Search

Objective: To determine the extent to which the use of the Theory of Change (ToC) as a methodological approach is appropriate to assess the medium and long term effects generated by the Maradol Papaya Program in the Mixteca Poblana region (Puebla, Mexico). Design/methodology/approximation: A case study was conducted with qualitative approach with a phenomenological approximation directed at the validation of the ToC as methodological tool for the assessment of programs, through Documental Research methods, observation and interviews with producers and key informants for the study. Results: The design of the route or pathway of change allowed a punctual definition of the key variables for its operation and measurement as part of the assessment exercise. The use of qualitative methods (in-depth interviews) allowed an appropriate valuation of qualitative variables, such as learning, identificaiton of quantitative variables (production volumes, production costs, etc.) that can be made with conventional methods (questionnaires) without this representing any methodological conflict. Limitations on the study/implications: Since it is a case study, its generalization is not appropriate. However, there are elements that can be suggested as a general premise, such as the recommendation of the use of mixed methods in the assessment of programs and projects. Findings/conclusions: The Theory of Change (ToC) is a valuable tool in identifying change variables through the design of the route or pathway change; however, this exercise has great validity and wealth if it is constructed in a participative way. The use of mixed methods (quantitative and qualitative) is suggested for this type of assessment.

For any body-time manifold (Formula presented.) there exists a groupoid, called the material groupoid, encoding all the material properties of the material evolution. A smooth distribution, the material distribution, is constructed to deal with the case in which the material groupoid is not a Lie groupoid. This new tool provides a unified framework to deal with general non-uniform material evolution., M. de Leon and V. M. Jiménez acknowledge the partial finantial support from MICINN Grant PID2019-106715GB-C21 and the ICMAT Severo Ochoa project CEX2019-000904-S.

Resumen Introduccion El hallazgo de lesiones de caracteristicas radiologicas indeterminadas y su manejo posterior constituye uno de los principales retos de la patologia mamaria. Lo mismo ocurre ante el diagnostico de entidades histologicas consideradas como de potencial maligno incierto. Los sistemas de categorizacion diagnostica nos ayudan a clasificar estas lesiones, pero poco se sabe sobre la concordancia entre las categorias radiologica e histologica. El objetivo de este estudio es valorar esta concordancia diagnostica entre lesiones BIRADS-3 y la categoria histologica B3, asi como revisar las recomendaciones actuales sobre su manejo. Material y metodo Se ha realizado un estudio retrospectivo y observacional de las biopsias de mama realizadas en lesiones radiologicas BIRADS-3, durante un periodo de 5 anos, recogiendose datos clinico-patologicos y de seguimiento. Resultados Se incluyeron un total de 267 lesiones BIRADS-3 biopsiadas con aguja gruesa, de las cuales 12 fueron tumores malignos (4,49%), 10 lesiones de potencial maligno incierto (3,75%) y las restantes de caracteristicas histologicas benignas. Conclusion Podemos afirmar que la categoria radiologica BIRADS-3 y la categoria de diagnostico histologico B3 no son equivalentes. Ante una tasa cercana al 10% de lesiones malignas o borderline que presentaban caracteristicas radiologicas indeterminadas en este estudio, planteamos valorar la indicacion de biopsia ante cualquier discordancia clinica y/o radiologica en pacientes con imagenes categorizadas como BIRADS-3.

In this paper, we study the integrability of contact Hamiltonian systems, both time-dependent and independent. In order to do so, we construct a Hamilton--Jacobi theory for these systems following two approaches, obtaining two different Hamilton--Jacobi equations. Compared to conservative Hamiltonian systems, contact Hamiltonian systems depend of one additional parameter. The fact of obtaining two equations reflects whether we are looking for solutions depending on this additional parameter or not. In order to illustrate the theory developed in this paper, we study three examples: the free particle with a linear external force, the freely falling particle with linear dissipation and the damped and forced harmonic oscillator., 27 pages

In this paper we present an application of the groupoid theory to the study of relevant case of material evolution phenomena, the \textit{process of morphogenesis}. Our theory is inspired by Walter Noll's theories of continuous distributions and provides a unifying and very simple framework of these phenomena. We present the explicit equation, the \textit{morphogenesis equation}, to calculate the \textit{material distributions} associated to this phenomenon., arXiv admin note: substantial text overlap with arXiv:2108.02865

We describe geometrically contact Lagrangian systems under impulsive forces and constraints, as well as instantaneous nonholonomic constraints which are not uniform along the configuration space. In both situations, the vector field describing the dynamics of a contact Lagrangian system is determined by defining projectors to evaluate the constraints by using a Riemannian metric. In particular, we introduce the Herglotz equations for contact Lagrangian systems subject to instantaneous nonholonomic constraints. Moreover, we provide a Carnot-type theorem for contact Lagrangian systems subject to impulsive forces and constraints, which characterizes the changes of energy due to contact-type dissipation and impulsive forces. We illustrate the applicability of the method with practical examples, in particular, a rolling cylinder on a springily surface and a rolling sphere on a non-uniform surface, both with dissipation., Comment: 23 pages

Cosymplectic geometry has been proven to be a very useful geometric background to describe time-dependent Hamiltonian dynamics. In this work, we address the globalization problem of locally cosymplectic Hamiltonian dynamics that failed to be globally defined. We investigate both the geometry of locally conformally cosymplectic (abbreviated as LCC) manifolds and the Hamiltonian dynamics constructed on such LCC manifolds. Further, we provide a geometric Hamilton-Jacobi theory on this geometric framework., Comment: 52 pages, 3 tables

We are proposing Tulczyjew¿s triple for contact dynamics. The most important ingredients of the triple, namely symplectic diffeomorphisms, special symplectic manifolds, and Morse families, are generalized to the contact framework. These geometries permit us to determine so-called generating family (obtained by merging a special contact manifold and a Morse family) for a Legendrian submanifold. Contact Hamiltonian and Lagrangian Dynamics are recast as Legendrian submanifolds of the tangent contact manifold. In this picture, the Legendre transformation is determined to be a passage between two different generators of the same Legendrian submanifold. A variant of contact Tulczyjew¿s triple is constructed for evolution contact dynamics., M. de León and M. Lainz acknowledge the partial finantial support from MICINN Grant PID2019-106715GB-C21 and the ICMAT Severo Ochoa project CEX2019-000904-S. M. Lainz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203. J.C. Marrero acknowledges the partial support from European Union (Feder) grant PGC2018-098265-B-C32.

The aim of this paper is to develop a Hamilton--Jacobi theory for contact Hamiltonian systems. We find several forms for a suitable Hamilton-Jacobi equation accordingly to the Hamiltonian and the evolution vector fields for a given Hamiltonian function. We also analyze the corresponding formulation on the symplectification of the contact Hamiltonian system, and establish the relations between these two approaches. In the last section, some examples are discussed., Comment: arXiv admin note: text overlap with arXiv:2011.05579

Open access version at https://arxiv.org/pdf/1810.04962.pdf, We discuss, in all generality, the reduction of a Hamilton — Jacobi theory for systems subject to nonholonomic constraints and invariant under the action of a group of symmetries. We consider nonholonomic systems subject to both linear and nonlinear constraints and with different positioning of such constraints with respect to the symmetries., This work has been partially supported by MINECO Grants MTM2016-76-072-P and the ICMAT Severo Ochoa projects SEV-2011-0087 and SEV-2015-0554. V.M. Jiménez wishes to thank MINECO for a FPI-PhD position.

In this paper, we continue the construction of variational integrators adapted to contact geometry started in Vermeeren et al. (J Phys A 52(44):445206, 2019), in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a discrete Lagrangian in the contact setting. This allows us to develop convenient numerical integrators for contact Lagrangian systems that are conformally contact by construction. The existence of an exact Lagrangian function is also discussed., Manuel Lainz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203. The authors are supported by Ministerio de Ciencia e Innovación (Spain) under Grants PID2019-106715GB-C21, MTM2016-76702-P and “Severo Ochoa Programme for Centres of Excellence” in R&D (SEV-2015-0554). A. Simoes is supported by the FCT (Portugal) research fellowship SFRH/BD/129882/2017 partially funded by the European Union (ESF). M. Lainz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203.

In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical points of the Herglotz action on this space of paths. This dynamics can be also obtained through an extended Lagrangian, including Lagrange multiplier terms. This theory has important applications in optimal control theory for Herglotz control problems, in which the cost function is given implicitly, through an ODE, instead of by a definite integral. Indeed, these control problems can be considered as particular cases of vakonomic contact systems, and we can use the Lagrangian theory of contact systems in order to understand their symmetries and dynamics., M. de León and M. Lainz acknowledge the partial finantial support from MINECO Grants MTM2016-76-072-P and the ICMAT Severo Ochoa project SEV-2015-0554. M. Lainz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203. M.C. Muñoz-Lecanda acknowledges the financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades project PGC2018-098265-B-C33 and the Secretary of University and Research of the Ministry of Business and Knowledge of the Catalan Government project 2017-SGR-932.

This paper is devoted to the study of mechanical systems subjected to external forces in the framework of symplectic geometry. We obtain Noether¿s theorem for Lagrangian systems with external forces, among other results regarding symmetries and conserved quantities. We particularize our results for the so-called Rayleigh dissipation, i.e., external forces that are derived from a dissipation function, and illustrate them with some examples. Moreover, we present a theory for the reduction in Lagrangian systems subjected to external forces, which are invariant under the action of a Lie group., The authors acknowledge financial support from the Spanish Ministry of Science and Innovation (MICINN), under Grant No. PID2019- 106715GB-C21, the “Severo Ochoa Programme for Centres of Excellence in R&D” (Grant No. CEX2019-000904-S), and the Spanish National Research Council (CSIC) through the “Ayuda extraordinaria a Centros de Excelencia Severo Ochoa” (Grant No. 20205-CEX001). M.L. wishes to thank the MICINN and the Institute of Mathematical Sciences (ICMAT) for FPI-Severo Ochoa Predoctoral Contract No. PRE2018-083203. A.L.-G. would like to thank the CSIC for its financial support through the JAE Intro scholarship JAEINT_20_01494. He would also like to acknowledge a renewal of the scholarship by the ICMAT.

We present several results on the inverse problem and equivalent contact Lagrangian systems. These problems naturally lead to consider smooth transformations on the z variable (i.e., reparametrizations of the action). We present the extended contact Lagrangian systems to formalize this notion. With this structure we define horizontal equivalence of Lagrangians, which generalizes the symplectic case. We also present some results on the inverse problem for extended contact systems., Manuel de León and Manuel Lainz acknowledge financial support from the Spanish Ministry of Science and Innovation (MICINN), under grants PID2019-106715GB-C21, “Severo Ochoa Programme for Centres of Excellence in R&D” (CEX2019-000904-S) and from the Spanish National Research Council (CSIC), through the “Ayuda extraordinaria a Centros de Excelencia Severo Ochoa” (20205-CEX001). Manuel Lainz wishes to thank MICINN and the Institute of Mathematical Sciences (ICMAT) for the FPI-Severo Ochoa predoctoral contract PRE2018-083203.

JOURNAL OF GEOMETRIC MECHANICS doi:10 3934/jgm 2021004 ©American Institute of Mathematical Sciences Volume 13, Number 1, March 2021 pp i{iii PREFACE TO THE SPECIAL ISSUE DEDICATED TO ANTHONY BLOCH This volume of JGM is dedicated to Tony Bloch on the occasion of his 65th birthday Perhaps PREFACE TO THE SPECIAL ISSUE DEDICATED TO ANTHONY BLOCH iii this was the time he managed to spare for his research amid the busy schedule as the Chair [Extracted from the article] Copyright of Journal of Geometric Mechanics is the property of American Institute of Mathematical Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )

In this article, we provide a Hamilton¿Jacobi formalism on locally conformally symplectic (lcs) manifolds. We are interested in the Hamilton¿Jacobi as an alternative method for formulating the dynamics, while our interest in the locally conformal character will account for physical theories described by Hamiltonians defined on well-behaved line bundles, whose dynamic takes place in open subsets of the general manifold. We present a lcs Hamilton¿Jacobi equation in subsets of the general manifold and then provide a global view by using the Lichnerowicz¿deRham differential. We show a comparison between the global and local description of a lcs Hamilton¿Jacobi theory, and how actually the local behavior can be glued to retrieve the global behavior of the Hamilton¿Jacobi theory. A particular example is the case of Gaussian isokinetic dynamics in which we apply our structure in certain submanifolds of the phase space., This work was partially supported by Grant No. PID2019-106715GB-C21 and “Severo Ochoa Programme for Centers of Excellence in R&D” (Grant No. CEX2019-000904-S)

In this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic bracket, which is an almost Jacobi bracket on the space of observables and provides the nonholonomic dynamics., This work has been partially supported by MINECO Grants MTM2016-76-072-P and the ICMAT Severo Ochoa project SEV-2015-0554. M. Lainz and V.M. Jimenez

We present a complete theory of higher-order autonomous contact mechanics, which allows us to describe higher-order dynamical systems with dissipation. The essential tools for the theory are the extended higher-order tangent bundles, ${\rm T}^kQ\times{\mathbb R}$, whose geometric structures are previously introduced in order to state the Lagrangian and Hamiltonian formalisms for these kinds of systems, including their variational formulation. The variational principle, the contact forms, and the geometric dynamical equations are obtained by using those structures and generalizing the standard formulation of contact Lagrangian and Hamiltonian systems. As an alternative approach, we develop a unified description that encompasses the Lagrangian and Hamiltonian equations as well as their relationship through the Legendre map; all of them are obtained from the contact dynamical equations and the constraint algorithm that is implemented because, in this formalism, the dynamical systems are always singular. Some interesting examples are finally analyzed using these geometric formulations., 39 pp. Minor changes. References updated

In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of thermodynamics, we show that the notion of evolution vector field is adequate to appropriately describe such systems. Our formulation naturally arises from the introduction of a skew-symmetric bracket to which numerical methods based on discrete gradients fit nicely. Moreover, we study the corresponding Lagrangian and Hamiltonian formalism, discussing the fundamental principles from which the equations are derived. An important class of systems that is naturally covered by our formalism are composed thermodynamic systems, which are described by at least two thermal variables and exchange heat between its components, The authors acknowledge financial support from the Spanish Ministry of Science and Innovation, under grants PID2019-106715GB-C21, MTM2016-76702-P, ?Severo Ochoa Programme for Centres of Excellence in R&D? (CEX2019- 000904-S) and from the Spanish National Research Council, through the ?Ayuda extraordinaria a Centros de Excelencia Severo Ochoa? (20205CEX001). A. Simoes is supported by the FCT (Portugal) research fellowship SFRH/BD/129882/2017 partially funded by the European Union (ESF)

In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been added to account for field theories that are scale invariant, flat spaces, and because some conformal fields can be exactly solved or classified. In particular, we will solve the example of a conformal scalar field using the geometric Hamilton–Jacobi theory that is explicitly proposed for conformal fields on a multisymplectic manifold. To complete the geometric approach to study field theories, we propose the Hamilton–Jacobi theory for conformal fields in a Cauchy data space, in which space and time are split separately and the dynamics is depicted in an infinite-dimensional manifold., This work has been partially supported by MINECO, Spain grants MTM2016-76-072-P and the ICMAT, Spain Severo Ochoa Project SEV-2011-0087 and SEV-2015-0554. OE grateful to Prof J. ?niatycki for many discussions on the field theory. The research of Marcin Zaj?c was financially supported by the University?s Integrated Development Programme (ZIP) of University of Warsaw, Poland co-financed by the European Social Fund under the Operational Programme Knowledge Education Development 2014?2020, action 3.5.

JOURNAL OF GEOMETRIC MECHANICSdoi:10.3934/jgm.2020028c©American Institute of Mathematical SciencesVolume12, Number3, September2020pp.i–ivPREFACE TO THE SPECIAL ISSUE DEDICATEDTO JAMES MONTALDIIn August 2018 we held a conference in Guanajuato, Mexico, where several col-laborators and students of James Montaldi had the privilege to homage his scien-tific contributions. James is best known as an expert in singularity and bifurcationtheory, who is a world reference in equivariant Hamiltonian systems, and has anexceptional talent to turn symmetries into insightful theorems about the dynamicsof mechanical systems. His unusual combination of mathematical depth, modesty,integrity and friendly personality, make him a greatly esteemed member of theextended geometric mechanics community.The programme of this exciting meeting, which lasted one week, incorporatedsome of the many areas in which James has worked over the years. During theconference, we heard testimonials of James’ mathematical sharpness, kindness andgenerosity as a supervisor and collaborator, accompanied with many nostalgic ref-erences of a meeting that he organised in Peyresq twenty years ago. This issue oftheJournal of Geometric Mechanicsis a continuation of our celebration of James’career and of our appreciation of having him as a teacher, colleague and friend.

By means of the Jacobi structure associated with a contact structure, we use the so-called evolution vector field to propose a new characterization of isolated thermodynamical systems with friction, a simple but important class of thermodynamical systems which naturally satisfy the first and second laws of thermodynamics, i.e. total energy preservation of isolated systems and non-decreasing total entropy, respectively. We completely clarify its qualitative dynamics, the underlying geometrical structures and we also show how to apply discrete gradient methods to numerically integrate the evolution equations for these systems.

The concept of material distribution is introduced as describing the geometric material structure of a general non-uniform body. Any smooth constitutive law is shown to give rise to a unique smooth integrable singular distribution. Ultimately, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform components. Thus, the constitutive law induces a unique partition of the body into smoothly uniform sub-bodies, laminates, filaments and isolated points., This work was supported by MINECO Grants MTM2013-42-870-P and the ICMAT Severo Ochoa projects SEV-2011-0087 and SEV2015-0554. V.M.J. wishes to thank MINECO for a FPI-PhD Position