As transformações de fase em cristais de cianeto de potássio (KCN) a 168&#176K e 83&#176K e suas ligas com KC1, foram estudadas através da absorção ótica no infravermelho do íon de impureza OCN&#8254 e dos íons CN&#8254 da rede. Por aplicação de tensão uniaxial foram obtidos pela primeira vez cristais únicos, da KCN-KCl, nas duas fases de mais baixa temperatura. A absorção ótica dicróica devida à vibração interna do íon CN&#8254 nesses monocristais, permitiu a determinação de seu arranjo estrutural direcional, de forma inequívoca, como também correções a modelo recentemente proposto para esse arranjamento, baseado em experiências com cristais de muitos domínios. O estudo do modo de flexão da impureza OCN&#8254 permitiu o seguimento das transformações de fase anteriormente observadas por meio de medidas de calor específico em cristais puros de KCN. A evolução dessas transformações em função da concentração do íon esférico de Cl&#8254 em substituição do íon elipsoidal CN&#8254 foi estudada numa larga faixa de concentrações. Um modelo para a fase de mais baixa temperatura e proposto com arranjo antiferroelétrico dos dipolos CN&#8254 e com distinção na sub-rede dos íons positivos. Em vista do modelo proposto, duas alternativas para as duas transições de fase poderiam ocorrer. Na transição de mais alta temperatura (168&#176K), ocorreria o alinhamento ferroelástico e antiferroelétrico, dos dipolos CN&#8254, e a transição de mais baixa temperatura (83&#176K) corresponderia somente à distorção na sub-rede dos íons positivos (e possivelmente dos negativos). Na outra possibilidade, a 168&#176K ocorreria somente um arranjo ferroelástico e a 83&#176K o arranjo antiferroelétrico e a distorção na rede. / The phase transformations in potassium cyanide crystals (KCN) at 168&#176K and 83&#176K and KCN-KCl mixed crystals, were studied through the I-r optical absorption of the CN&#8254 stretching mode and the OCN&#8254 impurity bending mode and Fermi resonance application of uniaxial stress in KCN-KCl mixed crystals gives, by the first time, oriented single crystals in the lower temperature phases. The dichroic optical absorption of the CN&#8254 stretching mode in these oriented single crystals allowed the explicit determination of the structural arrangement of the C\'N POT.-\' dipole. The results of our measurements are not in agreement recently proposed by Julian and Luty based on electrical experiments with polidomain crystals. The bending mode and Fermi resonances of the substitutional OC\'N POT.\'impurity give further information in agreement with previous specif heat measurements. The evolution of the phase transformation was studied as a function of the spheroidal Cl&#8254 íon concentration replacing the CN&#8254 ellipsoidal íon. A model for the lower temperature phase is proposed with antiferroelectric ordering of the CN&#8254 dipoles and additional distortion on positive and negative sub lattices. As a consequence of the proposed model the phase transitions, may occur in two different ways that can not be distinguished with the used techniques. In the first possibility during the higher temperature phase transition (168&#176K) would occur the ferroelastic and antiferroelectric alignement of the CN&#8254 dipoles and the lower phase transition (83&#176K) would be due to a lattice distortion as necessary to explain our results. In the other possibility the 168&#176K phase transition would occur only the ferroelastic transition;and at 83&#176K the antiferroelectric ordering of the CN&#8254 ions and the lattice distortion would occur

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.

In this study, we researched three kinds of surface treatment (no surface treatment, homogeneous alignment (HA) and vertical alignment (VA)) effect for the optoelectronic properties of cholesteric blue phase liquid crystals (BPLCs). We demonstrate the surface treatments have influence on the temperature range of BPLCs. The VA-BPLC possesses the widest temperature range, about 6.0 ¢J. The temperature range of both no surface treatment BPLC and HA-BPLC are about 5.5 ¢J. In the process of cooling, the surface treatments will restrain the change of the pitch of BPLC. Besides, surface treatment will let the crystalline of BPLC shipshape, so that it can reduce the scattering of the reflection light of BPLC. In the vertical electric field, the reflection wavelength of BPLC will be red-shift when the applied voltage increased. The reflection wavelength of the HA-BPLC can be tuned about 90 nm. The reflection wavelength of the VA-BPLC can be tuned about 120 nm. We have demonstrated the treatment of vertical alignment will reduce the operating voltage of BPLC.

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.

A recent line of works established a remarkable connection for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree \Delta undergoes a computational transition that coincides with the statistical physics uniqueness/non-uniqueness phase transition on the infinite \Delta-regular tree. Despite this clear picture for 2-spin systems, there is little known for multi-spin systems. We present the first analog of the above inapproximability results for multi-spin systems. The main difficulty in previous inapproximability results was analyzing the behavior of the model on random \Delta-regular bipartite graphs, which served as the gadget in the reduction. To this end one needs to understand the moments of the partition function. Our key contribution is connecting: (i) induced matrix norms, (ii) maxima of the expectation of the partition function, and (iii) attractive fixed points of the associated tree recursions (belief propagation). We thus obtain a generic analysis of the Gibbs distribution of any multi-spin system on random regular bipartite graphs. We also treat in depth the k-colorings and the q-state antiferromagnetic Potts models. Based on these findings, we prove that for \Delta constant and even k<\Delta, it is NP-hard to approximate within an exponential factor the number of k-colorings on triangle-free \Delta-regular graphs. We also prove an analogous statement for the antiferromagnetic Potts model. Our hardness results for these models complement the conjectured regime where the models are believed to have efficient approximation schemes. We systematize the approach to obtain a general theorem for the computational hardness of counting in antiferromagnetic spin systems, which we ultimately use to obtain the inapproximability results for the k-colorings and q-state antiferromagnetic Potts models, as well as (the previously known results for) antiferromagnetic 2-spin systems. The criterion captures in an appropriate way the statistical physics uniqueness phase transition on the tree.