Nontrivial Solutions of Quasilinear Equations In BV

The existence of a nontrivial critical point is proved for a functional containing an area-type term. Techniques of nonsmooth critical point theory are applied.

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

Estudo sobre a detecção de invariância de escala discreta em sistemas com criticalidade auto-organizada

Recent studies have shown evidence of log-periodic behavior in non-hierarchical systems. An interesting fact is the emergence of such properties on rupture and breakdown of complex materials and financial failures. These may be examples of systems with self-organized criticality (SOC). In this work we study the detection of discrete scale invariance or log-periodicity. Theoretically showing the effectiveness of methods based on the Fourier Transform of the log-periodicity detection not only with prior knowledge of the critical point before this point as well. Specifically, we studied the Brazilian financial market with the objective of detecting discrete scale invariance in Bovespa (Bolsa de Valores de S˜ao Paulo) index. Some historical series were selected periods in 1999, 2001 and 2008. We report evidence for the detection of possible log-periodicity before breakage, shown its applicability to the study of systems with discrete scale invariance likely in the case of financial crashes, it shows an additional evidence of the possibility of forecasting breakage

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

Phase diagram of the bosonic double-exchange model

The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic (AFM) superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

Interplay between double-exchange, superexchange, and Lifshitz localization in doped manganites

Considering the disorder caused in manganites by the substitution Mn→Fe or Ga, we accomplish a systematic study of doped manganites begun in previous papers. To this end, a disordered model is formulated and solved using the variational mean-field technique. The subtle interplay between double exchange, superexchange, and disorder causes similar effects on the dependence of T_(C) on the percentage of Mn substitution in the cases considered. Yet, in La_(2/3)Ca_(1/3)Mn_(1-y)Ga_(y)O_(3) our results suggest a quantum critical point (QCP) for y ≈ 0.1–0.2, associated to the localization of the electronic states of the conduction band. In the case of La_(x)Ca_(x)Mn_(1-y)Fe_(y)O_(3) (with x = 1/3,3/8) no such QCP is expected.

On the Origin of Natural Antibody

Natural IgM (nIgM) is constitutively present in the serum, where it aids in the early control of viral and bacterial expansions. nIgM also plays a significant role in the prevention of autoimmune disease by promoting the clearance of cellular debris. However, the cells that maintain high titers of nIgM in the circulation had not yet been identified. Several studies have linked serum nIgM with the presence of fetal-lineage B cells, and others have detected IgM secretion directly by B1a cells in various tissues. Nevertheless, a substantial contribution of undifferentiated B1 cells to nIgM titers is doubtful, as the ability to produce large quantities of antibody (Ab) is a function of the phenotype and morphology of differentiated plasma cells (PCs). No direct evidence exists to support the claim that a B1-cell population directly produces the bulk of circulating nIgM. The source of nIgM thus remained uncertain and unstudied.

In the first part of this study, I identified the primary source of nIgM. Using enzyme-linked immunosorbent spot (ELISPOT) assay, I determined that the majority of IgM Ab-secreting cells (ASCs) in naïve mice reside in the bone marrow (BM). Flow cytometric analysis of BM cells stained for intracellular IgM revealed that nIgM ASCs express IgM and the PC marker CD138 on their surface, but not the B1a cell marker CD5. By spinning these cells onto slides and staining them, following isolation by fluorescence-activated cell sorting (FACS), I found that they exhibit the typical morphological characteristics of terminally differentiated PCs. Transfer experiments demonstrated that BM nIgM PCs arise from a progenitor in the peritoneal cavity (PerC), but not isolated PerC B1a, B1b, or B2 cells. Immunoglobulin (Ig) gene sequence analysis and examination of B1-8i mice, which carry an Ig knockin that prohibits fetal B-cell development, indicated that nIgM PCs differentiate from fetal-lineage B cells. BrdU uptake experiments showed that the nIgM ASC compartment contains a substantial fraction of long-lived plasma cells (LLPCs). Finally, I demonstrated that nIgM PCs occupy a survival niche distinct from that used by IgG PCs.

In the second part of this dissertation, I characterized the unique survival niche of nIgM LLPCs, which maintain constitutive high titers of nIgM in the serum. By using genetically deficient or Ab-depleted mice, I found that neither T cells, type 2 innate lymphoid cells, nor mast cells, the three major hematopoietic producers of IL-5, were required for nIgM PC survival in the BM. However, IgM PCs associate strongly with IL-5-expressing BM stromal cells, which support their survival in vitro when stimulated. In vivo neutralization of IL-5 revealed that, like individual survival factors for IgG PCs, IL-5 is not the sole supporter of IgM PCs, but is likely one of several redundant molecules that together ensure uninterrupted signaling. Thus, the long-lived nIgM PC niche is not composed of hematopoietic sources of IL-5, but a stromal cell microenvironment that provides multiple redundant survival signals.

In the final part of my study, I identified and characterized the precursor of nIgM PCs, which I found in the first project to be resident in the PerC, but not a B1a, B1b, or B2 cell. By transferring PerC cells sorted based on expression of CD19, CD5, and CD11b, I found that only the CD19+CD5+CD11b- population contained cells capable of differentiating into nIgM PCs. Transfer of decreasing numbers of unfractionated PerC cells into Rag1 knockouts revealed an order-of-magnitude drop in the rate of serum IgM reconstitution between stochastically sampled pools of 106 and 3x105 PerC cells, suggesting that the CD19+CD5+CD11b- compartment comprises two cell types, and that interaction between the two necessary for nIgM-PC differentiation. By transferring neonatal liver, I determined that the early hematopoietic environment is required for nIgM PC precursors to develop. Using mice carrying a mutation that disturbs cKit expression, I also found that cKit appears to be required at a critical point near birth for the proper development of nIgM PC precursors.

The collective results of these studies demonstrate that nIgM is the product of BM-resident PCs, which differentiate from a PerC B cell precursor distinct from B1a cells, and survive long-term in a unique survival niche created by stromal cells. My work creates a new paradigm by which to understand nIgM, B1 cell, and PC biology.

Gas-solid coexistence of adhesive spheres

In this note, the authors investigate whether the gas-liquid critical point can remain stable with respect to solidification for narrow attractive interactions down to the Baxter limit. Using a crude cell theory, the authors estimate the necessary conditions for this to be true. Possible realizations are briefly discussed.

Fermion Mass Generation without Spontaneous Symmetry Breaking

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.

Default Invariance: Naïve Category of Law and Finance

Default invariance is the idea that default does not change at any scale of law and finance. Default is a conserved quantity in a universe where fundamental principles of law and finance operate. It exists at the micro-level as part of the fundamental structure of every financial transaction, and at the macro- level, as a fixed critical point within the relatively stable phases of the law and finance cycle. A key point is that default is equivalent to maximizing uncertainty at the micro-level and at the macro-level, is equivalent to the phase transition where unbearable fluctuations occur in all forms of risk transformation, including maturity, liquidity and credit. As such, default invariance is the glue that links the micro and macro structures of law and finance. In this essay, we apply naïve category theory (NCT), a type of mapping logic, to these types of phenomena. The purpose of using NCT is to introduce a rigorous (but simple) mathematical methodology to law and finance discourse and to show that these types of structural considerations are of prime practical importance and significance to law and finance practitioners. These mappings imply a number of novel areas of investigation. From the micro- structure, three macro-approximations are implied. These approximations form the core analytical framework which we will use to examine the phenomena and hypothesize rules governing law and finance. Our observations from these approximations are grouped into five findings. While the entirety of the five findings can be encapsulated by the three approximations, since the intended audience of this paper is the non-specialist in law, finance and category theory, for ease of access we will illustrate the use of the mappings with relatively common concepts drawn from law and finance, focusing especially on financial contracts, derivatives, Shadow Banking, credit rating agencies and credit crises.

The Helmholtzian Equation: Stabilizing Mechanisms for Quadratic Nonlinear Fields

Hexagonal Resonant Triad patterns are shown to exist as stable solutions of a particular type of nonlinear field where no cubic field nonlinearity is present. The zero ‘dc’ Fourier mode is shown to stabilize these patterns produced by a pure quadratic field nonlinearity. Closed form solutions and stability results are obtained near the critical point, complimented by numerical studies far from the critical point. These results are obtained using a neural field based on the Helmholtzian operator. Constraints on structure and parameters for a general pure quadratic neural field which supports hexagonal patterns are obtained.

Physical and chemical kinetics of structural build-up of cement suspensions

Abstract : The structural build-up of fresh cement-based materials has a great impact on their structural performance after casting. Accordingly, the mixture design should be tailored to adapt the kinetics of build-up given the application on hand. The rate of structural build-up of cement-based suspensions at rest is a complex phenomenon affected by both physical and chemical structuration processes. The structuration kinetics are strongly dependent on the mixture’s composition, testing parameters, as well as the shear history. Accurate measurements of build-up rely on the efficiency of the applied pre-shear regime to achieve an initial well-dispersed state as well as the applied stress during the liquid-solid transition. Studying the physical and chemical mechanisms of build-up of cement suspensions at rest can enhance the fundamental understanding of this phenomenon. This can, therefore, allow a better control of the rheological and time-dependent properties of cement-based materials. The research focused on the use of dynamic rheology in investigating the kinetics of structural build-up of fresh cement pastes. The research program was conducted in three different phases. The first phase was devoted to evaluating the dispersing efficiency of various disruptive shear techniques. The investigated shearing profiles included rotational, oscillatory, and combination of both. The initial and final states of suspension’s structure, before and after disruption, were determined by applying a small-amplitude oscillatory shear (SAOS). The difference between the viscoelastic values before and after disruption was used to express the degree of dispersion. An efficient technique to disperse concentrated cement suspensions was developed. The second phase aimed to establish a rheometric approach to dissociate and monitor the individual physical and chemical mechanisms of build-up of cement paste. In this regard, the non-destructive dynamic rheometry was used to investigate the evolutions of both storage modulus and phase angle of inert calcium carbonate and cement suspensions. Two independent build-up indices were proposed. The structural build-up of various cement suspensions made with different cement contents, silica fume replacement percentages, and high-range water reducer dosages was evaluated using the proposed indices. These indices were then compared to the well-known thixotropic index (Athix.). Furthermore, the proposed indices were correlated to the decay in lateral pressure determined for various cement pastes cast in a pressure column. The proposed pre-shearing protocol and build-up indices (phases 1 and 2) were then used to investigate the effect of mixture’s parameters on the kinetics of structural build-up in phase 3. The investigated mixture’s parameters included cement content and fineness, alkali sulfate content, and temperature of cement suspension. Zeta potential, calorimetric, spectrometric measurements were performed to explore the corresponding microstructural changes in cement suspensions, such as inter-particle cohesion, rate of Brownian flocculation, and nucleation rate. A model linking the build-up indices and the microstructural characteristics was developed to predict the build-up behaviour of cement-based suspensions The obtained results showed that oscillatory shear may have a greater effect on dispersing concentrated cement suspension than the rotational shear. Furthermore, the increase in induced shear strain was found to enhance the breakdown of suspension’s structure until a critical point, after which thickening effects dominate. An effective dispersing method is then proposed. This consists of applying a rotational shear around the transitional value between the linear and non-linear variations of the apparent viscosity with shear rate, followed by an oscillatory shear at the crossover shear strain and high angular frequency of 100 rad/s. Investigating the evolutions of viscoelastic properties of inert calcite-based and cement suspensions and allowed establishing two independent build-up indices. The first one (the percolation time) can represent the rest time needed to form the elastic network. On the other hand, the second one (rigidification rate) can describe the increase in stress-bearing capacity of formed network due to cement hydration. In addition, results showed that combining the percolation time and the rigidification rate can provide deeper insight into the structuration process of cement suspensions. Furthermore, these indices were found to be well-correlated to the decay in the lateral pressure of cement suspensions. The variations of proposed build-up indices with mixture’s parameters showed that the percolation time is most likely controlled by the frequency of Brownian collisions, distance between dispersed particles, and intensity of cohesion between cement particles. On the other hand, a higher rigidification rate can be secured by increasing the number of contact points per unit volume of paste, nucleation rate of cement hydrates, and intensity of inter-particle cohesion.

Phase Transitions in Engineered Ultracold Quantum Systems

The study of quantum degenerate gases has many applications in topics such as condensed matter dynamics, precision measurements and quantum phase transitions. We built an apparatus to create 87Rb Bose-Einstein condensates (BECs) and generated, via optical and magnetic interactions, novel quantum systems in which we studied the contained phase transitions. For our first experiment we quenched multi-spin component BECs from a miscible to dynamically unstable immiscible state. The transition rapidly drives any spin fluctuations with a coherent growth process driving the formation of numerous spin polarized domains. At much longer times these domains coarsen as the system approaches equilibrium. For our second experiment we explored the magnetic phases present in a spin-1 spin-orbit coupled BEC and the contained quantum phase transitions. We observed ferromagnetic and unpolarized phases which are stabilized by the spin-orbit coupling’s explicit locking between spin and motion. These two phases are separated by a critical curve containing both first-order and second-order transitions joined at a critical point. The narrow first-order transition gives rise to long-lived metastable states. For our third experiment we prepared independent BECs in a double-well potential, with an artificial magnetic field between the BECs. We transitioned to a single BEC by lowering the barrier while expanding the region of artificial field to cover the resulting single BEC. We compared the vortex distribution nucleated via conventional dynamics to those produced by our procedure, showing our dynamical process populates vortices much more rapidly and in larger number than conventional nucleation.

Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.