arXiv subjects

Andrés Rivera

Publications and source records attributed to Andrés Rivera.

16 recordsLinked to original sources

arXiv2026

FIMP dark matter in the scotogenic model at low-reheating temperatures

The scotogenic model offers an attractive framework that explains light neutrino masses while accommodating a viable dark matter candidate. In this work, we study the phenomenology of singlet fermion dark matter, $N_1$, produced via the freeze-in mechanism characterized by an instantaneous low reheating temperature, $T_{\text{rh}}$. We explore the model's viable parameter space, incorporating current bounds from lepton flavor violation ($μ\to e γ$) and direct detection limits. We show that low-reheating scenarios significantly reshape the viable region for $N_1$ dark matter, improving prospects for testing the scotogenic model in the FIMP scenario while keeping it consistent with current lepton flavor violation and cosmological bounds.

hep-ph↗

arXiv2026

Delay-induced dynamics in a nonlinear crime interaction model with periodic forcing

A nonlinear time-delay model is proposed to describe the interaction dynamics between criminal and non-criminal populations, combining social influence mechanisms, saturation effects represented by a Holling type II functional response, and time-dependent law-enforcement actions. The delay accounts for the latency between exposure to criminal behavior and behavioral response, introducing memory effects that naturally lead to a delay differential equations framework. Fundamental analytical properties, including positivity, global existence, and invariance of the feasible region, are established to ensure the mathematical consistency of the population interpretation. In the autonomous setting, explicit threshold conditions governing the stability of the criminal-free equilibrium and the emergence of coexistence states are derived, while the delay is shown to induce stability switches and oscillatory regimes through characteristic root crossings. In the non-autonomous case, topological degree arguments guaranty the existence of strictly positive periodic solutions, indicating that long-term dynamics depend primarily on the averaged law enforcement intensity measures rather than on short-term fluctuations. These results identify time delay as a key structural mechanism underlying recurrent patterns and complex temporal behavior in crime dynamics.

math.DS↗

arXiv2026

A Crime/S.I.R. optimal control problem

This paper presents and discusses a mathematical model inspired by control theory to derive optimal public policies for minimizing costs associated with the reduction and control of criminal activity in a population. Specifically, we analyze the optimal control problem \begin{equation*} \min G(u_1, u_2, u_3) = \int_{0}^{t_{\text{F}}} \left( I(t) - R(t) + \frac{B_1}{2} u_1^2(t) + \frac{B_2}{2} u_2^2(t) + \frac{B_3}{2} u_3^2(t) \right) \, dt. \end{equation*} where $I=I(t)$ and $R=R(t)$ satisfies the system of equations \begin{equation*} \left\{ \begin{aligned} \dot{S} &= Λ- (1-u_1)SI - μS + ((1+u_3)γ_2)I + ρΩR,\\ \dot{I} &= (1-u_1)SI - (μ+ δ_1)I - ((1+u_2)γ_1)I - ((1+u_3)γ_2)I + (1-Ω)ρR,\\ \dot{R} &= ((1+u_2)γ_1)I - (μ+ δ_2 + ρ)R. \end{aligned} \right. \end{equation*} Our approach assumes that the social and economic effects of criminal behavior can be modeled by a dynamic SIR-type system, which serves as a constraint on a cost functional associated with the strategies implemented by government and law enforcement authorities to reduce criminal behavior. Using optimal control theory, the proposed controls, i.e., preventive policies (such as community and social cohesion programs), are expected to have a significant and positive impact on crime reduction, generating opportunities for the most disadvantaged sectors of Cali society and contributing to long-term security. Given that resources to address this problem are limited, this research aims to determine an optimal combination of public interventions and policies that minimize criminality at the lowest possible economic cost, using an SIR model, tools from variational calculus, and optimal control theory.

eess.SY↗

arXiv2025

Periodic solutions in a tumor-immune competition system with time-delay and chemotherapy effects

The main purpose of this paper is to analyze the dynamics of the system of time-delay differential equations (DDEs) \begin{equation*} \begin{split} \dot{T}(t)&=T(t) f(t,T(t))-γE(t)T(t),\\ \dot{E}(t)&=σ+ \frac{pE(t)T(t-τ_1)}{g+a T(t-τ_1)}-\frac{mE(t)T(t-τ_2)}{g+a T(t-τ_2)}-ηE(t), \end{split} \end{equation*} where $T=T(t)$ and $E=E(t)$ represent the concentrations of tumor and effector cells at the time $t$. The coefficients $σ$, $μ$, $γ$, and $η$ are all positive, and $f(t, T)$ represents the relative growth rate of tumor cells, corresponding to a generalized logistic growth function that describes periodic time chemotherapeutic effects. The parameter $τ_1 \in \mathbb{R}_{\ge 0}$ is the response time delay of the immune system (mediated by effector cells) to an invasion of tumor cells, while $τ_2 \in \mathbb{R}_{\ge 0}$ represents the time delay of tumor cells in response to the appearance of effector cells.

math.DS↗

arXiv2025

Multi-component secluded WIMP dark matter and Dirac neutrino masses with an extra Abelian gauge symmetry

Scenarios for secluded WIMP dark matter models have been extensively studied in simplified versions. This paper shows a complete UV realization of a secluded WIMP dark matter model with an extra Abelian gauge symmetry that includes two-component dark matter candidates, where the dark matter conversion process plays a significant role in determining the relic density in the Universe. The model contains two new unstable mediators: a dark Higgs and a dark photon. It generates Dirac neutrino masses and can be tested in future direct detection experiments of dark matter. The model is also compatible with cosmological and theoretical constraints, including the branching ratio of Standard model particles into invisible, Big Bang nucleosynthesis restrictions, and the number of relativistic degrees of freedom in the early Universe, even without kinetic mixing.

hep-ph↗

arXiv2023

Periodic oscillations in electrostatic actuators under time delayed feedback controller

In this paper, we prove the existence of two positive $T$-periodic solutions of an electrostatic actuator modeled by the time-delayed Duffing equation $$\ddot{x}(t)+f_{D}(x(t),\dot{x}(t))+ x(t)=1- \dfrac{e \mathcal{V}^{2}(t,x(t),x_{d}(t),\dot{x}(t),\dot{x}_{d}(t))}{x^2(t)}, \qquad x(t)\in\,]0,\infty[ $$ where $x_{d}(t)=x(t-d)$ and $\dot{x}_{d}(t)=\dot{x}(t-d),$ denote position and velocity feedback respectively, and $$ \mathcal{V}(t,x(t),x_{d}(t),\dot{x}(t),\dot{x}_{d}(t))=V(t)+g_{1}(x(t)-x_{d}(t))+g_{2}(\dot{x}(t)-\dot{x}_{d}(t)),$$ is the feedback voltage with positive input voltage $V(t)\in C(\mathbb{R}/T\mathbb{Z})$ for $e\in \mathbb{R}^{+}, g_{1},g_{2}\in \mathbb{R}$, $d\in [0,T[$. The damping force $f_{D}(x,\dot{x})$ can be linear, i.e., $f_{D}(x,\dot{x}) = c\dot{x}$, $c\in\mathbb{R}^+$ or squeeze film type, i.e., $f_{D}(x,\dot{x}) = γ\dot{x}/x^{3}$, $γ\in\mathbb{R}^+$. The fundamental tool to prove our result is a local continuation method of periodic solutions from the non-delayed case $(d=0)$. Our approach provides new insights into the delay phenomenon on microelectromechanical systems and can be used to study the dynamics of a large class of delayed Liénard equations that govern the motion of several actuators, including the comb-drive finger actuator and the torsional actuator. Some numerical examples are provided to illustrate our results.

math.OC↗

arXiv2022

Dirac dark matter, neutrino masses, and dark baryogenesis

We present a gauged baryon number model as an example of models where all new fermions required to cancel out the anomalies help to solve phenomenological problems of the standard model (SM). Dark fermion doublets, along with the iso-singlet charged fermions, in conjunction with a set of SM-singlet fermions, participate in the generation of small neutrino masses through the Dirac-dark Zee mechanism. The other SM-singlets explain the dark matter in the Universe, while their coupling to an inert singlet scalar is the source of the $CP$ violation. In the presence of a strong first-order electroweak phase transition, this "dark" $CP$ violation allows for a successful electroweak baryogenesis mechanism.

hep-ph↗

arXiv2022

Periodic oscillations in a 2N-body problem

Hip-Hop solutions of the $2N$-body problem are solutions that satisfy at every instance of time, that the $2N$ bodies with the same mass $m$, are at the vertices of two regular $N$-gons, each one of these $N$-gons are at planes that are equidistant from a fixed plane $Π_0$ forming an antiprism. In this paper, we first prove that for every $N$ and every $m$ there exists a family of periodic hip-hop solutions. For every solution in these families the oriented distance to the plane $Π_0$, which we call $d(t)$, is an odd function that is also even with respect to $t=T$ for some $T>0.$ For this reason we call solutions in these families, double symmetric solutions. By exploring more carefully our initial set of periodic solutions, we numerically show that some of the branches stablished in our existence theorem have bifurcations that produce branches of solutions with the property that the oriented distance function $d(t)$ is not even with respect to any $T>0$, we call these solutions single symmetry solutions. We prove that no single symmetry solution is a choreography. We also display explicit double symmetric solutions that are choreographies.

math.DS↗

arXiv2022

Type-II two-Higgs-doublet model in noncommutative geometry

In noncommutative geometry (NCG) the spectral action principle predicts the standard model (SM) particle masses by constraining the scalar and Yukawa couplings at some heavy scale, but gives an inconsistent value for the Higgs mass. Nevertheless, the scalar sector in the NCG approach to the standard model, is in general composed of two Higgs doublets and its phenomenology remains unexplored. In this work, we present a type-II two-Higgs-doublet model in NCG, with a SM-like Higgs mass compatible with the 125~GeV experimental value and extra scalars within the alignment limit without decoupling with masses from 350 GeV.

hep-ph↗

arXiv2021

Lepton dark matter portal in the inert Zee model

The inert Zee model is an extension of the Zee model for neutrino masses. This new model explains the dark matter relic abundance, generates a one-loop neutrino masses and forbids tree-level Higgs-mediated flavor changing neutral currents. Although the dark matter phenomenology of the model is similar to that of the inert doublet model, the presence of new vector-like fermions opens the lepton portal as a new dark matter annihilation channel. We study the impact of such a new portal in the low mass regime and show the parameter space allowed by direct and indirect searches of dark matter. Remarkably, we show that the region for $m_{H^0} \lesssim$ 70 GeV is recovered for $λ_L \lesssim 10^{-3}$. We also show that future experiments like LZ and DARWIN could test a large region of the parameter space of the model.

hep-ph↗

arXiv2020

Inert doublet as multicomponent dark matter

In this work, we study multicomponent dark sectors comprised of a fermionic and a scalar dark matter candidate. In the scalar sector, we mostly focus on the Inert Doublet Model while in the fermionic sector we study three different models. For all of them, we investigate the impact that dark matter conversion and regular WIMP dark matter annihilating processes have on the relic abundance. We mostly recover the region between the electroweak scale and $\sim$ 550 GeV for the scalar dark matter mass, which is usually excluded in the Inert Doublet Model. We also consider current constraints from both direct detection and indirect detection experiments and include future prospects to probe the models. Additionally, we investigate constraints from collider searches on the fermionic dark matter candidates.

hep-ph↗

arXiv2020

Bifurcation of periodic orbits for the $N$-body problem, from a non geometrical family of solutions

Given two positive real numbers $M$ and $m$ and an integer $n>2$, it is well known that we can find a family of solutions of the $(n+1)$-body problem where the body with mass $M$ stays put at the origin and the other $n$ bodies, all with the same mass $m$, move on the $x$-$y$ plane following ellipses with eccentri\-city $e$. It is expected that this geometrical family that depends on $e$, has some bifurcations that produce solutions where the body in the center moves on the $z$-axis instead of staying put in the origin. By doing an analytic continuation of a periodic numerical solution of the $4$-body problem --the one displayed on the video http://youtu.be/2Wpv6vpOxXk --we surprisingly discovered that the origin of this periodic solution is not part of the geometrical family of elliptical solutions parametrized by the eccentricity $e$. It comes from a not so geometrical but easier to describe family. Having noticed this new family, the authors find an exact formula for the bifurcation point in this new family and use it to show the existence of a non-planar periodic solution for any pair of masses $M$, $m$, and any integer $n$. As a particular example, we find a solution where three bodies with mass $3$ move around a body with mass $7$ that moves up and down.

math.DS↗

arXiv2019

Phenomenological consistency of the singlet-triplet scotogenic model

We perform a complete analysis of the consistency of the singlet-triplet scotogenic model, where both dark matter and neutrino masses can be explained. We determine the parameter space that yields the proper thermal relic density been in agreement with neutrino physics, lepton flavor violation, direct and indirect dark matter searches. In particular, we calculate the dark matter annihilation into two photons, finding that the corresponding cross-section is below the present bounds reported by the Fermi-LAT and H.E.S.S. collaborations. We also determine the spin-dependent cross-section for dark matter elastic scattering with nucleons at one-loop level, finding that the next generation of experiments as LZ and DARWIN could test a small region of the parameter space of the model.

hep-ph↗

arXiv2019

Singlet-Doublet Dirac Dark Matter and Neutrino Masses

We examine an extension of the Standard Model that addresses the dark matter puzzle and generates Dirac neutrinos masses through the radiative seesaw mechanism. The new field content includes a scalar field that plays an important role in setting the relic abundance of dark matter. We analyze the phenomenology in the light of direct, indirect, and collider searches of dark matter. In this framework, the dark matter candidate is a Dirac particle that is a mixture of new singlet-doublet fields with mass $m_{χ_1^0}\lesssim 1.1\,\text{TeV}$. We find that the allowed parameter space of this model is broader than the well-known Majorana dark matter scenario.

hep-ph↗

arXiv2016

Quantitative stability of certain families of periodic solutions in the Sitnikov problem

The Sitnikov problem is a special case of the restricted three-body problem where the primaries moves in elliptic orbits of the two-body problem with eccentricity $e\in [0,1[$ and the massless body moves on a straight line perpendicular to the plane of motion of the primaries through their barycenter. It is well known that for the circular case ($e=0$) and a given $N\in \mathbb{N}$ there are a finite number of nontrivial symmetric $2Nπ$ periodic solutions all of them parabolic and unstable (in the Lyapunov sense) if we consider the corresponding autonomous equation like a $2π$-periodic equation. Using the method of global continuation of Leray-Schauder, J.Llibre and R.Ortega (J.Llibre $\&$ R. Ortega, 2008) proved that these families of periodic solutions can be continued from the known $2Nπ$-periodic solutions in the circular case for nonnecessarily small values of the eccentricity $e$ and in some cases for all values of $e\in \, [0,1[.$ However this approach does not say anything about the stability properties of this periodic solutions. In this document we present a new method that quantifies the mentioned bifurcating families and them stabilities properties at least in first approximation. Our approach proposes two general methods: The first one is to estimate the growing of the canonical solutions for one-parametric differential equation of the form \[ \ddot{x}+a(t,λ)x=0, \] with $a\in C^{1}([0,T] \times [0,Λ])$. The second one gives stability criteria for one-parametric Hill's equation of the form \[ \ddot{x}+q(t,λ)x=0, \quad (\ast) \] where $q(\cdot,λ)$ is $T$-periodic and $q\in C^{3}(\mathbb{R}\times [0,Λ])$, such that for $λ=0$ the equation $(*)$ is parabolic.

math.DS↗

arXiv2015

Radiative neutrino masses in the singlet-doublet fermion dark matter model with scalar singlets

When the singlet-doublet fermion dark matter model is extended with additional $Z_2$--odd real singlet scalars, neutrino masses and mixings can be generated at one-loop level. In this work, we discuss the salient features arising from the combination of the two resulting simplified dark matter models. When the $Z_2$-lightest odd particle is a scalar singlet, $\operatorname{Br}(μ\to e γ)$ could be measurable provided that the singlet-doublet fermion mixing is small enough. In this scenario, also the new decay channels of vector-like fermions into scalars can generate interesting leptonic plus missing transverse energy signals at the LHC. On the other hand, in the case of doublet-like fermion dark matter, scalar coannihilations lead to an increase in the relic density which allow to lower the bound of doublet-like fermion dark matter.

hep-ph↗