Investigating potential biases in observed and modeled metrics of aerosol-cloud-precipitation interactions

This study utilizes large eddy simulation, aircraft measurements, and satellite observations to identify factors that bias the absolute magnitude of metrics of aerosol-cloud-precipitation interactions for warm clouds. The metrics considered are precipitation susceptibility <i>S</i><sub>o</sub>, which examines rain rate sensitivity to changes in drop number, and a cloud-precipitation metric, χ, which relates changes in rain rate to those in drop size. While wide ranges in rain rate exist at fixed cloud drop concentration for different cloud liquid water amounts, χ and <i>S</i><sub>o</sub> are shown to be relatively insensitive to the growth phase of the cloud for large datasets that include data representing the full spectrum of cloud lifetime. Spatial resolution of measurements is shown to influence the liquid water path-dependent behavior of <i>S</i><sub>o</sub> and χ. Other factors of importance are the choice of the minimum rain rate threshold, and how to quantify rain rate, drop size, and the cloud condensation nucleus proxy. Finally, low biases in retrieved aerosol amounts owing to wet scavenging and high biases associated with above-cloud aerosol layers should be accounted for. The paper explores the impact of these effects for model, satellite, and aircraft data

Non-self similar blowup solutions to the higher dimensional Yang-Mills heat flows

In this paper, we consider the Yang-Mills heat flow on $\mathbb R^d \times SO(d)$ with $d \ge 11$. Under a certain symmetry preserved by the flow, the Yang-Mills equation can be reduced to: $$\partial_t u =\partial_r^2 u +\frac{d+1}{r} \partial_r u -3(d-2) u^2 - (d-2) r^2 u^3, \text{ and } (r,t) \in \mathbb R_+ \times \mathbb R_+.$$ We are interested in describing the singularity formation of this parabolic equation. We construct non-self-similar blowup solutions for $d \ge 11$ and prove that the asymptotic of the solution is of the form $$u(r,t) \sim \frac{1}{\lambda_\ell(t)} \mathcal{Q} \left( \frac{r}{\sqrt{\lambda_\ell (t)}} \right), \text{ as } t \to T ,$$ where $\mathcal{Q}$ is the ground state with boundary conditions $\mathcal{Q}(0)=-1, \mathcal{Q}'(0)=0$ and the blowup speed $\lambda_\ell$ verifies $$\lambda_\ell (t) = \left( C(u_0) +o_{t\to T}(1) \right) (T-t)^{\frac{2\ell }{\alpha}} \text{ as } t \to T,~~ \ell \in \mathbb{N}^*_+, ~~\alpha>1.$$ In particular, when $\ell = 1$, this asymptotic is stable whereas for $\ell \ge 2$ it becomes stable on a space of codimension $\ell-1$. Our approach here is not based on energy estimates but on a careful construction of time dependent eigenvectors and eigenvalues combined with maximum principle and semigroup pointwise estimates.Comment: 87 page

Sharp equivalent for the blowup profile to the gradient of a solution to the semilinear heat equation

In this paper, we consider the standard semilinear heat equation \begin{eqnarray*} \partial_t u = \Delta u + |u|^{p-1}u, \quad p >1. \end{eqnarray*} The determination of the (believed to be) generic blowup profile is well-established in the literature, with the solution blowing up only at one point. Though the blow-up of the gradient of the solution is a direct consequence of the single-point blow-up property and the mean value theorem, there is no determination of the final blowup profile for the gradient in the literature, up to our knowledge. In this paper, we refine the construction technique of Bricmont-Kupiainen 1994 and Merle-Zaag 1997, and derive the following profile for the gradient: %and derive construct a blowup solution to the above equation with the gradient's asymptotic $$\nabla u(x,T) \sim - \frac{\sqrt{2b}}{p-1} \frac{x}{|x| \sqrt{ |\ln|x||}} \left[\frac{b|x|^2}{2|\ln|x||} \right]^{-\frac{p+1}{2(p-1)}} \text{ as } x \to 0,$$ where $b =\frac{(p-1)^2}{4p}$, which is as expected the gradient of the well-known blowup profile of the solution.Comment: 23 page

Maximal LpL^p-regularity for stochastic evolution equations

We prove maximal $L^p$-regularity for the stochastic evolution equation \{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}. under the assumption that $A$ is a sectorial operator with a bounded $H^\infty$-calculus of angle less than $\frac12\pi$ on a space $L^q(\mathcal{O},\mu)$. The driving process $W_H$ is a cylindrical Brownian motion in an abstract Hilbert space $H$. For $p\in (2,\infty)$ and $q\in [2,\infty)$ and initial conditions $u_0$ in the real interpolation space \XAp we prove existence of unique strong solution with trajectories in L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to \g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their second variables with small enough Lipschitz constants. Extensions to the case where $A$ is an adapted operator-valued process are considered as well. Various applications to stochastic partial differential equations are worked out in detail. These include higher-order and time-dependent parabolic equations and the Navier-Stokes equation on a smooth bounded domain \OO\subseteq \R^d with $d\ge 2$. For the latter, the existence of a unique strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi

Decay of the Z Boson into Scalar Particles

In extensions of the standard model, light scalar particles are often possible because of symmetry considerations. We study the decay of the Z boson into such particles. In particular, we consider for illustration the scalar sector of a recently proposed model of the 17-keV neutrino which satisfies all laboratory, astrophysical, and cosmological constraints.Comment: 11 pages (2 figures, not included) (Revised, Oct 1992). Some equations have been corrected and 1 figure has been eliminate

The Antiquity of the Avesta

Paper read before the Bombay Branch of the Royal Asiatic Society, read 26th June 1896. Dr. Gerson Da Cunha in the Chair

Analyses of k_t distributions at RHIC by means of some selected statistical and stochastic models

The new data on k_t distributions obtained at RHIC are analysed by means of selected models of statistical and stochastic origin in order to estimate their importance in providing new information on hadronization process, in particular on the value of the temperature at freeze-out to hadronic phase.Comment: Modified version. One new figure, one new table and one reference addee

Calculation of class-b mosaic crystals reflactivity by Monte Carlo techniqye

The technique is proposed and implemented to calculate the reflectivity of such crystals by Monte Carlo modeling, corrently considering the multiple reflections of photons inside the crystal and the geometry of experiment for random distribution of the mosaicyesBelgorod State Universit