2D Samples Research Articles

Exact ground state for the four-electron problem in a 2D finite honeycomb lattice

Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact four-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspace in which the ground state is placed, than deduces by exact diagonalization in . The small subspace is obtained by the repeated application of the Hamiltonian on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of , till the obtained system of equations closes in itself. The procedure which can be applied in principle at fixed but arbitrary system size and number of particles is interesting on its own since it provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for . The diagonalization inside provides an incomplete image of the low lying part of the excitation spectrum, but provides the exact . Once the exact ground state is obtained, its properties can be easily analysed. The is found always as a singlet state whose energy, interestingly, saturates in the limit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state presents ‘Zittern’ (trembling) characteristics which are absent in 2D square Hubbard systems. Consequently, the manifestation of the local Coulomb repulsion in 2D square and honeycomb types of systems presents differences, which can be a real source in the differences in the many-body behaviour.

Color naming experiments using 2D and 3D rendered samples

AbstractThis article describes a color naming experiment using 2D and 3D rendered color samples. Conventional color naming experiments using a priori clues generally involve 2D clues such as color patches. However, in real‐world scenes, most objects have 3D shapes whose colors are affected by illumination effects such as shadows and gloss. We use 2D and 3D rendered samples as clues in the experiments, and analyze the relationship between color terms and object surfaces. First, we develop a color term collection system that can produce 218 test colors. We render the color images of a flat disk as a 2D sample and a sphere as a 3D sample on a calibrated display device. It is supposed that the 2D and 3D surfaces with the same object color are obtained under the same conditions of viewing and illumination. The results of color naming experiments show that there are differences for color terms between 2D and 3D samples. Important findings are as follows: (1) brighter color terms tend to be chosen for the 3D samples than the 2D samples, when observing achromatic colors, (2) achromatic color terms are chosen for 3D samples having low saturation, and (3) for chromatic colors, a darker color term is generally chosen in comparison to the corresponding 2D samples of the same color. These properties become more prominent by changing the illumination angle from 0° to 45° to the surface normal. © 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 270–280, 2015

Efficient solution of 3D Ginzburg-Landau problem for mesoscopic superconductors

The recently proposed approach for the solution of Ginzburg-Landau (GL) problem for 2D samples of arbitrary shape is, in this article, extended over 3D samples having the shape of (i) a prism with arbitrary base and (ii) a solid of revolution with arbitrary profile. Starting from the set of Laplace operator eigenfunctions of a 2D object, we construct an approximation to or the exact eigenfunctions of the Laplace operator of a 3D structure by applying an extrusion or revolution to these solutions. This set of functions is used as the basis to construct the solutions of the linearized GL equation. These solutions are then used as basis for the non-linear GL equation much like the famous LCAO method. To solve the non-linear equation, we used the Newton-Raphson method starting from the solution of the linear equation, i.e., the nucleation distribution of superconducting condensate. The vector potential approximations typically used in 2D cases, i.e., considering it as corresponding to applied constant field, are in the 3D case harder to justify. For that reason, we use a locally corrected Nystrom method to solve the second Ginzburg-Landau equation. The complete solution of GL problem is then achieved by solving self-consistently both equations.

Motion Tracking, Retrieval and 3D Reconstruction from Video

The work at hand presents a novel data-driven framework for 3D full body human motion reconstruction from uncalibrated monocular video data. To this end, we develop a knowledge base by taking 2D samples of the motion capture library from dierent viewing directions. This allows later steps to handle 2D query videos without any information on the viewing direction. We detect and track features from input video sequences by utilizing low-level image based feature detection techniques like MSER and SURF. This process is stabilized by back projection of high-level 3D prior information obtained from the motion capture library to the image plane. Extraction of suitable feature sets from both, input control signals and motion capture data, enables us to retrieve the best relevant prior poses from the motion capture library by employing fast motion retrieval techniques. Finally, 3D motion sequences are reconstructed by non-linear energy minimization, that takes into account multiple prior terms. Furthermore, we propose a method to estimate camera parameters from input video itself and sampling of motion capture library.

Lamellar coupled growth in the neopentylglycol-(D)camphor eutectic

Lamellar eutectic growth was investigated in the transparent organic alloy neopentylglycol-(D)camphor of eutectic composition (NPG-45.3wt% DC) using bulk (3D) and thin (2D) samples. Two types of eutectic grains were observed in the polycrystalline samples, either with lamellae well aligned to the direction of solidification or inclined at an angle of 21.5±1.5°. The well aligned grains were used for determining lamellar spacing as function of growth velocity V and temperature gradient G. Based on these data the Jackson–Hunt constant was evaluated to be KJH=1.60±0.15μm3s−1. For low growth velocity experiments the contact angles for (DC) and (NPG) lamellae at eutectic triple junctions were also evaluated, being θ(DC)=50.9±4.1° and θ(NPG)=41.8±4.7°, respectively. Using these values, as well as phase diagram data and the Gibbs–Thomson coefficients, the chemical coefficient of diffusion of (D)camphor in the eutectic liquid at eutectic temperature 53°C was estimated to be DL=97±15µm2s−1.

Isolated galaxies in hierarchical galaxy formation models – present-day properties and environmental histories

In this study, we have carried out a detailed, statistical analysis of isolated model galaxies, taking advantage of publicly available hierarchical galaxy formation models. To select isolated galaxies, we employ 2D methods widely used in the observational literature, as well as a more stringent 3D isolation criterion that uses the full 3D-real space information. In qualitative agreement with observational results, isolated model galaxies have larger fractions of late-type, star forming galaxies with respect to randomly selected samples of galaxies with the same mass distribution. We also find that the samples of isolated model galaxies typically contain a fraction of less than 15 per cent of satellite galaxies, that reside at the outskirts of their parent haloes where the galaxy number density is low. Projection effects cause a contamination of 2D samples of about 18 per cent, while we estimate a typical completeness of 65 per cent. Our model isolated samples also include a very small (few per cent) fraction of bulge dominated galaxies (B/T > 0.8) whose bulges have been built mainly by minor mergers. Our study demonstrates that about 65-70 per cent of 2D isolated galaxies that are classified as isolated at z = 0 have indeed been completely isolated since z = 1 and only 7 per cent have had more than 3 neighbours within a comoving radius of 1 Mpc. Irrespectively of the isolation criteria, roughly 45 per cent of isolated galaxies have experienced at least one merger event in the past (most of the mergers are minor, with mass ratios between 1:4 and 1:10). The latter point validates the approximation that isolated galaxies have been mainly influenced by internal processes.

Analysis of particle rolling and intrinsic rotations in copper powder during sintering

The common theoretical model used to describe the sintering process is the two particle model. This model describes comprehensively the growth of inter-particle contacts driven by the Laplace pressure. In three dimensions this model fails as cooperative material transport (i.e., movements of powder particles) occurs. The fundamental understanding of these processes is still rather sketchy and is derived from the observation of 1D or 2D samples. To observe and quantify cooperative material transport new experimental methods are needed, for example high resolution computer tomography in conjunction with photogrammetric image analysis. Single-crystal copper spheres were marked by drilling holes into the surface of each particle and two samples were prepared using the marked powder. One sample was heated continuously to 1,050 °C in a silica capillary and was analyzed by in situ synchrotron computer tomography (SCT) at the European synchrotron radiation facility in Grenoble. Free sintering was investigated by ex-situ SCT at Bessy II in Berlin. The novel technique of drilling holes into the sphere surfaces allows for the quantification of both intrinsic rotations and particle rolling by photogrammetry. The observed intrinsic rotations exceed the rolling by far and we conclude that the anisotropy of grain boundary energies results in grain boundary sliding. Furthermore, we present first computer simulations of sintering processes based on initial particle positions measured by SCT.

Fast Generation of Approximate Blue Noise Point Sets

AbstractPoisson‐disk sampling is a popular sampling method because of its blue noise power spectrum, but generation of these samples is computationally very expensive. In this paper, we propose an efficient method for fast generation of a large number of blue noise samples using a small initial patch of Poisson‐disk samples that can be generated with any existing approach. Our main idea is to convolve this set of samples with another to generate our final set of samples. We use the convolution theorem from signal processing to show that the spectrum of the resulting sample set preserves the blue noise properties. Since our method is approximate, we have error with respect to the true Poisson‐disk samples, but we show both mathematically and practically that this error is only a function of the number of samples in the small initial patch and is therefore bounded. Our method is parallelizable and we demonstrate an implementation of it on a GPU, running more than 10 times faster than any previous method and generating more than 49 million 2D samples per second. We can also use the proposed approach to generate multidimensional blue noise samples.

Radiolabeled gelatin type B analogues can be used for non-invasive visualisation and quantification of protein coatings on 3D porous implants

This study covers the quantification of the covalent attachment of gelatin type B (GelB) and the subsequent adsorption of Fibronectin (Fn) on poly-ε-caprolactone (PCL) surfaces, functionalised with 2-aminoethyl methacrylate (AEMA) by means of post-plasma UV-irradiation grafting. As typical surface characterisation tools do not allow quantification of deposited amounts of GelB or Fn, radiolabeled analogues were used for direct measurement of the amount of immobilized material. Bolton-Hunter GelB (BHG) and Fn were radioiodinated with (131)I and (125)I respectively and S-Hynic GelB (SHG) was labeled with (99m)Tc. Immobilisation of (131)I-BHG or (99m)Tc-SHG on both PCL and PCL-AEMA scaffolds was performed in analogy with earlier work. SPECT images on scaffolds coated with (99m)Tc-SHG conjugates were acquired on a U-SPECT II camera. There was a clear difference in the amount of deposited (131)I-BHG between blanco and AEMA-grafted PCL on 2D samples. No significant differences in immobilization behaviour were observed between (99m)Tc-SHG and (131)I-BHG. Subsequent immobilisation of Fn was successful and depended on the amounts of deposited GelB. SPECT imaging on cylindrical 3D scaffolds confirmed these findings and showed that the amount of immobilized (99m)Tc-SHG was depth dependant. The architecture of the scaffolds strongly influences the distribution of GelB within these structures. Furthermore, there is a clear difference in the homogeneity of the protein coating when different GelB immobilization protocols were applied. This study shows that radiolabeled compounds are a rapid and accurate tool in the quantitative and qualitative evaluation of the biofunctionalisation of AEMA grafted PCL scaffolds.

Development and Validation of a Fluorescence Method to Follow the Build-up of Short Peptide Sequences on Solid 2D Surfaces

The modification of material surfaces with short peptide sequences has become an essential step in many biotechnological and biomedical applications. Due to their simple architecture compared to more complex 3D substrates, 2D surfaces are of particular interest for high throughput applications and as model surfaces for dynamic or responsive surface modifications. The decoration of these surfaces with peptides is commonly accomplished by synthesizing the peptide first and subsequently transferring it onto the surface of the substrate. Recently, several procedures have been described for the synthesis of peptides directly onto a 2D surface, thereby simplifying and accelerating the modification of flat surfaces with peptides. However, the wider use of these techniques requires a routine method to monitor the amino acid build-up on the surface. Here, we describe a fast, inexpensive and nondestructive fluorescence based method which is readily accessible to follow the amino acid build-up on solid 2D samples.

Screening and edge states in two-dimensional metals in a magnetic field

The length λ0 at which the lateral electric-field component E ⊥ perpendicular to the boundary is conserved near the boundary of two-dimensional (2D) samples, which is covered by 2D electrons, has been determined. The existence of the finite such length follows from the self-consistent process of the screening of the external fields forming the boundaries of real 2D systems by the electrons of the metal. The effect of E ⊥ on the structure of magnetic edge states has been taken into account in the mean field approximation in a wide range of the external field from the semiclassical limit (ɛF ≫ ħωc), where ɛF is the Fermi energy of the 2D system and ħωc is the cyclotron energy to the quantum Hall effect (QHE) region (ɛF ≪ ħωc). The positions of the magnetic edge state peaks against the background of their ideal distribution along the perimeter of the 2D circle in the known problem of transverse magnetic focusing have been determined in the semiclassical limit. The systematic description of the structure of the skin layer with λ H ≥ λ0, consisting of the set of the so-called integer strips (overlapping or independent), which are carriers of the universal quantum conductance, has been proposed in the QHE regime. A relatively large probability of the overlapping of the fields of adjacent strips, as well as the possibility of describing coupled integer cascades, is remarkable. The existing data on the tunneling current through integer strips in the λ H layer providing suitable information on the actual state of the boundary of the 2D system have been commented. A natural analogy between the properties of magnetic edge states and a well-known problem of the details of the ballistic conductance σ‖(H) of narrow electron channels in the magnetic field H has been noticed. The formalisms of both problems are identical under the conditions λ H ≥ w, where 2w is the effective width of the quasi-one-dimensional channel. The existing information on the σ‖(H) dependence in a wide range of the magnetic field has been systematized. The attributes of the QHE observed in σ‖(H) convincingly indicate the reality of the formation of various modifications of integer strips in inhomogeneous 2D systems in the quantizing magnetic field.

Random nanoparticle deposition: inter-particle distances in 2D, 3D, and multilayer samples

We consider diluted assemblies of particles randomly distributed on a surface (2D samples), in a volume (3D samples) or in 2D layers separated with a spacer of thickness t (multilayer samples). Among various considerations on the inter-particle separations, a special interest is given to the nearest-neighbor distance distribution. We also discuss the influence of the particle size, by looking at the edge-to-edge distance, and analyze the particle distribution beyond the nearest-neighbor. Moreover, we investigate the particular case of multilayer samples, which to our knowledge has never been discussed. Finally, we experimentally illustrate the applicability of the random deposition model.

How Degradation of Calcium Phosphate Bone Substitute Materials is influenced by Phase Composition and Porosity

AbstractThe chemical composition of calcium phosphate (CaP) materials for the regenerative therapy of large bone defects is similar to that of bone. Additionally, calcium phosphates show an excellent biocompatibility. Besides the support of defect healing calcium phosphate implants should be completely degraded within an adequate time period to be replaced by newly formed bone. Although degradation of CaP‐implants occurs mainly by dissolution of the material, it is important to characterize the osteoclastic resorption as well, which is involved in native bone remodeling. The degradation of bone substitutes made of calcium phosphate ceramics is influenced by various parameters, such as defect size and localization, the general health situation, and age of the patient, but also material properties are important. Especially, the calcium phosphate composition is crucial for the degradation behavior of a calcium phosphate material. Additionally, at the cellular level the micro‐ and macroporosity, including interconnecting pores, influences both, the dissolution and the osteoclastic resorption. In our study, three different calcium phosphate materials (hydroxyapatite, tricalcium phosphate, and a biphasic calcium phosphate) and two different geometries (dense 2D samples and porous 3D scaffolds) are compared regarding their dissolution and resorption behavior. The results show, that the dissolution of CaP‐ceramics, as examined by the incubation in a degradation solution, depends mainly on the calcium phosphate phase but also on the porosity of the implant. Regarding the resorption, cell proliferation and differentiation of a monocytic cell line as well as the formation of resorption lacunas are analyzed. Cell proliferation is comparable on all phase compositions. Cell differentiation and resorption, however, are influenced by the calcium phosphate phase composition and by the implant porosity as well. By understanding these two mechanisms of degradation, bone substitute materials and, as a result, the bone regeneration of large bone defects using CaP‐ceramics can be improved.

Stress fields in granular solids: Effect of composition

We use the lattice element method to investigate stress fields at the sub-particle scale in granular solids composed of particles embedded in a cementing matrix. The stress distributions are found to be similar in 2D and 3D samples subjected to vertical loading with free lateral boundaries. We find that the number of strong forces falls off exponentially at high particle volume fractions where a percolating network of jammed particles occurs. The influence of the matrix volume fraction and particle/matrix stiffness ratio with respect to stress distribution is analyzed in 2D and 3D. We show that both decreasing the matrix volume fraction and increasing the stiffness ratio lead to increasingly broader distributions within a limit beyond which the distribution is independent of one or both of these parameters.

Basic colour names for 2D samples: effects of presentation media and illuminants

We have previously shown (Bloj et al., 2008; Abstracts Materials & Sensations 2008) that under particular conditions colour memory is independent of presentation media, and of the illuminants under which colours are viewed. In the present study we investigate whether colour naming is also unaffected by these two factors. Forty-eight colour samples from the Natural Colour System (NCS) collection were presented as real paper samples or as accurate computer simulations displayed on a calibrated monitor. The colour swatches could be presented under a daylight illuminant - two intensities, 85 ('D1') or 60 cd m(-2) ('D2') - or a purple illuminant, 45 cd m(-2) ('Lily'). The colour samples were shown in arrays of 16 (4 × 4 layout) and the observer's task was to assign one of the eleven basic colour terms to each of the samples. Six observers repeated this colour naming task five times for each presentation medium and illuminant. On average, in 73% of the cases the same colour term was assigned to surface and display colours. This level of agreement was highest for colour samples under daylight (D1-82%, D2-73%) and poor for Lily (65%). Although colour memory is unaffected by the nature of the colour stimulus, here we show that there are limitations to cross-media agreement in colour naming.

Two- and three-dimensional micromechanical viscoelastic finite element modeling of stone-based materials with X-ray computed tomography images

This paper presents 2D and 3D micromechanical finite element (FE) models to predict the viscoelastic properties including dynamic modulus and phase angle of stone-based materials (using an example of asphalt mixtures). Heterogeneous asphalt mixtures are consisted of very irregular aggregates, asphalt matrix and a small amount of air voids. The internal microstructure of asphalt mixtures was captured with X-ray computed tomography (CT) imaging techniques. The 2D and 3D digital samples were created with the reconfiguration of the scanned horizontal surface images. The FE mesh of digital samples was generated with the locations of image pixels within each aggregate and asphalt matrix. Along the boundary of these two phases, the aggregate and matrix FEs share the nodes to connect the deformation. The micromechanical FE model was accomplished by incorporating the captured microstructure and ingredient properties (viscoelastic asphalt matrix and elastic aggregates). The generalized Maxwell model was applied for viscoelastic asphalt matrix with calibrated parameters from the nonlinear regression analysis of the lab test data. The displacement-based FE simulations were conducted for the uniaxial compression under sinusoidal cyclic loading. Overall, the predicted dynamic modulus and phase angle from 2D and 3D micromechanical models were compared favorably with lab test data of the asphalt mixture specimens. The 3D simulation with digital samples generated better prediction than the 2D models. These results indicate that the developed micromechanical FE models have the ability to accurately predict the global viscoelastic properties of the stone-based materials.

Nonlinear Structured-Illumination Microscopy Using Photo-Switchable Labels

Periodically structured illumination light can extend the resolution of a light microscope beyond the classical limit by an amount equal to the spatial frequency, k1, of the illumination structure [1]. The wavelength and the laws of physics limit the set of frequencies that can be physically generated in a light intensity field in the same way as the set of frequencies that can be observed. Consequently, k1 cannot be much greater than the classic resolution limit itself, and therefore the resolution extension cannot exceed a factor of two. However, dramatically greater resolution extension is possible if the emission rate is made to be nonlinear with the incoming illumination intensity. This nonlinearity can cause the effective excitation to contain harmonics at multiples of k1, with correspondingly multiplied resolution-enhancing ability [3]. Photo-switching of fluorophores is a nearly ideal source of such nonlinearity. This phenomenon has produced modest resolution improvements when applied on one dimension and analyzed with real-space methods [4]. We are using it to develop high-resolution microscopy of 2D samples based on our frequency-space-based approach to nonlinear structured-illumination microscopy. Here we describe recent progress toward multidimensional super-resolution of biological samples using this technique. [1] M.G.L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,”J. Microsc.198, (2000). [2] R. Heintzmann, T.M. Jovin, and C. Cremer, “Saturated Patterned Excitation Microscopy - a Concept for Optical Resolution Improvement,”J. Opt. Soc. Am. A.19, (2002). [3] M.G.L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,”Proc. Nat. Acad. Sci. USA102, (2005). [4] M. A. Schwentker, H. Bock, M. Hofmann, S. Jakobs, J. Bewersdorf, C. Eggeling, and S.W. Hell, “Wide-Field Subdiffraction RESOLFT Microscopy Using Fluorescent Protein Photoswitching”, Microscopy Res. & Techn. 70, (2007).

Surface-enhanced Raman scattering: realization of localized surface plasmon resonance using unique substrates and methods

Surface-enhanced Raman scattering (SERS) enhancement and the reproducibility of the SERS signal strongly reflect the quality and nature of the SERS substrates because of diverse localized surface plasmon resonance (LSPR) excitations excited at interstitials or sharp edges. LSPR excitations are the most important ingredients for achieving huge enhancements in the SERS process. In this report, we introduce several gold and silver nanoparticle-based SERS-active substrates developed solely by us and use these substrates to investigate the influence of LSPR excitations on SERS. SERS-active gold substrates were fabricated by immobilizing colloidal gold nanoparticles on glass slides without using any surfactants or electrolytes, whereas most of the SERS-active substrates that use colloidal gold/silver nanoparticles are not free of surfactant. Isolated aggregates, chain-like elongated aggregates and two-dimensional (2D) nanostructures were found to consist mostly of monolayers rather than agglomerations. With reference to correlated LSPR and SERS, combined experiments were carried out on a single platform at the same spatial position. The isolated aggregates mostly show a broadened and shifted SPR peak, whereas a weak blue-shifted peak is observed near 430 nm in addition to broadened peaks centered at 635 and 720 nm in the red spectral region in the chain-like elongated aggregates. In the case of 2D nanostructures, several SPR peaks are observed in diverse frequency regions. The characteristics of LSPR and SERS for the same gold nanoaggregates lead to a good correlation between SPR and SERS images. The elongated gold nanostructures show a higher enhancement of the Raman signal than the the isolated and 2D samples. In the case of SERS-active silver substrates for protein detection, a new approach has been adopted, in contrast to the conventional fabrication method. Colloidal silver nanoparticles are immobilized on the protein functionalized glass slides, and further SERS measurements are carried out based on LSPR excitations. A new strategy for the detection of biomolecules, particularly glutathione, under aqueous conditions is proposed. Finally, supramolecular J-aggregates of ionic dyes incorporated with silver colloidal aggregates are characterized by SERS measurements and correlated to finite-difference time-domain analysis with reference to LSPR excitations.

The role of Sb and N ions on the morphology and localization of (Ga,In) (N,As) quantum wells

A comparative study of the influence of Sb and N ion concentration on the properties of GaInNAs (GINA) quantum wells (QWs) is presented. We find that for perfect two-dimensional (2D) QW there is no direct perceptible improvement in structural quality due to the introduction of Sb. Moreover, contrast variations in the QW suggest an inhomogeneous Sb incorporation. A different behaviour of the integrated photoluminescence (PL) intensity with temperature is observed when comparing the 2D samples grown with/without Sb. Regarding the GINA QWs exhibiting a three-dimensional (3D) morphology, we observe a significant improvement in structural quality for the samples grown with added Sb, as well as for those Sb-free samples but grown under a low N- ions density. Nevertheless, 2D and 3D samples show clear common properties: the GINA:Sb QWs exhibit an improved PL efficiency, but only at high temperatures. On the contrary, the Sb-free samples grown under a low N- ions concentration exhibit a brighter PL at all temperatures considered.

Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin copper oxide films

A central challenge in the physics of high-temperature superconductors is to understand superconductivity within a single copper oxide layer or bilayer, the fundamental structural unit, and how superconductivity is lost with underdoping of charge carriers. A seminal property of crystals and thick films1,2,3,4 is that when mobile holes are removed from optimally doped CuO2 planes, the transition temperature, Tc, and superfluid density, ns(0), decrease in a surprisingly correlated fashion. We elucidate the essential physics of strongly underdoped bilayers by studying two-dimensional (2D) samples near the critical doping level where superconductivity disappears. We report measurements of ns(T) in films of Y1−xCaxBa2Cu3O7−δ as thin as two copper oxide bilayers with Tc values as low as 3 K. In addition to seeing the 2D Kosterlitz–Thouless–Berezinski transition5,6 at Tc, we observe a remarkable scaling of Tc with ns(0), which indicates that the disappearance of superconductivity with underdoping is due to quantum fluctuations near a 2D quantum critical point.