Inhomogeneous Source Research Articles

Mathematical technology for solving the Kardar-Parisi-Zhang equation with a source

The description of an algorithm for numerical solution of the two-dimensional Kardar-Parisi-Zhang equation with fractal initial condition and spatially inhomogeneous stochastic source of particles has been presented. Using the Cole-Hopf substitution, the KardarParisi-Zhang equation is reduced to an auxiliary linear parabolic equation with a variable coefficient. This reduction provides both compatibility of the algorithm with the concept of mathematical technology and possibility of its practical realization on supercomputer using the MPI parallel programming technology and the ROOT framework. The required profile of the evolving surface is restored by the inverse substitution by solving the auxiliary equation, Opportunity of estimation of its autocorrelation function and its spectral power density, as well as the time dynamics of Shannon surface information, have been discussed.

Inhomogeneous Distribution of Components in Solid Protein Pharmaceuticals: Origins, Consequences, Analysis, and Resolutions.

Successful development of stable solid protein formulations usually requires the addition of one or several excipients to achieve optimal stability. In these products, there is a potential risk of an inhomogeneous distribution of the various ingredients, specifically the ratio of protein and stabilizer may vary. Such inhomogeneity can be detrimental for stability but is mostly neglected in literature. In the past, it was challenging to analyze inhomogeneous component distribution, but recent advances in analytical techniques have revealed new options to investigate this phenomenon. This paper aims to review fundamental aspects of the inhomogeneous distribution of components of freeze-dried and spray-dried protein formulations. Four key topics will be presented and discussed, including the sources of component inhomogeneity, its consequences on protein stability, the analytical methods to reveal component inhomogeneity, and possible solutions to prevent or mitigate inhomogeneity.

Generalized Fourier's law for nondiffusive thermal transport: Theory and experiment

Phonon heat conduction over length scales comparable to their mean free paths is a topic of considerable interest for basic science and thermal management technologies. Although the failure of Fourier's law beyond the diffusive regime is well understood, debate exists over the proper physical description of thermal transport in the ballistic to diffusive crossover. Here, we derive a generalized Fourier's law that links the heat flux and temperature fields, valid from ballistic to diffusive regimes and for general geometries, using the Peierls-Boltzmann transport equation within the relaxation time approximation. This generalized Fourier's law predicts that thermal conductivity not only becomes nonlocal at length scales smaller than phonon mean free paths, but also requires the inclusion of an inhomogeneous nonlocal source term that has been previously neglected. We demonstrate the validity of this generalized Fourier's law through direct comparison with time-domain thermoreflectance (TDTR) measurements in the nondiffusive regime without adjustable parameters. Furthermore, we show that interpreting experimental data without this generalized Fourier's law leads to inaccurate measurement of thermal transport properties.

Dielectric disorder in two-dimensional materials.

Understanding and controlling disorder is key to nanotechnology and materials science. Traditionally, disorder is attributed to local fluctuations of inherent material properties such as chemical and structural composition, doping or strain. Here, we present a fundamentally new source of disorder in nanoscale systems that is based entirely on the local changes of the Coulomb interaction due to fluctuations of the external dielectric environment. Using two-dimensional semiconductors as prototypes, we experimentally monitor dielectric disorder by probing the statistics and correlations of the exciton resonances, and theoretically analyse the influence of external screening and phonon scattering. Even moderate fluctuations of the dielectric environment are shown to induce large variations of the bandgap and exciton binding energies up to the 100 meV range, often making it a dominant source of inhomogeneities. As a consequence, dielectric disorder has strong implications for both the optical and transport properties of nanoscale materials and their heterostructures.

Homogenization of Plasma Emission Collection for Multichannel Spectrometers.

Laser-induced breakdown spectroscopy (LIBS) has recently demonstrated its unrivaled performance for broadband elemental imaging of surfaces. The dimensions of the laser sampling spot still being potentially larger than the interfaces of chemical domains, the plasma created at each location can be largely varying and inhomogeneous with contributions from the different sides of the interface. This variation can become problematic when imaging it on fiber bundles connected to multiple spectrometers. A spatially heterogeneous signal would lead to spatially dependent image on the fiber bundle causing inconsistent readings and loss of efficiency. Köhler illumination is used in this study to create a homogenous illumination, regardless of the source homogeneity, thus improving light collection efficiency. The performance of this approach was demonstrated with inhomogeneous spectral sources and applied to the LIBS analysis of a metallic interface, showing up to a sixfold improvement of the homogeneity of the plasma collection.

CaosDB—Research Data Management for Complex, Changing, and Automated Research Workflows

We present CaosDB, a Research Data Management System (RDMS) designed to ensure seamless integration of inhomogeneous data sources and repositories of legacy data in a FAIR way. Its primary purpose is the management of data from biomedical sciences, both from simulations and experiments during the complete research data lifecycle. An RDMS for this domain faces particular challenges: research data arise in huge amounts, from a wide variety of sources, and traverse a highly branched path of further processing. To be accepted by its users, an RDMS must be built around workflows of the scientists and practices and thus support changes in workflow and data structure. Nevertheless, it should encourage and support the development and observation of standards and furthermore facilitate the automation of data acquisition and processing with specialized software. The storage data model of an RDMS must reflect these complexities with appropriate semantics and ontologies while offering simple methods for finding, retrieving, and understanding relevant data. We show how CaosDB responds to these challenges and give an overview of its data model, the CaosDB Server and its easy-to-learn CaosDB Query Language. We briefly discuss the status of the implementation, how we currently use CaosDB, and how we plan to use and extend it.

Nonchiral Bosonization of Strongly Inhomogeneous Luttinger Liquids

Nonchiral bosonization (NCBT) is a nontrivial modification of the standard Fermi—Bose correspondence in one spatial dimension done to facilitate studying strongly inhomogeneous Luttinger liquids where the properties of free fermions plus the source of inhomogeneities are reproduced exactly. We introduce the NCBT formalism and discuss limit case checks, fermion commutation rules, point-splitting constraints, etc. We expand the Green’s functions obtained from NCBT in powers of the fermion—fermion interaction strength (only short-range forward scattering) and compare them with the corresponding terms obtained using standard fermionic perturbation theory. Finally, we substitute the Green’s functions obtained from NCBT in the Schwinger—Dyson equation, which is the equation of motion of the Green’s functions and serves as a nonperturbative confirmation of the method. We briefly discuss some other analytic approaches such as functional bosonization and numerical techniques like the density-matrix renormalization group, which can be used to obtain the correlation functions in one dimension.

The ASAS-SN Catalog of Variable Stars II: Uniform Classification of 412,000 Known Variables

The variable stars in the VSX catalog are derived from a multitude of inhomogeneous data sources and classification tools. This inhomogeneity complicates our understanding of variable star types, statistics, and properties, and it directly affects attempts to build training sets for current (and next) generation all-sky, time-domain surveys. We homogeneously analyze the ASAS-SN V-band light curves of ${\sim}412,000$ variables from the VSX catalog. The variables are classified using an updated random forest classifier with an $F_1$ score of 99.4\% and refinement criteria for individual classifications. We have derived periods for ${\sim}52,000$ variables in the VSX catalog that lack a period, and have reclassified ${\sim} 17,000$ sources into new broad variability groups with high confidence. We have also reclassified ${\sim} 94,000$ known variables with miscellaneous/generic classifications. The light curves, classifications, and a range of properties of the variables are all available through the ASAS-SN variable stars database (https://asas-sn.osu.edu/variables). We also include the V-band light curves for a set of ${\sim}4,000$ rare variables and transient sources, including cataclysmic variables, symbiotic binaries and flare stars.

A Review of Magneto-Elastic Interaction and Its Theoretical Descriptions in Type-II Superconductors

It is well known that the interaction between defect-induced strain field and vortex lattice (VL) gives rise to vortex pinning behaviors. Likewise, magneto-elastic (ME) interaction is caused by the difference between specific volumes of normal phase and superconducting (SC) phase. Acting as inhomogeneous strain sources, the normal-state vortex cores produce local deformation in the surrounding SC matter and thus affect VL energy. ME interaction belongs to the fundamental physics of interdependences between vortex matter and crystal lattice. The review starts with the effects of ME interaction on magnetization, vortex morphology and intervortex interaction. In Sect. 2, theoretical descriptions of ME interaction are classified in terms of different simplifications. The core ideas and outstanding results of these theories are given. It is followed by Sect. 3, where the correlation and difference between ME and pinning interaction are outlined. Although pinning differs from ME interaction in their formation mechanisms, the pinning interaction is established upon the vortex-induced strain field from Ginzburg-Landau (GL) viewpoint. Section 4 goes further with the GL treatment for solving ME and pinning problem; the general thoughts and steps can be found in this section. The last section gives some outlooks which involve pressure dependence of Tc and anisotropy.

On a backward problem for inhomogeneous time-fractional diffusion equations

In this paper, we consider a final value problem for time-fractional diffusion equation with inhomogeneous source. The main goal of our paper is to determine an approximated initial data from the observation data at final time by constructing a regularized solution using a mollification method. Under appropriate regularity assumptions of the exact solution, we give convergence rate between the reconstructed solution and the exact one. We also provide a numerical example to illustrate the main results.

Computational design of a high-efficiency accelerator grid for a miniature ion thruster by full-aperture ion optics simulations

Full-aperture ion optics simulations have been conducted for the inhomogeneous plasma source of a miniature ion propulsion system (MIPS) to design a high-efficiency accelerator grid that provides high degree of the neutral confinement and absence of direct ion impingement. The designed accelerator grid has flat upstream and smoothly curved downstream surfaces with straight holes for easy low-cost manufacture. The diameter of the accelerator aperture was changed from the nominal value of 0.40 mm to 0.25 mm, which decreased neutral leakage and increased the propellant utilization efficiency from 31 to 50%. The direct impingement of ions caused by decreasing the accelerator aperture diameter was compensated by reducing the thickness of the accelerator grid while taking into account the inhomogeneous ion beam current density profile of the MIPS. An off-design performance simulation was conducted to validate the proposed grid design; the obtained results showed that the ion beam could be accelerated smoothly even during throttling the beam current between 75 and 150%. A grid wear simulation was also performed to compare the changes in the propellant utilization efficiency between the nominal and high-efficiency grids caused by erosion. It was found that the propellant utilization efficiency of the high-efficiency grid was greater than that of the nominal grid within the first 5,000 h of operation and that its lifetime exceeded 10,000 h of the accumulated operation time. By using the proposed high-efficiency accelerator grid and MIPS plasma source, the propellant utilization efficiency was increased, while the accelerator impingement current became negligible.

A rule-based semantic approach for data integration, standardization and dimensionality reduction utilizing the UMLS: Application to predicting bariatric surgery outcomes

Utilization of existing clinical data for improving patient outcomes poses a number of challenging and complex problems involving lack of data integration, the absence of standardization across inhomogeneous data sources and computationally-demanding and time-consuming exploration of very large datasets. In this paper, we will present a robust semantic data integration, standardization and dimensionality reduction method to tackle and solve these problems. Our approach enables the integration of clinical data from diverse sources by resolving canonical inconsistencies and semantic heterogeneity as required by the National Library of Medicine's Unified Medical Language System (UMLS) to produce standardized medical data. Through a combined application of rule-based semantic networks and machine learning, our approach enables a large reduction in dimensionality of the data and thus allows for fast and efficient application of data mining techniques to large clinical datasets. An example application of the techniques developed in our study is presented for the prediction of bariatric surgery outcomes.

Prescribing psychotropic medications for children and adolescents by young psychiatrists attending the ECNP School of Neuropsychopharmacology

In this paper, we consider a final value problem for time-fractional diffusion equation with inhomogeneous source. The main goal of our paper is to determine an approximated initial data from the observation data at final time by constructing a regularized solution using a mollification method. Under appropriate regularity assumptions of the exact solution, we give convergence rate between the reconstructed solution and the exact one. We also provide a numerical example to illustrate the main results.

The quasi-boundary value method for identifying the initial value of heat equation on a columnar symmetric domain

In this paper, we consider an inverse problem for determining the initial value of heat equation with inhomogeneous source on a columnar symmetric domain. The quasi-boundary value regularization method is applied to solve this inverse problem. Under the a priori and a posteriori regularization parameter choice rules, the convergence estimates between the regularization solution and the exact solution are given. The numerical examples show this regularization method is effective and stable for dealing with this problem.

Influence of transversely inhomogeneous pseudo-thermal light source on lensless ghost imaging

The influence of a transversely inhomogeneous pseudo-thermal light source on lensless ghost imaging is investigated theoretically and experimentally. Based on classical optical theory, a model of lensless ghost imaging with an inside inclined light source is analyzed. We use the optical path difference between different transverse positions of the light beam to estimate the degree of inhomogeneity. The results indicate that the transversely inhomogeneous light source decreases the visibility and signal-to-noise ratio of the reconstructed image. Finally, we implement experiments to verify our results using inclined ground glass.

Ponderous impurities in a Luttinger liquid

In this work, analytical expressions for the Green function of a Luttinger liquid are derived with one and two mobile impurities (heavy particles) using a combination of bosonization and perturbative approaches. The calculations are done in the random phase approximation (RPA) limit using the powerful non-chiral bosonization technique (NCBT) which is nothing but the resummation of the most singular parts of the RPA terms of the Green function expanded out in powers of the forward scattering between fermions with the source of inhomogeneities treated exactly. The force acting on the heavy particle(s) is studied as a function of its terminal velocity, both in the linear and non-linear regime. Linear mobility (which is valid for impurities moving much slower than a certain crossover speed) has a power law temperature dependence whose exponent has a closed algebraic expression in terms of the various parameters in the problem. This expression interpolates between the ballistic regime of no-coupling with the fermions and the no-tunneling regime. When the speed of the impurity is much larger than this crossover speed, the applied force depends non-linearly on the speed and this too is a power law with a closely related exponent. The case of two mobile impurities is also studied whose mobility exhibits peculiar resonances when their mutual separation is appropriately chosen.

Periodic optical variability and debris accretion in white dwarfs: a test for a causal connection*

Recent Kepler photometry has revealed that about half of white dwarfs (WDs) have periodic, low-level (~ 1e-4 - 1e-3), optical variations. Hubble Space Telescope (HST) ultraviolet spectroscopy has shown that up to about one half of WDs are actively accreting rocky planetary debris, as evidenced by the presence of photospheric metal absorption lines. We have obtained HST ultraviolet spectra of seven WDs that have been monitored for periodic variations, to test the hypothesis that these two phenomena are causally connected, i.e. that the optical periodic modulation is caused by WD rotation coupled with an inhomogeneous surface distribution of accreted metals. We detect photospheric metals in four out of the seven WDs. However, we find no significant correspondence between the existence of optical periodic variability and the detection of photospheric ultraviolet absorption lines. Thus the null hypothesis stands, that the two phenomena are not directly related. Some other source of WD surface inhomogeneity, perhaps related to magnetic field strength, combined with the WD rotation, or alternatively effects due to close binary companions, may be behind the observed optical modulation. We report the marginal detection of molecular hydrogen in WD J1949+4734, only the fourth known WD with detected H_2 lines. We also re-classify J1926+4219 as a carbon-rich He-sdO subdwarf.

The truncation regularization method for identifying the initial value of heat equation on a spherical symmetric domain

In this paper, identifying the initial value for high dimension heat equation with inhomogeneous source on a spherical symmetric domain is investigated. The truncation regularization method is a powerful technique for solving this inverse problem. We prove the convergence estimates between the regularization solution and the exact solution under the prior and the posterior regularization parameter choice rulers. A numerical example is presented to validate the effectiveness of this method.

A truncation regularization method for a time fractional diffusion equation with an in-homogeneous source

In the present paper, we consider a time-fractional inverse diffusion problem with an in-homogeneous source, where data is given at x = 1 and the solution is required in the interval 0 < x < 1. This problem is ill-posed, i.e. the solution (if it exists) does not depend continuously on the data. We propose a regularization method to solve it based on the solution given by the Fourier method.

Numerical simulation of full-aperture-pair ion optics in a miniature ion thruster

The 211-aperture-pair two-grid ion optics of a miniature ion thruster is numerically simulated. Since the plasma in the miniature ion thruster is too inhomogeneous to introduce mirror or translational boundary conditions between apertures, all the apertures of the grid system are considered. The simulation is self-consistent, the ion current profile in the discharge chamber plasma is given by the particle-in-cell with Monte Carlo collision algorithm calculations, and all the ion beams extracted from the full-aperture-pair array were tracked including charge-exchange ions. A scheme for the construction of the full-aperture-pair simulation domain is proposed based on the array of a six-fold hexagonal single-aperture-pair simulation domain, which can be extended to other numbers of aperture pairs. Numerical results on accel impingement current and ion-beam profile are compared to experimental data and shown to be in reasonable agreement. Furthermore, the full-aperture-pair ion-optics model is compared with the single-aperture-pair ion-optics models used in the majority of previous ion-optics simulations, which showed that the full-aperture-pair ion-optics model yielded the most accurate predictions. These results suggest that the ion thruster grid system using an inhomogeneous plasma source can be designed more accurately and effectively using full-aperture-pair ion-optics simulations.