rich/dPMMA-rich structure. During the intermediate stage, the surface phase flows back into the middle layer inducing lateral phase coarsening. During the late stage, capillary fluctuations rupture the middle layer by spinodal dewetting, resulting in a final morphology with SAN-rich droplets encapsulated by dPMMA-rich wetting layers. Although regime II (R _g < l ₀ < 10 R _g) films also exhibit a tri-layer early stage, correlated holes in the middle layer spontaneously grow suggesting that this layer is too thin to support fully developed capillary fluctuations. Three stages of roughening are observed with a final morphology similar to regime III. In regime I (l ₀ < R _g), films roughen almost immediately after annealing in contrast to the other regimes. Initially, the surface roughness increases logarithmically with time before reaching a constant value of 2 R _g. The final average droplet height, 29.5 nm, is in good agreement with a simple interfacial energy model. Whereas the final morphology for regimes I, II and III are identical, the pathways by which films roughen are distinct suggesting that erroneous conclusions can be made by simply analyzing the final morphology.     

Photoproduction of Boson Pairs in a Radiation-Dominated Universe. II

The average number of pairs of scalar massive particles produced by a decaying photon in a radiation-dominated universe is calculated. The dependence of the expression obtained on the energy of the initial photon is investigated. Numerical estimates are found for the formative time t ₀ of the processes of decay of photons in an early universe and for the total number N ^(±) _{out pair} of photoproduced scalar pairs. The estimates are: t ₀ 3 min and N ^(±) _{out pair} 10³¹·N ^(±) ₀(0), where N ^(±) ₀(0) is the total number of pairs produced from the vacuum of a free quantized field.     

Critical behavior of the two-dimensional first passage time

We study the two-dimensional first passage problem in which bonds have zero and unit passage times with probabilityp and 1–p, respectively. We prove that as the zero-time bonds approach the percolation thresholdp _c, the first passage time exhibits the same critical behavior as the correlation function of the underlying percolation problem. In particular, if the correlation length obeys(p) ¦p–p _c¦^–v, then the first passage time constant satisfies(p)¦p–p _c¦^v. At p_c, where it has been asserted that the first passage time from 0 tox scales as ¦x¦ to a power with 0<<1, we show that the passage times grow like log ¦x¦, i.e., the fluid spreads exponentially rapidly.     

Note on the interfacial tension of phase-separated polymer solutions

Earlier theoretical calculations of the interfacial tension of phase-separated polymer solutions as a function of the degree of polymerizationN and the temperatureT, based partly on the mean-field approximation, had led toN ^–1/4(1–T/T _c )^3/2 for fixedN1 andT approaching the critical solution temperatureT _c It is here remarked that the scaling procedure of de Gennes then modifies this toN ^–0.37(1–T/T _c )^1.26, which is in close accord with the experimentalN ^–0.44(1–T/T _c )^1.26. The simplest mean-field picture yieldsN ^–1/2(1–T/T _c )^3/2.     

On the homotopical significance of the type of von Neumann algebra factors

The set of all projections and the set of all unitaries in a von Neumann algebra factorA are studied from the homotopical point of view relative to the operator norm topology.Two projectionsE andF can be deformed continuously to each other if and only ifEF and 1–E1–F where denotes the equivalence of projections inA in the sense of von Neumann. In other words, the relative dimension and co-dimension are a complete homotopical invariants of projections inA and label pathwise connected components of the set of projections.The first homotopy group ₁(U(A)) of unitaries inA is shown to be 0 forA of infinite type. For typeII ₁ and typeI _n factors, ₁(U(A)) are isomorphic to additive groups of realsR and integersZ, respectively, in which the first homotopy group ₁(F U(A)) of the center ofU(A) is imbedded asZ andnZ, respectively.     

Low temperature anharmonicity in Sn(CH3)4 due to methyl group reorientation: A Mössbauer study

The detailed temperature variation of the Mössbauer spectral intensity in Sn(CH₃)₄ displays a pronounced drop of the Debye temperature from _D 96K below the transition temperature (T _t 43K) to _D 76K above it. The transition atT _t is discussed in terms of recent INS and NMR results where increased motion of inequivalent CH₃ groups has been observed around the temperatureT _t .Supported by the U.S.-Israel Binational Science Foundation     

Dynamic short-range order observed in the (Zn)[Fe2]O4 spinel by neutron diffraction, μSR,and Mössbauer experiments

Using neutron diffraction (ND), muon-spin rotation/relaxation (SR), and⁵⁷Fe-Mössbauer spectroscopy (MS) we have investigated magnetic properties of the normal spinel (Zn)[Fe₂]O₄. In compounds which are slowly cooled from 1200°C to room temperature inversion is below detection limits. AtT _N = 10.5 K the spinel exhibits long-range antiferromagnetic order (LRO). The transition as seen in thermal-scan spectra by MS is very sharp. However, ND andSR experiments show that already at temperatures of 10T _N a short-range antiferromagnetic ordering (SRO) develops which extends through 70% of the sample volume just aboveT _N . BelowT _N SRO and LRO coexist. At 4.2 K still 25% of the sample is short-range ordered. The regions over which the SRO extends have a size of 3 nm. Their fluctuation rates are in the GHz range. Modern ab initio cluster calculations successfully describe the magnetic hyperfine fields as well as the electric field gradient (EFG) tensor at the Fe sites. Covalency of the Fe-O and Zn-O bonds is important. The physical origin of the regions exhibiting SRO, however, remains unresolved at this point.     

Local magnetic properties of ultrathin ferromagnetic fcc-Fe-films on Cu(001)

Conversion electron Mössbayer spectroscopy (CEMS) on three monolayers (ML) thick metastable fcc-Fe(001) films grown epitaxially on a Cu(001) substrate under different conditions shows that these films are characterized by a distributionP(B _hf) of magnetic hyperfine fieldsB _hf. The vast majority of⁵⁷Fe nuclei experience relatively large hyperfine fields at low temperature. The temperature dependence of the most probable fieldB _peak was found to follow aT ^3/2 spin-wave law below 300 K. It is shown from the relative line intensities that preferential Fe spin orientation perpendicular to the film plane exists in films grown at 120 K, while preferential in-plane spin orientation is found for a growth temperature of 300 K. Coating a low-temperature grown Fe film by 2 ML of Cu(001) drastically reduces the hyperfine field, in contrast to the case of room-temperature grown Cu-coated films.Dedicated to Professor Ulrich Gonser on the occasion of his 70th birthday     

Investigation of the plasma potential oscillations in the range of geodesic acoustic mode frequencies by heavy ion beam probing in tokamaks

Specific oscillations within a range of 20 kHz (20 kHz-mode) were investigated on the T-10 and TEXT tokamaks using Heavy Ion Beam Probe (HIBP) diagnostic. Regimes with ohmic heating on both machines, and with off-axis ECRH in T-10 were studied. It was shown that 20 kHz-modes are mainly the potential oscillations. The power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with a contrast range of (3–5). They are the manifestation of torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. It was shown that in TEXT the radial electric field oscillations exist in a limited radial range of 0.65 > < 0.95. The frequency of 20 kHz-mode is varied in the region of observation; it diminishes to the plasma edge. In T-10, after ECRH switch-on, the frequency increases, correlating with the growth of the electron temperature T _e. In both machines the frequency of the 20 kHz-mode varies with local T _e: f T _e ^1/2 , which is consistent with theoretical scaling for geodesic acoustic modes (GAM): f _GAM c _s/R T _e ^1/2 , where c _s is the speed of sound. The absolute frequencies are close to GAM values within a factor of unity.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Unstable neutrinos can do it!

We present a cosmological scenario with unstable neutrinos which decay into a light neutrino and a relativistic boson. Theoretical and observational constraints severely narrow the values of mass and of lifetime of neutrinos. However, within this range, we can construct models with (i) = 1, (ii) age of the universe 13 billion years (b.y.) and (iii)h ₀ –0.5. The dynamical modeling shows that (a) the initial condensates of primordial _L are disrupted by the decay, lowering their masses to acceptable values ~10¹² M, (b) the relativistic boson contributes nearly 0.25 to, and (c) there emerge two prominent scales in dark matter distribution, one with a mass ~10¹² M distributed over 200 kpc around galaxies and another component with density 10^–27 g cm^–3 distributed over 1 Mpc. The model agrees with observations at all scales.This essay received an honorable mention from the Gravity Research Foundation for 1986-Ed.     

Spin fluctuations in both the ordered and paramagnetic phases of MnSi! MnSi a heavy Fermi liquid?

Polarised neutrons and polarisation analysis have been used to determine the diffuse magnetic scattering from MnSi as a function of temperature. Measurements at 50 K (1.72T _c) and 100 K (3.45T _c) in the paramagnetic phase confirmed the presence of strong spatial correlations previously reported at 300 K (10T _c) and 580 K (20T _c). The spatial correlations between regions of spin density separated by 12 Å are of a ferromagnetic nature and determine the static susceptibility. Integration of the paramagnetic response over an inverse atomic volume yields a moment per manganese atom of 1.2 _B , a value considerably larger than the 0.4 _B observed in Bragg scattering and magnetisation measurements at 4.2 K. Measurements made at 11 K in the ordered magnetic phase reveal strong diffuse scattering corresponding to 0.8 _B per Mn atom. The increase in the diffuse scattering observed in the paramagnetic phase corresponds to the passage of the Bragg component into the background.The presence of significant scattering in the ordered phase and the very unusual wave vector dependence of the diffuse scattering observed at 11 K has been interpreted assuming MnSi to be a heavy Fermi liquid. Furthermore we believe these measurements give the first direct observation of the exchange hole.     

Hyperfine field of samarium in europium monoxide

The hyperfine magnetic field at samarium in europium monoxide at 4.2 K was measured using the time-differential perturbed angular correlation technique. The resultH _hf=147.9±9.7 T indicates a 4f contribution of 130±20 T which is 60% less than the free ion value for Sm³⁺. It is suggested that there exists crystal plus exchange field interactions causing admixtures of the first excited state of Sm³⁺ with its ground state.     

Electric quadrupole interaction at181Ta in RNi5 compounds

The time differential perturbed angular correlation measurements in PrNi₅, NdNi₅, GdNi₅, DyNi₅ and ErNi₅ rare-earth intermetallics with¹⁸¹Ta as probe nuclei have revealed that these impurity nuclei experience a non-axial electric quadrupole interaction. In all the cases, except in GdNi₅, the interaction frequency has a single value in the range 15–20 MHz with asymmetry parameter 0.98. In GdNi₅, however, there are two interaction frequencies (13.61 MHz and 26.89 MHz), the former being the dominant one (90%) with 0.35 and the latter (10%) with 0.98. It is concluded that in all cases the probe nuclei experiencing the highly asymmetric electric field gradient (efg) occupy the unique Ni(3g) site. Annealing studies have shown that in the case of GdNi₅ the interaction gets highly damped, while there is negligible effect in the other cases. The temperature variation of the efg in all cases seems to follow the empiricalT ^3/2 relation.