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We establish the Minimal Model Program for arithmetic threefolds whose residue characteristics are greater than five. In doing this, we generalize the theory of global F-regularity to mixed characteristic and identify certain stable sections of adjoint line bundles. Finally, by passing to graded rings, we generalize a special case of Fujita's conjecture to mixed characteristic. [ABSTRACT FROM AUTHOR]

We study the self-similar blow-up profiles associated to the following second-order reaction-diffusion equation with strong weighted reaction and unbounded weight: ∂ t ⁡ u = ∂ x ⁢ x ⁡ (u m) + | x | σ ⁢ u p , \partial_{t}u=\partial_{xx}(u^{m})+|x|^{\sigma}u^{p}, posed for x ∈ ℝ {x\in\mathbb{R}} , t ≥ 0 {t\geq 0} , where m > 1 {m>1} , 0 < p < 1 {0 2 ⁢ (1 - p) m - 1 {\sigma>\frac{2(1-p)}{m-1}}. As a first outcome, we show that finite time blow-up solutions in self-similar form exist for m + p > 2 {m+p>2} and σ in the considered range, a fact that is completely new: in the already studied reaction-diffusion equation without weights there is no finite time blow-up when p < 1 {p<1}. We moreover prove that, if the condition m + p > 2 {m+p>2} is fulfilled, all the self-similar blow-up profiles are compactly supported and there exist two different interface behaviors for solutions of the equation, corresponding to two different interface equations. We classify the self-similar blow-up profiles having both types of interfaces and show that in some cases global blow-up occurs, and in some other cases finite time blow-up occurs only at space infinity. We also show that there is no self-similar solution if m + p < 2 {m+p<2} , while the critical range m + p = 2 {m+p=2} with σ > 2 {\sigma>2} is postponed to a different work due to significant technical differences. [ABSTRACT FROM AUTHOR]

A new approximate solution relevant to case of rectangular (Langmuirian) adsorption isotherms has been developed on the basis of the integral-balance method with double integration technique. The solution is based on the model developed by Ruthven for slab and spherical adsorption pellets where the adsorption is controlled by the diffusion in macropores. This model results in a concentration-dependent diffusion coefficient with a quadratic nonlinearity of Fujita's type. The new approximate solution utilizes the concept of finite penetration depth of the diffusant penetration and almost shockwave shape of the concentration profiles. The solution is based on an assumed parabolic profile with unspecified exponent. The solution analysis allowed determining the optimal exponents of the concentration profile as a function of the nonlinearity parameter of the Fujita's concentration relationship. The approximate solutions have been compared to existing results from the literature and especially the data published by Ruthven and Crank, for concentration distributions and fractional uptakes in an adsorbent slab pellet. [ABSTRACT FROM AUTHOR]

Abstract We obtain a blow-up result for solutions to a semi-linear wave equation with scale-invariant dissipation and mass and power non-linearity, in the case in which the model has a "wave like" behavior. We perform a change of variables that transforms our starting equation in a strictly hyperbolic semi-linear wave equation with time-dependent speed of propagation. Applying Kato's lemma we prove a blow-up result for solutions to the transformed equation under some assumptions on the initial data. The limit case, that is, when the exponent p is exactly equal to the upper bound of the range of admissible values of p yielding blow-up needs special considerations. In this critical case an explicit integral representation formula for solutions of the corresponding linear Cauchy problem in 1d is derived. Finally, carrying out the inverse change of variables we get a non-existence result for global (in time) solutions to the original model. [ABSTRACT FROM AUTHOR]

Strong to violent tornadoes cause a disproportionate amount of damage, in part because the width and length of a tornado damage track are correlated to tornado intensity (as now estimated through enhanced Fujita scale ratings). The tendency expressed in the observational record is that the most intense tornadoes are often the widest. Herein the authors explore the simple hypothesis that wide intense tornadoes should form more readily out of wide rotating updrafts. This hypothesis is based on an application of Kelvin's circulation theorem, which is used to argue that the large circulation associated with a wide intense tornado is more plausibly associated with a wide mesocyclone. Because a mesocyclone is, strictly speaking, a rotating updraft, the mesocyclone width should increase with increasing updraft width. A simple mathematical model that is quantified using observations of mesocyclones supports this hypothesis, as do idealized numerical simulations of supercellular thunderstorms. [ABSTRACT FROM AUTHOR]

All the nuclear facility structures must be analyzed for tornado loads. This analysis was per-formed when designing the New Safe Confinement over the ruined Chernobyl power unit (NSC ChNPP). The standard methods of tornado analysis could not be applied due to its large size and geometric shape. Therefore, it was necessary to develop new calculation methods. The paper provides detailed information on the performed calculations and describes the conservative assumptions made when there was not enough information. The purpose of this paper is to analyze the gained experience of performing such an analysis of this unique structure, which may be of some interest. The following two complex problems are considered: • establishing the design tornado parameters; • developing an engineering methodology for the tornado analysis. Moreover, questions are formulated that should be clarified when carrying out similar designs.

Citing numerical simulations, climate alarmists believe that global warming will lead to more frequent and more intensive tornadoes. Considering temperature increase data in the contiguous USA, this study has investigated the trend of strong tornadoes in F3+ category in the 1954-2012 period. Statistically significant decrease of tornadoes per year at an average rate of 0.44 has been recorded, that is, 4.4 tornadoes per decade. Tornado increase has been recorded with F0 and F1 categories and the cause of this increase lies in meteorological and non-meteorological factors. By using upper and lower standard deviation values, the stages of tornado activity have been singled out. The 1957-1974 period may be considered as an active stage and the 1978-2009 period as an inactive stage. Upward trend of air temperature increase does not correspond with the downward trend of the number of F3+ tornado category, while the correlation coefficient between these two variables is R = −0.14. This fact does not correspond with the simulation results and output data of various numerical models anticipating an increase in the number and intensity of tornado events in the conditions of surface air temperature growth.

In this paper, we determine the Fujita critical exponent of the following time fractional subdiffusion equation with nonlinear memory 0CDtαu−△u=0It1−γ|u|p−1u,x∈RN,t>0,u(0,x)=u0(x),x∈RN,where 0 < α < 1, 0 ≤ γ < 1, γ ≤ α, p > 1, u0∈C0RN, 0It1−γ denotes left Riemann‐Liouville fractional integral of order 1 − γ. Let β = 1 − γ. We prove that, if 1 p∗ and ‖u0‖LqcRN is sufficiently small, where qc=Nα(p−1)2(α+β), then u exists globally. [ABSTRACT FROM AUTHOR]

The paper present description of the environmental conditions that favored the tornado event in the city of Blagoveshchensk at about 19:00 local time on July 31, 2011 as well as the tornado characteristics. The tornado was formed near the center of the city, then crossed it and caused significant damage. The tornado is classified in EF2 category of the Enhanced Fujita-Pearson scale. Atmospheric conditions near Blagoveshchensk on July 31, 2011 were favorable for the tornado initiation which occurred in the frontal zone of the cyclone over the warm underlying surface. The analysis of meteorological conditions during the tornado event are presented. A numerical study of the tornado was conducted to clarify its characteristics and environmental conditions during the event. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a time-weighted parabolic system coupled via nonlocal sources. Firstly, we give the critical Fujita exponent of solutions. Secondly, we propose the time-weighted blow-up profiles of solutions. Thirdly, the simultaneous and non-simultaneous blow-up of solutions are discussed under some conditions on the initial data. Fourthly, besides blow-up rates, we classify total blow-up and single point blow-up of solutions. At last, upper and lower bounds of blow-up time are studied according to precise blow-up phenomena. [ABSTRACT FROM AUTHOR]

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ABSTRACT: A tornado climatology in China was derived based on a recently completed data set with details on 4763 tornadoes in the period 1948–2012. The tornadoes were rated on the Fujita scale, and design basis tornado wind speeds were estimated. Annual tornadoes were estimated 108 (±44) in China, among which 0–4 exceed F3 on the Fujita scale. Three strongest tornadoes in the data set were rated F4. Assessing from frequency distribution of ratings, tornadoes in China could be mostly of the non‐supercell type. In average of all the country, most tornadoes occur in summer (June–August, about 64%). The peak month is July (31%). Geographically, the majority of tornadoes is distributed in eastern China, with the most frequent tornado occurrence being in the coastal provinces. There are southern type and northern type of tornado occurrence in eastern China. The former peaks in spring, while the latter peaks in summer. Two belts of design basis tornado wind speeds higher than 70 m s−1 were identified (on probability of 10−7 per year). One extends approximately along the coastline of China from south to north, while the other crosses this belt from east to west, approximately upstream of the Yangtze River. The Yangtze River Delta and Pearl River Delta have design basis tornado wind speeds higher than 90 m s−1, with maxima of 105 and 95 m s−1, respectively. However, by transferring into the enhanced Fujita scale, the wind speed is much lower, with the corresponding maxima being 82 and 76 m s−1 respectively. [ABSTRACT FROM AUTHOR]

Translation of tornadoes is an important feature in replicating the near-ground tornado flow field which has been simulated in previous studies based on Ward-type tornado simulators using relative motion of the ground plane. In this laboratory investigation, effects of translation on the near-ground tornado flow field were studied using the ISU Tornado Simulator that can physically translate over a ground plane. Two translation speeds, 0.15 m/s and 0.50 m/s, that scale up to those corresponding to slowly-moving tornadoes in the field were selected for this study. Compared with the flow field of a stationary tornado, the simulated tornado with translation had an influence on tine spatial distribution and magnitude of the horizontal velocities, early reversal of the radial inflow, and expansion of the core radius. Maximum horizontal velocities were observed to occur behind the center of the translating tornado and on the right side of its mean path. An increase in translation speed, resulted in reduction of maximum horizontal velocities at all heights. Comparison of the results with previous studies that used relative motion of the ground plane for simulating translating tornadoes, showed that translation has similar effects on the flow field at smaller radial distances (~2 core radius), but different effects at larger radial distances (~4 core radius). Further, it showed that the effect of translation on velocity profiles is noticeable at and above an elevation of ~0.6 core radius, unlike those in studies based on the relative motion of the ground plane. [ABSTRACT FROM AUTHOR]

The article presents a study on tropical cyclone (TC)–associated enhanced Fujita 3 (EF3) tornado in China. Topics discussed include the relationship between the condensation funnel, damage swath, and radar observations; TC tornadoes tend to be spawned from minisupercells in the right-front from their parent TC; and discusses the visual observations such as number of urban traffic surveillance videos of strong winds, and publicly available photographs.

Strong to violent tornadoes cause a disproportionate amount of damage, in part because the width and length of a tornado damage track are correlated to tornado intensity (as now estimated through enhanced Fujita scale ratings). The tendency expressed in the observational record is that the most intense tornadoes are often the widest. Herein the authors explore the simple hypothesis that wide intense tornadoes should form more readily out of wide rotating updrafts. This hypothesis is based on an application of Kelvin's circulation theorem, which is used to argue that the large circulation associated with a wide intense tornado is more plausibly associated with a wide mesocyclone. Because a mesocyclone is, strictly speaking, a rotating updraft, the mesocyclone width should increase with increasing updraft width. A simple mathematical model that is quantified using observations of mesocyclones supports this hypothesis, as do idealized numerical simulations of supercellular thunderstorms. [ABSTRACT FROM AUTHOR]

In this paper, we study the positive solutions for a semilinear equation in hyperbolic space. Using the heat semigroup and by constructing subsolutions and supersolutions, a Fujita-type result is established. [ABSTRACT FROM PUBLISHER]

Doppler radar data corresponding to five tornado events are analyzed using the Ground-Based Velocity Track Display method and the three-dimensional velocity field of nine volumetric samples is extracted. These samples are selected to cover a range of wind speeds (between 36 m/s and 64 m/s) and vortex structures representative of EF0 to EF3 tornadoes in a first attempt to generate a tornado wind field database. Tangential velocity profiles, swirl ratios and vortex structures, i.e. single-celled or two-celled vortex, are determined for each of these volumetric samples. Among the nine volumetric samples, two show single-celled characteristics, vortex breakdown bubble is evident in one and four demonstrate two-celled vortex characteristics. The radial profiles of the tangential velocity are in good agreement with a modified Rankine vortex model. The variation of maximum tangential velocities with height is very different when compared to the velocity variation in typical atmospheric boundary layer flows. The swirl ratios of the tornado volumetric samples are computed using the flow rate through the updrafts and the maximum circulation in the flows. [ABSTRACT FROM AUTHOR]

Tornado is one of the most hazardous external natural events which should be taken into account in the siting, design and safety evaluation of nuclear power plants. The tornado hazard has been assessed for a nuclear power plant located in the Southeast China in this paper. Using the original Fujita scale and grading by a number of experts, intensities of the tornado segments have been determined. The design-basis tornado wind speed, parameters and missiles generated have been evaluated following the methodology listed in the hChinese Nuclear Safety Guide HAD101/10. The results show that the overall cumulative frequency and intensity of tornadoes in the site area is not in a logarithm-linear relationship. The expected annual tornado occurrence frequencies of various F scales have been estimated by fitting higher intensity samples. The resulting wind speed corresponding to an exceedance frequency of 10-7 per year seems to be sensitive to the fitting samples. Considering the uncertainties, the intensity and frequency of tornadoes in the survey area, the ultimate design-basis tornado wind speed is taken to be 70.4 m/s, which is the lower limit wind speed of F3 scale. Moreover current problems in tornado hazard assessment in China are discussed. [ABSTRACT FROM AUTHOR]

Tornado is one of the most hazardous external natural events which should be taken into account in the siting, design and safety evaluation of nuclear power plants. The tornado hazard has been assessed for a nuclear power plant located in the Southeast China in this paper. Using the original Fujita scale and grading by a number of experts, intensities of the tornado segments have been determined. The design-basis tornado wind speed, parameters and missiles generated have been evaluated following the methodology listed in the hChinese Nuclear Safety Guide HAD101/10. The results show that the overall cumulative frequency and intensity of tornadoes in the site area is not in a logarithm-linear relationship. The expected annual tornado occurrence frequencies of various F scales have been estimated by fitting higher intensity samples. The resulting wind speed corresponding to an exceedance frequency of 10 -7 per year seems to be sensitive to the fitting samples. Considering the uncertainties, the intensity and frequency of tornadoes in the survey area, the ultimate design-basis tornado wind speed is taken to be 70.4 m/s, which is the lower limit wind speed of F3 scale. Moreover current problems in tornado hazard assessment in China are discussed. [ABSTRACT FROM AUTHOR]

We consider the nonlocal diffusion equation ∂ t u = J ⁎ u − u + u 1 + p in the whole of R N . We prove that the Fujita exponent dramatically depends on the behavior of the Fourier transform of the kernel J near the origin, which is linked to the tails of J . In particular, for compactly supported or exponentially bounded kernels, the Fujita exponent is the same as that of the nonlinear Heat equation ∂ t u = Δ u + u 1 + p . On the other hand, for kernels with algebraic tails, the Fujita exponent is either of the Heat type or of some related Fractional type, depending on the finiteness of the second moment of J . As an application of the result in population dynamics models, we discuss the hair trigger effect for ∂ t u = J ⁎ u − u + u 1 + p ( 1 − u ) . [ABSTRACT FROM AUTHOR]

On del Pezzo surfaces, we study effective ample R-divisors such that the complements of their supports are isomorphic to A¹-bundles over smooth affine curves. All considered varieties are assumed to be algebraic and defined over an algebraically closed field of characteristic 0 throughout this article. [ABSTRACT FROM AUTHOR]

In this study, a 13-yr climatology of tornado event and warning environments, including metrics of tornado intensity and storm morphology, is investigated with particular focus on the environments of tornadoes associated with quasi-linear convective systems and right-moving supercells. The regions of the environmental parameter space having poor warning performance in various geographical locations, as well as during different times of the day and year, are highlighted. Kernel density estimations of the tornado report and warning environments are produced for two parameter spaces: mixed-layer convective available potential energy (MLCAPE) versus 0-6-km vector shear magnitude (SHR6), and mixed-layer lifting condensation level (MLLCL) versus 0-1-km storm-relative helicity (SRH1). The warning performance is best in environments characteristic of severe convection (i.e., environments featuring large values of MLCAPE and SHR6). For tornadoes occurring during the early evening transition period, MLCAPE is maximized, MLLCL heights decrease, SHR6 and SRH1 increase, tornadoes rated as 2 or greater on the enhanced Fujita scale (EF2+) are most common, the probability of detection is relatively high, and false alarm ratios are relatively low. Overall, the parameter-space distributions of warnings and events are similar; at least in a broad sense, there is no systematic problem with forecasting that explains the high overall false alarm ratio, which instead seems to stem from the inability to know which storms in a given environment will be tornadic. [ABSTRACT FROM AUTHOR]

In this paper, we establish the blow-up theorems of Fujita type for a class of exterior problems of nonlinear diffusion equations subject to inhomogeneous Neumann boundary conditions. The critical Fujita exponents are determined and it is shown that the critical curve belongs to the blow-up case under any nontrivial initial data. [ABSTRACT FROM PUBLISHER]

The standard measure of the intensity of a tornado is the Fujita or Enhanced Fujita scale, which is based qualitatively on the damage caused by a tornado. An alternative measure of tornado intensity is the tornado path length, L. Here we examine the spatial-temporal clustering of severe tornadoes, which we define as having path lengths L ≥ 10 km. Of particular concern are tornado outbreaks when a large number of severe tornadoes occur in a day in a restricted region. We apply a spatial-temporal clustering analysis developed for earthquakes. We take all pairs of severe tornadoes in an outbreak, and for each pair plot the spatial lag (distance between touchdown points) against the temporal lag (time between touchdown points). We test our approach applying our analysis to the intense tornado outbreaks in the central United States on 26 and 27 April 2011, which resulted in over 300 fatalities. The patterns of spatial-temporal lag correlations that we obtain for the two days are strikingly different. On 26 April there were 45 severe tornadoes and our clustering analysis is dominated by a complex sequence of linear features. We associate each linear feature with multiple tornadoes generated by one discrete supercell thunderstorm. On 27 April there were 64 severe tornadoes and our clustering analysis is predominantly random with virtually no embedded linear patterns. We associate this pattern with a widespread complex of interacting supercell thunderstorms without long well defined paths of movement. [ABSTRACT FROM AUTHOR]

Considered are the formation conditions of the severe tornado in the South Urals (in the Republic of Bashkortostan) on August 29, 2014. It is noted that the tornado was associated with the supercell, and the synoptic conditions of its formation corresponded to the type 1 according to the classification proposed by A.I. Snitkovskii in 1987. Estimated are the tornado basic characteristics: the vortex funnel width is 150-200 m, and the maximum wind speed is 65 m/s. It is revealed that the tornado was of EF3 category following the enhanced Fujita scale. Proposed is the simple index of convective instability based on the data of ground-based observations for diagnosing the tornado genesis environments. [ABSTRACT FROM AUTHOR]

This paper deals with Cauchy problems of pseudo-parabolic equations with inhomogeneous terms. The aim of the paper is to study the influence of the inhomogeneous term on the asymptotic behavior of solutions. We at first determine the critical Fujita exponent and then give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity. Furthermore, the precise estimate of life span for the blow-up solution is obtained. Our results show that the asymptotic behavior of solutions is seriously affected by the inhomogeneous term. [ABSTRACT FROM AUTHOR]