Fazemos inicialmente uma breve exposição sobre os fundamentos da Termodinâmica Clássica Holotrópica, desenvolvida por N. Bernardes. Esta consiste em formular o problema da Termodinâmica tomando como grandeza fundamental a entropia de um universo ( - sistema Isolado); no caso de um universo clássico composto esta é igual a soma das entropias de suas partes. Postulamos um principio dinâmico suficiente para a validade da segunda lei da Termodinâmica, o qual implica que os máximos dessa soma são estados estacionários estáveis do universo. Somos levados naturalmente a perguntar o que acontece se a entropia do universo possuir mais do que um máximo; a resposta a isso é o tratamento que daremos ao fenômeno de transição de fase. Analisamos em detalhe o universo composto por um corpo pequeno (cuja entropia é por hipótese analítica) e reservatórios de calor e trabalho. Para que a entropia do universo possua mais que um máximo a entropia do corpo pequeno não pode ser côncava em todo seu domínio; assumindo uma forma particular para ela (deslocamento de Bernardes) analisaremos o equilíbrio entre duas fases e o comportamento em torno do ponto onde a curva de coexistência termina (ponto crítico isolado). Com isto será possível dar uma visão clara e bastante intuitiva do fenômeno de transição de fase dito \"de primeira ordem\". Tendo em mente o significado físico das transformadas de Legendre da entropia do corpo pequeno (transparente na formulação holotrópica) compreenderemos o sentido das descontinuidades de primeira e segunda ordem que afetam as funções termodinâmicas que descrevem o equilíbrio do universo, com o que não veremos razão alguma para classificar as transições de fase da maneira que assim fez Ehrenfest. Veremos também, e isto é muito importante, que a Termodinâmica Clássica não consegue explicar a singularidade no calor específico que se verifica experimentalmente num ponto crítico, sendo que esta falha é intrínseca ou à Termodinâmica clássica ou à hipótese da entropia do corpo pequeno ser contínua e diferenciável. / We make initially a short exposition about the fundaments of Holotropic classical thermodynamics, developed by N. Bernardes. This is the formulation of the thermodynamic problem taking the entropy of a universe (isolated system) as the fundamental variable. In a classical composite universe it is the sum of the entropies of its parts. We postulate a dynamic principle sufficient for the validity of the second law of Thermodynamics, which implies that the maxima of that sum are stable stationary states of the universe. We arrive at the question about what occurs when the entropy of the universe possesses more than one maximum; the answer is the treatment we will give to the phenomena of phase transition. We analyze in detail the universe composed by a small body (whose entropy is analytical by hypothesis) and heat and work reservoirs. The entropy of the small body must be not concave in all of its dominium for the entropy of universe to have more than one maximum; we make a particular choice for it (Bernardes displacement) in order to analyze equilibrium between two phases and the behavior around the point where the coexistence curve terminates (isolated critical point). With this it will be possible to have a clear and intuitive grasp of the phenomena called \"first order\" phase transition. Keeping in mind the physical meaning of the Legendre transforms of the entropy of the small body we will understand the meaning of the first and second order discontinuities that affect the thermodynamic functions which describe the equilibrium state of the universe. We will see no reason to classify phase transitions the way Ehrenfest did. We will see also, and this is a very important thing, that classical Thermodynamics cannot explain the singularity that occurs in specific heat at a critical point. This failure is intrinsic to classical Thermodynamics or to the hypothesis that the small body entropy is a continuous and differentiable function.

Fazemos inicialmente uma breve exposição sobre os fundamentos da Termodinâmica Clássica Holotrópica, desenvolvida por N. Bernardes. Esta consiste em formular o problema da Termodinâmica tomando como grandeza fundamental a entropia de um universo ( - sistema Isolado); no caso de um universo clássico composto esta é igual a soma das entropias de suas partes. Postulamos um principio dinâmico suficiente para a validade da segunda lei da Termodinâmica, o qual implica que os máximos dessa soma são estados estacionários estáveis do universo. Somos levados naturalmente a perguntar o que acontece se a entropia do universo possuir mais do que um máximo; a resposta a isso é o tratamento que daremos ao fenômeno de transição de fase. Analisamos em detalhe o universo composto por um corpo pequeno (cuja entropia é por hipótese analítica) e reservatórios de calor e trabalho. Para que a entropia do universo possua mais que um máximo a entropia do corpo pequeno não pode ser côncava em todo seu domínio; assumindo uma forma particular para ela (deslocamento de Bernardes) analisaremos o equilíbrio entre duas fases e o comportamento em torno do ponto onde a curva de coexistência termina (ponto crítico isolado). Com isto será possível dar uma visão clara e bastante intuitiva do fenômeno de transição de fase dito \"de primeira ordem\". Tendo em mente o significado físico das transformadas de Legendre da entropia do corpo pequeno (transparente na formulação holotrópica) compreenderemos o sentido das descontinuidades de primeira e segunda ordem que afetam as funções termodinâmicas que descrevem o equilíbrio do universo, com o que não veremos razão alguma para classificar as transições de fase da maneira que assim fez Ehrenfest. Veremos também, e isto é muito importante, que a Termodinâmica Clássica não consegue explicar a singularidade no calor específico que se verifica experimentalmente num ponto crítico, sendo que esta falha é intrínseca ou à Termodinâmica clássica ou à hipótese da entropia do corpo pequeno ser contínua e diferenciável. / We make initially a short exposition about the fundaments of Holotropic classical thermodynamics, developed by N. Bernardes. This is the formulation of the thermodynamic problem taking the entropy of a universe (isolated system) as the fundamental variable. In a classical composite universe it is the sum of the entropies of its parts. We postulate a dynamic principle sufficient for the validity of the second law of Thermodynamics, which implies that the maxima of that sum are stable stationary states of the universe. We arrive at the question about what occurs when the entropy of the universe possesses more than one maximum; the answer is the treatment we will give to the phenomena of phase transition. We analyze in detail the universe composed by a small body (whose entropy is analytical by hypothesis) and heat and work reservoirs. The entropy of the small body must be not concave in all of its dominium for the entropy of universe to have more than one maximum; we make a particular choice for it (Bernardes displacement) in order to analyze equilibrium between two phases and the behavior around the point where the coexistence curve terminates (isolated critical point). With this it will be possible to have a clear and intuitive grasp of the phenomena called \"first order\" phase transition. Keeping in mind the physical meaning of the Legendre transforms of the entropy of the small body we will understand the meaning of the first and second order discontinuities that affect the thermodynamic functions which describe the equilibrium state of the universe. We will see no reason to classify phase transitions the way Ehrenfest did. We will see also, and this is a very important thing, that classical Thermodynamics cannot explain the singularity that occurs in specific heat at a critical point. This failure is intrinsic to classical Thermodynamics or to the hypothesis that the small body entropy is a continuous and differentiable function.

No description available.

A recent breakthrough in information theory known as compressive sensing is one component of an ongoing revolution in data acquisition and processing that guides one to acquire less data yet still recover the same amount of information as traditional techniques, meaning less resources such as time, detector cost, or power are required. Starting from these basic principles, this thesis explores the application of these techniques to imaging. The first laboratory example we introduce is a simple infrared camera. Then we discuss the application of compressive sensing techniques to hyperspectral microscopy, specifically Raman microscopy, which should prove to be a powerful technique to bring the acquisition time for such microscopies down from hours to minutes. Next we explore a novel sensing architecture that uses partial circulant matrices as sensing matrices, which results in a simplified, more robust imaging system. The results of these imaging experiments lead to questions about the performance and fundamental nature of sparse signal recovery with partial circulant compressive sensing matrices. Thus, we present the results of a suite of numerical experiments that show some surprising and suggestive results that could stimulate further theoretical and applied research of partial circulant compressive sensing matrices. We conclude with a look ahead to adaptive sensing procedures that allow real-time, interactive optical signal processing to further reduce the resource demands of an imaging system.

Dimerized antiferromagnetic spin-1/2 chains and ladders demonstrate quantum critical phase transition, the existence or absence of which is dependent on the dimerization and the dimerization pattern of the chain and the ladder, respectively. The gapped phases can not be distinguished by the conventional Landau long-range order parameters. However, they possess non-local topological string order parameters which can be used to classify different phases. We utilize the self-consistent free fermionic approximation and some standard results for exactly solved models to analytically calculate the string order parameters of dimerized spin chains. As a complement parameter the gapped phases possess the topological number, called the winding number and they are characterized by different integer values of the winding number. In order to calculate the string order parameters and winding numbers in dimerized spin chains and two-leg ladders we use analytical methods such as the Jordan-Wigner transformation, mean-field approximation, duality transformations, and some standard results available for the exactly 1D solve models. It is shown that the winding number provides the complementary framework to the string order parameter to characterize the topological gapped phases.

No description available.

No description available.

We have investigated several topics in the area of manganites including oxygen disorder, grain boundaries, low field magnetoresistance, magnetoresistive anisotropy and magnetic properties. Studied materials were in the form of polycrystalline samples and epitaxial thin films. The studied compounds were Sm(1-x)Sr(x)MnO3 (SSMO) and La(1-x)Ca(x)MnO3 (LCMO). 1-We have studied the effects of oxygen disorder and grain boundary disorder in the SSMO system close to half hole doping level. The temperature dependencies of resistivity and magnetoresistance were measured as a function of the vacuum annealing time. We observed a logarithmic increase of the resistivity as a function of vacuum annealing time. We have shown that an increasing grain boundary disorder softens the magnetic phase transition from a first order phase transition into a second order transition. Furthermore, the peaks in the resistivity and specific heat are broadened and there is an increase in the charge-carrier scattering rates in the metallic state. On the other hand, the polaronic hopping activation energies in the insulating state changed slightly as a function of grain boundary disorder. The origin of these phenomena is discussed. Magnetoresistive anisotropy has been studied as a function of the grain size. Results showed a strong grain size dependence of anisotropic electrical transport in granular samples of manganites. 2-We investigated the anisotropic magnetoresistance (AMR) in ultrathin LCMO films grown on various substrates. It was found that depending on the strain state, the AMR in some of these systems exceeds 100% and can even change sign. These changes are dramatic when compared to the few percent change in AMR in conventional ferromagnets. The mechanism behind these changes in the AMR is discussed. We have also studied the effects of strain on resistive peak broadening with a simple percolation model. We have shown that strain associated with a lattice mismatched substrate in thin films can cause new electronic behavior, not found in bulk materials or thicker films of the same chemical composition. Resistivity of the ultra thin films exhibit strong relaxation effects when measured as a function of time in a constant magnetic field.

In the practice of solid state chemistry, structural phase transitions are fairly common events. Nonetheless, their understanding, in terms of both: A rationalization of the observed changes in symmetry pattern and; An understanding of the mechanisms allowing for a particular transformation, are outstanding problems. The thermodynamic classification of phase transitions distinguishes between first and second order transitions, on the basis of the discontinuous behavior of quantities related to first or second derivatives of the free energy, respectively. Small atomic displacements are typically associated with second order phase transitions, and latent heat changes amount to a few calories per gram only. Additionally, the symmetries of the phases surrounding the transition are typically in the relation of a group and a subgroup. Reconstructive phase transitions, on the contrary, involve breaking of (large) parts of the bond scaffolding of the initial structure, and exhibit drastic changes at the transition point, with large latent heat and hysteresis effects. The corresponding atomic displacements can be in the order of the lattice parameters, and no group-subgroup is found, between the symmetry of the phases. These type of transitions have generally a strong first-order character. Landau theory accounts for continuous, second-order phase transitions. As a phenomenological theory, it does not establish the existence of a phase transition, which remains an experimental fact. It only bridges microscopic characteristics, like space-group symmetries and structural changes, or phonon softening effects, with measurable macroscopic quantities. Therein, distortions are carried by an order parameter, which fully specifies the form of the analytical variational free energy. The latter is continuous and derivable with respect to temperature, pressure and atomic displacement, at the transition point. First order, non-continuous phase transitions are still within the scope of Landau theory in the mentioned special case of the existence of a group-to-(isotropic) subgroup relationship. In the majority of cases, however, and for the most interesting phase transitions (for basic and applied research), such a relationship is missing, making the choice of an order parameter less straightforward. Most of the allotropic transformations of the elements, many intermetallic systems, and numerous insulating systems belongs to this class. This class also includes most interesting and fundamental electronic effects, like metallization in perovskites or spinel oxides for example. This very simple fact of a missing symmetry condition has helped reinforcing the opinion of first-order phase transitions being a world apart, and possibly contributed to discouraging a firm theory to develop, able to account for their transformation mechanisms and the change of physical properties across phase transition. The thermodynamic distinction between first and second order phase transitions is too narrow, as, in case of first order phase transitions, it embraces both weakly discontinuous transition and reconstructive ones, where bonds are being strongly modified. Especially, a mean to qualify the distance between two structures (geometric, with respect to symmetry, a.s.o.), is missing. Clearly, a group-subgroup relationship may, and typically does imply shortest shifting distances, as a tiny atomic displacement can already do for a symmetry lowering. Naively, missing such a relation means no constraints, and apparently no means to conclude at a connection of two structures in general, let alone a full mechanistic analysis. First order phase transitions proceed by nucleation and subsequent growth of the new phase from the initial one. Different from (second-order) continuous phase transitions, they do imply coexistence of the transforming motifs. The discontinuity in some order parameter between the two phases is driven by lowering of the free energy as the new phase forms. However, close to the transition, the original phase remains metastable, and a fluctuation is needed to cause the formation of the new phase to set in. Such a process responds to thermal changes, and depending on the height of the nucleation barrier, its rate may be slower or faster. In the former case, large deviations from equilibrium may be required to achieve transformation to the stable phase, which means that large hysteresis effects will be observed in the course of transformation. The intent of this work consists in giving a face to the intermediate configurations appearing in first order phase transitions, in solid-solid reconstructive processes. Apart of a mechanistic elucidation, consisting in answering the question “Which atomic displacements bring structural motif A into structural motif B ?”, another purpose of this work is a rather pedagogical one, that is, showing that first-order phase transitions can be understood in detail, not only in principle but in fact. The core of the examples illustrated in this work is concerned with phase transformations where pressure represents the thermodynamic controlling parameter. Pressure is extensively used in chemical synthesis, as a mean to achieve novel properties, optical or mechanical just to mention a few. Additionally, reports on novel high-pressure polymorphs are regularly appearing. In this sense, pressure is a relevant parameter for approaching fundamental questions in solid state chemistry.

The magnetocaloric and thermomagnetic properties of the Ni1-xCrxMnGe1.05 (for x = 0, 0.035, 0.070, 0.105, 0.110, 0.115, and 0.120) system have been studied by X-ray diffraction, differential scanning calorimetry (DSC), resistivity and magnetization measurements. A change in crystal structure from orthorhombic to hexagonal was observed in the XRD data with an increase in chromium concentrations. The values of the cell parameters and volume of the unit cell for hexagonal phase were determined. It was found that the partial substitution of Cr for Ni in Ni1-xCrxMnGe1.05 results in a first order magnetostructural transition from antiferromagnetic to ferromagnetic (FM) at TM of about132 K, 100 K, and 110 K for x= 0.105, 0.115, and 0.120, respectively. A FM to paramagnetic second order transition has been observed at TC around 200K. A magnetic entropy change of = 4.5 J/kg K, 5.6 J/Kg K, and 5.06 J/Kg K was observed in the vicinity of TC for x = 0.105, 0.115, and 0.120 respectively at ΔH = 5T. The values of the latent heat and corresponding total entropy changes have been determined from Differential Scanning Calorimetry (DSC) measurements. Magnetoresistance values of about -5% were measured near TC for x =0.105. The maximum value of refrigeration capacity (RC) and relative cooling power (RCP) was found to be 155 J/Kg and 175 J/Kg respectively for x = 0.120. A concentration-dependent (T-x) phase diagram of transition temperatures has been constructed using the magnetic and DSC data. The structural, magnetic and magnetocaloric properties of GdNi2Mnx system (for x = 0.5, 0.6, 0.8, 1.0, 1.2, 1.4, 1.5) have been studied by x-ray diffraction and magnetization measurements. A mixture of the Laves phase C15 and a phase with rhombohedral structure PuNi3- type (space group R m) was observed in the XRD data. A second order magnetic phase transition from ferromagnetic (FM) to paramagnetic (PM) was found, characterized by a long-range exchange interaction as predicted by mean field theory. The maximum value of magnetic entropy changes, -∆SM, near TC for ∆H = 5T, was found to be 3.1 J/KgK, 2.8 J/KgK, 2.9 J/KgK, and 2.5 J/Kg K for x = 0.8, 1.2, 1.4, and 1.5 respectively. In spite of the low values of ΔSM, the RC and RCP value was found to be 176 J/Kg and 220 J/Kg for the GdNi2Mn0.8 compound, respectively.