The concerted emergence of well-known spatial and temporal ecological patterns in an evolutionary food web model in **space**

**space**and

**time**, from species abundance distributions to the waxing and waning of geographic ranges. Expand abstract.

**space**and

**time**. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these models revolve around speciation, dispersal, and extinction, but they usually neglect trophic structure. Here, we propose and study a spatially extended evolutionary food web model that allows us to study large spatial systems with several trophic layers. Our computer simulations show that the model gives rise simultaneously to several biodiversity patterns in

**space**and time, from species abundance distributions to the waxing and waning of geographic ranges. We find that trophic position in the network plays a crucial role when it comes to the

**time**evolution of range sizes, because the trophic context restricts the occurrence and survival of species especially on higher trophic levels.

4/10 relevant

bioRxiv

The linearly damped nonlinear Schr\"odinger equation with localized driving: spatiotemporal decay estimates and the emergence of extreme wave events

**spaces**and a

**time**-weighted energy method. Expand abstract.

**spaces**and a

**time**-weighted energy method. Numerical simulations examining the dynamics (in the presence of physically relevant examples of driver types and driving amplitude/linear loss regimes), showcase that the suggested decaying rates, are proved relevant in describing the transient dynamics of the solutions, prior their decay: they support the emergence of waveforms possessing an algebraic

**space**-

**time**localization (reminiscent of the Peregrine soliton) as first events of the dynamics, but also effectively capture the

**space**-

**time**asymptotics of the numerical solutions.

5/10 relevant

arXiv

C4 **Space**-Time.. A Window to New Physics?

**space**-

**time**in the symplectic 8-d real space-time (symplectic R8 is algebraically isomorphic to C4), we derive the usual geodesic equation of a charged particle in gravitational eld, plus new information which is interpreted. Expand abstract.

**space**-

**time**to a 4-d complex

**space**-time, can serve us to describe geometrically electromagnetism and unify it with gravity, in a different way that Kaluza-Klein theories do. Specically, the electromagnetic eld Aμ, is included in the free geodesic equation of C4. By embedding our usual 4-d real

**space**-

**time**in the symplectic 8-d real

**space**-

**time**(symplectic R8 is algebraically isomorphic to C4), we derive the usual geodesic equation of a charged particle in gravitational eld, plus new information which is interpreted. Afterwards, we explore the consequences of the formulation of a "special relativity" in the at R8.

10/10 relevant

Preprints.org

A **space**-**time** hybridizable discontinuous Galerkin method for linear
free-surface waves

**space**-

**time**HDG formulation makes use of weighted inner products. Expand abstract.

**space**-

**time**hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic

**space**-

**time**meshes. We consider a mixed formulation which immediately allows us to compute the velocity of the fluid. In order to show well-posedness, our

**space**-

**time**HDG formulation makes use of weighted inner products. We perform an a priori error analysis in which the dependence on the

**time**step and spatial mesh size is explicit. We provide two numerical examples: one that verifies our analysis and a wave maker simulation.

10/10 relevant

arXiv

Global Existence of Strong Solutions to the Kinetic Cucker--Smale Model Coupled with the Stokes Equations

**space**and using space-

**time**estimates for the linear non-stationary Stokes equations, we present a complete analysis on existence of global-in-time strong solutions to the coupled model, without any smallness requirements on initial data. Expand abstract.

**time**strong solutions to the kinetic Cucker--Smale model coupled with the Stokes equations in the whole

**space**. By introducing a weighted Sobolev

**space**and using

**space**-

**time**estimates for the linear non-stationary Stokes equations, we present a complete analysis on existence of global-in-

**time**strong solutions to the coupled model, without any smallness requirements on initial data.

4/10 relevant

arXiv

Waves of **space**-**time** from a collapsing compact object

**time**dependent collapse of a spherically symmetric compact object with initial mass $M_1+M_2$ and final mass $M_2$ and the waves of

**space**-

**time**emitted during the collapse via back-reaction effects. We obtain exact analytical solutions for the waves of

**space**-

**time**in an example in which $M_1=M_2=(M_1+M_2)/2$. The wavelengths of the

**space**-

**time**emitted waves during the collapse have the cut (we use natural units $c=\hbar=1$): $\lambda < (2/b)$, $(1/b)$-being the

**time**scale that describes the decay of the compact object.

10/10 relevant

arXiv

On the initial value problem for the electromagnetic wave equation in
Friedmann-Robertson-Walker **space**-times

**space**-

**times**for curvature $K=0$ and $K=-1$. Deriving a solution expression in the form of spherical means we deduce and compare two properties of the Maxwell propagator namely, decay rates, as well as continuity through the

**space**-

**time**singularity to that of the scalar wave equation presented by Abbasi and Craig [1].

10/10 relevant

arXiv

Existence of global weak solutions to the Navier-Stokes equations in
weighted **spaces**

**space**$\mathring M^{2,2}_{\mathcal C}$ introduced in [Z. Bradshaw and I. Kukavica, Existence of suitable weak solutions to the Navier-Stokes equations for intermittent data, J. Math. Fluid Mech. to appear]. This class is strictly larger than currently available

**spaces**of initial data for global existence and includes all locally square integrable discretely self-similar data. We also identify a sub-class of data for which solutions exhibit eventual regularity on a parabolic set in

**space**-time.

4/10 relevant

arXiv

Monitoring the prolonged TNF stimulation in **space** and **time** with topological-functional networks

4/10 relevant

bioRxiv

On the numerical approximations of the periodic Schr\"odinger equation

**space**-

**time**integrability properties observed by Bourgain in the continuous case are satisfied at the numerical level uniformly with respect to the mesh size. For the simplest finite differences scheme we show that, as mesh size tends to zero, the blow-up in the $L^4$

**time**-

**space**norm occurs, a phenomenon due to the presence of numerical spurious high frequencies. To recover the uniformity of this property we introduce two methods: a spectral filtering of initial data and a viscous scheme. For both of them we prove a $L^4$

**time**-

**space**estimate, uniform with respect to the mesh size. {Warning 2019}: This paper was submitted to M2AN in 2007 and it was assigned the number 2007-29. It passed a first review round ( three reviews :-) ) without decision ("It is only after the consideration of a thoroughly revised version of your manuscript and a new iteration with all the referees that I will be in position to make my final decision.") After completing the PhD, I tried to publish the papers resulting from the thesis and I didn't spent too much

**time**on other related problems (the periodic case for example). It was only recently that I discovered some interest in the subject from other authors and I decided to upload it on arxiv.org. Use with caution as there is no revision of the text in the last twelve years.

4/10 relevant

arXiv