Physics

Intersaccadic periods of fixation are characterized by incessant retinal motion due to small eye movements. While these movements are often disregarded as noise, the temporal modulations they introduce to retinal receptors are significant. However, analysis of these input modulations is challenging because the intersaccadic eye motion is close to the resolution limits of most eyetrackers, including widespread pupil-based video systems. Here, we analyzed in depth the limits of two high-precision eyetrackers, the Dual-Purkinje Image and the scleral search coil, and compared the intersaccadic eye movements of humans to those of a non-human primate. By means of a model eye we determined that the resolution of both techniques is sufficient to reliably measure intersaccadic ocular activity up to approximately 80 Hz. Our results show that the characteristics of ocular drift are remarkably similar in the two species and that a clear deviation from a scale-invariant spectrum occurs in the range between 50-100 Hz, generally attributed to ocular tremor. The amplitude of this deviation differs on the two axes of motion. In addition to our experimental observations, we suggest basic guidelines to evaluate the performance of eyetrackers and to optimize experimental conditions for the measurement of ocular drift and tremor.

Superlattice standing waves arising on the surface of ferrofluids that are driven by an ac magnetic field are investigated experimentally. Several different types are obtained through successive spatial period doublings, which are mediated by resonant mode interactions. The observed superlattices are quite diverse, depending on the relevant base Fourier modes, the orientation and the number of emerged subharmonic modes, and the phase difference among the involved modes all together. On the other hand, their temporal evolutions are all either period-1 ͑harmonic͒ or period-2 ͑subharmonic͒.

A lo largo de este trabajo se ha realizado un estudio pormenorizado de las vibraciones en sistemas simples cuyas condiciones de contorno eran dependientes del tiempo, obteniendo soluciones tanto por el método convencional de resolución (capítulos 2 y 3), como trabajando con condiciones de contorno variables con el tiempo (capítulo 4). Se han representado gráficamente todas las soluciones obtenidas, y por último se ha realizado la comparación de resultados de ambos métodos.

Attenuation correction is an essential requirement of positron emission tomography (PET) image reconstruction to allow for accurate quantification. However, attenuation correction is particularly challenging for PET-MRI as neither PET nor magnetic resonance imaging (MRI) can directly image tissue attenuation properties. MRI-based computed tomography (CT) synthesis has been proposed as an alternative to physics based and segmentation-based approaches that assign a population-based tissue density value in order to generate an attenuation map. We propose a novel deep fully convolutional neural network that generates synthetic CTs in a recursive manner by gradually reducing the residuals of the previous network, increasing the overall accuracy and generalisability, while keeping the number of trainable parameters within reasonable limits. The model is trained on a database of 20 preacquired MRI/CT pairs and a four-fold random bootstrapped validation with a 80:20 split is performed. Quantitative results show that the proposed framework outperforms a state-of-the-art atlas-based approach decreasing the Mean Absolute Error (MAE) from 131HU to 68HU for the synthetic CTs and reducing the PET reconstruction error from 14.3% to 7.2%.

Thin liquid films on surfaces are part of our everyday life, they serve e.g. as coatings or lubricants. The stability of a thin layer is governed by interfacial forces, described by the effective interface potential, and has been subject of many studies in the last decades. In recent years, the dynamics of thin liquid films came into focus since results on the reduction of the glass transition temperature raised new questions on the behavior of especially polymeric liquids in confined geometries. The new focus was fired by theoretical models that proposed significant implication of the boundary condition at the solid/liquid interface on the dynamics of dewetting and the form of a liquid front. Our study reflects these recent developments and adds new experimental data to corroborate the theoretical models. To probe the solid/liquid boundary condition experimentally, different ways are possible, each bearing advantages and disadvantages, which will be discussed. Studying liquid flow on a variety of different substrates entails a view on the direct implications of the substrate, the experimental focus of this study is the variation of the polymer chain length: The results demonstrate that inter-chain entanglements and in particular their density close to the interface, originating from non-bulk conformations, govern liquid slip of a polymer.

Probing the fluid dynamics of thin films is an excellent tool to study the solid/liquid boundary condition. There is no need for external stimulation or pumping of the liquid due to the fact that the dewetting process, an internal mechanism, acts as a driving force for liquid flow. Viscous dissipation within the liquid and slippage balance interfacial forces. Thereby, friction at the solid/liquid interface plays a key role towards the flow dynamics of the liquid. Probing the temporal and spatial evolution of growing holes or retracting straight fronts gives, in combination with theoretical models, information of the liquid flow field and especially the boundary condition at the interface. We review the basic models and experimental results obtained during the last years with exclusive regard to polymers as ideal model liquids for fluid flow. Moreover, concepts that aim on explaining slippage on the molecular scale are summarized and discussed.

We have studied the adsorption kinetics of the protein amylase at solid/liquid interfaces. Offering substrates with tailored properties, we are able to separate the impact of short-and long-range interactions. By means of a colloidal Monte Carlo approach including conformational changes of the adsorbed proteins induced by density fluctuations, we develop a scenario that is consistent with the experimentally observed three-step kinetics on specific substrates. Our observations show that not only the surface chemistry determines the properties of an adsorbed protein layer but also the van der Waals contributions of a composite substrate may lead to non-negligible effects.

Silanization bases on the adsorption, selfassembly and covalent binding of silane molecules onto surfaces, resulting in a densely packed selfassembled monolayer (SAM). Following standard recipes, however, the quality of the monolayer is often variable and therefore unsatisfactory. The process of self-assembly is highly affected by the chemicals involved in the wet-chemical process, by the ambient parameters during preparation such as humidity or temperature and by possibly present contaminants (or impurities). Here, we present a reliable, efficient, and wet-chemical recipe for the preparation of ultra-smooth, highly ordered alkylterminated silane SAMs on Si wafers.

Adhesion is a key issue for researchers of various fields, it is therefore of uppermost importance to understand the parameters that are involved. Commonly, only surface parameters are employed to determine the adhesive forces between materials. Yet, van der Waals forces act not only between atoms in the vicinity of the surface, but also between atoms in the bulk material. In this review, we describe the principles of van der Waals interactions and outline experimental and theoretical studies investigating the influence of the subsurface material on adhesion. In addition, we present a collection of data indicating that silicon wafers with native oxide layers are a good model substrate to study van der Waals interactions with coated materials.

Abstract: We have studied the adsorption kinetics of the protein amylase at solid/liquid interfaces. Offering substrates with tailored properties, we are able to separate the impact of short-and long-range interactions. By means of a colloidal Monte Carlo approach ...

Silanization bases on the adsorption, selfassembly and covalent binding of silane molecules onto surfaces, resulting in a densely packed selfassembled monolayer (SAM). Following standard recipes, however, the quality of the monolayer is often variable and therefore unsatisfactory. The process of self-assembly is highly affected by the chemicals involved in the wet-chemical process, by the ambient parameters during preparation such as humidity or temperature and by possibly present contaminants (or impurities). Here, we present a reliable, efficient, and wet-chemical recipe for the preparation of ultra-smooth, highly ordered alkylterminated silane SAMs on Si wafers.

We have investigated the reduction of the glass transition temperature, Tg, for thin supported films of particularly small molecular weight (MW = 2 kg/mol) polystyrene, and found good agreement with earlier studies on larger molecules. By combining the eigenmodes of the films with mode coupling theory, we arrive at a simple and predictive model which is in quantitative agreement with the data. Its only fitting parameter is the shear modulus governing the relevant fluctuations. The weak dependence of the latter upon the molecular weight of the polymer is in accordance with the general observation that the reduction of Tg is largely independent of chain length at sufficiently low molecular weight.

It is shown that the intrinsic stress in solvent cast polymer coatings plays a key role in the nucleation of holes in the film. Nucleation is important because it is meanwhile clear that heterogeneous nucleation is the only relevant rupture mechanism for the technologically relevant thickness regime well above 100 nm. The most striking feature is that in contrast to what has been widely believed, the number density of holes scales not algebraically, but exponentially with the film thickness.

We present a detailed theoretical study, based on density-functional calculations, of Na adsorption on TiO 2 (110) for coverage equal to 1/8, 1/4, and 1/2 monolayers. Two competing threefold adsorption sites are found. In the framework of the Bader theory, we analyze the electron distribution, the interfacial electron transfer, and the screening processes as a function of the coverage and the actual adsorption geometry. At low coverage, the Na atoms bind preferentially to two bridging and one in-plane O atoms. The adsorbed sodium atoms are nearly fully ionized. The excess electron states have a nonbonding Ti character and are delocalized over a few surface and subsurface sites. Such a behavior, which is at variance with the common belief that the excess states should be essentially localized on the surface fivefold titanium, is discussed in terms of the surface electrostatic potential and the atomic relaxations. According to our calculations, the onset of covalent interactions between Na atoms occurs for coverage slightly below 1/2 of monolayer, depending on the specific adsorption configuration. It is accompanied by a reduction of the positive Bader charge of the Na atoms and by a weakening of the ionic Na-O bond strength, which results in decreasing Na adsorption energies. At 1/2 monolayer coverage, the adsorption energies are practically insensitive to the details of the Na distribution among the low-energy adsorption sites, which suggests that Na-induced surface reconstructions might be affected by the intrinsic quality of the surface and the actual deposition conditions.

Generalized Ginzburg-Landau models of complex-vector order parameters are investigated by the mean-field approximation and the renormalization-group theory. Mean-field results for the possible ordered phases and their domains of stability are presented. The availability of large regions on the phase diagram in which the phase transitions are of first order is established. The fixed points of the renormalization-group equations and their stability properties are investigated up to second order in @=4d. Except for systems with cubic anisotropy, the renormalization-group equations do not have stable fixed points, and this indicates the presence of fluctuation-driven first- order transitions. For cubic symmetries a new critical behavior is reported. The results are related to superconductivity in high-T, oxides and heavy-fermion systems.

A renormalized-field theory for the critical behavior of ferromagnets with dipolar interactions and uniaxial anisotropy is developed to the one-loop order whereby the (reduced) dipolar g and uniaxial m couplings are studied on equal footing. A generalized minimal subtraction scheme is used to study the attractors and the renormalized flow of the P coupling constant and, subsequently, to determine the Kouvel-Fisher efFective exponent p & for the longitudinal susceptibility for arbitrary values of m and g. Despite the difficulties brought about by the generality of treatment, the investigation was carried out analytically throughout. The crossover transitions between the four nontrivial fixed points (Heisenberg, Ising, uniaxial dipolar, and isotropic dipolar), as exemplified by p &, are determined in detail to the one-loop order of the theory. In particular, all previous predictions concerning the discussed features of criticality in dipolar ferromagnets are obtained as specific cases of the present study. The problems arising in an attempt to fix the physical scale in a renormalized-field theoretical treatment of crossover behavior are discussed in view of finding a quantitative interpretation of recent experimental results on Gd and Fe&4NdgB.

A unified thermodynamic treatment is presented for reorientation transitions in ultrathin ferromagnetic films, driven by temperature or thickness variations. Since the physical mechanism underlying such transitions is the competition between surface, bulk, and shape anisotropy, the natural and proper scenery to examine the problem is the anisotropy space of the corresponding system. The recently developed anisotropy-flow concept is then applied to detect and characterize the possible thickness-and temperature-driven reorientation transitions, consistent with the standard, though not universally valid, assumption for the additive separation of the bulk and surface contributions. Three generic types of transition are easily identified with a number of subcases each. Each generic scenario is seen to come about as a simple consequence of the route which the system follows in the anisotropy space under variations of the driving parameter. The relevant characteristic thicknesses are easily identified. We find that, as a rule, there exist two borderlines in the ferromagnetic part of the T-d diagram of the system; these should lead in principle to a much richer structure of the diagram in question than has been reported so far. ͓S0163-1829͑96͒07329-8͔

The problem of higher-order Ne ´el anisotropies is solved by exploiting the addition theorem for spherical functions. A key advantage of the present approach is the orthonormal character of the expansion of the magnetic energy that simplifies the formalism and makes possible the treatment of nonideal morphologies as well. Explicit expressions for second-, fourth-, and sixth-order anisotropies are obtained for ideal bulk of fcc and bcc symmetry as well as for ͑001͒, ͑110͒, and ͑111͒ surfaces with nearest-neighbor ͑NN͒ Ne ´el interactions. The systematic examination of the pair model involves partition by species of inequivalent sites, interaction spheres, and orders in the multipole expansion. It enables us to to treat also next-nearest-neighbor ͑NNN͒ pair interactions to the same high orders as the NN ones. The analysis sheds light onto the peculiar cases of bcc͑100͒ and bcc͑111͒ surfaces where one finds no symmetry breaking ͑no second-order contributions͒ with NN interactions only. With the extension to NNN's, it is demonstrated that bcc͑111͒ surfaces exhibit a particularly high symmetry and acquire no second-order anisotropy contributions from NNN interactions, whereas the latter induce a second-order symmetry breaking in the bcc͑100͒ case. ͓S0163-1829͑98͒05734-8͔

The effect of quenched random fields on the zero‐temperature critical behaviour is studied by the means of the Wilson‐Fisher renormalisation‐group recursion relations to first order in the ϵ‐expansion. A number of quantum models is considered. The simultaneous influence of both, the random‐field and the classical‐to‐quantum dimensional crossover phenomena on the quantum critical behaviour is investigated. A special attention is paid to the properties of some reasonable particular forms of Gaussian random correlations which might be of relevance to the description of natural systems.

The question whether the Halperin-Lubensky-Ma result for a fluctuationinduced weakly first-order phase transition in superconductors holds in the presence of quenched impurities is considered. The renormalisation-group recursion relations have a new stable fixed point for 1 < n c 366, which describes a real critical behaviour in the range 2 < D,(n) < d < 4 of space dimensionalities d ( n / 2 is the number of components of the complex order parameter). Some features of the new fixed point are discussed. The critical exponents are presented for 1 < n C 366.

The influence of long-range correlated quenched impurities of a power-law decay type upon the phase transition in a model system of a superconductor is investigated. Direct renormalisation group &-analysis yields a fixed point which is stable over a domain in a specific parameter connected with the long-range character of the correlations. The critical exponents are calculated to first order in E. The existence of a stable fixed point is interpreted as signalling a second-order phase transition near four dimensions of space.

The influence of external field on thin ferromagnetic films with spin-reorientation transitions (SRTs) is explored in the presence of different orders of thickness-dependent uniaxial anisotropy. The two principal configurations are addressed and the first two anisotropy contributions are examined. A simple and natural representation of the field-induced SRTs has been found. It preserves the linearity of the thickness-driven trajectories even with field. The crosspoints of these trajectories with the phase borderlines correspond to crossover thicknesses of a linear type for positive second-order anisotropy contributions and of both linear and nonlinear types for negative second-order anisotropies. In the latter case, the nonlinear boundaries correlate with the coexistence of phases which brings about first-order-like reorientations and concommittant hysteresis effects. Practical schemes are proposed for the determination of the complete set of anisotropy parameters from measured field dependences of the crossover thicknesses. Indez Tens-Anisotropy, ultrathin films

A procedure is put forward for the specification of a suitable phase diagram for a uniaxial system with higher-order anisotropy which undergoes a spin-reorientation transition via coherent rotation of magnetization in an applied field of arbitrary strength and direction. The approach generalizes recent studies for a field applied in one of the principal directions. The analysis is valid for bulk and thin-film systems and is relevant to all experimental techniques that involve the implementation of an external field. The representation is especially promising in the context of thickness-driven transitions in ultrathin systems. It is generally valid, beyond the uniaxial restriction, for any remagnetization process which takes place within a given plane.

We study the microcanonical description of string gases in the presence of D-branes. We obtain exact expressions for the single string density of states and draw the regions in phase space where asymptotic approximations are valid. We are able to describe the whole range of energies including the SYM phase of the D-branes and we remark the importance of the infrared cut-off used in the high energy approximations. With the complete expression we can obtain the density of states of the multiple string gas and study its thermal properties, showing that the Hagedorn temperature is maximum for every system and there is never a phase transition whenever there is thermal contact among the strings attached to different D-branes.

A simple superposition model was used to define the relationship between molecular weight distribution and shear viscosity for linear polymeric systems. Gel permeation chromatography data for molecular weight distributions were fitted using statistical distribution functions. A simple superposition model was then employed to calculate the shear viscosity for the systems investigated. The effect of polydispersity on the shape of the flow curves was calculated. The simplicity of the model makes feasible its use in numerical simulations of complex geometries as encountered in polymer processing equipment. The present study also sheds some light on the relationship between entanglement and disentanglement phenomena in polymeric systems.

The flow fields in polymer processing exhibit complex behavior with chaotic characteristics, due in part to the non-linearity of the field equations describing them. In chaotic flows fluid elements are highly sensitive to their initial positions and velocities. A fundamental understanding of such characteristics is essential for optimization and design of equipment used for distributive mixing. In this work we analyze the flow in a twin-flight single screw extruder, obtained through 3-D FEM numerical simulations. We study particle motion and, implicitly, mixing in the extruder. Here, particles are massless points whose presence does not affect the flow field or other particle motion. We visualize chaos through Poincaré sections and calculate Lyapunov exponents as a measure of divergence of initial conditions, signaling chaotic features of flow. We use entropic measures to probe disorder or system homogeneity. The time evolution of the Renyi entropy of β = 1 for the 3-D spatial distribution of particles using different initial conditions are followed. The Kolmogorov-Sinai entropy rate, calculated by the sum of positive Lyapunov exponents, is correlated with the rate of evolution of entropy. In the same context we also examine the eccentric Couette flow. We find that the Renyi entropy dependence on time is logarithmic. To gain further understanding of this numerical observation, we analyze analytically the diffusion with drift entropy and find that it also depends logarithmically on time. Using the logarithmic coefficient of the Shannon entropy (ß = 1), as a measure of the overall rate of mixing, we find that the eccentric Couette device has the highest rate of mixing, followed by the twin-flight single screw extruder, and by the 1-D diffusion with drift.

Purpose: To evaluate the mechanical accuracy and the robustness of position alignment under x-ray-based image guidance of a treatment chair with six degrees of freedom (6DTC) which was developed for patient treatment in an upright posture at fixed horizontal beam lines in particle (proton, carbon ion, or others) radiotherapy facilities. The positional accuracy including translational and axial rotational accuracy of the 6DTC was evaluated by using a Vicon Motion Capture System (VMCS). Stability of the chair rotation isocenter was determined by a CCD camera with an in-house developed software. The tests were carried out to examine two key motion components of the 6DTC: a floor/rail-mount 360 • -rotating platform and a 6-degree-of-freedom (6DOF) platform. The measurement results were compared to that of a commercial clinical robot couch. The accuracy of position alignment, simulating the actual clinical protocol, through an Image-guided Radiation Therapy (IGRT) system was studied at the pre-treatment position and beam specific treatment position. The translational accuracy was 0.12 mm (SD 0.07 mm) for the 6DOF platform. The rotational accuracy was 0.04 • (SD 0.03 • ) and 0.02 • (SD 0.02 • ) for the 6DOF platform and the 360 • -rotating platform, respectively. The displacement between the chair rotation center and the room isocenter center was no more than 0.18 mm in all three rotational axes. Combined with an x-ray-based IGRT system, the treatment alignment test with a rigid phantom yielded a total positional accuracy of 0.23 mm (SD 0.17 mm) and 0.14 • (SD 0.14 • ) at treatment position. Conclusions: On the basis of the rigid phantom study, the 6DTC showed comparable accuracy to the robot treatment couch. Combining with the IGRT, the 6DTC can provide position alignment with submillimeter accuracy for rigid phantom in upright posture.

Computational models have become an essential part of exploratory protocols in cell biology, as a complement to in vivo or in vitro experiments. These virtual models have the twofold advantage of enabling access to new types of data and validate complex theories. The design of mechanically functionalized biomaterials or scaffolds, to promote cell proliferation and invasion in the absence or in the complement of synthetic chemical coatings, can certainly benefit from these hybrid testing approaches. The underlying fundamental process of cell migration and in particular its dependence on the cell mechanical/geometrical environment remains crudely understood. Currently at least two theories explain the migration patterns observed by cells on curved topographies, involving either polymerization dynamics of actin or assembly dynamics of focal adhesions. We recently proposed a third mechanism relying on nucleus mechanosensitivity, which has been tested extensively experimentally and compu...

The study and understanding of functionality and its link with surface topography requires surfaces that enable us to decouple the examined effect. The sinusoidal function offers an easy solution for the decoupling of amplitude and frequency. However, the corresponding surfaces would require very good characteristics: shape regularity, low waviness and low microroughness. This study thoroughly characterized sinusoidal surface (egg-box shapes) having periods ranging from 30 μm to 300 μm and peak-to-valley amplitudes comprised between 3 and 30 μm. The microroughness of the examined surfaces was quantified with the arithmetic mean deviation Sa and was found to be around 1 nm for most examined surfaces. The waviness of the surfaces, which was also quantified with Sa, was lower than 0.15 μm for all the surfaces. The relative error computed for the period of the sinusoidal surfaces was lower than 1.3%. Finally, the shape regularity was assessed by comparing the measurements to a mathemati...

Cells have evolved multiple mechanisms to apprehend and adapt finely to their environment. Here we report a new cellular ability, which we term &quot;curvotaxis&quot; that enables the cells to respond to cell-scale curvature variations, a ubiquitous trait of cellular biotopes. We develop ultra-smooth sinusoidal surfaces presenting modulations of curvature in all directions, and monitor cell behavior on these topographic landscapes. We show that adherent cells avoid convex regions during their migration and position themselves in concave valleys. Live imaging combined with functional analysis shows that curvotaxis relies on a dynamic interplay between the nucleus and the cytoskeleton-the nucleus acting as a mechanical sensor that leads the migrating cell toward concave curvatures. Further analyses show that substratum curvature affects focal adhesions organization and dynamics, nuclear shape, and gene expression. Altogether, this work identifies curvotaxis as a new cellular guiding m...

In this paper we propose a new methodology to characterize the morphological properties of a surface in relation with its functionality (tribological properties, surface coating adhesion, brightness, wettability…). We create a software based on experimental design and surface profile recording. Using an appropriate database structure, the roughness parameters are automatically computed at different scales. The surface files are saved in a hard disk directory and roughness parameters are computed at different scales. Finally, a statistical analysis system proposes the roughness parameter (or the pair of roughness parameters) that better describe(s) the functionality of the surface and the spatial scales at which the parameter(s) is (are) the more relevant.

The purpose of this article is to localize underwater objects based on the noise reflection of the propeller rotation in cavitation mode. In the proposed method, the propeller noise, which plays the role of pings in active sonar, is modeled by the Wittekind method. As such, an echo is continuously received by a vertical and uniform linear hydrophone array due to reflection from the underwater targets. The challenges associated with the underwater channels are simulated by the ocean model in COMSOL. Specifically, to model the propagation of underwater acoustic in this channel, the Helmholtz equation is solved using COMSOL. Finally, localization is performed by comparing the Delay & Sum algorithm and the multiple signal classification (MUSIC) algorithm in MATLAB. According to the simulation results, the proposed method is able to detect the position of the target and the propeller approximately, although the multipath phenomenon causes adverse effects on the results. The narrowband MU...

Filopodial protrusion initiates cell migration, which decides the fate of cells in biological environments. In order to understand the structural stability of ultra-slender filopodial protrusion, we have developed an explicit modeling strategy that can study both static and dynamic characteristics of microfilament bundles. Our study reveals that the stability of filopodial protrusions is dependent on the density of F-actin crosslinkers. This cross-linkage strategy is a requirement for the optimization of cell structures, resulting in the provision and maintenance of adequate bending stiffness and buckling resistance while mediating the vibration. This cross-linkage strategy explains the mechanical stability of filopodial protrusion and helps understand the mechanisms of mechanically induced cellular activities.

The quest for Kitaev quantum spin liquids has led to great interest in honeycomb quantum magnets with strong spin-orbit coupling. It has been recently proposed that even Mott insulators with 3d transition metal ions, having nominally weak spin-orbit coupling, can realize such exotic physics. Motivated by this, we study the rhombohedral honeycomb cobaltates CoTiO3, BaCo2(PO4)2, and BaCo2(AsO4)2, using ab initio density functional theory, which takes into account realistic crystal field distortions and chemical information, in conjunction with exact diagonalization numerics. We show that these Co 2+ magnets host J eff = 1/2 local moments with highly anisotropic g-factors, and we extract their full spin Hamiltonians including longer-range and anisotropic exchange couplings. For CoTiO3, we find a nearest-neighbor easy-plane ferromagnetic XXZ model with additional bond-dependent anisotropies and interlayer exchange, which supports three-dimensional (3D) Dirac nodal line magnons. In contrast, for BaCo2(PO4)2 and BaCo2(AsO4)2, we find a strongly suppressed interlayer coupling, and significant frustration from additional third-neighbor antiferromagnetic exchange mediated by P/As. Such bond-anisotropic J1-J3 spin models can support collinear zig-zag or coplanar spiral ground states. We discuss their dynamical spin correlations which reveal a gapped Goldstone mode, and argue that the effective parameters of the pseudospin-1/2 models in these two materials may be strongly renormalized by coupling to a low energy spin-exciton. Our results call for re-examining proposals for realizing Kitaev spin liquids in the honeycomb cobaltates.

A teacher affects eternity; he can never tell where his influence stops -Henry Adams To paddy, Thanks to all my colleagues, who helped in this adventure of life, love and gravitation. and to the people who started me off on this adventure and my friends who kept me on this songline until it was done.

Thanu Padmanabhan was a renowned Indian theoretical physicist known for his research in general relativity, cosmology, and quantum gravity. In an extraordinary career spanning forty-two years, he published more than three hundred research articles, wrote ten highly successful technical and popular books, and mentored nearly thirty graduate students and post-doctoral fellows. He is best known for his deep work investigating gravitation as an emergent thermodynamic phenomenon. He was an outstanding teacher, and an indefatigable populariser of science, who travelled very widely to motivate and inspire young students. Paddy, as he was affectionately known, was also a close friend to his students and collaborators, treating them as part of his extended academic family.

We discuss the late time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) which connect the nonlinear and linear two point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed towards a universal profile which does not change its shape at late times. We begin by clarifying the relation between the density profiles of the individual halos and the slope of the correlation function and discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profile which preserves the shape at late times, then the correlation function should grow as a 2 [in a Ω = 1 universe] even at nonlinear scales. We prove that such exact solutions do not exist; however, there exists a class of solutions ("psuedo-linear profiles", PLP's for short) which evolve as a 2 to a good approximation. It turns out that the PLP's are the correlation functions which arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering is a minimum and hence can act as building blocks of the nonlinear universe. We discuss the implications of this result.

We investigate the evolution of non-linear density perturbations by taking into account the effects of deviations from spherical symmetry of a system. Starting from the standard spherical top hat model in which these effects are ignored, we introduce a physically motivated closure condition which specifies the dependence of the additional terms on the density contrast, d . The modified equation can be used to model the behaviour of an overdense region over a sufficiently large range of d . The key new idea is a Taylor series expansion in (1/d ) to model the non-linear epoch. We show that the modified equations quite generically lead to the formation of stable structures in which the gravitational collapse is halted at around the virial radius. The analysis also allows us to connect up the behaviour of individual overdense regions with the non-linear scaling relations satisfied by the two-point correlation function.