EDP - Equacions en Derivades Parcials i Aplicacions
http://hdl.handle.net/2117/79726
2024-02-29T22:32:23ZMacroscopic descriptions of follower-leader systems
http://hdl.handle.net/2117/374082
Macroscopic descriptions of follower-leader systems
Bernardi, Sara; Estrada Rodríguez, Gissell; Gimperlein, Heiko; Painter, Kevin J.
The fundamental derivation of macroscopic model equations to describe swarms based on microscopic movement laws and mathematical analyses into their self-organisation capabilities remains a challenge from the perspective of both modelling and analysis. In this paper we clarify relevant continuous macroscopic model equations that describe follower-leader interactions for a swarm where these two populations are fixed. We study the behaviour of the swarm over long and short time scales to shed light on the number of leaders needed to initiate swarm movement, according to the homogeneous or inhomogeneous nature of the interaction (alignment) kernel. The results indicate the crucial role played by the interaction kernel to model transient behaviour
2022-10-06T11:37:42ZBernardi, SaraEstrada Rodríguez, GissellGimperlein, HeikoPainter, Kevin J.The fundamental derivation of macroscopic model equations to describe swarms based on microscopic movement laws and mathematical analyses into their self-organisation capabilities remains a challenge from the perspective of both modelling and analysis. In this paper we clarify relevant continuous macroscopic model equations that describe follower-leader interactions for a swarm where these two populations are fixed. We study the behaviour of the swarm over long and short time scales to shed light on the number of leaders needed to initiate swarm movement, according to the homogeneous or inhomogeneous nature of the interaction (alignment) kernel. The results indicate the crucial role played by the interaction kernel to model transient behaviourMotility switching and front–back synchronisation in polarised cells
http://hdl.handle.net/2117/373927
Motility switching and front–back synchronisation in polarised cells
Estrada Rodríguez, Gissell; Perthame, Benoit
The combination of protrusions and retractions in the movement of polarized cells leads to understand the effect of possible synchronisation between the two ends of the cells. This syn- chronisation, in turn, could lead to different dynamics such as normal and fractional diffusion. Departing from a stochastic single cell trajectory, where a “memory effect” induces persistent movement, we derive a kinetic-renewal system at the mesoscopic scale. We investigate various scenarios with different levels of complexity, where the two ends of the cell move either indepen- dently or with partial or full synchronisation. We study the relevant macroscopic limits where we obtain diffusion, drift-diffusion or fractional diffusion, depending on the initial system. This article clarifies the form of relevant macroscopic equations that describe the possible effects of synchronised movement in cells, and sheds light on the switching between normal and fractional diffusion.
2022-10-04T12:12:28ZEstrada Rodríguez, GissellPerthame, BenoitThe combination of protrusions and retractions in the movement of polarized cells leads to understand the effect of possible synchronisation between the two ends of the cells. This syn- chronisation, in turn, could lead to different dynamics such as normal and fractional diffusion. Departing from a stochastic single cell trajectory, where a “memory effect” induces persistent movement, we derive a kinetic-renewal system at the mesoscopic scale. We investigate various scenarios with different levels of complexity, where the two ends of the cell move either indepen- dently or with partial or full synchronisation. We study the relevant macroscopic limits where we obtain diffusion, drift-diffusion or fractional diffusion, depending on the initial system. This article clarifies the form of relevant macroscopic equations that describe the possible effects of synchronised movement in cells, and sheds light on the switching between normal and fractional diffusion.Cosmology intertwined: a review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies
http://hdl.handle.net/2117/367803
Cosmology intertwined: a review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies
Abdalla, Elcio; Abellan, Guillermo Franco; Aboubrahim, Amin; Agnello, Adriano; Akarsu, Özgür; Akrami, Yashar; Alestas, George; Aloni, Daniel; Amendola, Luca; Anchordoqui, Luis A.; Haro Cases, Jaume
The standard Λ Cold Dark Matter (ΛCDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant , the – tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the tension between the Planck CMB estimate of the Hubble constant and the SH0ES collaboration measurements. After showing the evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density , and the amplitude or rate of the growth of structure ( ). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the – tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questions
2022-05-27T12:14:34ZAbdalla, ElcioAbellan, Guillermo FrancoAboubrahim, AminAgnello, AdrianoAkarsu, ÖzgürAkrami, YasharAlestas, GeorgeAloni, DanielAmendola, LucaAnchordoqui, Luis A.Haro Cases, JaumeThe standard Λ Cold Dark Matter (ΛCDM) cosmological model provides a good description of a wide range of astrophysical and cosmological data. However, there are a few big open questions that make the standard model look like an approximation to a more realistic scenario yet to be found. In this paper, we list a few important goals that need to be addressed in the next decade, taking into account the current discordances between the different cosmological probes, such as the disagreement in the value of the Hubble constant , the – tension, and other less statistically significant anomalies. While these discordances can still be in part the result of systematic errors, their persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the necessity for new physics or generalisations beyond the standard model. In this paper, we focus on the tension between the Planck CMB estimate of the Hubble constant and the SH0ES collaboration measurements. After showing the evaluations made from different teams using different methods and geometric calibrations, we list a few interesting new physics models that could alleviate this tension and discuss how the next decade's experiments will be crucial. Moreover, we focus on the tension of the Planck CMB data with weak lensing measurements and redshift surveys, about the value of the matter energy density , and the amplitude or rate of the growth of structure ( ). We list a few interesting models proposed for alleviating this tension, and we discuss the importance of trying to fit a full array of data with a single model and not just one parameter at a time. Additionally, we present a wide range of other less discussed anomalies at a statistical significance level lower than the – tensions which may also constitute hints towards new physics, and we discuss possible generic theoretical approaches that can collectively explain the non-standard nature of these signals. Finally, we give an overview of upgraded experiments and next-generation space missions and facilities on Earth that will be of crucial importance to address all these open questionsTopics in cosmology — clearly explained by means of simple examples
http://hdl.handle.net/2117/366576
Topics in cosmology — clearly explained by means of simple examples
Haro Cases, Jaume; Elizalde Rius, Emilio
This is a very comprehensible review of some key issues in modern cosmology. Simple mathematical examples and analogies are used, whenever available. The starting point is the well-known Big Bang cosmology (BBC). We deal with the mathematical singularities appearing in this theory and discuss some ways to remove them. Next, and before introducing the inflationary paradigm by means of clear examples, we review the horizon and flatness problems of the old BBC model. We then consider the current cosmic acceleration and, as a procedure to deal with both periods of cosmic acceleration in a unified way, we study quintessential inflation. Finally, the reheating stage of the universe via gravitational particle production, which took place after inflation ended, is discussed in clear mathematical terms, by involving the so-called a-attractors in the context of quintessential inflation
2022-04-29T08:58:38ZHaro Cases, JaumeElizalde Rius, EmilioThis is a very comprehensible review of some key issues in modern cosmology. Simple mathematical examples and analogies are used, whenever available. The starting point is the well-known Big Bang cosmology (BBC). We deal with the mathematical singularities appearing in this theory and discuss some ways to remove them. Next, and before introducing the inflationary paradigm by means of clear examples, we review the horizon and flatness problems of the old BBC model. We then consider the current cosmic acceleration and, as a procedure to deal with both periods of cosmic acceleration in a unified way, we study quintessential inflation. Finally, the reheating stage of the universe via gravitational particle production, which took place after inflation ended, is discussed in clear mathematical terms, by involving the so-called a-attractors in the context of quintessential inflationUnderstanding gravitational particle production in quintessential inflation
http://hdl.handle.net/2117/362823
Understanding gravitational particle production in quintessential inflation
Haro Cases, Jaume; Pan, Supriya; Aresté Saló, Llibert
The diagonalization method, introduced by a group of Russian scientists at the beginning of seventies, is used to compute the energy density of superheavy massive particles produced due to a sudden phase transition from inflation to kination in quintessential inflation models, the models unifying inflation with quintessence originally proposed by Peebles-Vilenkin. These superheavy particles must decay in lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field, in order to have a hot universe after inflation. In the present article we show that, in order that the overproduction of Gravitational Waves (GWs) during this phase transition does not disturb the Big Bang Nucleosynthesis (BBN) success, the decay has to be produced after the end of the kination regime, obtaining a maximum reheating temperature in the TeV regime
2022-02-22T09:23:03ZHaro Cases, JaumePan, SupriyaAresté Saló, LlibertThe diagonalization method, introduced by a group of Russian scientists at the beginning of seventies, is used to compute the energy density of superheavy massive particles produced due to a sudden phase transition from inflation to kination in quintessential inflation models, the models unifying inflation with quintessence originally proposed by Peebles-Vilenkin. These superheavy particles must decay in lighter ones to form a relativistic plasma, whose energy density will eventually dominate the one of the inflaton field, in order to have a hot universe after inflation. In the present article we show that, in order that the overproduction of Gravitational Waves (GWs) during this phase transition does not disturb the Big Bang Nucleosynthesis (BBN) success, the decay has to be produced after the end of the kination regime, obtaining a maximum reheating temperature in the TeV regimeA review of quintessential inflation
http://hdl.handle.net/2117/362538
A review of quintessential inflation
Haro Cases, Jaume; Aresté Saló, Llibert
Some of the most important quintessential inflation scenarios, such as the Peebles–Vilenkin model, are described in detail. These models are able to explain the early- and late-time accelerated expansions of our universe, and the phase transition from the end of inflation to the beginning of kination where the adiabatic evolution of the universe was broken in order to produce enough particles to reheat the universe with a viable temperature, thereby aligning with the Hot Big Bang universe. In addition, while considering the reheating to be due to the gravitational production of superheavy particles conformally coupled to gravity, we checked that the considered scenarios do not suffer problems due to the overproduction of gravitational waves at the end of inflation, and thus the validity of Big Bang nucleosynthesis is preserved
2022-02-17T09:18:18ZHaro Cases, JaumeAresté Saló, LlibertSome of the most important quintessential inflation scenarios, such as the Peebles–Vilenkin model, are described in detail. These models are able to explain the early- and late-time accelerated expansions of our universe, and the phase transition from the end of inflation to the beginning of kination where the adiabatic evolution of the universe was broken in order to produce enough particles to reheat the universe with a viable temperature, thereby aligning with the Hot Big Bang universe. In addition, while considering the reheating to be due to the gravitational production of superheavy particles conformally coupled to gravity, we checked that the considered scenarios do not suffer problems due to the overproduction of gravitational waves at the end of inflation, and thus the validity of Big Bang nucleosynthesis is preservedPointwise monotonicity of heat kernels
http://hdl.handle.net/2117/361251
Pointwise monotonicity of heat kernels
Alonso Orán, Diego; Chamizo, Fernando; Martínez Martínez, Ángel David; Mas Blesa, Albert
In this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.
2022-02-01T13:52:33ZAlonso Orán, DiegoChamizo, FernandoMartínez Martínez, Ángel DavidMas Blesa, AlbertIn this paper we present an elementary proof of a pointwise radial monotonicity property of heat kernels that is shared by the Euclidean spaces, spheres and hyperbolic spaces. The main result was discovered by Cheeger and Yau in 1981 and rediscovered in special cases during the last few years. It deals with the monotonicity of the heat kernel from special points on revolution hypersurfaces. Our proof hinges on a non straightforward but elementary application of the parabolic maximum principle. As a consequence of the monotonicity property, we derive new inequalities involving classical special functions.Quintessential inflation and cosmological seesaw mechanism: reheating and observational constraints
http://hdl.handle.net/2117/352892
Quintessential inflation and cosmological seesaw mechanism: reheating and observational constraints
Aresté Saló, Llibert; Benistry, David; Guendelman, Eduardo I.; Haro Cases, Jaume
Recently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the class of a-attractors and depicting correctly the early and late time accelerations of our universe. The potential emphasizes a cosmological seesaw mechanism (CSSM) that produces a large inflationary vacuum energy in one side of the potential and a very small value of dark energy on the right hand side of the potential. Here we show that the model agrees with the recent observations and with the reheating constraints. Therefore the model gives a reasonable scenario beyond the standard ¿CDM that includes the inflationary epoch
2021-10-01T11:20:20ZAresté Saló, LlibertBenistry, DavidGuendelman, Eduardo I.Haro Cases, JaumeRecently a new kind of quintessential inflation coming from the Lorentzian distribution has been introduced in [1,2]. The model leads to a very simple potential, which basically depends on two parameters, belonging to the class of a-attractors and depicting correctly the early and late time accelerations of our universe. The potential emphasizes a cosmological seesaw mechanism (CSSM) that produces a large inflationary vacuum energy in one side of the potential and a very small value of dark energy on the right hand side of the potential. Here we show that the model agrees with the recent observations and with the reheating constraints. Therefore the model gives a reasonable scenario beyond the standard ¿CDM that includes the inflationary epochDiscrepancy of minimal riesz energy points
http://hdl.handle.net/2117/352747
Discrepancy of minimal riesz energy points
Mas Blesa, Albert; Marzo Sánchez, Jordi
We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished manuscript where estimates for the spherical cap discrepancy of the logarithmic energy minimizers in S2 were obtained. Our result improves previously known bounds for 0=s<2 and s¿1 in S2, where s=0 is Wolff’s result, and for d-t0<s<d with t0˜2.5 when d=3 and s¿d-1.
2021-09-30T11:52:50ZMas Blesa, AlbertMarzo Sánchez, JordiWe find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz s-energy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished manuscript where estimates for the spherical cap discrepancy of the logarithmic energy minimizers in S2 were obtained. Our result improves previously known bounds for 0=s<2 and s¿1 in S2, where s=0 is Wolff’s result, and for d-t0<s<d with t0˜2.5 when d=3 and s¿d-1.a-attractors in quintessential inflation motivated by supergravity
http://hdl.handle.net/2117/352204
a-attractors in quintessential inflation motivated by supergravity
Aresté Saló, Llibert; Benistry, David; Guendelman, Eduardo I.; Haro Cases, Jaume
An exponential kind of quintessential inflation potential motivated by supergravity is studied. This type belongs to the class of a-attractor models. The model was studied for the first time by Dimopoulos and Owen in [J. Cosmol. Astropart. Phys. 06 (2017) 027], in which the authors introduced a negative cosmological constant in order to ensure a zero-vacuum energy density at late times. However, in this paper, we disregard this cosmological constant, showing that the obtained results are very close to the ones obtained recently in the context of Lorentzian quintessential inflation and thus depicting with great accuracy the early- and late-time acceleration of our Universe. The model is compatible with the recent observations. Finally, we review the treatment of the a-attractor and we show that our potential depicts the late time cosmic acceleration with an effective equation of state equal to -1
2021-09-24T11:54:50ZAresté Saló, LlibertBenistry, DavidGuendelman, Eduardo I.Haro Cases, JaumeAn exponential kind of quintessential inflation potential motivated by supergravity is studied. This type belongs to the class of a-attractor models. The model was studied for the first time by Dimopoulos and Owen in [J. Cosmol. Astropart. Phys. 06 (2017) 027], in which the authors introduced a negative cosmological constant in order to ensure a zero-vacuum energy density at late times. However, in this paper, we disregard this cosmological constant, showing that the obtained results are very close to the ones obtained recently in the context of Lorentzian quintessential inflation and thus depicting with great accuracy the early- and late-time acceleration of our Universe. The model is compatible with the recent observations. Finally, we review the treatment of the a-attractor and we show that our potential depicts the late time cosmic acceleration with an effective equation of state equal to -1