arXiv subjects

Andrea Signori

Publications and source records attributed to Andrea Signori.

At least 19 recordsLinked to original sources

arXiv2026

Proton-Proton to Antinucleon Cross Sections for Cosmic Ray Applications

We present predictions of inclusive antiproton and antineutron production cross sections in proton-proton collisions relevant to primary and secondary antiproton production in cosmic ray interactions with interstellar matter. Our predictions are based on collinear factorisation in Quantum Chromodynamics and are accurate to next-to-leading order in the perturbative expansion of the strong coupling. We assess the relevance of cross sections measured at collider experiments, such as NA49 at the CERN SPS and ALICE at the LHC, to the kinetic energy ranges accessed by cosmic ray detectors. We characterise the associated uncertainties due to the input parton distribution and fragmentation functions, and to missing higher orders. We critically examine the ~30% excess of antineutron over antiproton production in proton-proton collisions preliminarily reported by the NA49 experiment by combining our predictions with a data-driven model. Our results do not support the NA49 finding, and point to a mild excess of a few percent. We finally show that the NA49 result could only be reconciled with our framework by invoking sizeable differences between antiproton and antineutron production in the poorly constrained region of small transverse momenta of the produced hadron.

hep-ph↗

arXiv2026

Introduction to transverse momentum imaging

This set of notes complements the lectures and recitation sessions discussed in the following graduate schools: HUGS at Jefferson Lab (years 2018, 2019, 2021), the International School and Workshop on Probing Hadron Structure at the Electron-Ion Collider at ICTS (2024), Frontiers in Nuclear and Hadronic Physics at GGI (2025), and the International Workshop and School on Hadron Structure and Strong Interactions at Nanjing University (2025).

hep-ph↗

arXiv2026

On a Mullins-Sekerka model for the growth of active droplets modelling protocells: Stability analysis and numerical computations

Mullins-Sekerka models with chemical reactions can lead to scenarios where droplets grow, become unstable, split, grow and undergo further division. These grow and division cycles have been proposed as a model for protocells and are believed to play a fundamental role in living systems by providing chemical compartments which are important in the organization of living systems. This paper analyses chemically active Mullins-Sekerka models. Existence of radially symmetric solutions is shown and a detailed stability analysis in radial as well as planar situations is given. In particular, we also analyze multilayered solutions leading to shell-type situations. Finally, we introduce a numerical method based on a parametric finite element approach that explicitly accounts for topological changes, thereby allowing for droplet splitting and merging. Several numerical simulations verify the findings of the theoretical stability analysis and show complex dynamical behavior, including multiple instabilities, splittings of droplets and appearance of shell-type solutions.

math.AP↗

arXiv2026

Optimal velocity control of a Brinkman-Cahn-Hilliard system with curvature effects

We address an optimal control problem governed by a system coupling a Brinkman-type momentum equation for the velocity field with a sixth-order Cahn-Hilliard equation for the phase variable, incorporating curvature effects in the free energy. The control acts as a distributed velocity control, allowing for the manipulation of the flow field and, consequently, the phase separation dynamics. We establish the existence of optimal controls, prove the Fr\'echet differentiability of the control-to-state operator, and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. We also discuss the aspect of sparsity. Beyond its analytical novelty, this work provides a rigorous control framework for Brinkman-Cahn-Hilliard systems incorporating a curvature regularization, offering a foundation for applications in microfluidic design and controlled pattern formation.

math.OC↗

arXiv2025

Optimal Control of a Navier-Stokes-Cahn-Hilliard System for Membrane-fluid Interaction

We consider an optimal control problem for a two-dimensional Navier-Stokes-Cahn-Hilliard system arising in the modeling of fluid-membrane interaction. The fluid dynamics is governed by the incompressible Navier-Stokes equations, which are nonlinearly coupled with a sixth-order Cahn-Hilliard type equation representing the deformation of a flexible membrane through a phase-field variable. Building on the previously established existence and uniqueness of global strong solutions for the coupled system, we introduce an external forcing term acting on the fluid as the control variable. Then we seek to minimize a tracking-type cost functional, demonstrating the existence of an optimal control and deriving the associated first-order necessary optimality conditions. A key issue is to establish sufficient regularity for solutions of the adjoint system, which is crucial for the rigorous derivation of optimality conditions in the fluid dynamic setting.

math.AP↗

arXiv2025

On Brinkman flows with curvature-induced phase separation in binary mixtures

The mathematical analysis of diffuse-interface models for multiphase flows has attracted significant attention due to their ability to capture complex interfacial dynamics, including curvature effects, within a unified, energetically consistent framework. In this work, we study a novel Brinkman-Cahn-Hilliard system, coupling a sixth-order phase-field evolution with a Brinkman-type momentum equation featuring variable shear viscosity. The Cahn-Hilliard equation includes a nonconservative source term accounting for mass exchange, and the velocity equation contains a non divergence-free forcing term. We establish the existence of weak solutions in a divergence-free variational framework, and, in the case of constant mobility and shear viscosity, prove uniqueness and continuous dependence on the forcing. Additionally, we analyze the Darcy limit, providing existence results for the corresponding reduced system.

math.AP↗

arXiv2025

On a phenotype-structured phase-field model of nutrient-limited tumour growth

Phase-field models of tumour growth have proved useful as theoretical tools to investigate cancer invasion. A key implicit assumption underlying mathematical models of this type which have so far been proposed, though, is that cells in the tumour are identical. This assumption ignores both the fact that cells in the same tumour may express different characteristics to different extents, exhibiting heterogeneous phenotypes, and the fact that cells may undergo phenotypic changes, with their characteristics evolving over time. To address such a limitation, in this paper we incorporate inter-cellular phenotypic heterogeneity and the evolution of cell phenotypes into the phase-field modelling framework. This is achieved by formulating a phenotype-structured phase-field model of nutrient-limited tumour growth. For this model, we first establish a well-posedness result under general assumptions on the model functions, which encompass a wide spectrum of biologically relevant scenarios. We then present a sample of numerical solutions to showcase key features of spatiotemporal and evolutionary cell dynamics predicted by the model. We conclude with a brief overview of modelling and analytical research perspectives.

math.AP↗

arXiv2025

On a non-local phase-field model for tumour growth with single-well Lennard-Jones potential

In the present work, we develop a comprehensive and rigorous analytical framework for a non-local phase-field model that describes tumour growth dynamics. The model is derived by coupling a non-local Cahn-Hilliard equation with a parabolic reaction-diffusion equation, which accounts for both phase segregation and nutrient diffusion. Previous studies have only considered symmetric potentials for similar models. However, in the biological context of cell-to-cell adhesion, single-well potentials, like the so-called Lennard-Jones potential, seem physically more appropriate. The Cahn-Hilliard equation with this kind of potential has already been analysed. Here, we take a step forward and consider a more refined model. First, we analyse the model with a viscous relaxation term in the chemical potential and subject to suitable initial and boundary conditions. We prove the existence of solutions, a separation property for the phase variable, and a continuous dependence estimate with respect to the initial data. Finally, via an asymptotic analysis, we recover the existence of a weak solution to the initial and boundary value problem without viscosity, provided that the chemotactic sensitivity is small enough.

math.AP↗

arXiv2025

On a Cahn-Hilliard equation for the growth and division of chemically active droplets modeling protocells

The Cahn-Hilliard model with reaction terms can lead to situations in which no coarsening is taking place and, in contrast, growth and division of droplets occur which all do not grow larger than a certain size. This phenomenon has been suggested as a model for protocells, and a model based on the modified Cahn-Hilliard equation has been formulated. We introduce this equation and show the existence and uniqueness of solutions. Then formally matched asymptotic expansions are used to identify a sharp interface limit using a scaling of the reaction term which becomes singular when the interfacial thickness tends to zero. We compute planar solutions and study their stability under non-planar perturbations. Numerical computations for the suggested model are used to validate the sharp interface asymptotics. In addition, the numerical simulations show that the reaction terms lead to diverse phenomena such as growth and division of droplets in the obtained solutions, as well as the formation of shell-like structures.

math.AP↗

arXiv2025

Unveiling the Collins-Soper kernel in inclusive DIS at threshold

We revisit the factorization of inclusive deep inelastic scattering near the kinematic threshold to explicitly track off-lightcone effects. Particle production develops around two opposite near-lightcone directions like in transverse-momentum-dependent processes, and the Collins-Soper kernel emerges as a universal function in the rapidity evolution of the relevant parton correlators. We clarify outstanding issues regarding soft radiation and rapidity divergences, and uncover a new way to calculate the Collins-Soper kernel on the lattice with collinear operators.

hep-ph↗

arXiv2025

The anisotropic Cahn--Hilliard equation with degenerate mobility: Existence of weak solutions

This paper presents an existence result for the anisotropic Cahn--Hilliard equation characterized by a potentially concentration-dependent degenerate mobility taking into account an anisotropic energy. The model allows for the degeneracy of the mobility at specific concentration values, demonstrating that the solution remains within physically relevant bounds. The introduction of anisotropy leads to highly nonlinear terms making energy and entropy estimates rather involved. As the mobility degenerates in the pure phases, the degenerate Cahn--Hilliard equation describes surface diffusion and is an important model to model solid-state dewetting (SSD) of thin films. We show existence of weak solutions for the anisotropic degenerate Cahn--Hilliard equation by using suitable energy and entropy type estimates.

math.AP↗

arXiv2024

Solvability and optimal control of a multi-species Cahn-Hilliard-Keller-Segel tumor growth model

This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn-Hilliard-Keller-Segel tumor growth model, which incorporates complex biological processes such as species diffusion, chemotaxis, angiogenesis, and nutrient consumption, resulting in a highly nonlinear system of nonlinear partial differential equations. The modeling derivation and corresponding analysis have been addressed in a previous contribution. Building on this foundation, the scope of this study involves investigating a distributed control problem with the goal of optimizing a tracking-type cost functional. This latter aims to minimize the deviation of tumor cell location from desired target configurations while penalizing the costs associated with implementing control measures, akin to introducing a suitable medication. Under appropriate mathematical assumptions, we demonstrate that sufficiently regular solutions exhibit continuous dependence on the control variable. Furthermore, we establish the existence of optimal controls and characterize the first-order necessary optimality conditions through a suitable variational inequality.

math.AP↗

arXiv2024

Flavor dependence of unpolarized quark Transverse Momentum Distributions from a global fit

We present an extraction of the unpolarized transverse-momentum-dependent parton distribution and fragmentation functions that takes into account possible differences between quark flavors and final-state hadrons. The extraction is based on experimental measurements from Drell-Yan processes and semi-inclusive deep-inelastic scattering, whose combination is essential to distinguish flavor differences. The analysis is carried out at N$^3$LL accuracy. The extracted flavor-dependent distributions give a very good description of the data ($\chi^2/N_{\rm dat} = 1.08$). The resulting uncertainties take fully into account also the uncertainties in the determination of the corresponding collinear distributions.

hep-ph↗

arXiv2024

Complex pattern formation governed by a Cahn-Hilliard-Swift-Hohenberg system: Analysis and numerical simulations

This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting system leads to complex patterns involving a separation into phases as typical of the Cahn-Hilliard equation and small scale stripes and dots as seen in the Swift-Hohenberg equation. We introduce singular potentials of logarithmic type to enhance the model's accuracy in adhering to essential physical constraints. The paper establishes the existence and uniqueness of weak solutions within this extended framework. The insights gained contribute to a deeper understanding of phase separation in complex systems, with potential applications in materials science and related fields. We introduce a stable finite element approximation based on an obstacle formulation. Subsequent numerical simulations demonstrate that the model allows for complex structures as seen in pigment patterns of animals and in porous polymeric materials.

math.AP↗

arXiv2024

Cahn-Hilliard equations with singular potential, reaction term and pure phase initial datum

We consider local and nonlocal Cahn-Hilliard equations with constant mobility and singular potentials including, e.g., the Flory-Huggins potential, subject to no-flux (or periodic) boundary conditions. The main goal is to show that the presence of a suitable class of reaction terms allows to establish the existence of a weak solution to the corresponding initial and boundary value problem even though the initial condition is a pure state. In other words, the separation process takes place even in presence of a pure phase, provided that it is triggered by a convenient reaction term. This fact was already observed by the authors in a previous contribution devoted to a specific biological model. In this context, we generalize the previously-mentioned concept by examining the essential assumptions required for the reaction term to apply the new strategy. Also, we explore the scenario involving the nonlocal Cahn-Hilliard equation and provide illustrative examples that contextualize within our abstract framework.

math.AP↗

arXiv2024

Curvature effects in pattern formation: well-posedness and optimal control of a sixth-order Cahn-Hilliard equation

This work investigates the well-posedness and optimal control of a sixth-order Cahn-Hilliard equation, a higher-order variant of the celebrated and well-established Cahn-Hilliard equation. The equation is endowed with a source term, where the control variable enters as a distributed mass regulator. The inclusion of additional spatial derivatives in the sixth-order formulation enables the model to capture curvature effects, leading to a more accurate depiction of isothermal phase separation dynamics in complex materials systems. We provide a well-posedness result for the aforementioned system when the corresponding nonlinearity of double-well shape is regular and then analyze a corresponding optimal control problem. For the latter, existence of optimal controls is established, and the first-order necessary optimality conditions are characterized via a suitable variational inequality. These results aim at contributing to improve the understanding of the mathematical properties and control aspects of the sixth-order Cahn-Hilliard equation, offering potential applications in the design and optimization of materials with tailored microstructures and properties.

math.AP↗

arXiv2023

Two-phase flows through porous media described by a Cahn--Hilliard--Brinkman model with dynamic boundary conditions

We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for the volume averaged velocity field as well as a convective Cahn--Hilliard equation with dynamic boundary conditions for the phase-field, which describes the location of the two fluids within the domain. The dynamic boundary conditions are incorporated to model the interaction of the fluids with the wall of the container more precisely. In particular, they allow for a dynamic evolution of the contact angle between the interface separating the fluids and the boundary, and also for a convection-induced motion of the corresponding contact line. For our model, we first prove the existence of global-in-time weak solutions in the case where regular potentials are used in the Cahn--Hilliard subsystem. In this case, we can further show the uniqueness of the weak solution under suitable additional assumptions. Moreover, we further prove the existence of weak solutions in the case of singular potentials. Therefore, we regularize such singular potentials by a Yosida approximation, such that the results for regular potentials can be applied, and eventually pass to the limit in this approximation scheme.

math.AP↗

arXiv2023

Analysis of a multi-species Cahn-Hilliard-Keller-Segel tumor growth model with chemotaxis and angiogenesis

We introduce a multi-species diffuse interface model for tumor growth, characterized by its incorporation of essential features related to chemotaxis, angiogenesis and proliferation mechanisms. We establish the weak well-posedness of the system within an appropriate variational framework, accommodating various choices for the nonlinear potentials. One of the primary novelties of the work lies in the rigorous establishment of the existence of a weak solution through the introduction of delicate approximation schemes. To our knowledge, this represents a novel advancement for both the intricate Cahn-Hilliard-Keller-Segel system and the Keller-Segel subsystem with source terms. Moreover, when specific conditions are met, such as having more regular initial data, a smallness condition on the chemotactic constant with respect to the magnitude of initial conditions and potentially focusing solely on the two-dimensional case, we provide regularity results for the weak solutions. Finally, we derive a continuous dependence estimate, which, in turn, leads to the uniqueness of the smoothed solution as a natural consequence.

math.AP↗