A variational approech to stationary and rotating Bose-Einstein condensates

Cataloged from PDF version of article.After the experimental demonstration of Bose-Einstein condensation (BEC) in alkali gases [6, 7, 18], the number of theoretical and experimental papers on ultracold atomic physics increased enormously [48]. BEC experiments provide a way to manipulate quantum many-body systems, and measure their properties precisely. Although the theory of BEC is simpler compared to other many-body systems due to strong correlation, a fully analytical treatment is generally not possible. Therefore, variational methods, which give approximate analytical solutions, are widely used. With this motivation, in this thesis we study on BEC in stationary and rotating regimes using variational methods. All the atoms in the condensate can be described with a single wave function, and in the dilute regime this wave function satisfies a single nonlinear equation (the Gross-Pitaevskii equation) which resembles the nonlinear Schr¨odinger equation in nonlinear optics. A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser [41, 43] having a similar behavior in the limiting cases of nonlinearity with ground state density profile of BECs, is used as the trial wave function to solve the Gross-Pitaevskii equation with variational principle for a wide range of the interaction parameter. The simple form of the ansatz allowed us to modify it for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground state wave function and energy are in very good agreement with the analytical solutions in the limiting cases of interaction and numerical solutions for the intermediate regime. In the second part, we consider a rapidly rotating two-component BoseEinstein condensate containing a vortex lattice. We calculate the dispersion relation for small oscillations of vortex positions (Tkachenko modes) in the mean-field quantum Hall regime, taking into account the coupling of these modes with density excitations. Using an analytic form for the density of the vortex lattice, we numerically calculate the elastic constants for different lattice geometries. We also apply this method to the calculation the elastic constant for the single-component triangular lattice. For a two-component BEC, there are two kinds of Tkachenko modes, which we call acoustic and optical in analogy with phonons. For all lattice types, acoustic Tkachenko mode frequencies have quadratic wave-number dependence at long-wavelengths, while the optical Tkachenko modes have linear dependence. For triangular lattices the dispersion of the Tkachenko modes are isotropic, while for other lattice types the dispersion relations show directional dependence consistent with the symmetry of the lattice. Depending on the intercomponent interaction there are five distinct lattice types, and four structural phase transitions between them. Two of these transitions are second-order and are accompanied by the softening of an acoustic Tkachenko mode. The remaining two transitions are first-order and while one of them is accompanied by the softening of an optical mode, the other does not have any dramatic effect on the Tkachenko spectrum. We also find an instability of the vortex lattice when the intercomponent repulsion becomes stronger than the repulsion within the components.Keçeli, MuratM.S

Ansatz from Non-Linear Optics Applied to Trapped Bose-Einstein Condensates

A simple analytical ansatz, which has been used to describe the intensity profile of the similariton laser (a laser with self-similar propagation of ultrashort pulses), is used as a variational wave function to solve the Gross-Pitaevskii equation for a wide range of interaction parameters. The variational form interpolates between the noninteracting density profile and the strongly interacting Thomas-Fermi profile smoothly. The simple form of the ansatz is modified for both cylindrically symmetric and completely anisotropic harmonic traps. The resulting ground-state density profile and energy are in very good agreement with both the analytical solutions in the limiting cases of interaction and the numerical solutions in the intermediate regime.Comment: 4 pages, 3 figures, published versio

Dijagnostička točnost sastojaka mlijeka kod dijagnostike gravidnosti u krava srednje i kasne laktacije

The aims of this study were to establish a cut-off point by evaluating the usability of the somatic cell count (SCC) and milk components (fat, fat-free dry matter (FFDM), protein, lactose, freezing point, electrical conductivity and pH) to observe the pregnancy status, and to determine the practical usage of these parameters as diagnostic biomarker of pregnancy status. In the present study, primiparous Holstein cows (n=133) were included in the mid and late lactation. Milk samples were collected in sterile tubes for SCC and milk components analysis. In each lactation period, SCC, milk yield and milk component parameters were analysed by Student\u27s t test according to pregnancy status. Receiver operating characteristic curves were used to determine the predictive threshold using SCC and milk component parameters to discriminate between pregnant and non-pregnant cows. SCC levels were similar for all cows in the mid and late-lactation. In the mid lactation, FFDM, protein, lactose and electrical conductivity were higher and milk yield, fat, freezing point and pH were lower in pregnant cows (p<0.05). In the late lactation, FFDM, protein, lactose and electrical conductivity were significantly higher and milk yield, fat and pH were significantly lower in pregnant cows (p<0.05). Furthermore, fat, FFDM, protein, lactose, freezing point, electrical conductivity, and pH were the best predictors for pregnancy diagnosis in mid-lactating cows with the AUC values of 0.840, 0.768, 0.780, 0.772, 0.693, 0.792, and 0.901 respectively. Furthermore, fat, FFDM, protein, lactose, electrical conductivity, and pH could be useful diagnostic tools for pregnancy determination in late lactating cows with the AUC values of 0.869, 0.684, 0.661, 0.689, 0.756, and 0.841 respectively. In conclusion, the milk components could be used as rapid, easily accessible, and inexpensive markers for the evaluation of the diagnosis of pregnancy status in primiparous Holstein cows.Ciljevi ove studije bili su utvrditi granične vrijednosti procjenom mogućnosti upotrebe broja somatskih stanica (SCC) i pojedinih fizikalno-kemijskih parametara mlijeka (udio masti, bezmasne suhe tvari (FFDM), proteina, laktoze, točke zamrzavanja, električne vodljivosti i pH) za promatranje statusa gravidnosti kao i u svrhu korištenja navedenih parametara kao bioloških markera u dijagnozi statusa gravidnosti. U ovu su studiju bile uključene prvotelke holstein pasmine (n=133) u srednjoj i kasnoj laktaciji. Uzorci mlijeka sakupljani su u sterilne epruvete za analizu SCC i fizikalno-kemijskih parametara. U svakom razdoblju laktacije, SCC, prinos mlijeka i fizikalno-kemijski parametri analizirani su Student t-testom u odnosu na status gravidnosti. Za određivanje prediktivnog praga korištene su krivulje odnosa specifičnosti i osjetljivosti klasifikatora (ROC), korištenjem SCC i fizikalno-kemijskih parametara mlijeka za razlikovanje gravidnih i negravidnih krava. Za sve krave u srednjoj i kasnoj laktaciji razine SCC bile su slične. Sredinom laktacije, FFDM, udjeli proteina i laktoze te električna vodljivost bili su viši, a prinos mlijeka, udio masti, točka ledišta i pH bili su niži u gravidnih krava (p<0,05). U kasnoj laktaciji, FFDM, udjeli proteina i laktoze te električna vodljivost bili su značajno viši, a prinos mlijeka, udio masti i pH bili su značajno niži u gravidnih krava (p<0,05). Udjeli masti, proteina i laktoze, FFDM, točka ledišta, električna vodljivost i pH bili su najbolji prediktori za dijagnozu gravidnosti kod krava u srednjoj laktaciji s vrijednostima površina ispod ROC krivulje (AUC) 0,840, 0,768, 0,780, 0,772, 0,693, 0,792 i 0,901. Udjeli masti, proteina i laktoze, FFDM, električna vodljivost i pH mogu biti korisni dijagnostički alati za određivanje gravidnosti kod krava u kasnoj laktaciji s AUC vrijednostima 0,869, 0,684, 0,661, 0,689, 0,756 i 0,841. Zaključno, komponente mlijeka mogu se koristiti kao brzi, lako dostupni i jeftini markeri za procjenu dijagnoze statusa gravidnosti kod prvotelki holstein krava

ELSI -- An open infrastructure for electronic structure solvers

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. Finally, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets. Program summary: Program title: ELSI Interface CPC Library link to program files: http://dx.doi.org/10.17632/473mbbznrs.1 Licensing provisions: BSD 3-clause Programming language: Fortran 2003, with interface to C/C++ External routines/libraries: BLACS, BLAS, BSEPACK (optional), EigenExa (optional), ELPA, FortJSON, LAPACK, libOMM, MPI, MAGMA (optional), MUMPS (optional), NTPoly, ParMETIS (optional), PETSc (optional), PEXSI, PT-SCOTCH (optional), ScaLAPACK, SLEPc (optional), SuperLU_DIST Nature of problem: Solving the electronic structure from given Hamiltonian and overlap matrices in electronic structure calculations. Solution method: ELSI provides a unified software interface to facilitate the use of various electronic structure solvers including cubic scaling dense eigensolvers, linear scaling density matrix methods, and other approaches

The frequency of Duchenne muscular dystrophy/Becker muscular dystrophy and Pompe disease in children with isolated transaminase elevation: results from the observational VICTORIA study

IntroductionElevated transaminases and/or creatine phosphokinase can indicate underlying muscle disease. Therefore, this study aims to determine the frequency of Duchenne muscular dystrophy/Becker muscular dystrophy (DMD/BMD) in male children and Pompe disease (PD) in male and female children with isolated hypertransaminasemia.MethodsThis multi-center, prospective study enrolled patients aged 3–216 months with serum alanine transaminase (ALT) and/or aspartate transaminase (AST) levels &gt;2× the upper limit of normal (ULN) for ≥3 months. Patients with a known history of liver or muscle disease or physical examination findings suggestive of liver disease were excluded. Patients were screened for creatinine phosphokinase (CPK) levels, and molecular genetic tests for DMD/BMD in male patients and enzyme analysis for PD in male and female patients with elevated CPK levels were performed. Genetic analyses confirmed PD. Demographic, clinical, and laboratory characteristics of the patients were analyzed.ResultsOverall, 589 patients [66.8% male, mean age of 63.4 months (standard deviation: 60.5)] were included. In total, 251 patients (188 male and 63 female) had CPK levels above the ULN. Of the patients assessed, 47% (85/182) of male patients were diagnosed with DMD/BMD and 1% (3/228) of male and female patients were diagnosed with PD. The median ALT, AST, and CPK levels were statistically significantly higher, and the questioned neurological symptoms and previously unnoticed examination findings were more common in DMD/BMD patients than those without DMD/BMD or PD (p &lt; 0.001).DiscussionQuestioning neurological symptoms, conducting a complete physical examination, and testing for CPK levels in patients with isolated hypertransaminasemia will prevent costly and time-consuming investigations for liver diseases and will lead to the diagnosis of occult neuromuscular diseases. Trial RegistrationClinicaltrials.gov NCT04120168

Valence: A Massively Parallel Implementation of the Variational Subspace Valence Bond Method

This work describes the software package, Valence, for the calculation of molecularenergies using the variational subspace valence bond (VSVB) method. VSVB is a highly scalable ab initio electronic structure method based on non-orthogonal orbitals. Important features of practical value include: Valence bond wave functions of Hartree–Fock quality can be constructed with a single determinant; excited states can be modeled with a single configuration or determinant; wave functions can be constructed automatically by combining orbitals from previous calculations. The opensource software package includes tools to generate wave functions, a database of generic orbitals, example input files, and a library build intended for integration with other packages. We also describe the interface to an external software package, enabling the computation of optimized molecular geometries and vibrational frequencies

The effects of vertically coronally advanced flap and free gingival graft techniques on shallow vestibule: a randomized comparative prospective trial

Objectives: The present study aimed to compare the influence of vertically coronally advanced flap (V-CAF) and free gingival graft (FGG) techniques on shallow vestibule depth (VD). Materials and methods: Parallel-arm randomized clinical trial was conducted on 38 sites treated with either FGG or V-CAF. Periodontal variables (VD, recession depth and width, probing depth, clinical attachment level, keratinized tissue height (KTH), and tissue thickness (TT)), clinician- and patient-based subjective variables were assessed. Results: All periodontal variables showed significant improvements in both groups at all follow-up intervals compared to baseline (p < 0.05). Both groups increased VD compared to baseline. RC and CRC were similar after treatment for both techniques. FGG provided a greater increase in KTH (p < 0.001) and VD (VD1, p = 0.02 and VD2, p < 0.001) while V-CAF exhibited more TT gain (p = 0.002). Except overall tissue appearance that was better in V-CAF (p < 0.001), no inter-group significant difference existed in patient-based variables. Conclusions: Both techniques were significantly effective in VD increasing. While both techniques were equally successful in RC, V-CAF provided higher TT gain and better tissue appearance. V-CAF can be chosen instead of FGG in the treatment of recessions with shallow VD. Clinical relevance: It can be recommended to prefer V-CAF instead of FGG in the treatment of shallow vestibule. Trial registration number: NCT05777811 (clinicaltrials.gov)

Dual delivery of platelet-derived growth factor and bone morphogenetic factor-6 on titanium surface to enhance the early period of implant osseointegration

Objective: To test the surface properties and in vitro effects of a new sequential release system on MC3T3-E1 cells for improved osseointegration. Background: BMP6-loaded anodized titanium coated with PDGF containing silk fibroin (SF) may improve osseointegration. Methods: Titanium surfaces were electrochemically anodized, and SF layer was covered via electrospinning. Five experimental groups (unanodized Ti (Ti), anodized Ti (AnTi), anodized + BMP6-loaded Ti (AnTi-BMP6), anodized + BMP6 loaded + silk fibroin-coated Ti (AnTi-BMP6-SF), and anodized + BMP6-loaded + silk fibroin with PDGF-coated Ti (AnTi-BMP6-PDGF-SF)) were tested. After SEM characterization, contact angle analysis, and FTIR analysis, the amount of released PDGF and BMP6 was detected using ELISA. Cell proliferation (XTT), mineralization, and gene expression (RUNX2 and ALPL) were also evaluated. Results: After successful anodization and loading of PDGF and BMP6, contact angle measurements showed hydrophobicity for TiO2 and hydrophilicity for protein-adsorbed surfaces. In FTIR, protein-containing surfaces exhibited amide-I, amide-II, and amide-III bands at 1600 cm-1-1700 cm-1, 1520 cm-1-1540 cm-1, and 1220 cm-1-1300 cm-1 spectrum levels with a significant peak in BMP6- and/or SF-loaded groups at 1100 cm-1. PDGF release and BMP6 release were delayed, and relatively slower release was detected in SF-coated surfaces. Higher MC3T3-E1 proliferation and mineralization and lower gene expression of RUNX2 and ALPL were detected in AnTi-BMP6-PDGF-SF toward day 28. Conclusion: The new system revealed a high potential for an improved early osseointegration period by means of a better factor release curve and contribution to the osteoblastic cell proliferation, mineralization, and associated gene expression. © 2020 John Wiley & Sons A/S. Published by John Wiley & Sons Lt

Cyanoacrylate and hyaluronic acid combination on palatal donor site management after de-epithelialized graft harvesting

BackgroundAlthough soft tissue substitutes showed promising improvement in the past decade, epithelialized gingival graft (EGG) is still widely used in periodontal plastic surgery applications. Donor site management after EGG harvesting has been challenging for clinicians. This study aimed to compare the effectiveness of cyanoacrylate, hyaluronic acid, and their combination in palatal donor site management after EGG harvesting. MethodsData from 89 patients were included and categorized as gelatin sponge (GS), gelatin sponge with either cyanoacrylate (GS + CY), hyaluronic acid (GS + HA), or both (GS + CY + HA). The data of pain perception (PP), quantity of analgesics (QA), secondary bleeding (SB), epithelization level (EL), and color match (CM) were assessed retrospectively. ResultsThe GS + CY and GS + HA + CY groups showed lower PP scores compared to the GS and GS + HA groups (p < 0.05). The QA was higher in the GS group compared to the GS + CY and GS + HA + CY groups (p < 0.001). All study groups showed greater EL than GS group on day 7 (p < 0.001). On day 14, full EL was present in 81% of the patients in the GS + HA + CY group, which was higher than the other groups (p < 0.001). All study groups reported lower SB in the first 3 days, which was lower compared to the GS group (p < 0.001) and showed higher CM scores than the GS group on days 7 and 14 (p < 0.001). ConclusionsCY application reduces pain and analgesic intake and HA may support the wound healing with increased EL. Using the CY-HA combination provides additional benefits for donor site management