1,721,385 research outputs found
Optimality conditions for an extended tumor growth model with double obstacle potential via deep quench approach
Full text linkIn this work, we investigate a distributed optimal control problem for an extended phase field system of Cahn–Hilliard type which physical context is that of tumor growth dynamics. In a previous contribution, the author has already studied the corresponding problem for the logarithmic potential. Here, we try to extend the analysis by taking into account a non-smooth singular nonlinearity, namely the double obstacle potential. Due to its non-smoothness behavior, the standard procedure to characterize the necessary conditions for the optimality cannot be performed. Therefore, we follow a different strategy which in the literature is known as the “deep quench” approach in order to obtain some optimality conditions that have to be interpreted in a more general framework. We establish the existence of optimal controls and some first-order optimality conditions for the system are derived by employing suitable approximation schemes
Gluon TMDs in Quarkonium Production
Full text linkI report on our investigations into the impact of (un)polarized transverse momentum dependent parton distribution functions (TMD PDFs or TMDs) for gluons at hadron colliders, especially at A Fixed Target Experiment at the LHC (AFTER@LHC). In the context of high energy proton-proton collisions, we look at final states with low mass (e.g. ηb) in order to investigate the nonperturbative part of TMD PDFs. We study the factorization theorem for the qTspectrum of ηb produced in proton-proton collisions relying on the effective field theory approach, defining the tools to perform phenomenological investigations at next-to-next-to-leading log and next-to-leading order accuracy in the perturbation theory. We provide predictions for the unpolarized cross section and comment on the possibility of extracting nonperturbative information about the gluon content of the proton once data at low transverse momentum are available
Optimal treatment for a phase field system of Cahn-Hilliard type modeling tumor growth by asymptotic scheme
Full text linkWe consider a particular phase field system which physical context is that of tumor growth dynamics. The model we deal with consists of a Cahn-Hilliard equation governing the evolution of the phase variable which takes into account the tumor cells proliferation in the tissue coupled with a reaction-diffusion equation for the nutrient. This model has already been investigated from the viewpoint of well-posedness, long-time behavior, and asymptotic analyses as some parameters go to zero. Starting from these results, we aim to face a related optimal control problem by employing suitable asymptotic schemes. In this direction, we assume some quite general growth conditions for the involved potential and a smallness restriction for a parameter appearing in the system we are going to face. We provide the existence of optimal controls and a necessary condition for optimality is addressed
Penalisation of long treatment time and optimal control of a tumour growth model of Cahn-Hilliard type with singular potential
Full text linkA distributed optimal control problem for a diffuse interface model, which physical context is that of tumour growth dynamics, is addressed. The system we deal with comprises a Cahn-Hilliard equation for the tumour fraction coupled with a reaction-diffusion for a nutrient species surrounding the tumourous cells. The cost functional to be minimised possesses some objective terms and it also penalises long treatments time, which may affect harm to the patients, and big aggregations of tumourous cells. Hence, the optimisation problem leads to the optimal strategy which reduces the time exposure of the patient to the medication and at the same time allows the doctors to achieve suitable clinical goals
Vanishing parameter for an optimal control problem modeling tumor growth
Full text linkA distributed optimal control problem for a phase field system which physical context is that of tumor growth is discussed. The system we are going to take into account consists of a Cahn-Hilliard equation for the phase variable (relative concentration of the tumor) coupled with a reaction-diffusion equation for the nutrient. The cost functional is of standard tracking-type and the control variable models the intensity at which it is possible to dispense medication. The model we deal with presents two small and positive parameters which are introduced in previous contributions as relaxation terms. Here, starting from the already investigated optimal control problem for the relaxed model, we aim at confirming the existence of optimal control and characterizing the first-order necessary optimality condition, via asymptotic schemes, when one of the two occurring parameters goes to zero
Existence of weak solutions to multiphase Cahn–Hilliard–Darcy and Cahn–Hilliard–Brinkman models for stratified tumor growth with chemotaxis and general source terms
Full text linkWe investigate a multiphase Cahn–Hilliard model for tumor growth with general source terms. The multiphase approach allows us to consider multiple cell types and multiple chemical species (oxygen and/or nutrients) that are consumed by the tumor. Compared to classical two-phase tumor growth models, the multiphase model can be used to describe a stratified tumor exhibiting several layers of tissue (e.g., proliferating, quiescent and necrotic tissue) more precisely. Our model consists of a convective Cahn–Hilliard type equation to describe the tumor evolution, a velocity equation for the associated volume-averaged velocity field, and a convective reaction-diffusion type equation to describe the density of the chemical species. The velocity equation is either represented by Darcy’s law or by the Brinkman equation. We first construct a global weak solution of the multiphase Cahn–Hilliard–Brinkman model. After that, we show that such weak solutions of this system converge to a weak solution of the multiphase Cahn–Hilliard–Darcy system as the viscosities tend to zero in some suitable sense. This means that the existence of a global weak solution to the Cahn–Hilliard–Darcy system is also established
On the connection between quark propagation and hadronization
Full text linkWe investigate the properties and structure of the recently discussed “fully inclusive jet correlator”, namely, the gauge-invariant field correlator characterizing the final state hadrons produced by a free quark as this propagates in the vacuum. Working at the operator level, we connect this object to the single-hadron fragmentation correlator of a quark, and exploit a novel gauge invariant spectral decomposition technique to derive a complete set of momentum sum rules for quark fragmentation functions up to twist-3 level; known results are recovered, and new sum rules proposed. We then show how one can explicitly connect quark hadronization and dynamical quark mass generation by studying the inclusive jet’s gauge-invariant mass term. This mass is, on the one hand, theoretically related to the integrated chiral-odd spectral function of the quark, and, on the other hand, is experimentally accessible through the E and twist-3 fragmentation function sum rules. Thus, measurements of these fragmentation functions in deep inelastic processes provide one with an experimental gateway into the dynamical generation of mass in Quantum Chromodynamics
Nonperturbative Uncertainties on the Transverse Momentum Distribution of Electroweak Bosons and on the Determination of the W Boson Mass at the LHC
Full text linkIn this contribution we present an overview of recent results concerning the impact of a possible flavour dependence of the intrinsic quark transverse momentum on electroweak observables. In particular, we focus on the spectrum of electroweak gauge bosons produced in proton-proton collisions at the LHC and on the direct determination of the boson mass. We show that these effects are comparable in size to other nonperturbative effects commonly included in phenomenological analyses and should thus be included in precise theoretical predictions for present and future hadron colliders
On the nonlocal Cahn–Hilliard equation with nonlocal dynamic boundary condition and boundary penalization
Full text linkThe Cahn–Hilliard equation is one of the most common models to describe phase segregation processes in binary mixtures. Various dynamic boundary conditions have already been introduced in the literature to model interactions of the materials with the boundary more precisely. To take long-range interactions into account, we propose a new model consisting of a nonlocal Cahn–Hilliard equation with a nonlocal dynamic boundary condition comprising an additional boundary penalization term. We rigorously derive our model as the gradient flow of a nonlocal free energy with respect to a suitable inner product of order H−1 containing both bulk and surface contributions. In the main model, the chemical potentials are coupled by a Robin type boundary condition depending on a specific relaxation parameter. We prove weak and strong well-posedness of this system, and we investigate the singular limits attained when this relaxation parameter tends to zero or infinity
On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport
Full text linkThis paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell adhesion by a non-local term and may be seen as non-local variants of the corresponding local model proposed by Garcke et al (2016). The model in consideration couples a non-local Cahn-Hilliard equation for the tumor phase variable with a reaction-diffusion equation for the nutrient concentration, and takes into account also significant mechanisms such as chemotaxis and active transport. The system depends on two relaxation parameters: a viscosity coefficient and parabolic-regularization coefficient on the chemical potential. The first part of the paper is devoted to the analysis of the system with both regularizations. Here, a rich spectrum of results is presented. Weak well-posedness is first addressed, also including singular potentials. Then, under suitable conditions, existence of strong solutions enjoying the separation property is proved. This allows also to obtain a refined stability estimate with respect to the data, including both chemotaxis and active transport. The second part of the paper is devoted to the study of the asymptotic behavior of the system as the relaxation parameters vanish. The asymptotics are analyzed when the parameters approach zero both separately and jointly, and exact error estimates are obtained. As a by-product, well-posedness of the corresponding limit systems is established
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