Blow Ups Research Articles

Biogeographic patterns of daily wildfire spread and extremes across North America

IntroductionClimate change is predicted to increase the frequency of extreme single-day fire spread events, with major ecological and social implications. In contrast with well-documented spatio-temporal patterns of wildfire ignitions and perimeters, daily progression remains poorly understood across continental spatial scales, particularly for extreme single-day events (“blow ups”). Here, we characterize daily wildfire spread across North America, including occurrence of extreme single-day events, duration and seasonality of fire and extremes, and ecoregional climatic niches of fire in terms of Actual Evapotranspiration (AET) and Climatic Water Deficit (CWD) annual climate normals.MethodsRemotely sensed daily progression of 9,636 wildfires ≥400 ha was used to characterize ecoregional patterns of fire growth, extreme single-day events, duration, and seasonality. To explore occurrence, extent, and impacts of single-day extremes among ecoregions, we considered complementary ecoregional and continental extreme thresholds (Ecoregional or Continental Mean Daily Area Burned + 2SD). Ecoregional spread rates were regressed against AET and CWD to explore climatic influence on spread.ResultsWe found three-fold differences in mean Daily Area Burned among 10 North American ecoregions, ranging from 260 ha day−1 in the Marine West Coast Forests to 751 ha day−1 in Mediterranean California. Ecoregional extreme thresholds ranged from 3,829 ha day−1 to 16,626 ha day−1, relative to a continental threshold of 7,173 ha day−1. The ~3% of events classified as extreme cumulatively account for 16–55% of total area burned among ecoregions. We observed four-fold differences in mean fire duration, ranging from 2.7 days in the Great Plains to 10.5 days in Northwestern Forested Mountains. Regions with shorter fire durations also had greater daily area burned, suggesting a paradigm of fast-growing short-duration fires in some regions and slow-growing long-duration fires elsewhere. CWD had a weak positive relationship with spread rate and extreme thresholds, and there was no pattern for AET.DiscussionRegions with shorter fire durations had greater daily area burned, suggesting a paradigm of fast-growing short-duration fires in some regions and slow-growing long-duration fires elsewhere. Although climatic conditions can set the stage for ignition and influence vegetation and fuels, finer-scale mechanisms likely drive variation in daily spread. Daily fire progression offers valuable insights into the regional and seasonal distributions of extreme single-day spread events, and how these events shape net fire effects.

Seshadri constants on some blow-ups of projective spaces

Let [Formula: see text] denote the blow-up of [Formula: see text] along [Formula: see text] general lines and [Formula: see text] general points. In this paper, we focus on [Formula: see text]-very ample line bundles on [Formula: see text] and investigate their Seshadri constants with some restrictions on [Formula: see text]. Additionally, we compute the nef cone of [Formula: see text] for [Formula: see text] and study the Seshadri constants of some ample line bundles on it. We also examine the Seshadri constants of some ample line bundles on [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text].

Blowing-ups of beam shape coefficients of Gaussian beams using finite series in generalized Lorenz–Mie theory

Compact closed-form expressions of the beam shape coefficients (BSCs) of Gaussian beams are obtained in the generalized Lorenz–Mie theory through the finite series (FS) method. As a result, such expressions have made it possible to more deeply understand the behaviour of the BSCs and, therefore, the scattering of Gaussian beams beyond the paraxial approximation. The blowing up, in particular, of FS BSCs which has been observed for several paraxial beams is now mathematically justified as a phenomenon that is independent of numerical precision. Furthermore, numerical results demonstrate how such blow ups are related to the ratio between the beam waist radius and its wavelength.

Singular impasse points of planar constrained differential systems

Planar analytic constrained differential systems (or impasse systems) are given by $A(x)\dot{x} = F(x), \quad x\in\mathbb{R}^{2}$, where $F$ is a vector field and $A$ is a matrix valued function. This class of systems differs from classical ODE's due to existence of the so called impasse set $\Delta=\{x:{\rm det} A (x) = 0\}$. The dynamics near smooth impasse points is well known in the literature. In this paper, we use Newton polygon and weighted blow ups in order to study its phase portrait near singular points of $\Delta$. Moreover, we apply our results in electric circuit problems.

The Nirenberg Problem on Half Spheres: A Bubbling-off Analysis

Abstract In this paper, we perform a refined blow-up analysis of finite energy approximated solutions to a Nirenberg-type problem on half spheres. The latter consists of prescribing, under minimal boundary conditions, the scalar curvature to be a given function. In particular, we give a precise location of blow-up points and blow-up rates. Such an analysis shows that the blow-up picture of the Nirenberg problem on half spheres is far more complicated that in the case of closed spheres. Indeed, besides the combination of interior and boundary blow ups, there are nonsimple blow-up points for subcritical solutions having zero or nonzero weak limit. The formation of such nonsimple blowups is governed by a vortex problem, unveiling an unexpected connection with Euler equations in fluid dynamic and mean fields type equations in mathematical physics.

Non simple blow ups for the Nirenberg problem on half spheres

<p style='text-indent:20px;'>In this paper we study a Nirenberg type problem on standard half spheres <inline-formula><tex-math id="M1">\begin{document}$ (\mathbb{S}^n_+,g_0) $\end{document}</tex-math></inline-formula> consisting of finding conformal metrics of prescribed scalar curvature and zero boundary mean curvature. This problem amounts to solve the following boundary value problem involving the critical Sobolev exponent:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} (\mathcal{P}) \quad \begin{cases} - \Delta_{g_0} u \, + \, \frac{n(n-2)}{4} u \, = K \, u^{\frac{n+2}{n-2}},\, u > 0 \quad \mbox{in } \mathbb{S}^n_+, \\ \frac{\partial u}{\partial \nu }\, = \, 0 \quad \mbox{on } \partial \mathbb{S}^n_+, \end{cases} \end{equation*} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M2">\begin{document}$ K \in C^3(\mathbb{S}^n_+) $\end{document}</tex-math></inline-formula> is a positive function. We construct, under generic conditions on the function <inline-formula><tex-math id="M3">\begin{document}$ K $\end{document}</tex-math></inline-formula>, finite energy solutions of a subcritical approximation of <inline-formula><tex-math id="M4">\begin{document}$ (\mathcal{P}) $\end{document}</tex-math></inline-formula> on half spheres of dimension <inline-formula><tex-math id="M5">\begin{document}$ n \geq 5 $\end{document}</tex-math></inline-formula>, which exhibit multiple blow up of <i>cluster-type</i> at the same boundary point. These solutions may have zero or non zero weak limit and may develop clusters at different boundary points. Such a blow up phenomena on half spheres drastically contrast with the case of the Nirenberg problem on spheres, where non simple blow up for finite energy solutions cannot occur and unveils an unexpected connection with vortex type problems arising in Euler equations in fluid dynamic and mean fields type equations in mathematical physics. We construct also, under suitable conditions on the restriction of <inline-formula><tex-math id="M6">\begin{document}$ K $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M7">\begin{document}$ \partial \mathbb{S}^n_+ $\end{document}</tex-math></inline-formula>, approximate solutions of arbitrarily large energy and Morse index.</p>

Approximations of kinetic equations of swarm formation: Convergence and exact solutions

In the present paper we study Euler–type approximations along characteristics for a class of kinetic equations that describe swarm formations in the case when the interactions rate is variable. The proposed numerical schemes preserve essential properties of the kinetic equations and in particular preserve the probabilistic measure and are able to approximate the solution almost to the appearance of blow-ups. The blow–ups are referred here to the self–organization swarm behavior. Moreover we define a class of exact solutions — traveling wave–type equilibrium solutions that we called TWES.

BLOW UP AT INFINITY OF WEAK SOLUTIONS FOR A HIGHER-ORDER PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY

The main goal of this work is to study the inital boundary value problem for a higher-order parabolic equation with logarithmic source term u_{t}+(-\Delta )^{m}u=uln (u). We obtain blow-up at infinity of weak solutions, by employing potential well technique. This improves and extends some previous studies.

Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system

AbstractWe consider a degenerate chemotaxis model with two-species and two-stimuli in dimensiond≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time on and below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species.

Assessing the Potential for Pyroconvection and Wildfire Blow Ups

Fire meteorologists have few tools for assessing atmospheric stability in the context of wildfires. Most tools at our disposal were developed for assessing thunderstorms and general convection, and so they ignore heat and moisture supplied by the wildfire. We propose a simple parcel-based model that can be used to assess how the atmosphere will affect a growing wildfire plume by also taking into account the heat and moisture released from the fire. From this model, we can infer trends in day to day atmospheric stability as it relates to fire plumes. We can also infer how significant the appearance of a pyrocumulus cloud on the top of a fire column is. In some cases, the appearance of a pyrocumulus indicates that the fire is near if not already blowing up, whereas in other cases environmental conditions remain too stable to have a significant effect. A qualitative application of the model is demonstrated through application to a 2017 wildfire case in Western Montana.

The Hilbert scheme of a pair of linear spaces

Let mathcal {H}_{a,b}^n denote the component of the Hilbert scheme whose general point parameterizes an a-plane union a b-plane meeting transversely in {mathbf {P}}^n. We show that mathcal {H}_{a,b}^n is smooth and isomorphic to successive blow ups of mathbf {Gr}(a,n) times mathbf {Gr}(b,n) or text {Sym}^2 mathbf {Gr}(a,n) along certain incidence correspondences. We classify the subschemes parameterized by mathcal {H}_{a,b}^n and show that this component has a unique Borel fixed point. We also study the birational geometry of this component. In particular, we describe the effective and nef cones of mathcal {H}_{a,b}^n and determine when the component is Fano. Moreover, we show that mathcal {H}_{a,b}^n is a Mori dream space for all values of a, b, n.

Very functorial, very fast, and very easy resolution of singularities

The main proposition, Theorem 1.2, is the existence for excellent Deligne–Mumford champ of characteristic zero of a resolution functor independent of the resolution process itself. Received wisdom was that this was impossible, but the counterexamples overlooked the possibility of using weighted blow ups. The fundamental local calculations take place in complete local rings, and are elementary in nature, while being self contained and wholly independent of Hironaka’s methods and all derivatives thereof, i.e. existing technology. Nevertheless Abramovich et al. (Functorial embedded resolution via weighted blowing ups, 2019. arXiv:1906.07106 ), have varied existing technology to obtain even shorter proofs of all the main theorems in the pure dimensional geometric case. Excellent patching is more technical than varieties over a field, and so easier geometric arguments are pointed out when they exist.

Stability of valuations and Kollár components

We prove that among all Kollár components obtained by plt blow ups of a klt singularity o \in (X,D) , there is at most one that is (log-)K-semistable. We achieve this by showing that if such a Kollár component exists, it uniquely minimizes the normalized volume function introduced in [Li18] among all divisorial valuations. Conversely, we show that any divisorial minimizer of the normalized volume function yields a K-semistable Kollár component. We also prove that for any klt singularity, the infimum of the normalized volume function is always approximated by the normalized volumes of Kollár components.

Bounded negativity and Harbourne constants on ruled surfaces

Let X be a smooth projective surface and let $${\mathcal {C}}$$ be an arrangement of curves on X. The Harbourne constant of $${\mathcal {C}}$$ was defined as a way to investigate the occurrence of curves of negative self-intersection on blow ups of X. This is related to the bounded negativity conjecture which predicts that the self-intersection number of all reduced curves on a surface is bounded below by a constant. We consider a geometrically ruled surface X over a smooth curve and give lower bounds for the Harbourne constants of transversal arrangements of curves on X. We also define a global Harbourne constant as the infimum of Harbourne constants for arrangements of a specific type and give a lower bound for it.

Rationality of Seshadri constants on general blow ups of [formula omitted

Let X be a projective surface and let L be an ample line bundle on X. The global Seshadri constant ε(L) of L is defined as the infimum of Seshadri constants ε(L,x) as x∈X varies. It is an interesting question to ask if ε(L) is a rational number for any pair (X,L). We study this question when X is a blow up of P2 at r≥0 very general points and L is an ample line bundle on X. For each r we define a submaximality threshold which governs the rationality or irrationality of ε(L). We state a conjecture which strengthens the SHGH Conjecture and assuming that this conjecture is true we determine the submaximality threshold.

Lagrangian Floer homology on symplectic blow ups

We show how to compute the Lagrangian Floer homology in the one-point blow up of the proper transform of Lagrangians submanifolds, solely in terms of information of the base manifold. As an example we present an alternative computation of the Lagrangian quantum homology in the one-point blow up of (CP^2,\omega) of the proper transform of the Clifford torus.

Sunday School for Cyborgs

Sunday School for Cyborgs R. John Williams (bio) Cyborg Theology: Humans, Technology, and God Scott A. Midson I. B. Taurus www.bloomsbury.com/uk/cyborg-theology-9781784537876/ 272 Pages; Cloth, £63.00 It takes no great sleuth to deduce that strange religious things are afoot in Silicon Valley. Massive financial investments, for instance, have been devoted to solving the "modest problem of death"—with immortality hovering just on the horizon. Re-wire the human DNA! Upload your consciousness to the machine! There are architectural signs of a new religiosity as well: Apple's secretive, four-story corporate building, built in the form of a "perfect circle," with a mega-church like auditorium at the center, and monastic cubicles where the smart phones we carry with us everywhere, like digital totems, are lovingly crafted for the masses. Archive.org, which has nowhere near Apple's budget (but all the same religious fervor), took the cheaper route and purchased a now-defunct Christian Science Church building in San Francisco's Richmond District. Visitors are greeted by a temple-like white stone facade adorned with Roman columns. Inside, on the walls of the "chapel," where organ pipes once hummed, archive. org's massive servers sparkle with little blue lights, reflecting against the stained-glass windows like so much digital incense—the churning of data from all over the world, terabytes of zeros-and-ones constantly in flux. Weirdest of all, in the pews of the chapel, curiously still in place, rows of little statues stand unblinking: colorful, human forms made of some kind of plaster or papier-mâché (if you work for longer than three years for archive.org, they commission a local artist to create a likeness of you, which will stand thereafter in the chapel). It feels definitively sacred. More to the point, a deep quasi-religious fervor burns in the hearts and minds of those who inhabit these techno-Delphic spaces. The "Reformed Church of Google" (Google it; it's real) is probably a clever joke among Valley atheists ("Googlists believe Google should rightfully be given the title of 'God,' as She exhibits a great many of the characteristics traditionally associated with such Deities in a scientifically provable manner"), but there is certainly no shortage of true belief infiltrating the burgeoning field of AI and its massively expanding digital infrastructures. Look at any fictional or documentary portrayal of contemporary technoculture, and you'll find an increasingly cyborg-ish mythos performing the kind of devotional energies formerly devoted to the world's great religions. FX's television series Devs (2020), directed by Alex Garland, of Ex Machina (2014) fame, is only the most obvious example: the big reveal, no real spoiler here, is that Devs doesn't stand for the company's "development" program; it stands for Deus. For those in the know, flashes of this god-in-the-machine zeal show up in even the most unexpected situations. Late last year, a friend of mine, a coder working at a startup in San Francisco, happened to be standing near a steel grate close to her favorite Sushi restaurant when one of PG&E's electricity transformers exploded underground. It was deeply traumatic. If she'd been standing just a few feet to her left, she could have died (it is common knowledge that PG&E refuses to spend the money necessary to safely maintain its own equipment, hence occasional blow ups and failures). She tweeted about it, hoping to understand what had happened, but she was unprepared for what some of her fellow digerati messaged her: "it's a sign," someone wrote, convinced that the "Singularity" was coming: "you have been prepared for this moment." It was evidence, they insisted, that a new digital "magic" was out there. Put simply, San Francisco has long since become Pynchon's San Narciso; the sacral-synth sounds of Blade Runner's Los Angeles trickle down from every loudspeaker; the techno-priesthood is in place; the apps are our sacrament; [End Page 9] the prophesied forms of Minority Report's (2002) "precog temple," creepily personalized ads, and zoom-screen surveillance are our everyday reality; John Lilly's sensory...

Finite morphisms and simultaneous reduction of the multiplicity

AbstractLet X be a singular algebraic variety defined over a perfect field k, with quotient field . Let be the highest multiplicity of X and let be the set of points of multiplicity s. If is a regular center and is the blow up at Y, then the highest multiplicity of X1 is less than or equal to s. A sequence of blow ups at regular centers , say , is said to be a simplification of the multiplicity if the maximum multiplicity of is strictly lower than that of X, that is, if is empty. In characteristic zero there is an algorithm which assigns to each X a unique simplification of the multiplicity. However, the problem remains open when the characteristic is positive. In this paper we will study finite dominant morphisms between singular varieties of generic rank (i.e., ). We will see that, when imposing suitable conditions on β, there is a strong link between the strata of maximum multiplicity of X and , say and respectively. In such case, we will say that the morphism is strongly transversal. When is strongly transversal one can obtain information about the simplification of the multiplicity of X from that of and vice versa. Finally, we will see that given a singular variety X and a finite field extension L of of rank , one can construct (at least locally, in étale topology) a strongly transversal morphism , where has quotient field L.

Circle actions on almost complex manifolds with 4 fixed points

Let the circle act on a compact almost complex manifold $M$. In this paper, we classify the fixed point data of the action if there are 4 fixed points and the dimension of the manifold is at most 6. First, if $\dim M=2$, then $M$ is a disjoint union of rotations on two 2-spheres. Second, if $\dim M=4$, we prove that the action alikes a circle action on a Hirzebruch surface. Finally, if $\dim M=6$, we prove that six types occur for the fixed point data; $\mathbb{CP}^3$ type, complex quadric in $\mathbb{CP}^4$ type, Fano 3-fold type, $S^6 \cup S^6$ type, and two unknown types that might possibly be realized as blow ups of a manifold like $S^6$. When $\dim M=6$, we recover the result by Ahara in which the fixed point data is determined if furthermore $\mathrm{Todd}(M)=1$ and $c_1^3(M)[M] \neq 0$, and the result by Tolman in which the fixed point data is determined if furthermore the base manifold admits a symplectic structure and the action is Hamiltonian.

Energy identity for stationary Yang Mills

Given a principal bundle $$P\rightarrow M$$ over a Riemannian manifold with compact structure group G, let us consider a stationary Yang–Mills connection A with energy $$\int _M |F_A|^2\le \Lambda $$ . If we consider a sequence of such connections $$A_i$$ , then it is understood by Tian (Ann Math 151(1):193–268, 2000) that up to subsequence we can converge $$A_i\rightarrow A$$ to a singular limit connection such that the energy measures converge $$|F_{A_i}|^2 dv_g\rightarrow |F_A|^2dv_g +\nu $$ , where $$\nu =e(x)d\lambda ^{n-4}$$ is the $$n-4$$ rectifiable defect measure. Our main result is to show, without additional assumptions, that for $$n-4$$ a.e. point the energy density e(x) may be computed explicitly as the sum of the bubble energies arising from blow ups at x. Each of these bubbles may be realized as a Yang Mills connection over $$S^4$$ itself. This energy quantization was proved in Riviere (Commun Anal Geom 10(4):683–708, 2002) assuming a uniform $$L^1$$ hessian bound on the curvatures in the sequence. In fact, our second main theorem is to show this hessian bound holds automatically. Precisely, given a connection A as above we have the a-priori estimate $$\int _M |\nabla ^2 F_A| < C(\Lambda ,\dim G,M)$$ for the curvature. It is important to note this result is proved in tandem with the energy quantization, and not before it. Indeed, we will in fact prove an effective version of the energy identity, and it is this effective version which will lead to both the $$L^1$$ hessian bound and the classical energy quantization results. In the course of the proof we will provide a quantitative version of the bubble tree decomposition which hold in all dimensions with effective estimates for a fixed stationary connections. To produce strongest estimates in the paper we introduce an $$\epsilon $$ -gauge condition, which generalizes the usual Coulomb gauge and which will exist, with effective control, even over singular regions. On these $$\epsilon $$ -gauges we will provide a new superconvexity estimate which will be a key tool in analyzing higher-dimensional annular regions.