Optical trapping of a cube

The successful development and optimisation of optically-driven micromachines will be greatly enhanced by the ability to computationally model the optical forces and torques applied to such devices. In principle, this can be done by calculating the light-scattering properties of such devices. However, while fast methods exist for scattering calculations for spheres and axisymmetric particles, optically-driven micromachines will almost always be more geometrically complex. Fortunately, such micromachines will typically possess a high degree of symmetry, typically discrete rotational symmetry. Many current designs for optically-driven micromachines are also mirror-symmetric about a plane. We show how such symmetries can be used to reduce the computational time required by orders of magnitude. Similar improvements are also possible for other highly-symmetric objects such as crystals. We demonstrate the efficacy of such methods by modelling the optical trapping of a cube, and show that even simple shapes can function as optically-driven micromachines.

Effects of cation substitutions on the physical properties of M2M1T2O6 pyroxenes

In this PhD study, the effects of the cation substitutions on the physical properties of pyroxenes have been discussed. The results of this work extend the knowledge on pyroxenes with different chemical compositions. These properties might be used in the development of ceramic pigments, advanced materials and for the mineralogical phase identification. First of all, the crystallographic differences between Ge and Si pyroxenes have been examined. The structure of C2/c Ca rich Ge clinopyroxenes is very close to the low pressure C2/c structural configuration found in Ca-rich Si-pyroxenes. The shear of the unit cell is very similar, and the difference between a Ge end member and the corresponding Si-rich one is less than 1°. Instead, a remarkable difference exists between Ca-poor Si and Ge clinopyroxenes. First, Ca-poor Ge pyroxenes do not display a P21/c symmetry, but retain the C2/c symmetry; second, the observed C2/c structure shows, at room pressure, the configuration with highly kinked tetrahedral chains characteristic of the high pressure C2/c symmetry of Si Ca-poor pyroxenes. In orthopyroxenes, with Pbca symmetry, Ge-pyroxenes have volume larger than Si-pyroxenes. Samples along the system CaCoGe2O6 - CoCoGe2O6 have been synthesized at three different temperatures: 1050 °C, 1200 °C and 1250 °C. The aim of these solid state syntheses was to obtain a solid solution at ambient pressure, since the analogues Si-system needs high pressure. Unfortunately, very limited solution occurs because the structure forms of the two end member (high temperature for CaCoGe2O6 and high pressure CoCoGe2O6) are incompatible. The phase diagram of this system has been sketched and compared to that of Si. The cobalt end member (CoCoGe2O6) is stable at ambient pressure in two symmetries: at 1050 °C C2/c and 1200 °C Pbca. The impurity phase formed during these experiments is cobalt spinel. Raman spectroscopy has been used to investigate the vibrational properties of Ca-pyroxenes CaCoGe2O6, CaMgGe2O6, CaMgSi2O6 and CaCoSi2O6. A comparison between silicate and germanate pyroxenes shows significant changes in peak positions of the corresponding modes caused mainly by the difference of the Ge-Si atomic weight along with the distortion and compression of the coordination polyhedra. Red shift in Raman spectra of germanates has been calculated by a rough scale factor calculated by a simple harmonic oscillator model, considering the different bond lengths for 4-coordinated Si ~ 1.60- 1.65 Å vs Ge–O distance ~1.70 - 1.80 Å. The Raman spectra of CaMgGe2O6 and CaCoGe2O6 have been classified, in analogy with silicate (Wang et al., 2001) counterparts, in different ranges: - R1 (880-640 cm-1): strong T-O stretching modes of Ge and non-bridging O1 and O2 atoms within the GeO4 tetrahedron; - R2 (640-480 cm-1): stretching/bending modes of Ge-Obr-Ge bonds (chain stretching and chain bending); - R4 (480-360 cm-1): O-Ge-O vibrations; - R3 (360-240 cm-1): motions of the cations in M2 and M1 sites correlated with tetrahedral chain motion and tilting tetrahedra; - R5 (below 240 cm-1): lattice modes. The largest shift with respect to CaMgSi2O6 - CaCoSi2O6 is shown by the T-O stretching and chain modes. High-pressure Raman spectroscopy (up to about 8 GPa) on the same samples of Ca-pyroxenes using an ETH-type diamond anvil cell shows no phase transition within the P-ranges investigated, as all the peak positions vary linearly as a function of pressure. Our data confirm previous experimental findings on Si-diopside (Chopelas and Serghiou, 2000). In the investigated samples, all the Raman peaks shift upon compression, but the major changes in wavenumber with pressure are attributed to the chain bending (Ge-Obr-Ge bonds) and tetrahedra stretching modes (Ge-Onbr). Upon compression, the kinking angle, the bond lengths and T-T distances between tetrahedra decrease and consequently the wavenumber of the bending chain mode and tetrahedra stretching mode increases. Ge-pyroxenes show the higher P-induced peak-position shifts, being more compressible than corresponding silicates. The vibrational properties of CaM2+Ge2O6 (M2+ =Mg, Mn, Fe, Co, Ni, Zn) are reported for the first time. The wavenumber of Ge-Obr-Ge bending modes decreases linearly with increasing ionic radius of the M1 cation. No simple correlation has been found with M1 atomic mass or size or crystallographic parameters for the peak at ~850 cm-1 and in the low wavenumber regions. The magnetic properties of the system CaCoSi2O6 - CoCoSi2O6 have been investigated by magnetometry. The join is always characterized by 1 a.p.f.u. of cobalt in M1 site and this causes a pure collinear antiferromagnetic behaviour of the intra-chain superexchange interaction involving Co ions detected in all the measurements, while the magnetic order developed by the cobalt ions in M2 site (intra-chain) is affected by weak ferromagnetism, due to the non-collinearity of their antiferromagnetic interaction. In magnetically ordered systems, this non-collinearity effect promotes a spin canting of anti-parallel aligned magnetic moments and thus is a source of weak ferromagnetic behaviour in an antiferromagnetic. The weak ferromagnetism can be observed only for the samples with Co content higher than 0.5 a.p.f.u. in M2, when the concentration is sufficiently high to create a long range order along the M2 chain which is magnetically independent of M1 chain. The ferromagnetism was detected both in the M(T) at 10 Oe and M(H).

Phase transitions in wave turbulence

We consider turbulence within the Gross-Pitaevsky model and look into the creation of a coherent condensate via an inverse cascade originating at small scales. The growth of the condensate leads to a spontaneous breakdown of statistical symmetries of overcondensate fluctuations: First, isotropy is broken, then a series of phase transitions marks the changing symmetry from twofold to threefold to fourfold. We describe respective anisotropic flux flows in the k space. At the highest level reached, we observe a short-range positional and long-range orientational order (as in a hexatic phase). In other words, the more one pumps the system, the more ordered the system becomes. The phase transitions happen when the system is pumped by an instability term and does not occur when pumped by a random force. We thus demonstrate nonuniversality of an inverse-cascade turbulence with respect to the nature of small-scale forcing.

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.

Anisotropia magnética em nanofilmes com assimetria cristalográfica

This Thesis comprises a theoretical study about the influence of the magnetocrystalline anisotropy on the static and dynamic magnetic properties of nanofilms: monolayers and trilayers coupled through the bilinear and biquadratic exchange fields, for situations in which the systems are grown in unusual [hkl] asymmetric directions. Using a theory based on a realistic phenomenological model for description of nanometric systems, we consider the total free magnetic energy including the Zeeman interaction, cubic and uniaxial anisotropies, demagnetizing and surface anysotropy energies, as well as the exchange terms. Numerical calculations are conducted by minimizing the total magnetic energy from the determination of equilibrium static configurations. We consider experimental parameters found in the literature to illustrate our results for Fe/Cr/Fe trilayer systems. In particular, a total of six different magnetic scenarios are analyzed for three regimens of exchange fields and the [211] and [321] asymmetric growth directions. After numerically minimize the total energy, we use the equilibrium configurations to calculate magnetization and magnetoresistance curves with the respective magnetic phases and corresponding critical fields. These results are also used to establish the boundary for occurrence of saturated states. Within the context of the spin waves, we solve the equation of motion for these systems in order to find the respective associated dispersion relations. The results show similar magnetization and magnetoresistance curves for both [211] and [321] growth scenarios, including an equivalent magnetic transition behavior. However, the combination of those peculiar symmetries and influence of the exchange energies results in attractive properties, including the generation of magnetic states as a function of the asymmetric degree imposed in the [hkl] growth orientations. There is also an increasing incompatibility between the values of saturation fields of magnetization and magnetoresistance for the cases in which a magnetic field acts along intermediate cubic anisotropic axes, particularly in the situations where the bilinear and biquadratic exchange fields are comparable. The dispersion relations and static results are consistent, the corresponding magnetic states are also present in both acoustic and optical modes. Furthermore, Goldstone excitations are also observed for that particular cases of a magnetic field acting in the intermediate axes, an effect related to transitions of second order and to the spontaneous symmetry breaking imposed by the combination of the biquadratic energy with the cubic and uniaxial anisotropies.

Disformal scalars as dark matter candidates: Branon phenomenology

Scalar particles coupled to the Standard Model fields through a disformal coupling arise in different theories, such as massive gravity or braneworld models. We will review the main phenomenology associated with such particles. Distinctive disformal signatures could be measured at colliders and with astrophysical observations. The phenomeno-logical relevance of the disformal coupling demands the introduction of a set of symmetries, which may ensure the stability of these new degrees of freedom. In such a case, they constitute natural dark matter candidates since they are generally massive and weakly coupled. We will illustrate these ideas by paying particular attention to the branon case, since these questions arise naturally in braneworld models with low tension, where they were first discussed.

Ordered magnetic dipoles: controlling anisotropy in nanomodulated continuous ferromagnetic films

In this paper, the research focus is how to entangle magnetic dipoles to control/engineer magnetic properties of different devices at a submicron/nano scale. Here, we report the generation of synthetic arrays of tunable magnetic dipoles in a nanomodulated continuous ferromagnetic film. In-plane magnetic field rotations in modulated Ni 45Fe 55 revealed various rotational symmetries of magnetic anisotropy due to dipolar interaction with a crossover from lower to higher fold as a function of modulation geometry. Additionally, the effect of aspect ratio on symmetry shows a novel phase shift of anisotropy, which could be critical to manipulate the overall magnetic properties of the patterned film. The tendency to form vortex is in fact found to be very small, which highlights that the strong coupling between metastable dipoles is more favorable than vortex formation to minimize energy in this nanomodulated structure. This has further been corroborated by the observation of step hysteresis, magnetic force microscopy images of tunable magnetic dipoles, and quantitative micromagnetic simulations. An analytical expression has been derived to estimate the overall anisotropy accurately for nanomodulated film having low magnetocrystaline anisotropy. Derived mathematical expressions based on magnetic dipolar interaction are found to be in good agreement with our results.

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.

Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

'A piece of fine meshwork': the intertwining fiction of Philip Roth and Edna O'Brien

This thesis comprises a comparative analysis of the works the Irish author Edna O’Brien and her contemporary and friend, the Jewish-American author Philip Roth. It investigates the striking biographical, textual and stylistic symmetries between two writers from very different cultures and literary traditions. The thesis begins with the, until now, undetected intertextual nexuses between Roth’s fiction and O’Brien’s. These allusions significantly alter the readings of a number of their novels, while at the same time indicating wider transatlantic frames of reference now apparent in their work. O’Brien has, since the beginning of her career, been in frequent correspondence with all of the pre-eminent Jewish-American authors of her time, and her work conducts a dialogue with key Jewish-American texts. Conversely, Roth’s fiction—like O’Brien’s, obviously indebted to Joyce—has frequently alluded to other seminal Irish authors. The literary and personal relationship of Roth and O’Brien symbolize myriad links between Jewish and Irish literary cultures. In O’Brien’s (and wider Irish) fiction, the Jew is often positioned as an exotic but dangerous “Other”. Equally, throughout the Jewish canon Irish Catholics are frequently employed as foils. Roth and O’Brien investigate difference by depicting relationships that cross these boundaries. Through understanding the complex interrelations at play between the fiction of Roth and O’Brien, and between their work and that of a wider pantheon of Irish and American writers, this thesis will reposition both as transnational authors while developing a culturally sensitive, textually nuanced account of their transatlantic literary relations.

Scotogenic model for co-bimaximal mixing

We present a scotogenic model, i.e. a one-loop neutrino mass model with dark right-handed neutrino gauge singlets and one inert dark scalar gauge doublet eta, which has symmetries that lead to co-bimaximal mixing, i.e. to an atmospheric mixing angle theta(23) = 45 degrees and to a CP-violating phase delta = +/-pi/2, while the mixing angle theta(13) remains arbitrary. The symmetries consist of softly broken lepton numbers L-alpha (alpha = e, mu, tau), a non-standard CP symmetry, and three L-2 symmetries. We indicate two possibilities for extending the model to the quark sector. Since the model has, besides eta, three scalar gauge doublets, we perform a thorough discussion of its scalar sector. We demonstrate that it can accommodate a Standard Model-like scalar with mass 125 GeV, with all the other charged and neutral scalars having much higher masses.

Gait Regulation for Bipedal Locomotion

This work explores regulation of forward speed, step length, and slope walking for the passive-dynamic class of bipedal robots. Previously, an energy-shaping control for regulating forward speed has appeared in the literature; here we show that control to be a special case of a more general time-scaling control that allows for speed transitions in arbitrary time. As prior work has focused on potential energy shaping for fully actuated bipeds, we study in detail the shaping of kinetic energy for bipedal robots, giving special treatment to issues of underactuation. Drawing inspiration from features of human walking, an underactuated kinetic-shaping control is presented that provides efficient regulation of walking speed while adjusting step length. Previous results on energetic symmetries of bipedal walking are also extended, resulting in a control that allows regulation of speed and step length while walking on any slope. Finally we formalize the optimal gait regulation problem and propose a dynamic programming solution seeded with passive-dynamic limit cycles. Observations of the optimal solutions generated by this method reveal further similarities between passive dynamic walking and human locomotion and give insight into the structure of minimum-effort controls for walking.

The tetrahexahedric angular Calogero model

The spherical reduction of the rational Calogero model (of type A n−1 and after removing the center of mass) is considered as a maximally superintegrable quantum system, which describes a particle on the (n−2)-sphere subject to a very particular potential. We present a detailed analysis of the simplest non-separable case, n=4, whose potential is singular at the edges of a spherical tetrahexahedron. A complete set of independent conserved charges and of Hamiltonian intertwiners is constructed, and their algebra is elucidated. They arise from the ring of polynomials in Dunkl-deformed angular momenta, by classifying the subspaces invariant and antiinvariant under all Weyl reflections, respectively.

Generalized cluster states based on finite groups

We define generalized cluster states based on finite group algebras in analogy to the generalization of the toric code to the Kitaev quantum double models. We do this by showing a general correspondence between systems with CSS structure and finite group algebras, and applying this to the cluster states to derive their generalization. We then investigate properties of these states including their projected entangled pair state representations, global symmetries, and relationship to the Kitaev quantum double models. We also discuss possible applications of these states.

Estudo de modelos simplificados com interações de longo alcance no ensemble microcanônico

Tese (doutorado)Universidade de Brasília, Instituto de Física, Programa de Pós-Graduação em Física, 2015.