First-passage and extreme-value statistics of a particle subject to a constant force plus a random force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.Comment: Contains an analysis of the extreme-value statistics not included in first versio

Blackbody Radiation and the Scaling Symmetry of Relativistic Classical Electron Theory with Classical Electromagnetic Zero-Point Radiation

It is pointed out that relativistic classical electron theory with classical electromagnetic zero-point radiation has a scaling symmetry which is suitable for understanding the equilibrium behavior of classical thermal radiation at a spectrum other than the Rayleigh-Jeans spectrum. In relativistic classical electron theory, the masses of the particles are the only scale-giving parameters associated with mechanics while the action-angle variables are scale invariant. The theory thus separates the interaction of the action variables of matter and radiation from the scale-giving parameters. Classical zero-point radiation is invariant under scattering by the charged particles of relativistic classical electron theory. The basic ideas of the matter -radiation interaction are illustrated in a simple relativistic classical electromagnetic example.Comment: 18 page

Variational Approximations in a Path-Integral Description of Potential Scattering

Using a recent path integral representation for the T-matrix in nonrelativistic potential scattering we investigate new variational approximations in this framework. By means of the Feynman-Jensen variational principle and the most general ansatz quadratic in the velocity variables -- over which one has to integrate functionally -- we obtain variational equations which contain classical elements (trajectories) as well as quantum-mechanical ones (wave spreading).We analyse these equations and solve them numerically by iteration, a procedure best suited at high energy. The first correction to the variational result arising from a cumulant expansion is also evaluated. Comparison is made with exact partial-wave results for scattering from a Gaussian potential and better agreement is found at large scattering angles where the standard eikonal-type approximations fail.Comment: 35 pages, 3 figures, 6 tables, Latex with amsmath, amssymb; v2: 28 pages, EPJ style, misprints corrected, note added about correct treatment of complex Gaussian integrals with the theory of "pencils", matches published versio

Controls on the fate and speciation of Np(V) during iron (oxyhydr)oxide crystallization

The speciation and fate of neptunium as Np(V)O2+ during the crystallization of ferrihydrite to hematite and goethite was explored in a range of systems. Adsorption of NpO2+ to iron(III) (oxyhydr)oxide phases was reversible and, for ferrihydrite, occurred through the formation of mononuclear bidentate surface complexes. By contrast, chemical extractions and X-ray absorption spectroscopy (XAS) analyses showed the incorporation of Np(V) into the structure of hematite during its crystallization from ferrihydrite (pH 10.5). This occurred through direct replacement of octahedrally coordinated Fe(III) by Np(V) in neptunate-like coordination. Subsequent analyses on mixed goethite and hematite crystallization products (pH 9.5 and 11) showed that Np(V) was incorporated during crystallization. Conversely, there was limited evidence for Np(V) incorporation during goethite crystallization at the extreme pH of 13.3. This is likely due to the formation of a Np(V) hydroxide precipitate preventing incorporation into the goethite particles. Overall these data highlight the complex behavior of Np(V) during the crystallization of iron(III) (oxyhydr)oxides, and demonstrate clear evidence for neptunium incorporation into environmentally important mineral phases. This extends our knowledge of the range of geochemical conditions under which there is potential for long-term immobilization of radiotoxic Np in natural and engineered environments

Uranium fate during crystallization of magnetite from ferrihydrite in conditions relevant to the disposal of radioactive waste

Uranium incorporation into magnetite and its behaviour during subsequent oxidation has been investigated at high pH to determine the uranium retention mechanism(s) on formation and oxidative perturbation of magnetite in systems relevant to radioactive waste disposal. Ferrihydrite was exposed to U(VI)aq containing cement leachates (pH 10.5-13.1) and crystallization of magnetite was induced via addition of Fe(II)aq. A combination of XRD, chemical extraction and XAS techniques provided direct evidence that U(VI) was reduced and incorporated into the magnetite structure, possibly as U(V), with a significant fraction recalcitrant to oxidative remobilization. Immobilization of U(VI) by reduction and incorporation into magnetite at high pH, and with significant stability upon reoxidation, has clear and important implications for limiting uranium migration in geological disposal of radioactive wastes. © 2016 by Walter de Gruyter Berlin/Boston

Incorporation and retention of 99-Tc(IV) in magnetite under high pH conditions

Technetium incorporation into magnetite and its behavior during subsequent oxidation has been investigated at high pH to determine the technetium retention mechanism(s) on formation and oxidative perturbation of magnetite in systems relevant to radioactive waste disposal. Ferrihydrite was exposed to Tc(VII)(aq) containing cement leachates (pH 10.5-13.1), and crystallization of magnetite was induced via addition of Fe(II)aq. A combination of X-ray diffraction (XRD), chemical extraction, and X-ray absorption spectroscopy (XAS) techniques provided direct evidence that Tc(VII) was reduced and incorporated into the magnetite structure. Subsequent air oxidation of the magnetite particles for up to 152 days resulted in only limited remobilization of the incorporated Tc(IV). Analysis of both X-ray absorption near edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) data indicated that the Tc(IV) was predominantly incorporated into the magnetite octahedral site in all systems studied. On reoxidation in air, the incorporated Tc(IV) was recalcitrant to oxidative dissolution with less than 40% remobilization to solution despite significant oxidation of the magnetite to maghemite/goethite: All solid associated Tc remained as Tc(IV). The results of this study provide the first direct evidence for significant Tc(IV) incorporation into the magnetite structure and confirm that magnetite incorporated Tc(IV) is recalcitrant to oxidative dissolution. Immobilization of Tc(VII) by reduction and incorporation into magnetite at high pH and with significant stability upon reoxidation has clear and important implications for limiting technetium migration under conditions where magnetite is formed including in geological disposal of radioactive wastes

Statistical properties of the Burgers equation with Brownian initial velocity

We study the one-dimensional Burgers equation in the inviscid limit for Brownian initial velocity (i.e. the initial velocity is a two-sided Brownian motion that starts from the origin x=0). We obtain the one-point distribution of the velocity field in closed analytical form. In the limit where we are far from the origin, we also obtain the two-point and higher-order distributions. We show how they factorize and recover the statistical invariance through translations for the distributions of velocity increments and Lagrangian increments. We also derive the velocity structure functions and we recover the bifractality of the inverse Lagrangian map. Then, for the case where the initial density is uniform, we obtain the distribution of the density field and its $n$-point correlations. In the same limit, we derive the $n-$point distributions of the Lagrangian displacement field and the properties of shocks. We note that both the stable-clustering ansatz and the Press-Schechter mass function, that are widely used in the cosmological context, happen to be exact for this one-dimensional version of the adhesion model.Comment: 42 pages, published in J. Stat. Phy

GONADOTROPHIN RESPONSES TO GnRH PULSES IN HYPOGONADOTROPHIC HYPOGONADISM: LH RESPONSIVENESS IS MAINTAINED IN THE PRESENCE OF LUTEAL PHASE CONCENTRATIONS OF OESTROGEN AND PROGESTERONE

LH pulse secretion changes during the menstrual cycle from a rapid regular pattern in the follicular phase to a slower and irregular pattern in the luteal phase. To determine whether the irregular LH pulse pattern in the luteal phase reflects altered GnRH secretion or altered pituitary responsiveness to GnRH, we gave low dose GnRH pulses (25 ng/kg i.v.) every 2 h or every hour for 10 or 12 d to three women with isolated GnRH deficiency. After 4 d of GnRH alone, oestradiol (E 2 ) was given and after 6 d progesterone (P) was added to mimic the hormonal milieu of the luteal phase. LH and FSH were measured every 4 h throughout and also every 20 min for 6 or 12 h, before and after GnRH alone (day 0 and day 4), after E 2 (day 6), and after E 2 + P (day 10 and day 12). Both GnRH pulse frequencies resulted in a rapid increase in plasma FSH to peaks on day 4 (every 2 h) and day 2 and 3 (every hour). FSH concentrations then declined as plasma E 2 rose to 50–80 pg/ml reflecting the selective inhibitory effect of E 2 on FSH release. Plasma LH was also increased after the hourly GnRH injections and this regimen was associated with a more rapid rise in E 2 reflecting follicular maturation. In contrast to the differences in mean hormone concentrations, administration of GnRH at both frequencies resulted in sustained one-on-one responsiveness of LH that was maintained in the presence of both oestrogen and progesterone at mid-luteal phase concentrations. We conclude that the slow frequency of LH pulses observed during the luteal phase reflects decreased GnRH pulse frequency rather than impaired pituitary responsiveness to GnRH.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74947/1/j.1365-2265.1987.tb00786.x.pd

The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero-temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics.Comment: 21 page