Epistemology of Experimental Gravity - Scientific Rationality

The evolution of gravitational tests from an epistemological perspective framed in the concept of rational reconstruction of Imre Lakatos, based on his methodology of research programmes. Unlike other works on the same subject, the evaluated period is very extensive, starting with Newton's natural philosophy and up to the quantum gravity theories of today. In order to explain in a more rational way the complex evolution of the gravity concept of the last century, I propose a natural extension of the methodology of the research programmes of Lakatos that I then use during the paper. I believe that this approach offers a new perspective on how evolved over time the concept of gravity and the methods of testing each theory of gravity, through observations and experiments. I argue, based on the methodology of the research programmes and the studies of scientists and philosophers, that the current theories of quantum gravity are degenerative, due to the lack of experimental evidence over a long period of time and of self-immunization against the possibility of falsification. Moreover, a methodological current is being developed that assigns a secondary, unimportant role to verification through observations and/or experiments. For this reason, it will not be possible to have a complete theory of quantum gravity in its current form, which to include to the limit the general relativity, since physical theories have always been adjusted, during their evolution, based on observational or experimental tests, and verified by the predictions made. Also, contrary to a widespread opinion and current active programs regarding the unification of all the fundamental forces of physics in a single final theory, based on string theory, I argue that this unification is generally unlikely, and it is not possible anyway for a unification to be developed based on current theories of quantum gravity, including string theory. In addition, I support the views of some scientists and philosophers that currently too much resources are being consumed on the idea of developing quantum gravity theories, and in particular string theory, to include general relativity and to unify gravity with other forces, as long as science does not impose such research programs. DOI: 10.13140/RG.2.2.35350.7072

MODELLING SUPERFLUID NEUTRON STARS APPLICATIONS TO PULSAR GLITCHES

In this dissertation I discuss how observations of the maximum glitch occurred in a certain pulsar provides a test for the microscopic physics of neutron star interiors, in particular the pinning forces (a parameter which effectively describes the strength of the vortex-lattice interaction at the mesoscopic scale). Conversely, by fixing the input parameters by taking estimates from recent literature, it is possible to estimate the mass of a glitching pulsar. A proof of concept of this thesis is given by constructing a quantitative model for pulsar rotational dynamics that can consistently encode state of the art models of the pinning force between vortices and ions in the crust, as well as the stratified structure of a neutron star. This point is far from being secondary as most studies on pulsar glitches are based on body-averaged models or differential models that tacitly assume a cylindrical symmetry, not consistent with the spherically layered structure

Notes in Pure Mathematics & Mathematical Structures in Physics

These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.Comment: Small improvements and addition

Elastocapillary Phenomena in Soft Elastic Solids

Soft elastic solids play an important role in a wide range of applications such as in tissue scaffolds to grow artificial organs, in wearable contact lenses, as adhesives, in soft robotics and even as prototypical models to understand the mechanics of growth and morphology of organs. For a soft elastic material like hydrogel with its shear modulus in the range of tens of pascals, its surface tension also contributes to the mechanics of its deformation in addition to its elasticity. As opposed to a hard solid that is very difficult to deform, for the case of these soft solids, even a weak force like gravity can bring about significant deformation. Many of these aspects of the deformation and behavior of these ultrasoft materials are still not very well understood. Thus, the objectives of this dissertation were to understand the role of elastocapillarity (i.e, joint roles of solid surface tension and elasticity) and elastobuoyancy (i.e, joint roles of gravity and elasticity) that manifest in such solids. In this dissertation, we studied the role elastocapillarity in adhesion-induced instability in thin elastic films bonded to rigid substrates and also in surface oscillation modes of soft gel spheres set to vibration; the elastobuoyancy effect; elasticity mediated interaction of particles in soft solids as well as on thin films supported over a pool of liquid. We also presented some new results on how soft spherical gels undergo restricted spreading on rigid substrates with varying surface energies. In the first section, we studied how a thin confined layer of a soft elastic film loses adhesion from a rigid substrate by forming interfacial instabilities when a tensile stress is applied to it. We performed experiments to quantify the characteristic lengthscale of the patterns formed and found that they were significantly larger than the wavelengths of purely elastic instabilities. A linear stability analysis of the elastic field equations by taking into account the role of surface tension showed that the amplification of the wavelength is due to the role of elastocapillarity where the surface tension, elasticity, and film thickness contribute jointly in a non-trivial way. In addition, we found experimentally as well as theoretically that the stress required to adhesively fracture these films is much larger than Griffith’s fracture stress for stiffer elastic films, which is also due to the effect of elastocapillarity. We also studied the surface fluctuation of sessile hydrogel spheres subjected to mechanically-induced Gaussian white noise to understand the role of elastocapillarity in their oscillation modes. An important finding of this study is that they give a direct evidence that the surface tension of these elastic hydrogels is almost like that of water, which is the integral solvent in the swollen network of the polymeric gel. In the subsequent section, we introduced the new phenomenon of Elastobuoyancy. When a rigid sphere is placed on the surface of an ultrasoft hydrogel, it plunges into the soft substrate to an equilibrium depth where the elastic strain energy of the surrounding medium balances its weight. We refer to this state of the sphere as ‘Elastobuoyant’. By performing systematic experiments where we varied the sphere size and the elasticity of the substrate, we obtained scaling laws of the depth as a function of the radii, elastic modulus and the spheres buoyant weight, which were also supported by asymptotic analyses of the same. Following the section on elastobuoyancy, we reported a new set of principles to design self-assembly of particles by using the combined roles of surface tension, elasticity, and gravity in soft substrates. We used three different systems to study this elastic interaction macroscopically: (i) elastobuoyant assembly of particles suspended inside a soft elastic gel, (ii) elastocapillary assembly of particles floating on the surface of soft gels analogous to capillary attraction of objects on the surface of liquids, and (iii) assembly of particles on the surface of thin elastic membranes supported over a viscous liquid. In the second last chapter in this thesis, we presented some results on how soft elastic gel spheres spread on rigid substrates with different surface energies. Our observations indicate that their contact angles are slightly greater than those of equivalent liquid drops on similar substrates. The contact angles of these gel spheres increase as a function of elasticity and decrease when surface energy increases. We derived an expression for the excess elastic tension in the gel spheres at the crack tip by using an approach that is similar to estimating the viscous dissipation at the contact line during spreading of liquids. By using a general constitutive law where the elastic energy is not limited to the square of the strains, the singularity at the crack tip is artificially removed thereby forcing the gel to assume a liquid-like behavior. Our experimental results agreed reasonably well with the model. In the last chapter, we summarized the doctoral research and presented suggestions for future investigations. There are several appendices in this thesis that have interesting observations from partially completed projects that need additional research and analysis in the future

Periodic time dependent Hamiltonian systems and applications

[eng] A dynamical system is one that evolves with time. This definition is so diffuse that seems to be completely useless, however, gives a good insight of the vast range of applicability of this field of Mathematics has. It is hard to track back in the history of science to find the origins of this discipline. The works by Fibonacci, in the twelfth century, concerning the population growth rate of rabbits can be already considered to belong to the above mentioned field. Newton's legacy changed the prism through the humankind watched the universe and established the starting shot of several areas of knowledge including the study of difierential equations. Newton's second law relates the acceleration, the second derivative of the position of a body with the net force acting upon it. The formulation of the law of universal gravitation settled the many body problem, the fundamental question around the field of celestial mechanics has grown. Newton itself solved the two body problem, providing an analytical proof of Kepler's laws. In the subsequent years a number of authors, among of them Euler and Lagrange, exhausted Newton's powerful ideas but none of them was able to find a closed solution of the many body problem. By the end of the nineteenth century, Poincaré changed again the point of view: The French mathematician realized that the many body problem could not be solved in the sense his predecessors expected, however, many other fundamental questions could be addressed by studying the solutions of not quantitatively but by means of their geometrical and topological properties. The ideas that bloomed in Poincaré's mind are nowadays a source of inspiration for modern scientist facing problems located along all the spectrum of human knowledge. Poincaré understood that invariant structures organize the long term behaviour of the solutions of the system. Invariant objects are, therefore, the skeleton of the dynamics. These invariant structures and their linear normal behaviour are to be analyzed carefully and this shall lead to a good insight on global aspects of the phase space. For nonintegrable systems the task of studying invariant objects and their stability is, in general, a problem which is hard to be handled rigorously. Usually, the hypotheses needed to prove specific statements on the solutions of the systems reduce the applicability of the results. This is especially relevant in physical problems: Indeed, we cannot, for instance, choose the mass of Sun to be suficiently small. The advent of the computers changed the way to undertake studies of dynamical systems. The task of writing programs for solving, numerically, problems related to specific examples is, at the present time, as important as theoretical studies. This has two main consequences: On the first hand, more involved models can be chosen to study real problems and this allow us to understand better the relation between abstract concepts and physical phenomena. Secondly, even when facing fundamental questions on dynamics, the numerical studies give us data from which build our theoretical developments. Nowadays, a large number of commercial (or public) software packages helps scientist to study simple problems avoiding the tedious work to master numerical algorithms and programming languages. These programs are coded to work in the largest possible number of different situations, therefore, they do not have the eficiency that programs written specifically for a certain purpose have. Some of the computations presented in this dissertation cannot be performed by using commercial software or, at least, not in a reasonable amount of time. For this reason, a large part of the work presented here has to do with coding and debugging programs to perform numerical computations. These programs are written to be highly eficient and adapted to each problem. At the same time, the design is done so that specific blocks of the code can be used for other computations, that is, there exist a commitment between eficiency and reusability which is hard to achieve without having full control on the code. Under these guiding principles we undertake the study of applied dynamical systems according to the following stages: From a particular problem we get a simple model, then perform a number of numerical experiments that permits us to understand the invariant objects of the system, with that information, we can isolate the relevant phenomena and identify the key elements playing a role on it. Next, we try to find an even simpler model in which we can develop theoretical arguments and produce theorems that, with more effort, can be generalized or related to other problems which, in principle, seem to be difierent to the original one. Paraphrasing Carles Simó, from a physical problem we can take the lift to the abstract world, use theoretical arguments, come out with conclusions and, finally, lift down to the real world and apply these conclusions to specific problems (maybe not only the original one). This methodology has been developed in the last decades over the world when it turned out to outstand among the most powerful approaches to cope with problems in applied mathematics. The group of Dynamical Systems from Barcelona has been one of the bulwarks of this development from the late seventies to the present days. Following the guidelines presented in the previous section, we concern with several problems, mostly from the field of celestial mechanics but we also deal with a phenomenon coming from high energy physics. All these situations can be modeled by means of periodically time dependent Hamiltonian systems. To cope with those investigations, we develop software which can be used to perform computations in any periodically perturbed Hamiltonian system. We split the contents of this dissertation in two parts. The first one is devoted to general tolos to handle periodically time dependent Hamiltonians, even though we fill this first part with a number of illustrating examples, the goal is to keep the exposition in the abstract setting. Most of the contents of Part I deal with the development of software used to be applied in the second part. Some of the software has not been applied to the specific contents of Part II, this is left for future work. We also devote a whole chapter to some theoretical issues that, while are motivated by physical problems, they fall out of the category of periodic time dependent Hamiltonians. This splitting of contents has the intention of reecting, somehow, the basic methodological principles presented in the previous paragraph, keeping separated the abstract and the physical world but keeping in mind the lift

From Logic to Realism to Brighter Future for Humanity

This collection of articles explores a wide range of subject, from Godel’s incompleteness theorem, to possible technocalypse and neutrofuturology. Articles on historical debates on irrational number to electroculture, on vortex particle, or on different Neutrosophic applications are included

PSA 2016

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2016

PSA 2016

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2016

Evolutionary Computation

This book presents several recent advances on Evolutionary Computation, specially evolution-based optimization methods and hybrid algorithms for several applications, from optimization and learning to pattern recognition and bioinformatics. This book also presents new algorithms based on several analogies and metafores, where one of them is based on philosophy, specifically on the philosophy of praxis and dialectics. In this book it is also presented interesting applications on bioinformatics, specially the use of particle swarms to discover gene expression patterns in DNA microarrays. Therefore, this book features representative work on the field of evolutionary computation and applied sciences. The intended audience is graduate, undergraduate, researchers, and anyone who wishes to become familiar with the latest research work on this field