Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1972-01-01

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.

A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

DTIC Science & Technology

NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

Validity of GNRB® arthrometer compared to Telos™ in the assessment of partial anterior cruciate ligament tears.

PubMed

Lefevre, N; Bohu, Y; Naouri, J F; Klouche, S; Herman, S

2014-02-01

The main goal of this study was to compare the results of the GNRB(®) arthrometer to those of Telos™ in the diagnosis of partial thickness tears of the anterior cruciate ligament (ACL). A prospective study performed January-December 2011 included all patients presenting with a partial or full-thickness ACL tears without ACL reconstruction and with a healthy contralateral knee. Anterior laxity was measured in all patients by the Telos™ and GNRB(®) devices. This series included 139 patients, mean age 30.7 ± 9.3 years. Arthroscopic reconstruction was performed in 109 patients, 97 for complete tears and 12 single bundle reconstructions for partial thickness tears. Conservative treatment was proposed in 30 patients with a partial thickness tear. The correlation between the two devices was evaluated by the Spearman coefficient. The optimal laxity thresholds were determined with ROC curves, and the diagnostic value of the tests was assessed by the area under the curve (AUC). The differential laxities of full and partial thickness tears were significantly different with the two tests. The correlation between the results of laxity measurement with the two devices was fair, with the strongest correlation between Telos™ 250 N and GNRB(®) 250 N (r = 0.46, p = 0.00001). Evaluation of the AUC showed that the informative value of all tests was fair with the best results with the GNRB(®) 250 N: AUC = 0.89 [95 % CI 0.83-0.94]. The optimal differential laxity threshold with the GNRB(®) 250 N was 2.5 mm (Se = 84 %, Sp = 81 %). The diagnostic value of GNRB(®) was better than Telos™ for ACL partial thickness tears.

Motor impulsivity differentiates between psychiatric inpatients with multiple versus single lifetime suicide attempts.

PubMed

Colborn, Victoria A; LaCroix, Jessica M; Neely, Laura L; Tucker, Jennifer; Perera, Kanchana; Daruwala, Samantha E; Grammer, Geoffrey; Weaver, Jennifer; Ghahramanlou-Holloway, Marjan

2017-07-01

A history of multiple suicide attempts conveys greater risk for suicide than a single attempt. Impulsivity may partially explain the association between multiple attempts and increased risk. We examined trait impulsivity, ability to engage in goal-directed behaviors, and impulse control among psychiatrically hospitalized United States military personnel and their dependents. Individuals with a history of multiple versus single attempts had significantly higher motor impulsivity, indicating spur of the moment action. Providers are encouraged to directly assess and treat motor impulsivity among suicidal individuals. Further research should explore whether motor impulsivity is a mechanism of change in psychosocial suicide prevention interventions. Copyright © 2017. Published by Elsevier B.V.

Lactobacillus strain diversity based on partial hsp60 gene sequences and design of PCR-restriction fragment length polymorphism assays for species identification and differentiation.

PubMed

Blaiotta, Giuseppe; Fusco, Vincenzina; Ercolini, Danilo; Aponte, Maria; Pepe, Olimpia; Villani, Francesco

2008-01-01

A phylogenetic tree showing diversities among 116 partial (499-bp) Lactobacillus hsp60 (groEL, encoding a 60-kDa heat shock protein) nucleotide sequences was obtained and compared to those previously described for 16S rRNA and tuf gene sequences. The topology of the tree produced in this study showed a Lactobacillus species distribution similar, but not identical, to those previously reported. However, according to the most recent systematic studies, a clear differentiation of 43 single-species clusters was detected/identified among the sequences analyzed. The slightly higher variability of the hsp60 nucleotide sequences than of the 16S rRNA sequences offers better opportunities to design or develop molecular assays allowing identification and differentiation of either distant or very closely related Lactobacillus species. Therefore, our results suggest that hsp60 can be considered an excellent molecular marker for inferring the taxonomy and phylogeny of members of the genus Lactobacillus and that the chosen primers can be used in a simple PCR procedure allowing the direct sequencing of the hsp60 fragments. Moreover, in this study we performed a computer-aided restriction endonuclease analysis of all 499-bp hsp60 partial sequences and we showed that the PCR-restriction fragment length polymorphism (RFLP) patterns obtainable by using both endonucleases AluI and TacI (in separate reactions) can allow identification and differentiation of all 43 Lactobacillus species considered, with the exception of the pair L. plantarum/L. pentosus. However, the latter species can be differentiated by further analysis with Sau3AI or MseI. The hsp60 PCR-RFLP approach was efficiently applied to identify and to differentiate a total of 110 wild Lactobacillus strains (including closely related species, such as L. casei and L. rhamnosus or L. plantarum and L. pentosus) isolated from cheese and dry-fermented sausages.

On the hierarchy of partially invariant submodels of differential equations

NASA Astrophysics Data System (ADS)

Golovin, Sergey V.

2008-07-01

It is noted that the partially invariant solution (PIS) of differential equations in many cases can be represented as an invariant reduction of some PISs of the higher rank. This introduces a hierarchic structure in the set of all PISs of a given system of differential equations. An equivalence of the two-step and the direct ways of construction of PISs is proved. The hierarchy simplifies the process of enumeration and analysis of partially invariant submodels to the given system of differential equations. In this framework, the complete classification of regular partially invariant solutions of ideal MHD equations is given.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1989-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of partial differential equation solutions in the least squares norm.

Solution of differential equations by application of transformation groups

NASA Technical Reports Server (NTRS)

Driskell, C. N., Jr.; Gallaher, L. J.; Martin, R. H., Jr.

1968-01-01

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations.

Numerical solution of differential equations by artificial neural networks

NASA Technical Reports Server (NTRS)

Meade, Andrew J., Jr.

1995-01-01

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks (ANN's) are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed by the author to mate the adaptability of the ANN with the speed and precision of the digital computer. This method has been successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Design of TIR collimating lens for ordinary differential equation of extended light source

NASA Astrophysics Data System (ADS)

Zhan, Qianjing; Liu, Xiaoqin; Hou, Zaihong; Wu, Yi

2017-10-01

The source of LED has been widely used in our daily life. The intensity angle distribution of single LED is lambert distribution, which does not satisfy the requirement of people. Therefore, we need to distribute light and change the LED's intensity angle distribution. The most commonly method to change its intensity angle distribution is the free surface. Generally, using ordinary differential equations to calculate free surface can only be applied in a point source, but it will lead to a big error for the expand light. This paper proposes a LED collimating lens based on the ordinary differential equation, combined with the LED's light distribution curve, and adopt the method of calculating the center gravity of the extended light to get the normal vector. According to the law of Snell, the ordinary differential equations are constructed. Using the runge-kutta method for solution of ordinary differential equation solution, the curve point coordinates are gotten. Meanwhile, the edge point data of lens are imported into the optical simulation software TracePro. Based on 1mm×1mm single lambert body for light conditions, The degrees of collimating light can be close to +/-3. Furthermore, the energy utilization rate is higher than 85%. In this paper, the point light source is used to calculate partial differential equation method and compared with the simulation of the lens, which improve the effect of 1 degree of collimation.

Reciprocal links among differential parenting, perceived partiality, and self-worth: a three-wave longitudinal study.

PubMed

Shebloski, Barbara; Conger, Katherine J; Widaman, Keith F

2005-12-01

This study examined reciprocal links between parental differential treatment, siblings' perception of partiality, and self-worth with 3 waves of data from 384 adolescent sibling dyads. Results suggest that birth-order status was significantly associated with self-worth and perception of maternal and paternal differential treatment. There was a consistent across-time effect of self-worth on perception of parental partiality for later born siblings, but not earlier born siblings, and a consistent effect of differential treatment on perception of partiality for earlier born but not later born siblings. The results contribute new insight into the associations between perception of differential parenting and adolescents' adjustment and the role of birth order. Copyright 2006 APA, all rights reserved).

Process-Based Expansion and Neural Differentiation of Human Pluripotent Stem Cells for Transplantation and Disease Modeling

PubMed Central

Stover, Alexander E.; Brick, David J.; Nethercott, Hubert E.; Banuelos, Maria G.; Sun, Lei; O’Dowd, Diane K.; Schwartz, Philip H.

2014-01-01

Robust strategies for developing patient-specific, human, induced pluripotent stem cell (iPSC)-based therapies of the brain require an ability to derive large numbers of highly defined neural cells. Recent progress in iPSC culture techniques includes partial-to-complete elimination of feeder layers, use of defined media, and single-cell passaging. However, these techniques still require embryoid body formation or coculture for differentiation into neural stem cells (NSCs). In addition, none of the published methodologies has employed all of the advances in a single culture system. Here we describe a reliable method for long-term, single-cell passaging of PSCs using a feeder-free, defined culture system that produces confluent, adherent PSCs that can be differentiated into NSCs. To provide a basis for robust quality control, we have devised a system of cellular nomenclature that describes an accurate genotype and phenotype of the cells at specific stages in the process. We demonstrate that this protocol allows for the efficient, large-scale, cGMP-compliant production of transplantable NSCs from all lines tested. We also show that NSCs generated from iPSCs produced with the process described are capable of forming both glia defined by their expression of S100β and neurons that fire repetitive action potentials. PMID:23893392

Mathematical Methods for Physics and Engineering Third Edition Paperback Set

NASA Astrophysics Data System (ADS)

Riley, Ken F.; Hobson, Mike P.; Bence, Stephen J.

2006-06-01

Prefaces; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics; Index.

Spatial complexity of solutions of higher order partial differential equations

NASA Astrophysics Data System (ADS)

Kukavica, Igor

2004-03-01

We address spatial oscillation properties of solutions of higher order parabolic partial differential equations. In the case of the Kuramoto-Sivashinsky equation ut + uxxxx + uxx + u ux = 0, we prove that for solutions u on the global attractor, the quantity card {x epsi [0, L]:u(x, t) = lgr}, where L > 0 is the spatial period, can be bounded by a polynomial function of L for all \\lambda\\in{\\Bbb R} . A similar property is proven for a general higher order partial differential equation u_t+(-1)^{s}\\partial_x^{2s}u+ \\sum_{k=0}^{2s-1}v_k(x,t)\\partial_x^k u =0 .

Lactobacillus Strain Diversity Based on Partial hsp60 Gene Sequences and Design of PCR-Restriction Fragment Length Polymorphism Assays for Species Identification and Differentiation▿ †

PubMed Central

Blaiotta, Giuseppe; Fusco, Vincenzina; Ercolini, Danilo; Aponte, Maria; Pepe, Olimpia; Villani, Francesco

2008-01-01

A phylogenetic tree showing diversities among 116 partial (499-bp) Lactobacillus hsp60 (groEL, encoding a 60-kDa heat shock protein) nucleotide sequences was obtained and compared to those previously described for 16S rRNA and tuf gene sequences. The topology of the tree produced in this study showed a Lactobacillus species distribution similar, but not identical, to those previously reported. However, according to the most recent systematic studies, a clear differentiation of 43 single-species clusters was detected/identified among the sequences analyzed. The slightly higher variability of the hsp60 nucleotide sequences than of the 16S rRNA sequences offers better opportunities to design or develop molecular assays allowing identification and differentiation of either distant or very closely related Lactobacillus species. Therefore, our results suggest that hsp60 can be considered an excellent molecular marker for inferring the taxonomy and phylogeny of members of the genus Lactobacillus and that the chosen primers can be used in a simple PCR procedure allowing the direct sequencing of the hsp60 fragments. Moreover, in this study we performed a computer-aided restriction endonuclease analysis of all 499-bp hsp60 partial sequences and we showed that the PCR-restriction fragment length polymorphism (RFLP) patterns obtainable by using both endonucleases AluI and TacI (in separate reactions) can allow identification and differentiation of all 43 Lactobacillus species considered, with the exception of the pair L. plantarum/L. pentosus. However, the latter species can be differentiated by further analysis with Sau3AI or MseI. The hsp60 PCR-RFLP approach was efficiently applied to identify and to differentiate a total of 110 wild Lactobacillus strains (including closely related species, such as L. casei and L. rhamnosus or L. plantarum and L. pentosus) isolated from cheese and dry-fermented sausages. PMID:17993558

On the Solution of Elliptic Partial Differential Equations on Regions with Corners

DTIC Science & Technology

2015-07-09

In this report we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations . We observe...that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of...efficient numerical algorithms. The results are illustrated by a number of numerical examples. On the solution of elliptic partial differential equations on

General linear methods and friends: Toward efficient solutions of multiphysics problems

NASA Astrophysics Data System (ADS)

Sandu, Adrian

2017-07-01

Time dependent multiphysics partial differential equations are of great practical importance as they model diverse phenomena that appear in mechanical and chemical engineering, aeronautics, astrophysics, meteorology and oceanography, financial modeling, environmental sciences, etc. There is no single best time discretization for the complex multiphysics systems of practical interest. We discuss "multimethod" approaches that combine different time steps and discretizations using the rigourous frameworks provided by Partitioned General Linear Methods and Generalize-structure Additive Runge Kutta Methods..

Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2006-03-01

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Recessive Loci Pps-1 and OM Differentially Regulate PISTILLATA-1 and APETALA3-1 Expression for Sepal and Petal Development in Papaver somniferum

PubMed Central

Singh, Sharad K.; Shukla, Ashutosh K.; Dhawan, Om P.; Shasany, Ajit K.

2014-01-01

The involvement of PISTILLATA (PI) and APETALA (AP) transcription factors in the development of floral organs has previously been elucidated but little is known about their upstream regulation. In this investigation, two novel mutants generated in Papaver somniferum were analyzed - one with partially petaloid sepals and another having sepaloid petals. Progeny from reciprocal crosses of respective mutant parent genotypes showed a good fit to the monogenic Mendelian inheritance model, indicating that the mutant traits are likely controlled by the single, recessive nuclear genes named “Pps-1” and “OM” in the partially petaloid sepal and sepaloid petal phenotypes, respectively. Both paralogs of PISTILLATA (PapsPI-1 and PapsPI-3) were obtained from the sepals and petals of P. somniferum. Ectopic expression of PapsPI-1 in tobacco resulted in a partially petaloid sepal phenotype at a low frequency. Upregulation of PapsPI-1 and PapsAP3-1 in the petal and the petal part of partially petaloid sepal mutant and down-regulation of the same in sepaloid petal mutant indicates a differential pattern of regulation for flowering-related genes in various whorls. Similarly, it was found that the recessive mutation OM in sepaloid petal mutant downregulates PapsPI-1 and PapsAP3-1 transcripts. The recessive nature of the mutations was confirmed by the segregation ratios obtained in this analysis. PMID:24979593

The solids-flux theory--confirmation and extension by using partial differential equations.

PubMed

Diehl, Stefan

2008-12-01

The solids-flux theory has been used for half a century as a tool for estimating concentration and fluxes in the design and operation of secondary settling tanks during stationary conditions. The flux theory means that the conservation of mass is used in one dimension together with the batch-settling flux function according to the Kynch assumption. The flux theory results correspond to stationary solutions of a partial differential equation, a conservation law, with discontinuous coefficients modelling the continuous-sedimentation process in one dimension. The mathematical analysis of such an equation is intricate, partly since it cannot be interpreted in the classical sense. Recent results, however, make it possible to partly confirm and extend the previous flux theory statements, partly draw new conclusions also on the dynamic behaviour and the possibilities and limitations for control. We use here a single example of an ideal settling tank and a given batch-settling flux in a whole series of calculations. The mathematical results are adapted towards the application and many of them are conveniently presented in terms of operating charts.

Moving finite elements in 2-D

NASA Technical Reports Server (NTRS)

Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.

1983-01-01

The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.

Proglucagons in vertebrates: Expression and processing of multiple genes in a bony fish.

PubMed

Busby, Ellen R; Mommsen, Thomas P

2016-09-01

In contrast to mammals, where a single proglucagon (PG) gene encodes three peptides: glucagon, glucagon-like peptide 1 and glucagon-like peptide 2 (GLP-1; GLP-2), many non-mammalian vertebrates carry multiple PG genes. Here, we investigate proglucagon mRNA sequences, their tissue expression and processing in a diploid bony fish. Copper rockfish (Sebastes caurinus) express two independent genes coding for distinct proglucagon sequences (PG I, PG II), with PG II lacking the GLP-2 sequence. These genes are differentially transcribed in the endocrine pancreas, the brain, and the gastrointestinal tract. Alternative splicing identified in rockfish is only one part of this complex regulation of the PG transcripts: the system has the potential to produce two glucagons, four GLP-1s and a single GLP-2, or any combination of these peptides. Mass spectrometric analysis of partially purified PG-derived peptides in endocrine pancreas confirms translation of both PG transcripts and differential processing of the resulting peptides. The complex differential regulation of the two PG genes and their continued presence in this extant teleostean fish strongly suggests unique and, as yet largely unidentified, roles for the peptide products encoded in each gene. Copyright © 2016 Elsevier Inc. All rights reserved.

Tumoral stem cell reprogramming as a driver of cancer: Theory, biological models, implications in cancer therapy.

PubMed

Vicente-Dueñas, Carolina; Hauer, Julia; Ruiz-Roca, Lucía; Ingenhag, Deborah; Rodríguez-Meira, Alba; Auer, Franziska; Borkhardt, Arndt; Sánchez-García, Isidro

2015-06-01

Cancer is a clonal malignant disease originated in a single cell and characterized by the accumulation of partially differentiated cells that are phenotypically reminiscent of normal stages of differentiation. According to current models, therapeutic strategies that block oncogene activity are likely to selectively target tumor cells. However, recent evidences have revealed that cancer stem cells could arise through a tumor stem cell reprogramming mechanism, suggesting that genetic lesions that initiate the cancer process might be dispensable for tumor progression and maintenance. This review addresses the impact of these results toward a better understanding of cancer development and proposes new approaches to treat cancer in the future. Copyright © 2014 Elsevier Ltd. All rights reserved.

Differential cross sections for ionizations of H and H2 by 75 keV proton impact

NASA Astrophysics Data System (ADS)

Igarashi, A.; Gulyás, L.

2018-02-01

We have calculated total, partial and fully differential cross sections (FDCSs) for ionizations of H and H2 by 75 keV proton impact within the framework of the continuum-distorted-wave-eikonal-initial-state (CDW-EIS) approximation. Applying the single active electron model, the interaction between the projectile and the target ion is taken into account in the impact parameter picture. Extension of the CDW-EIS model to the molecular target is performed using the two-effective center approximation. The obtained results are compared with those of experimental and other theoretical data when available. The agreements between the theories and the experimental data are generally reasonable except for some cases of the FDCSs.

High-Throughput Screening Enhances Kidney Organoid Differentiation from Human Pluripotent Stem Cells and Enables Automated Multidimensional Phenotyping.

PubMed

Czerniecki, Stefan M; Cruz, Nelly M; Harder, Jennifer L; Menon, Rajasree; Annis, James; Otto, Edgar A; Gulieva, Ramila E; Islas, Laura V; Kim, Yong Kyun; Tran, Linh M; Martins, Timothy J; Pippin, Jeffrey W; Fu, Hongxia; Kretzler, Matthias; Shankland, Stuart J; Himmelfarb, Jonathan; Moon, Randall T; Paragas, Neal; Freedman, Benjamin S

2018-05-15

Organoids derived from human pluripotent stem cells are a potentially powerful tool for high-throughput screening (HTS), but the complexity of organoid cultures poses a significant challenge for miniaturization and automation. Here, we present a fully automated, HTS-compatible platform for enhanced differentiation and phenotyping of human kidney organoids. The entire 21-day protocol, from plating to differentiation to analysis, can be performed automatically by liquid-handling robots, or alternatively by manual pipetting. High-content imaging analysis reveals both dose-dependent and threshold effects during organoid differentiation. Immunofluorescence and single-cell RNA sequencing identify previously undetected parietal, interstitial, and partially differentiated compartments within organoids and define conditions that greatly expand the vascular endothelium. Chemical modulation of toxicity and disease phenotypes can be quantified for safety and efficacy prediction. Screening in gene-edited organoids in this system reveals an unexpected role for myosin in polycystic kidney disease. Organoids in HTS formats thus establish an attractive platform for multidimensional phenotypic screening. Copyright © 2018 Elsevier Inc. All rights reserved.

Construction and accuracy of partial differential equation approximations to the chemical master equation.

PubMed

Grima, Ramon

2011-11-01

The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

Stepwise Analysis of Differential Item Functioning Based on Multiple-Group Partial Credit Model.

ERIC Educational Resources Information Center

Muraki, Eiji

1999-01-01

Extended an Item Response Theory (IRT) method for detection of differential item functioning to the partial credit model and applied the method to simulated data using a stepwise procedure. Then applied the stepwise DIF analysis based on the multiple-group partial credit model to writing trend data from the National Assessment of Educational…

Soliton solutions for ABS lattice equations: I. Cauchy matrix approach

NASA Astrophysics Data System (ADS)

Nijhoff, Frank; Atkinson, James; Hietarinta, Jarmo

2009-10-01

In recent years there have been new insights into the integrability of quadrilateral lattice equations, i.e. partial difference equations which are the natural discrete analogues of integrable partial differential equations in 1+1 dimensions. In the scalar (i.e. single-field) case, there now exist classification results by Adler, Bobenko and Suris (ABS) leading to some new examples in addition to the lattice equations 'of KdV type' that were known since the late 1970s and early 1980s. In this paper, we review the construction of soliton solutions for the KdV-type lattice equations and use those results to construct N-soliton solutions for all lattice equations in the ABS list except for the elliptic case of Q4, which is left to a separate treatment.

XMDS2: Fast, scalable simulation of coupled stochastic partial differential equations

NASA Astrophysics Data System (ADS)

Dennis, Graham R.; Hope, Joseph J.; Johnsson, Mattias T.

2013-01-01

XMDS2 is a cross-platform, GPL-licensed, open source package for numerically integrating initial value problems that range from a single ordinary differential equation up to systems of coupled stochastic partial differential equations. The equations are described in a high-level XML-based script, and the package generates low-level optionally parallelised C++ code for the efficient solution of those equations. It combines the advantages of high-level simulations, namely fast and low-error development, with the speed, portability and scalability of hand-written code. XMDS2 is a complete redesign of the XMDS package, and features support for a much wider problem space while also producing faster code. Program summaryProgram title: XMDS2 Catalogue identifier: AENK_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENK_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 872490 No. of bytes in distributed program, including test data, etc.: 45522370 Distribution format: tar.gz Programming language: Python and C++. Computer: Any computer with a Unix-like system, a C++ compiler and Python. Operating system: Any Unix-like system; developed under Mac OS X and GNU/Linux. RAM: Problem dependent (roughly 50 bytes per grid point) Classification: 4.3, 6.5. External routines: The external libraries required are problem-dependent. Uses FFTW3 Fourier transforms (used only for FFT-based spectral methods), dSFMT random number generation (used only for stochastic problems), MPI message-passing interface (used only for distributed problems), HDF5, GNU Scientific Library (used only for Bessel-based spectral methods) and a BLAS implementation (used only for non-FFT-based spectral methods). Nature of problem: General coupled initial-value stochastic partial differential equations. Solution method: Spectral method with method-of-lines integration Running time: Determined by the size of the problem

For numerical differentiation, dimensionality can be a blessing!

NASA Astrophysics Data System (ADS)

Anderssen, Robert S.; Hegland, Markus

Finite difference methods, such as the mid-point rule, have been applied successfully to the numerical solution of ordinary and partial differential equations. If such formulas are applied to observational data, in order to determine derivatives, the results can be disastrous. The reason for this is that measurement errors, and even rounding errors in computer approximations, are strongly amplified in the differentiation process, especially if small step-sizes are chosen and higher derivatives are required. A number of authors have examined the use of various forms of averaging which allows the stable computation of low order derivatives from observational data. The size of the averaging set acts like a regularization parameter and has to be chosen as a function of the grid size h. In this paper, it is initially shown how first (and higher) order single-variate numerical differentiation of higher dimensional observational data can be stabilized with a reduced loss of accuracy than occurs for the corresponding differentiation of one-dimensional data. The result is then extended to the multivariate differentiation of higher dimensional data. The nature of the trade-off between convergence and stability is explicitly characterized, and the complexity of various implementations is examined.

Identifying States along the Hematopoietic Stem Cell Differentiation Hierarchy with Single Cell Specificity via Raman Spectroscopy.

PubMed

Ilin, Yelena; Choi, Ji Sun; Harley, Brendan A C; Kraft, Mary L

2015-11-17

A major challenge for expanding specific types of hematopoietic cells ex vivo for the treatment of blood cell pathologies is identifying the combinations of cellular and matrix cues that direct hematopoietic stem cells (HSC) to self-renew or differentiate into cell populations ex vivo. Microscale screening platforms enable minimizing the number of rare HSCs required to screen the effects of numerous cues on HSC fate decisions. These platforms create a strong demand for label-free methods that accurately identify the fate decisions of individual hematopoietic cells at specific locations on the platform. We demonstrate the capacity to identify discrete cells along the HSC differentiation hierarchy via multivariate analysis of Raman spectra. Notably, cell state identification is accurate for individual cells and independent of the biophysical properties of the functionalized polyacrylamide gels upon which these cells are cultured. We report partial least-squares discriminant analysis (PLS-DA) models of single cell Raman spectra enable identifying four dissimilar hematopoietic cell populations across the HSC lineage specification. Successful discrimination was obtained for a population enriched for long-term repopulating HSCs (LT-HSCs) versus their more differentiated progeny, including closely related short-term repopulating HSCs (ST-HSCs) and fully differentiated lymphoid (B cells) and myeloid (granulocytes) cells. The lineage-specific differentiation states of cells from these four subpopulations were accurately identified independent of the stiffness of the underlying biomaterial substrate, indicating subtle spectral variations that discriminated these populations were not masked by features from the culture substrate. This approach enables identifying the lineage-specific differentiation stages of hematopoietic cells on biomaterial substrates of differing composition and may facilitate correlating hematopoietic cell fate decisions with the extrinsic cues that elicited them.

Time Parallel Solution of Linear Partial Differential Equations on the Intel Touchstone Delta Supercomputer

NASA Technical Reports Server (NTRS)

Toomarian, N.; Fijany, A.; Barhen, J.

1993-01-01

Evolutionary partial differential equations are usually solved by decretization in time and space, and by applying a marching in time procedure to data and algorithms potentially parallelized in the spatial domain.

Recent disruption of an asteroid from the Eos family

NASA Astrophysics Data System (ADS)

Novaković, B.; Tsirvoulis, G.

2014-07-01

A key difficulty with searching for partially differentiated asteroids arises from the fact that a crust covers the exterior of the body, and, consequently, should hide the melted interior. This motivates an alternative approach of examining members of asteroid families, i.e., fragments of single large bodies, many of which were in the size regime capable of igneous differentiation, that have been disrupted by catastrophic collisions. Such families could provide a stratigraphic cross section across the interior of the parent asteroid [1]. With more than 10,000 known members, the Eos dynamical family is one of the most numerous and earliest recognized asteroid families [2]. Interestingly, the estimated ˜220-km-diameter parent body [3] is well within the size range capable of differentiation. Thus, existing family members should contain fragments of the deep interior. The Eos family has the highest diversity of taxonomic classes than any other known family [4]. Many members are of K spectral type, which is uncommon outside the family, and is similar to the spectra of CV, CK, CO, and CR carbonaceous chondrites [5]. This diversity leads to the suggestion that the Eos parent body was partially differentiated [4,6]. Thus, the Eos family may not only be a remnant of a partially differentiated parent body, but it could be the source of the CV-CK meteorite group. Here we report the discovery of a young subfamily of the Eos asteroid family. It may help understanding the mineralogical nature of the Eos asteroid family and of its parent body. By applying the hierarchical clustering method [7], we find an extremely compact 16-body cluster within the borders of the Eos family. We name the cluster (6733) 1992 EF, after its largest member. The statistical significance of this new cluster is estimated to be above 99%, indicating that its members share a common origin. All members of the cluster are found to be dynamically stable over long timescales. Backward numerical orbital integrations are used to set an upper limit of the age of the cluster to be only 4 Myr.

Mathematical Modelling of Continuous Biotechnological Processes

ERIC Educational Resources Information Center

Pencheva, T.; Hristozov, I.; Shannon, A. G.

2003-01-01

Biotechnological processes (BTP) are characterized by a complicated structure of organization and interdependent characteristics. Partial differential equations or systems of partial differential equations are used for their behavioural description as objects with distributed parameters. Modelling of substrate without regard to dispersion…

Fault Tolerant Optimal Control.

DTIC Science & Technology

1982-08-01

subsystem is modelled by deterministic or stochastic finite-dimensional vector differential or difference equations. The parameters of these equations...is no partial differential equation that must be solved. Thus we can sidestep the inability to solve the Bellman equation for control problems with x...transition models and cost functionals can be reduced to the search for solutions of nonlinear partial differential equations using ’verification

Differential geometry techniques for sets of nonlinear partial differential equations

NASA Technical Reports Server (NTRS)

Estabrook, Frank B.

1990-01-01

An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.

A procedure to construct exact solutions of nonlinear fractional differential equations.

PubMed

Güner, Özkan; Cevikel, Adem C

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions.

Algebraic and geometric structures of analytic partial differential equations

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2016-11-01

We study the problem of the compatibility of nonlinear partial differential equations. We introduce the algebra of convergent power series, the module of derivations of this algebra, and the module of Pfaffian forms. Systems of differential equations are given by power series in the space of infinite jets. We develop a technique for studying the compatibility of differential systems analogous to the Gröbner bases. Using certain assumptions, we prove that compatible systems generate infinite manifolds.

User's guide to PMESH: A grid-generation program for single-rotation and counterrotation advanced turboprops

NASA Technical Reports Server (NTRS)

Warsi, Saif A.

1989-01-01

A detailed operating manual is presented for a grid generating program that produces 3-D meshes for advanced turboprops. The code uses both algebraic and elliptic partial differential equation methods to generate single rotation and counterrotation, H or C type meshes for the z - r planes and H type for the z - theta planes. The code allows easy specification of geometrical constraints (such as blade angle, location of bounding surfaces, etc.), mesh control parameters (point distribution near blades and nacelle, number of grid points desired, etc.), and it has good runtime diagnostics. An overview is provided of the mesh generation procedure, sample input dataset with detailed explanation of all input, and example meshes.

Modern aspects of homogeneous-heterogeneous reactions and variable thickness in nanofluids through carbon nanotubes

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Ahmed, Sohail; Muhammad, Taseer; Alsaedi, Ahmed

2017-10-01

This article examines homogeneous-heterogeneous reactions and internal heat generation in Darcy-Forchheimer flow of nanofluids with different base fluids. Flow is generated due to a nonlinear stretchable surface of variable thickness. The characteristics of nanofluid are explored using CNTs (single and multi walled carbon nanotubes). Equal diffusion coefficients are considered for both reactants and auto catalyst. The conversion of partial differential equations (PDEs) to ordinary differential equations (ODEs) is done via appropriate transformations. Optimal homotopy approach is implemented for solutions development of governing problems. Averaged square residual errors are computed. The optimal solution expressions of velocity, temperature and concentration are explored through plots by using several values of physical parameters. Further the coefficient of skin friction and local Nusselt number are examined through graphs.

Algorithm-enabled partial-angular-scan configurations for dual-energy CT.

PubMed

Chen, Buxin; Zhang, Zheng; Xia, Dan; Sidky, Emil Y; Pan, Xiaochuan

2018-05-01

We seek to investigate an optimization-based one-step method for image reconstruction that explicitly compensates for nonlinear spectral response (i.e., the beam-hardening effect) in dual-energy CT, to investigate the feasibility of the one-step method for enabling two dual-energy partial-angular-scan configurations, referred to as the short- and half-scan configurations, on standard CT scanners without involving additional hardware, and to investigate the potential of the short- and half-scan configurations in reducing imaging dose and scan time in a single-kVp-switch full-scan configuration in which two full rotations are made for collection of dual-energy data. We use the one-step method to reconstruct images directly from dual-energy data through solving a nonconvex optimization program that specifies the images to be reconstructed in dual-energy CT. Dual-energy full-scan data are generated from numerical phantoms and collected from physical phantoms with the standard single-kVp-switch full-scan configuration, whereas dual-energy short- and half-scan data are extracted from the corresponding full-scan data. Besides visual inspection and profile-plot comparison, the reconstructed images are analyzed also in quantitative studies based upon tasks of linear-attenuation-coefficient and material-concentration estimation and of material differentiation. Following the performance of a computer-simulation study to verify that the one-step method can reconstruct numerically accurately basis and monochromatic images of numerical phantoms, we reconstruct basis and monochromatic images by using the one-step method from real data of physical phantoms collected with the full-, short-, and half-scan configurations. Subjective inspection based upon visualization and profile-plot comparison reveals that monochromatic images, which are used often in practical applications, reconstructed from the full-, short-, and half-scan data are largely visually comparable except for some differences in texture details. Moreover, quantitative studies based upon tasks of linear-attenuation-coefficient and material-concentration estimation and of material differentiation indicate that the short- and half-scan configurations yield results in close agreement with the ground-truth information and that of the full-scan configuration. The one-step method considered can compensate effectively for the nonlinear spectral response in full- and partial-angular-scan dual-energy CT. It can be exploited for enabling partial-angular-scan configurations on standard CT scanner without involving additional hardware. Visual inspection and quantitative studies reveal that, with the one-step method, partial-angular-scan configurations considered can perform at a level comparable to that of the full-scan configuration, thus suggesting the potential of the two partial-angular-scan configurations in reducing imaging dose and scan time in the standard single-kVp-switch full-scan CT in which two full rotations are performed. The work also yields insights into the investigation and design of other nonstandard scan configurations of potential practical significance in dual-energy CT. © 2018 American Association of Physicists in Medicine.

An asymptotically exact reduced PDE model for the magnetorotational instability: derivation and numerical simulations

NASA Astrophysics Data System (ADS)

Jamroz, Ben; Julien, Keith; Knobloch, Edgar

2008-12-01

Taking advantage of disparate spatio-temporal scales relevant to astrophysics and laboratory experiments, we derive asymptotically exact reduced partial differential equation models for the magnetorotational instability. These models extend recent single-mode formulations leading to saturation in the presence of weak dissipation, and are characterized by a back-reaction on the imposed shear. Numerical simulations performed for a broad class of initial conditions indicate an initial phase of growth dominated by the optimal (fastest growing) magnetorotational instability fingering mode, followed by a vertical coarsening to a box-filling mode.

Optimal moving grids for time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Wathen, A. J.

1992-01-01

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Constructing general partial differential equations using polynomial and neural networks.

PubMed

Zjavka, Ladislav; Pedrycz, Witold

2016-01-01

Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations

PubMed Central

Güner, Özkan; Cevikel, Adem C.

2014-01-01

We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space fractional Burgers equation, and the time fractional fmKdV equation. As a result, we obtain some new exact solutions. PMID:24737972

On implicit abstract neutral nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernández, Eduardo, E-mail: lalohm@ffclrp.usp.br; O’Regan, Donal, E-mail: donal.oregan@nuigalway.ie

2016-04-15

In this paper we continue our developments in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) on the existence of solutions for abstract neutral differential equations. In particular we extend the results in Hernández and O’Regan (J Funct Anal 261:3457–3481, 2011) for the case of implicit nonlinear neutral equations and we focus on applications to partial “nonlinear” neutral differential equations. Some applications involving partial neutral differential equations are presented.

Oscillation of certain higher-order neutral partial functional differential equations.

PubMed

Li, Wei Nian; Sheng, Weihong

2016-01-01

In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.

The Manifest Association Structure of the Single-Factor Model: Insights from Partial Correlations

ERIC Educational Resources Information Center

Salgueiro, Maria de Fatima; Smith, Peter W. F.; McDonald, John W.

2008-01-01

The association structure between manifest variables arising from the single-factor model is investigated using partial correlations. The additional insights to the practitioner provided by partial correlations for detecting a single-factor model are discussed. The parameter space for the partial correlations is presented, as are the patterns of…

Pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations

NASA Astrophysics Data System (ADS)

Al-Islam, Najja Shakir

In this Dissertation, the existence of pseudo almost periodic solutions to some systems of nonlinear hyperbolic second-order partial differential equations is established. For that, (Al-Islam [4]) is first studied and then obtained under some suitable assumptions. That is, the existence of pseudo almost periodic solutions to a hyperbolic second-order partial differential equation with delay. The second-order partial differential equation (1) represents a mathematical model for the dynamics of gas absorption, given by uxt+a x,tux=Cx,t,u x,t , u0,t=4 t, 1 where a : [0, L] x RR , C : [0, L] x R x RR , and ϕ : RR are (jointly) continuous functions ( t being the greatest integer function) and L > 0. The results in this Dissertation generalize those of Poorkarimi and Wiener [22]. Secondly, a generalization of the above-mentioned system consisting of the non-linear hyperbolic second-order partial differential equation uxt+a x,tux+bx,t ut+cx,tu=f x,t,u, x∈ 0,L,t∈ R, 2 equipped with the boundary conditions ux,0 =40x, u0,t=u 0t, uxx,0=y 0x, x∈0,L, t∈R, 3 where a, b, c : [0, L ] x RR and f : [0, L] x R x RR are (jointly) continuous functions is studied. Under some suitable assumptions, the existence and uniqueness of pseudo almost periodic solutions to particular cases, as well as the general case of the second-order hyperbolic partial differential equation (2) are studied. The results of all studies contained within this text extend those obtained by Aziz and Meyers [6] in the periodic setting.

Reversible effects of oxygen partial pressure on genes associated with placental angiogenesis and differentiation in primary-term cytotrophoblast cell culture.

PubMed

Debiève, F; Depoix, C; Gruson, D; Hubinont, C

2013-09-01

Timely regulated changes in oxygen partial pressure are important for placental formation. Disturbances could be responsible for pregnancy-related diseases like preeclampsia and intrauterine growth restriction. We aimed to (i) determine the effect of oxygen partial pressure on cytotrophoblast differentiation; (ii) measure mRNA expression and protein secretion from genes associated with placental angiogenesis; and (iii) determine the reversibility of these effects at different oxygen partial pressures. Term cytotrophoblasts were incubated at 21% and 2.5% O2 for 96 hr, or were switched between the two oxygen concentrations after 48 hr. Real-time PCR and enzyme-linked immunosorbent assays (ELISAs) were used to evaluate cell fusion and differentiation, measuring transcript levels for those genes involved in cell fusion and placental angiogenesis, including VEGF, PlGF, VEGFR1, sVEGFR1, sENG, INHA, and GCM1. Cytotrophoblasts underwent fusion and differentiation in 2.5% O2 . PlGF expression was inhibited while sVEGFR1 expression increased. VEGF and sENG mRNA expressions increased in 2.5% compared to 21% O2 , but no protein was detected in the cell supernatants. Finally, GCM1 mRNA expression increased during trophoblast differentiation at 21% O2 , but was inhibited at 2.5% O2 . These mRNA expression effects were reversed by returning the cells to 21% O2 . Thus, low-oxygen partial pressure does not inhibit term-cytotrophoblast cell fusion and differentiation in vitro. Lowering the oxygen partial pressure from 21% to 2.5% caused normal-term trophoblasts to reversibly modify their expression of genes associated with placental angiogenesis. This suggests that modifications observed in pregnancy diseases such as preeclampsia or growth retardation are probably due to an extrinsic effect on trophoblasts. Copyright © 2013 Wiley Periodicals, Inc.

Lattice Boltzmann model for high-order nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations.

PubMed

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes

NASA Astrophysics Data System (ADS)

Ul Haq, Rizwan; Nadeem, Sohail; Khan, Z. H.; Noor, N. F. M.

2015-01-01

In the present study, thermal conductivity and viscosity of both single-wall and multiple-wall Carbon Nanotubes (CNT) within the base fluids (water, engine oil and ethylene glycol) of similar volume have been investigated when the fluid is flowing over a stretching surface. The magnetohydrodynamic (MHD) and viscous dissipation effects are also incorporated in the present phenomena. Experimental data consists of thermo-physical properties of each base fluid and CNT have been considered. The mathematical model has been constructed and by employing similarity transformation, system of partial differential equations is rehabilitated into the system of non-linear ordinary differential equations. The results of local skin friction and local Nusselt number are plotted for each base fluid by considering both Single Wall Carbon Nanotube (SWCNT) and Multiple-Wall Carbon Nanotubes (MWCNT). The behavior of fluid flow for water based-SWCNT and MWCNT are analyzed through streamlines. Concluding remarks have been developed on behalf of the whole analysis and it is found that engine oil-based CNT have higher skin friction and heat transfer rate as compared to water and ethylene glycol-based CNT.

Entropy and convexity for nonlinear partial differential equations

PubMed Central

Ball, John M.; Chen, Gui-Qiang G.

2013-01-01

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue. PMID:24249768

Oxidation Behavior of Carbon Fiber-Reinforced Composites

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2008-01-01

OXIMAP is a numerical (FEA-based) solution tool capable of calculating the carbon fiber and fiber coating oxidation patterns within any arbitrarily shaped carbon silicon carbide composite structure as a function of time, temperature, and the environmental oxygen partial pressure. The mathematical formulation is derived from the mechanics of the flow of ideal gases through a chemically reacting, porous solid. The result of the formulation is a set of two coupled, non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined at each time step using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual finite element method, allowing for the solution of the differential equations numerically.

Entropy and convexity for nonlinear partial differential equations.

PubMed

Ball, John M; Chen, Gui-Qiang G

2013-12-28

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

Differential phase measurements of D-region partial reflections

NASA Technical Reports Server (NTRS)

Wiersma, D. J.; Sechrist, C. F., Jr.

1972-01-01

Differential phase partial reflection measurements were used to deduce D region electron density profiles. The phase difference was measured by taking sums and differences of amplitudes received on an array of crossed dipoles. The reflection model used was derived from Fresnel reflection theory. Seven profiles obtained over the period from 13 October 1971 to 5 November 1971 are presented, along with the results from simultaneous measurements of differential absorption. Some possible sources of error and error propagation are discussed. A collision frequency profile was deduced from the electron concentration calculated from differential phase and differential absorption.

Adaptive Grid Generation for Numerical Solution of Partial Differential Equations.

DTIC Science & Technology

1983-12-01

numerical solution of fluid dynamics problems is presented. However, the method is applicable to the numer- ical evaluation of any partial differential...emphasis is being placed on numerical solution of the governing differential equations by finite difference methods . In the past two decades, considerable...original equations presented in that paper. The solution of the second problem is more difficult. 2 The method of Thompson et al. provides control for

Diagnostic Accuracy of Copeptin in the Differential Diagnosis of the Polyuria-polydipsia Syndrome: A Prospective Multicenter Study.

PubMed

Timper, Katharina; Fenske, Wiebke; Kühn, Felix; Frech, Nica; Arici, Birsen; Rutishauser, Jonas; Kopp, Peter; Allolio, Bruno; Stettler, Christoph; Müller, Beat; Katan, Mira; Christ-Crain, Mirjam

2015-06-01

The polyuria-polydipsia syndrome comprises primary polydipsia (PP) and central and nephrogenic diabetes insipidus (DI). Correctly discriminating these entities is mandatory, given that inadequate treatment causes serious complications. The diagnostic "gold standard" is the water deprivation test with assessment of arginine vasopressin (AVP) activity. However, test interpretation and AVP measurement are challenging. The objective was to evaluate the accuracy of copeptin, a stable peptide stoichiometrically cosecreted with AVP, in the differential diagnosis of polyuria-polydipsia syndrome. This was a prospective multicenter observational cohort study from four Swiss or German tertiary referral centers of adults >18 years old with the history of polyuria and polydipsia. A standardized combined water deprivation/3% saline infusion test was performed and terminated when serum sodium exceeded 147 mmol/L. Circulating copeptin and AVP levels were measured regularly throughout the test. Final diagnosis was based on the water deprivation/saline infusion test results, clinical information, and the treatment response. Fifty-five patients were enrolled (11 with complete central DI, 16 with partial central DI, 18 with PP, and 10 with nephrogenic DI). Without prior thirsting, a single baseline copeptin level >21.4 pmol/L differentiated nephrogenic DI from other etiologies with a 100% sensitivity and specificity, rendering a water deprivation testing unnecessary in such cases. A stimulated copeptin >4.9 pmol/L (at sodium levels >147 mmol/L) differentiated between patients with PP and patients with partial central DI with a 94.0% specificity and a 94.4% sensitivity. A stimulated AVP >1.8 pg/mL differentiated between the same categories with a 93.0% specificity and a 83.0% sensitivity. This study was limited by incorporation bias from including AVP levels as a diagnostic criterion. Copeptin is a promising new tool in the differential diagnosis of the polyuria-polydipsia syndrome, and a valid surrogate marker for AVP. Primary Funding Sources: Swiss National Science Foundation, University of Basel.

A boundary value approach for solving three-dimensional elliptic and hyperbolic partial differential equations.

PubMed

Biala, T A; Jator, S N

2015-01-01

In this article, the boundary value method is applied to solve three dimensional elliptic and hyperbolic partial differential equations. The partial derivatives with respect to two of the spatial variables (y, z) are discretized using finite difference approximations to obtain a large system of ordinary differential equations (ODEs) in the third spatial variable (x). Using interpolation and collocation techniques, a continuous scheme is developed and used to obtain discrete methods which are applied via the Block unification approach to obtain approximations to the resulting large system of ODEs. Several test problems are investigated to elucidate the solution process.

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

Necessary and sufficient conditions are found under which operators of the form Sigma (m, j=1) x (2) sub j + X sub O can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

Canonical coordinates for partial differential equations

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type.

Comparison of Th1- and Th2-associated immune reactivities stimulated by single versus multiple vaccination of mice with irradiated Schistosoma mansoni cercariae

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caulada-Benedetti, Z.; Al-Zamel, F.; Sher, A.

1991-03-01

Mice immunized against Schistosoma mansoni by a single percutaneous exposure to radiation-attenuated parasite larvae demonstrate partial resistance to challenge infection that has been shown to correlate with development of cell-mediated immunity, whereas mice hyperimmunized by multiple exposure to attenuated larvae produce antibodies capable of transferring partial protection to naive recipients. Measurement of Ag-specific lymphokine responses in these animals suggested that the difference in resistance mechanisms may be due to the differential induction of Th subset response by the two immunization protocols. Thus, upon Ag stimulation, singly immunized mice predominantly demonstrated responses associated with Th1 reactivity, including IL-2 and IFN-gamma production,more » whereas multiply immunized animals showed increased IL-5, IL-4, and IgG1 antibody production associated with enhanced Th2 response. These responses demonstrated some degree of organ compartmentalization, with splenocytes demonstrating higher Th1-related lymphokine production and cells from draining lymph nodes showing stronger proliferation and Th2 type reactivity. However, hyperimmunized mice also continued to demonstrate substantial Th1-associated immune reactivity. Moreover, in vivo Ag challenge elicited activated larvacidal macrophages in hyperimmunized animals. These observations indicate that protective cell-mediated mechanisms associated with induction of CD4+ Th1 cell reactivity predominate in singly vaccinated mice. Further vaccination stimulates Th2 responses, such as enhanced IgG1 production, that may also contribute to protective immunity.« less

Modeling biological gradient formation: combining partial differential equations and Petri nets.

PubMed

Bertens, Laura M F; Kleijn, Jetty; Hille, Sander C; Heiner, Monika; Koutny, Maciej; Verbeek, Fons J

2016-01-01

Both Petri nets and differential equations are important modeling tools for biological processes. In this paper we demonstrate how these two modeling techniques can be combined to describe biological gradient formation. Parameters derived from partial differential equation describing the process of gradient formation are incorporated in an abstract Petri net model. The quantitative aspects of the resulting model are validated through a case study of gradient formation in the fruit fly.

Computed tear film and osmolarity dynamics on an eye-shaped domain

PubMed Central

Li, Longfei; Braun, Richard J.; Driscoll, Tobin A.; Henshaw, William D.; Banks, Jeffrey W.; King-Smith, P. Ewen

2016-01-01

The concentration of ions, or osmolarity, in the tear film is a key variable in understanding dry eye symptoms and disease. In this manuscript, we derive a mathematical model that couples osmolarity (treated as a single solute) and fluid dynamics within the tear film on a 2D eye-shaped domain. The model includes the physical effects of evaporation, surface tension, viscosity, ocular surface wettability, osmolarity, osmosis and tear fluid supply and drainage. The governing system of coupled non-linear partial differential equations is solved using the Overture computational framework, together with a hybrid time-stepping scheme, using a variable step backward differentiation formula and a Runge–Kutta–Chebyshev method that were added to the framework. The results of our numerical simulations provide new insight into the osmolarity distribution over the ocular surface during the interblink. PMID:25883248

Single-bubble sonoluminescence in sulfuric acid and water: bubble dynamics, stability, and continuous spectra.

PubMed

Puente, Gabriela F; García-Martínez, Pablo; Bonetto, Fabián J

2007-01-01

We present theoretical calculations of an argon bubble in a liquid solution of 85%wt sulfuric acid and 15%wt water in single-bubble sonoluminescence. We used a model without free parameters to be adjusted. We predict from first principles the region in parameter space for stable bubble evolution, the temporal evolution of the bubble radius, the maximum temperature, pressures, and the light spectra due to thermal emissions. We also used a partial differential equation based model (hydrocode) to compute the temperature and pressure evolutions at the center of the bubble during maximum compression. We found the behavior of this liquid mixture to be very different from water in several aspects. Most of the models in sonoluminescence were compared with water experimental results.

Development of programmable artificial neural networks

NASA Technical Reports Server (NTRS)

Meade, Andrew J.

1993-01-01

Conventionally programmed digital computers can process numbers with great speed and precision, but do not easily recognize patterns or imprecise or contradictory data. Instead of being programmed in the conventional sense, artificial neural networks are capable of self-learning through exposure to repeated examples. However, the training of an ANN can be a time consuming and unpredictable process. A general method is being developed to mate the adaptability of the ANN with the speed and precision of the digital computer. This method was successful in building feedforward networks that can approximate functions and their partial derivatives from examples in a single iteration. The general method also allows the formation of feedforward networks that can approximate the solution to nonlinear ordinary and partial differential equations to desired accuracy without the need of examples. It is believed that continued research will produce artificial neural networks that can be used with confidence in practical scientific computing and engineering applications.

Multiscale Simulations of Magnetic Island Coalescence

NASA Technical Reports Server (NTRS)

Dorelli, John C.

2010-01-01

We describe a new interactive parallel Adaptive Mesh Refinement (AMR) framework written in the Python programming language. This new framework, PyAMR, hides the details of parallel AMR data structures and algorithms (e.g., domain decomposition, grid partition, and inter-process communication), allowing the user to focus on the development of algorithms for advancing the solution of a systems of partial differential equations on a single uniform mesh. We demonstrate the use of PyAMR by simulating the pairwise coalescence of magnetic islands using the resistive Hall MHD equations. Techniques for coupling different physics models on different levels of the AMR grid hierarchy are discussed.

Testing for Differential Item Functioning with Measures of Partial Association

ERIC Educational Resources Information Center

Woods, Carol M.

2009-01-01

Differential item functioning (DIF) occurs when an item on a test or questionnaire has different measurement properties for one group of people versus another, irrespective of mean differences on the construct. There are many methods available for DIF assessment. The present article is focused on indices of partial association. A family of average…

THREE-POINT BACKWARD FINITE DIFFERENCE METHOD FOR SOLVING A SYSTEM OF MIXED HYPERBOLIC-PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS. (R825549C019)

EPA Science Inventory

A three-point backward finite-difference method has been derived for a system of mixed hyperbolic_¯¯parabolic (convection_¯¯diffusion) partial differential equations (mixed PDEs). The method resorts to the three-point backward differenci...

Magnetic Evidence for a Partially Differentiated Carbonaceous Chondrite Parent Body and Possible Implications for Asteroid 21 Lutetia

NASA Astrophysics Data System (ADS)

Weiss, Benjamin; Carporzen, L.; Elkins-Tanton, L.; Shuster, D. L.; Ebel, D. S.; Gattacceca, J.; Binzel, R. P.

2010-10-01

The origin of remanent magnetization in the CV carbonaceous chondrite Allende has been a longstanding mystery. The possibility of a core dynamo like that known for achondrite parent bodies has been discounted because chondrite parent bodies are assumed to be undifferentiated. Here we report that Allende's magnetization was acquired over several million years (Ma) during metasomatism on the parent planetesimal in a > 20 microtesla field 8-9 Ma after solar system formation. This field was present too recently and directionally stable for too long to have been the generated by the protoplanetary disk or young Sun. The field intensity is in the range expected for planetesimal core dynamos (Weiss et al. 2010), suggesting that CV chondrites are derived from the outer, unmelted layer of a partially differentiated body with a convecting metallic core (Elkins-Tanton et al. 2010). This suggests that asteroids with differentiated interiors could be present today but masked under chondritic surfaces. In fact, CV chondrites are spectrally similar to many members of the Eos asteroid family whose spectral diversity has been interpreted as evidence for a partially differentiated parent asteroid (Mothe-Diniz et al. 2008). CV chondrite spectral and polarimetric data also resemble those of asteroid 21 Lutetia (e.g., Belskaya et al. 2010), recently encountered by the Rosetta spacecraft. Ground-based measurements of Lutetia indicate a high density of 2.4-5.1 g cm-3 (Drummond et al. 2010), while radar data seem to rule out a metallic surface composition (Shepard et al. 2008). If Rosetta spacecraft measurements confirm a high density and a CV-like surface composition for Lutetia, then we propose Lutetia may be an example of a partially differentiated carbonaceous chondrite parent body. Regardless, the very existence of primitive achondrites, which contain evidence of both relict chondrules and partial melting, are prima facie evidence for the formation of partially differentiated bodies.

Differential Curing In Fiber/Resin Laminates

NASA Technical Reports Server (NTRS)

Webster, Charles N.

1989-01-01

Modified layup schedule counteracts tendency toward delamination. Improved manufacturing process resembles conventional process, except prepregs partially cured laid on mold in sequence in degree of partial cure decreases from mold side to bag side. Degree of partial cure of each layer at time of layup selected by controlling storage and partial-curing temperatures of prepreg according to Arrhenius equation for rate of gel of resin as function of temperature and time from moment of mixing. Differential advancement of cure in layers made large enough to offset effect of advance bag-side heating in oven or autoclave. Technique helps prevent entrapment of volatile materials during manufacturing of fiber/resin laminates.

Phylogenetic Distribution of Leaf Spectra and Optically Derived Functional Traits in the American Oaks

NASA Astrophysics Data System (ADS)

Cavender-Bares, J.; Meireles, J. E.; Couture, J. J.; Kaproth, M.; Townsend, P. A.

2015-12-01

Detecting functional traits of species, genotypes and phylogenetic lineages is critical in monitoring functional biodiversity remotely. We examined the phylogenetic distribution of leaf spectra across the American Oaks for 35 species under greenhouse conditions as well as genetic variation in leaf spectra across Central American populations of a single species grown in common gardens in Honduras. We found significant phylogenetic signal in the leaf spectra (Blomberg's K > 1.0), indicating similarity in spectra among close relatives. Across species, full range leaf spectra were used in a Partial Least Squares Discriminant Analysis (PLS-DA) that allowed species calibration (kappa statistic = 0.55). Validation of the model used to detect species (kappa statistic = 0.4) indicated reasonably good detection of individual species within the same the genus. Among four populations from Belize, Costa Rica, Honduras, and Mexico within a single species (Quercus oleoides), leaf spectra were also able to differentiate populations. Ordination of population-level data using dissimilarities of predicted foliar traits, including leaf mass per area (LMA), lignin content, fiber content, chlorophyll a+b, and C:N ratio in genotypes in either watered or unwatered conditions showed significant differentiation among populations and treatments. These results provide promise for remote detection and differentiation of plant functional traits among plant phylogenetic lineages and genotypes, even among closely related populations and species.

Dynamics of temporally localized states in passively mode-locked semiconductor lasers

NASA Astrophysics Data System (ADS)

Schelte, C.; Javaloyes, J.; Gurevich, S. V.

2018-05-01

We study the emergence and the stability of temporally localized structures in the output of a semiconductor laser passively mode locked by a saturable absorber in the long-cavity regime. For large yet realistic values of the linewidth enhancement factor, we disclose the existence of secondary dynamical instabilities where the pulses develop regular and subsequent irregular temporal oscillations. By a detailed bifurcation analysis we show that additional solution branches that consist of multipulse (molecules) solutions exist. We demonstrate that the various solution curves for the single and multipeak pulses can splice and intersect each other via transcritical bifurcations, leading to a complex web of solutions. Our analysis is based on a generic model of mode locking that consists of a time-delayed dynamical system, but also on a much more numerically efficient, yet approximate, partial differential equation. We compare the results of the bifurcation analysis of both models in order to assess up to which point the two approaches are equivalent. We conclude our analysis by the study of the influence of group velocity dispersion, which is only possible in the framework of the partial differential equation model, and we show that it may have a profound impact on the dynamics of the localized states.

A homotopy analysis method for the nonlinear partial differential equations arising in engineering

NASA Astrophysics Data System (ADS)

Hariharan, G.

2017-05-01

In this article, we have established the homotopy analysis method (HAM) for solving a few partial differential equations arising in engineering. This technique provides the solutions in rapid convergence series with computable terms for the problems with high degree of nonlinear terms appearing in the governing differential equations. The convergence analysis of the proposed method is also discussed. Finally, we have given some illustrative examples to demonstrate the validity and applicability of the proposed method.

Parent Ratings of ADHD Symptoms: Generalized Partial Credit Model Analysis of Differential Item Functioning across Gender

ERIC Educational Resources Information Center

Gomez, Rapson

2012-01-01

Objective: Generalized partial credit model, which is based on item response theory (IRT), was used to test differential item functioning (DIF) for the "Diagnostic and Statistical Manual of Mental Disorders" (4th ed.), inattention (IA), and hyperactivity/impulsivity (HI) symptoms across boys and girls. Method: To accomplish this, parents completed…

An electric-analog simulation of elliptic partial differential equations using finite element theory

USGS Publications Warehouse

Franke, O.L.; Pinder, G.F.; Patten, E.P.

1982-01-01

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct. ?? 1982.

Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.

PubMed

Baranwal, Vipul K; Pandey, Ram K; Singh, Om P

2014-01-01

We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.

Isolation of stress responsive Psb A gene from rice (Oryza sativa l.) using differential display.

PubMed

Tyagi, Aruna; Chandra, Arti

2006-08-01

Differential display (DD) experiments were performed on drought-tolerant rice (Oryza sativa L.) genotype N22 to identify both upregulated and downregulated partial cDNAs with respect to moisture stress. DNA polymorphism was detected between drought-stressed and control leaf tissues on the DD gels. A partial cDNA showing differential expression, with respect to moisture stress was isolated from the gel. Northern blotting analysis was performed using this cDNA as a probe and it was observed that mRNA corresponding to this transcript was accumulated to high level in rice leaves under water deficit stress. At the DNA sequence level, the partial cDNA showed homology with psb A gene encoding for Dl protein.

Genetic differentiation among North Atlantic killer whale populations.

PubMed

Foote, Andrew D; Vilstrup, Julia T; De Stephanis, Renaud; Verborgh, Philippe; Abel Nielsen, Sandra C; Deaville, Robert; Kleivane, Lars; Martín, Vidal; Miller, Patrick J O; Oien, Nils; Pérez-Gil, Monica; Rasmussen, Morten; Reid, Robert J; Robertson, Kelly M; Rogan, Emer; Similä, Tiu; Tejedor, Maria L; Vester, Heike; Víkingsson, Gísli A; Willerslev, Eske; Gilbert, M Thomas P; Piertney, Stuart B

2011-02-01

Population genetic structure of North Atlantic killer whale samples was resolved from differences in allele frequencies of 17 microsatellite loci, mtDNA control region haplotype frequencies and for a subset of samples, using complete mitogenome sequences. Three significantly differentiated populations were identified. Differentiation based on microsatellite allele frequencies was greater between the two allopatric populations than between the two pairs of partially sympatric populations. Spatial clustering of individuals within each of these populations overlaps with the distribution of particular prey resources: herring, mackerel and tuna, which each population has been seen predating. Phylogenetic analyses using complete mitogenomes suggested two populations could have resulted from single founding events and subsequent matrilineal expansion. The third population, which was sampled at lower latitudes and lower density, consisted of maternal lineages from three highly divergent clades. Pairwise population differentiation was greater for estimates based on mtDNA control region haplotype frequencies than for estimates based on microsatellite allele frequencies, and there were no mitogenome haplotypes shared among populations. This suggests low or no female migration and that gene flow was primarily male mediated when populations spatially and temporally overlap. These results demonstrate that genetic differentiation can arise through resource specialization in the absence of physical barriers to gene flow. © 2010 Blackwell Publishing Ltd.

Dynamic analysis and numerical experiments for balancing of the continuous single-disc and single-span rotor-bearing system

NASA Astrophysics Data System (ADS)

Wang, Aiming; Cheng, Xiaohan; Meng, Guoying; Xia, Yun; Wo, Lei; Wang, Ziyi

2017-03-01

Identification of rotor unbalance is critical for normal operation of rotating machinery. The single-disc and single-span rotor, as the most fundamental rotor-bearing system, has attracted research attention over a long time. In this paper, the continuous single-disc and single-span rotor is modeled as a homogeneous and elastic Euler-Bernoulli beam, and the forces applied by bearings and disc on the shaft are considered as point forces. A fourth-order non-homogeneous partial differential equation set with homogeneous boundary condition is solved for analytical solution, which expresses the unbalance response as a function of position, rotor unbalance and the stiffness and damping coefficients of bearings. Based on this analytical method, a novel Measurement Point Vector Method (MPVM) is proposed to identify rotor unbalance while operating. Only a measured unbalance response registered for four selected cross-sections of the rotor-shaft under steady-state operating conditions is needed when using the method. Numerical simulation shows that the detection error of the proposed method is very small when measurement error is negligible. The proposed method provides an efficient way for rotor balancing without test runs and external excitations.

Simplified combustion noise theory yielding a prediction of fluctuating pressure level

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The first order equations for the conservation of mass and momentum in differential form are combined for an ideal gas to yield a single second order partial differential equation in one dimension and time. Small perturbation analysis is applied. A Fourier transformation is performed that results in a second order, constant coefficient, nonhomogeneous equation. The driving function is taken to be the source of combustion noise. A simplified model describing the energy addition via the combustion process gives the required source information for substitution in the driving function. This enables the particular integral solution of the nonhomogeneous equation to be found. This solution multiplied by the acoustic pressure efficiency predicts the acoustic pressure spectrum measured in turbine engine combustors. The prediction was compared with the overall sound pressure levels measured in a CF6-50 turbofan engine combustor and found to be in excellent agreement.

Egg phenotype differentiation in sympatric cuckoo Cuculus canorus gentes.

PubMed

Antonov, Anton; Stokke, B G; Vikan, J R; Fossøy, F; Ranke, P S; Røskaft, E; Moksnes, A; Møller, A P; Shykoff, J A

2010-06-01

The brood parasitic common cuckoo Cuculus canorus consists of gentes, which typically parasitize only a single host species whose eggs they often mimic. Where multiple cuckoo gentes co-exist in sympatry, we may expect variable but generally poorer mimicry because of host switches or inter-gens gene flow via males if these also contribute to egg phenotypes. Here, we investigated egg trait differentiation and mimicry in three cuckoo gentes parasitizing great reed warblers Acrocephalus arundinaceus, marsh warblers Acrocephalus palustris and corn buntings Miliaria calandra breeding in close sympatry in partially overlapping habitat types. The three cuckoo gentes showed a remarkable degree of mimicry to their three host species in some but not all egg features, including egg size, a hitherto largely ignored feature of egg mimicry. Egg phenotype matching for both background and spot colours as well as for egg size has been maintained in close sympatry despite the possibility for gene flow.

Generalized Lie symmetry approach for fractional order systems of differential equations. III

NASA Astrophysics Data System (ADS)

Singla, Komal; Gupta, R. K.

2017-06-01

The generalized Lie symmetry technique is proposed for the derivation of point symmetries for systems of fractional differential equations with an arbitrary number of independent as well as dependent variables. The efficiency of the method is illustrated by its application to three higher dimensional nonlinear systems of fractional order partial differential equations consisting of the (2 + 1)-dimensional asymmetric Nizhnik-Novikov-Veselov system, (3 + 1)-dimensional Burgers system, and (3 + 1)-dimensional Navier-Stokes equations. With the help of derived Lie point symmetries, the corresponding invariant solutions transform each of the considered systems into a system of lower-dimensional fractional partial differential equations.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Concatenons as the solutions for non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Kudryashov, N. A.; Volkov, A. K.

2017-07-01

New class of solutions for nonlinear partial differential equations is introduced. We call them the concaten solutions. As an example we consider equations for the description of wave processes in the Fermi-Pasta-Ulam mass chain and construct the concatenon solutions for these equation. Stability of the concatenon-type solutions is investigated numerically. Interaction between the concatenon and solitons is discussed.

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Analytical solutions for coupling fractional partial differential equations with Dirichlet boundary conditions

NASA Astrophysics Data System (ADS)

Ding, Xiao-Li; Nieto, Juan J.

2017-11-01

In this paper, we consider the analytical solutions of coupling fractional partial differential equations (FPDEs) with Dirichlet boundary conditions on a finite domain. Firstly, the method of successive approximations is used to obtain the analytical solutions of coupling multi-term time fractional ordinary differential equations. Then, the technique of spectral representation of the fractional Laplacian operator is used to convert the coupling FPDEs to the coupling multi-term time fractional ordinary differential equations. By applying the obtained analytical solutions to the resulting multi-term time fractional ordinary differential equations, the desired analytical solutions of the coupling FPDEs are given. Our results are applied to derive the analytical solutions of some special cases to demonstrate their applicability.

Comparative Metabolomic Analysis of the Green Microalga Chlorella sorokiniana Cultivated in the Single Culture and a Consortium with Bacteria for Wastewater Remediation.

PubMed

Chen, Taojing; Zhao, Quanyu; Wang, Liang; Xu, Yunfeng; Wei, Wei

2017-11-01

Co-culture of microalgae with many types of bacteria usually comes out with significant different treatment efficiencies for COD, nitrogen, and phosphorus in wastewater remediation, compared with the single culture. In order to understand the mechanism behind, a comparative experiment was designed in this study, using the green microalgae species Chlorella sorokiniana in the single culture and a consortium with a bacterium, Pseudomonas H4, for nutrient removal. Comparative metabolome profile analysis was conducted to reveal the Chlorella cell responses to the synergistic growth with the bacteria, and possible relations between the metabolic regulation of microalgae and the nutrient degradation were discussed. The detectable differential metabolites of Chlorella belonged to several classes, including carbohydrates, fatty acids, amino acids, phosphates, polyols, etc. The orthogonal partial least squares discriminant analysis (OPLS-DA) model of the identified metabolites suggests the metabolism in this alga was significantly affected by the bacteria, corresponding to different treatment behaviors.

Spectroscopic signature of mouse embryonic stem cell-derived hepatocytes using synchrotron Fourier transform infrared microspectroscopy

NASA Astrophysics Data System (ADS)

Thumanu, Kanjana; Tanthanuch, Waraporn; Ye, Danna; Sangmalee, Anawat; Lorthongpanich, Chanchao; Parnpai, Rangsun; Heraud, Philip

2011-05-01

Stem cell-based therapy for liver regeneration has been proposed to overcome the persistent shortage in the supply of suitable donor organs. A requirement for this to succeed is to find a rapid method to detect functional hepatocytes, differentiated from embryonic stem cells. We propose Fourier transform infrared (FTIR) microspectroscopy as a versatile method to identify the early and last stages of the differentiation process leading to the formation of hepatocytes. Using synchrotron-FTIR microspectroscopy, the means of identifying hepatocytes at the single-cell level is possible and explored. Principal component analysis and subsequent partial least-squares (PLS) discriminant analysis is applied to distinguish endoderm induction from hepatic progenitor cells and matured hepatocyte-like cells. The data are well modeled by PLS with endoderm induction, hepatic progenitor cells, and mature hepatocyte-like cells able to be discriminated with very high sensitivity and specificity. This method provides a practical tool to monitor endoderm induction and has the potential to be applied for quality control of cell differentiation leading to hepatocyte formation.

Partial slip effect in the flow of MHD micropolar nanofluid flow due to a rotating disk - A numerical approach

NASA Astrophysics Data System (ADS)

Ramzan, Muhammad; Chung, Jae Dong; Ullah, Naeem

The aim of present exploration is to study the flow of micropolar nanofluid due to a rotating disk in the presence of magnetic field and partial slip condition. The governing coupled partial differential equations are reduced to nonlinear ordinary differential equations using appropriate transformations. The differential equations are solved numerically by using Maple dsolve command with option numeric which utilize Runge-Kutta fourth-fifth order Fehlberg technique. A comparison to previous study is also added to validate the present results. Moreover, behavior of different parameters on velocity, microrotation, temperature and concentration of nanofluid are presented via graphs and tables. It is noted that the slip effect and magnetic field decay the velocity and microrotation or spin component.

The Uniform Convergence of Eigenfunction Expansions of Schrödinger Operator in the Nikolskii Classes {H}_{p}^{\\alpha }(\\bar{\\Omega })

NASA Astrophysics Data System (ADS)

Jamaludin, N. A.; Ahmedov, A.

2017-09-01

Many boundary value problems in the theory of partial differential equations can be solved by separation methods of partial differential equations. When Schrödinger operator is considered then the influence of the singularity of potential on the solution of the partial differential equation is interest of researchers. In this paper the problems of the uniform convergence of the eigenfunction expansions of the functions from corresponding to the Schrödinger operator with the potential from classes of Sobolev are investigated. The spectral function corresponding to the Schrödinger operator is estimated in closed domain. The isomorphism of the Nikolskii classes is applied to prove uniform convergence of eigenfunction expansions of Schrödinger operator in closed domain.

Low-Degree Partial Melting Experiments of CR and H Chondrite Compositions: Implications for Asteroidal Magmatism Recorded in GRA 06128 and GRA 06129 T

NASA Technical Reports Server (NTRS)

Usui, T.; Jones, John H.; Mittlefehldt, D. W.

2010-01-01

Studies of differentiated meteorites have revealed a diversity of differentiation processes on their parental asteroids; these differentiation mechanisms range from whole-scale melting to partial melting without the core formation [e.g., 1]. Recently discovered paired achondrites GRA 06128 and GRA 06129 (hereafter referred to as GRA) represent unique asteroidal magmatic processes. These meteorites are characterized by high abundances of sodic plagioclase and alkali-rich whole-rock compositions, implying that they could originate from a low-degree partial melt from a volatile-rich oxidized asteroid [e.g., 2, 3, 4]. These conditions are consistent with the high abundances of highly siderophile elements, suggesting that their parent asteroid did not segregate a metallic core [2]. In this study, we test the hypothesis that low-degree partial melts of chondritic precursors under oxidizing conditions can explain the whole-rock and mineral chemistry of GRA based on melting experiments of synthesized CR- and H-chondrite compositions.

The application of Legendre-tau approximation to parameter identification for delay and partial differential equations

NASA Technical Reports Server (NTRS)

Ito, K.

1983-01-01

Approximation schemes based on Legendre-tau approximation are developed for application to parameter identification problem for delay and partial differential equations. The tau method is based on representing the approximate solution as a truncated series of orthonormal functions. The characteristic feature of the Legendre-tau approach is that when the solution to a problem is infinitely differentiable, the rate of convergence is faster than any finite power of 1/N; higher accuracy is thus achieved, making the approach suitable for small N.

In vitro Multi-Species Biofilms of Methicillin-Resistant Staphylococcus aureus and Pseudomonas aeruginosa and Their Host Interaction during In vivo Colonization of an Otitis Media Rat Model

PubMed Central

Yadav, Mukesh K.; Chae, Sung-Won; Go, Yoon Young; Im, Gi Jung; Song, Jae-Jun

2017-01-01

Staphylococcus aureus (SA) and Pseudomonas aeruginosa (PA) are known to cause biofilm-related infections. MRSA and PA have been frequently isolated from chronically infected wounds, cystic fibrosis, chronic suppurative otitis media (CSOM), and from indwelling medical devices, and these bacteria co-exist; however, their interaction with each-other or with the host is not well known. In this study, we investigated MRSA and PA multi-species biofilm communities in vitro and their interaction with the host during in vivo colonization using an OM rat-model. In-vitro biofilm formation and in-vivo colonization were studied using CV-microtiter plate assay and OM rat-model respectively. The biofilms were viewed under scanning electron microscope and bacteria were enumerated using cfu counts. The differential gene expressions of rat mucosa colonized with single or multi-species of MRSA or PA were studied using RNA-sequencing of total transcriptome. In multi-species in-vitro biofilms PA partially inhibited SA growth. However, no significant inhibition of MRSA was detected during in-vivo colonization of multi-species in rat bullae. A total of 1,797 genes were significantly (p < 0.05) differentially expressed in MRSA or PA or MRSA + PA colonized rat middle ear mucosa with respect to the control. The poly-microbial colonization of MRSA and PA induced the differential expression of a significant number of genes that are involved in immune response, inflammation, signaling, development, and defense; these were not expressed with single species colonization by either MRSA or PA. Genes involved in defense, immune response, inflammatory response, and developmental process were exclusively up-regulated, and genes that are involved in nervous system signaling, development and transmission, regulation of cell growth and development, anatomical and system development, and cell differentiation were down-regulated after multi-species inoculation. These results indicate that poly-microbial colonization induces a host response that is different from that induced by single species infection. PMID:28459043

Coolant side heat transfer with rotation: User manual for 3D-TEACH with rotation

NASA Technical Reports Server (NTRS)

Syed, S. A.; James, R. H.

1989-01-01

This program solves the governing transport equations in Reynolds average form for the flow of a 3-D, steady state, viscous, heat conducting, multiple species, single phase, Newtonian fluid with combustion. The governing partial differential equations are solved in physical variables in either a Cartesian or cylindrical coordinate system. The effects of rotation on the momentum and enthalpy calculations modeled in Cartesian coordinates are examined. The flow of the fluid should be confined and subsonic with a maximum Mach number no larger than 0.5. This manual describes the operating procedures and input details for executing a 3D-TEACH computation.

Regularization of moving boundaries in a laplacian field by a mixed Dirichlet-Neumann boundary condition: exact results.

PubMed

Meulenbroek, Bernard; Ebert, Ute; Schäfer, Lothar

2005-11-04

The dynamics of ionization fronts that generate a conducting body are in the simplest approximation equivalent to viscous fingering without regularization. Going beyond this approximation, we suggest that ionization fronts can be modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact uniformly propagating solutions of this problem in 2D and construct a single partial differential equation governing small perturbations of these solutions. For some parameter value, this equation can be solved analytically, which shows rigorously that the uniformly propagating solution is linearly convectively stable and that the asymptotic relaxation is universal and exponential in time.

Photodynamic therapy influence on anti-cancer immunity

NASA Astrophysics Data System (ADS)

Isaeva, O. G.; Osipov, V. A.

2010-02-01

The system of partial differential equations describing tumor-immune dynamics with angiogenesis taken into account is presented. For spatially homogeneous case, the steady state analysis of the model is carried out. The effects of single photodynamic impact are numerically simulated. In the case of strong immune response we found that the photodynamic therapy (PDT) gives rise to the substantial shrinkage of tumor size which is accompanied by the increase of IL-2 concentration. On the contrary, the photodynamic stimulation of weak immune response is shown to be insufficient to reduce the tumor. These findings indicate the important role of anti-cancer immune response in the long-term tumor control after PDT.

Photodynamic therapy influence on anti-cancer immunity

NASA Astrophysics Data System (ADS)

Isaeva, O. G.; Osipov, V. A.

2009-10-01

The system of partial differential equations describing tumor-immune dynamics with angiogenesis taken into account is presented. For spatially homogeneous case, the steady state analysis of the model is carried out. The effects of single photodynamic impact are numerically simulated. In the case of strong immune response we found that the photodynamic therapy (PDT) gives rise to the substantial shrinkage of tumor size which is accompanied by the increase of IL-2 concentration. On the contrary, the photodynamic stimulation of weak immune response is shown to be insufficient to reduce the tumor. These findings indicate the important role of anti-cancer immune response in the long-term tumor control after PDT.

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.

1982-01-01

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

Trigonometric Integrals via Partial Fractions

ERIC Educational Resources Information Center

Chen, H.; Fulford, M.

2005-01-01

Parametric differentiation is used to derive the partial fractions decompositions of certain rational functions. Those decompositions enable us to integrate some new combinations of trigonometric functions.

Exp-function method for solving fractional partial differential equations.

PubMed

Zheng, Bin

2013-01-01

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional Sharma-Tasso-Olver (STO) equation. As a result, some new exact solutions for them are successfully established.

Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr.; Rajiyah, H.

1991-01-01

Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

Normalized cDNA libraries

DOEpatents

Soares, Marcelo B.; Efstratiadis, Argiris

1997-01-01

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3' noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to moderate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library.

Normalized cDNA libraries

DOEpatents

Soares, M.B.; Efstratiadis, A.

1997-06-10

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3{prime} noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to moderate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library. 4 figs.

Topics in spectral methods

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1985-01-01

After detailing the construction of spectral approximations to time-dependent mixed initial boundary value problems, a study is conducted of differential equations of the form 'partial derivative of u/partial derivative of t = Lu + f', where for each t, u(t) belongs to a Hilbert space such that u satisfies homogeneous boundary conditions. For the sake of simplicity, it is assumed that L is an unbounded, time-independent linear operator. Attention is given to Fourier methods of both Galerkin and pseudospectral method types, the Galerkin method, the pseudospectral Chebyshev and Legendre methods, the error equation, hyperbolic partial differentiation equations, and time discretization and iterative methods.

Effect of evaporative surface cooling on thermographic assessment of burn depth

NASA Technical Reports Server (NTRS)

Anselmo, V. J.; Zawacki, B. E.

1977-01-01

Differences in surface temperature between evaporating and nonevaporating, partial- and full-thickness burn injuries were studied in 20 male, white guinea pigs. Evaporative cooling can disguise the temperature differential of the partial-thickness injury and lead to a false full-thickness diagnosis. A full-thickness burn with blister intact may retain enough heat to result in a false partial-thickness diagnosis. By the fourth postburn day, formation of a dry eschar may allow a surface temperature measurement without the complication of differential evaporation. For earlier use of thermographic information, evaporation effects must be accounted for or eliminated.

Solving Differential Equations in R: Package deSolve

EPA Science Inventory

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines appr...

A higher order numerical method for time fractional partial differential equations with nonsmooth data

NASA Astrophysics Data System (ADS)

Xing, Yanyuan; Yan, Yubin

2018-03-01

Gao et al. [11] (2014) introduced a numerical scheme to approximate the Caputo fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 by directly approximating the integer-order derivative with some finite difference quotients in the definition of the Caputo fractional derivative, see also Lv and Xu [20] (2016), where k is the time step size. Under the assumption that the solution of the time fractional partial differential equation is sufficiently smooth, Lv and Xu [20] (2016) proved by using energy method that the corresponding numerical method for solving time fractional partial differential equation has the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. However, in general the solution of the time fractional partial differential equation has low regularity and in this case the numerical method fails to have the convergence rate O (k 3 - α), 0 < α < 1 uniformly with respect to the time variable t. In this paper, we first obtain a similar approximation scheme to the Riemann-Liouville fractional derivative with the convergence rate O (k 3 - α), 0 < α < 1 as in Gao et al. [11] (2014) by approximating the Hadamard finite-part integral with the piecewise quadratic interpolation polynomials. Based on this scheme, we introduce a time discretization scheme to approximate the time fractional partial differential equation and show by using Laplace transform methods that the time discretization scheme has the convergence rate O (k 3 - α), 0 < α < 1 for any fixed tn > 0 for smooth and nonsmooth data in both homogeneous and inhomogeneous cases. Numerical examples are given to show that the theoretical results are consistent with the numerical results.

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Lineage divergence detected in the malaria vector Anopheles marajoara (Diptera: Culicidae) in Amazonian Brazil

PubMed Central

2010-01-01

Background Cryptic species complexes are common among anophelines. Previous phylogenetic analysis based on the complete mtDNA COI gene sequences detected paraphyly in the Neotropical malaria vector Anopheles marajoara. The "Folmer region" detects a single taxon using a 3% divergence threshold. Methods To test the paraphyletic hypothesis and examine the utility of the Folmer region, genealogical trees based on a concatenated (white + 3' COI sequences) dataset and pairwise differentiation of COI fragments were examined. The population structure and demographic history were based on partial COI sequences for 294 individuals from 14 localities in Amazonian Brazil. 109 individuals from 12 localities were sequenced for the nDNA white gene, and 57 individuals from 11 localities were sequenced for the ribosomal DNA (rDNA) internal transcribed spacer 2 (ITS2). Results Distinct A. marajoara lineages were detected by combined genealogical analysis and were also supported among COI haplotypes using a median joining network and AMOVA, with time since divergence during the Pleistocene (<100,000 ya). COI sequences at the 3' end were more variable, demonstrating significant pairwise differentiation (3.82%) compared to the more moderate 2.92% detected by the Folmer region. Lineage 1 was present in all localities, whereas lineage 2 was restricted mainly to the west. Mismatch distributions for both lineages were bimodal, likely due to multiple colonization events and spatial expansion (~798 - 81,045 ya). There appears to be gene flow within, not between lineages, and a partial barrier was detected near Rio Jari in Amapá state, separating western and eastern populations. In contrast, both nDNA data sets (white gene sequences with or without the retention of the 4th intron, and ITS2 sequences and length) detected a single A. marajoara lineage. Conclusions Strong support for combined data with significant differentiation detected in the COI and absent in the nDNA suggest that the divergence is recent, and detectable only by the faster evolving mtDNA. A within subgenus threshold of >2% may be more appropriate among sister taxa in cryptic anopheline complexes than the standard 3%. Differences in demographic history and climatic changes may have contributed to mtDNA lineage divergence in A. marajoara. PMID:20929572

Lump solutions to nonlinear partial differential equations via Hirota bilinear forms

NASA Astrophysics Data System (ADS)

Ma, Wen-Xiu; Zhou, Yuan

2018-02-01

Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is the Hirota bilinear formulation and the primary object is the class of positive multivariate quadratic functions. A complete determination of quadratic functions positive in space and time is given, and positive quadratic functions are characterized as sums of squares of linear functions. Necessary and sufficient conditions for positive quadratic functions to solve Hirota bilinear equations are presented, and such polynomial solutions yield lump solutions to nonlinear partial differential equations under the dependent variable transformations u = 2(ln ⁡ f) x and u = 2(ln ⁡ f) xx, where x is one spatial variable. Applications are made for a few generalized KP and BKP equations.

Boundary-fitted coordinate systems for numerical solution of partial differential equations - A review

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W.

1982-01-01

A comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given. Some general mathematical framework and error analysis common to such coordinate systems is also included. The general categories of generating systems are those based on conformal mapping, orthogonal systems, nearly orthogonal systems, systems produced as the solution of elliptic and hyperbolic partial differential equations, and systems generated algebraically by interpolation among the boundaries. Also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation. Dynamically adaptive coordinate systems, coupled with the physical solution, and time-dependent systems that follow moving boundaries are treated. References reporting experience using such coordinate systems are reviewed as well as those covering the system development.

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.

Shift-connected SIMD array architectures for digital optical computing systems, with algorithms for numerical transforms and partial differential equations

NASA Astrophysics Data System (ADS)

Drabik, Timothy J.; Lee, Sing H.

1986-11-01

The intrinsic parallelism characteristics of easily realizable optical SIMD arrays prompt their present consideration in the implementation of highly structured algorithms for the numerical solution of multidimensional partial differential equations and the computation of fast numerical transforms. Attention is given to a system, comprising several spatial light modulators (SLMs), an optical read/write memory, and a functional block, which performs simple, space-invariant shifts on images with sufficient flexibility to implement the fastest known methods for partial differential equations as well as a wide variety of numerical transforms in two or more dimensions. Either fixed or floating-point arithmetic may be used. A performance projection of more than 1 billion floating point operations/sec using SLMs with 1000 x 1000-resolution and operating at 1-MHz frame rates is made.

Family Structure and the Intergenerational Transmission of Educational Advantage*

PubMed Central

Martin, Molly A.

2013-01-01

I examine whether the effect of parents’ education on children’s educational achievement and attainment varies by family structure and, if so, whether this can be explained by differential parenting practices. Using data from the National Education Longitudinal Study of 1988, I find that as parents’ education increases, children in single mother families experience a lower boost in their achievement test scores, likelihood of attending any post-secondary schooling, likelihood of completing a four-year college degree, and years of completed schooling relative to children living with both biological parents. Differences in parents’ educational expectations, intergenerational closure, and children’s involvement in structured leisure activities partially explain these status transmission differences by family structure. The findings imply that, among children with highly educated parents, children of single mothers are less likely to be highly educated themselves relative to children who grow up with both biological parents. PMID:23017695

Novel Gas Sensor Arrays Based on High-Q SAM-Modified Piezotransduced Single-Crystal Silicon Bulk Acoustic Resonators

PubMed Central

Zhao, Yuan; Yang, Qingrui; Chang, Ye; Pang, Wei; Zhang, Hao; Duan, Xuexin

2017-01-01

This paper demonstrates a novel micro-size (120 μm × 200 μm) piezoelectric gas sensor based on a piezotransduced single-crystal silicon bulk acoustic resonator (PSBAR). The PSBARs operate at 102 MHz and possess high Q values (about 2000), ensuring the stability of the measurement. A corresponding gas sensor array is fabricated by integrating three different self-assembled monolayers (SAMs) modified PSBARs. The limit of detection (LOD) for ethanol vapor is demonstrated to be as low as 25 ppm with a sensitivity of about 1.5 Hz/ppm. Two sets of identification code bars based on the sensitivities and the adsorption energy constants are utilized to successfully discriminate isopropanol (IPA), ethanol, hexane and heptane vapors at low and high gas partial pressures, respectively. The proposed sensor array shows the potential to form a portable electronic nose system for volatile organic compound (VOC) differentiation. PMID:28672852

Novel Gas Sensor Arrays Based on High-Q SAM-Modified Piezotransduced Single-Crystal Silicon Bulk Acoustic Resonators.

PubMed

Zhao, Yuan; Yang, Qingrui; Chang, Ye; Pang, Wei; Zhang, Hao; Duan, Xuexin

2017-06-26

This paper demonstrates a novel micro-size (120 μm × 200 μm) piezoelectric gas sensor based on a piezotransduced single-crystal silicon bulk acoustic resonator (PSBAR). The PSBARs operate at 102 MHz and possess high Q values (about 2000), ensuring the stability of the measurement. A corresponding gas sensor array is fabricated by integrating three different self-assembled monolayers (SAMs) modified PSBARs. The limit of detection (LOD) for ethanol vapor is demonstrated to be as low as 25 ppm with a sensitivity of about 1.5 Hz/ppm. Two sets of identification code bars based on the sensitivities and the adsorption energy constants are utilized to successfully discriminate isopropanol (IPA), ethanol, hexane and heptane vapors at low and high gas partial pressures, respectively. The proposed sensor array shows the potential to form a portable electronic nose system for volatile organic compound (VOC) differentiation.

When push comes to shove: Exclusion processes with nonlocal consequences

NASA Astrophysics Data System (ADS)

Almet, Axel A.; Pan, Michael; Hughes, Barry D.; Landman, Kerry A.

2015-11-01

Stochastic agent-based models are useful for modelling collective movement of biological cells. Lattice-based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes. An alternative motility mechanism to simple exclusion is formulated, in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local. This mechanism is termed shoving. A nonlinear diffusion equation is derived for a single population of shoving agents using mean-field continuum approximations. A continuum model is also derived for a multispecies problem with interacting subpopulations, which either obey the shoving rules or the simple exclusion rules. Numerical solutions of the derived partial differential equations compare well with averaged simulation results for both the single species and multispecies processes in two dimensions, while some issues arise in one dimension for the multispecies case.

Family structure and the intergenerational transmission of educational advantage.

PubMed

Martin, Molly A

2012-01-01

I examine whether the effect of parents' education on children's educational achievement and attainment varies by family structure and, if so, whether this can be explained by differential parenting practices. Using data from the National Education Longitudinal Study of 1988, I find that as parents' education increases, children in single mother families experience a lower boost in their achievement test scores, likelihood of attending any post-secondary schooling, likelihood of completing a 4-year college degree, and years of completed schooling relative to children living with both biological parents. Differences in parents' educational expectations, intergenerational closure, and children's involvement in structured leisure activities partially explain these status transmission differences by family structure. The findings imply that, among children with highly educated parents, children of single mothers are less likely to be highly educated themselves relative to children who grow up with both biological parents. Copyright © 2011 Elsevier Inc. All rights reserved.

An approximation theory for nonlinear partial differential equations with applications to identification and control

NASA Technical Reports Server (NTRS)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Research on Nonlinear Dynamical Systems.

DTIC Science & Technology

1983-01-10

Applied Math., to appear. [26] Variational inequalities and flow in porous media, LCDS’Lecture Notes, Brown University #LN 82-1, July 1982. [27] On...approximation schemes for parabolic and hyperbolic systems of partial differential equations, including higher order equations of elasticity based on the...51,58,59,63,64,69]. Finally, stability and bifurcation in parabolic partial differential equations is the focus of [64,65,67,72,73]. In addition to these broad

Impact of parenchymal loss on renal function after laparoscopic partial nephrectomy under warm ischemia.

PubMed

Bagheri, Fariborz; Pusztai, Csaba; Farkas, László; Kallidonis, Panagiotis; Buzogány, István; Szabó, Zsuzsanna; Lantos, János; Imre, Marianna; Farkas, Nelli; Szántó, Árpád

2016-12-01

To elucidate the impact of renal parenchymal loss and the ischemic reperfusion injury (RI) on the renal function after laparoscopic partial nephrectomy (LPN) under warm ischemia (WI). Thirty-five patients with a single polar renal mass ≤4 cm and normal contralateral kidney underwent LPN. Transperitoneal LPN with WI using en bloc hilar occlusion was performed. The total differential renal function (T-DRF) using 99m Tc-dimercaptosuccinic acid was evaluated preoperatively and postoperatively over a period of 1 year. A special region of interest (ROI) was selected on the non-tumorous pole of the involved kidney, and was compared with the same ROI in the contralateral kidney. The latter comparison was defined as partial differential renal function (P-DRF). Any postoperative decline in the P-DRF of the operated kidney was attributed to the RI. Subtraction of the P-DRF decline from the T-DRF decline was attributed to the parenchymal loss caused by the resection of the tumor and suturing of the normal parenchyma. The mean WI time was 22 min, and the mean weight of resected specimen was 18 g. The mean postoperative eGFR declined to 87 ml/min/1.73 m 2 from its baseline mean value of 97 ml/min/1.73 m 2 (p value = 0.075). Mean postoperative T-DRF and P-DRF of the operated kidney declined by 7 and 3 %, respectively. After LPN of small renal mass, decline in renal function is primarily attributed to parenchymal loss caused by tumor resection and suturing of the normal parenchyma rather than the RI.

Geometric properties of commutative subalgebras of partial differential operators

NASA Astrophysics Data System (ADS)

Zheglov, A. B.; Kurke, H.

2015-05-01

We investigate further algebro-geometric properties of commutative rings of partial differential operators, continuing our research started in previous articles. In particular, we start to explore the simplest and also certain known examples of quantum algebraically completely integrable systems from the point of view of a recent generalization of Sato's theory, developed by the first author. We give a complete characterization of the spectral data for a class of 'trivial' commutative algebras and strengthen geometric properties known earlier for a class of known examples. We also define a kind of restriction map from the moduli space of coherent sheaves with fixed Hilbert polynomial on a surface to an analogous moduli space on a divisor (both the surface and the divisor are part of the spectral data). We give several explicit examples of spectral data and corresponding algebras of commuting (completed) operators, producing as a by-product interesting examples of surfaces that are not isomorphic to spectral surfaces of any (maximal) commutative ring of partial differential operators of rank one. Finally, we prove that any commutative ring of partial differential operators whose normalization is isomorphic to the ring of polynomials k \\lbrack u,t \\rbrack is a Darboux transformation of a ring of operators with constant coefficients. Bibliography: 39 titles.

Partial differential equation methods for stochastic dynamic optimization: an application to wind power generation with energy storage.

PubMed

Johnson, Paul; Howell, Sydney; Duck, Peter

2017-08-13

A mixed financial/physical partial differential equation (PDE) can optimize the joint earnings of a single wind power generator (WPG) and a generic energy storage device (ESD). Physically, the PDE includes constraints on the ESD's capacity, efficiency and maximum speeds of charge and discharge. There is a mean-reverting daily stochastic cycle for WPG power output. Physically, energy can only be produced or delivered at finite rates. All suppliers must commit hourly to a finite rate of delivery C , which is a continuous control variable that is changed hourly. Financially, we assume heavy 'system balancing' penalties in continuous time, for deviations of output rate from the commitment C Also, the electricity spot price follows a mean-reverting stochastic cycle with a strong evening peak, when system balancing penalties also peak. Hence the economic goal of the WPG plus ESD, at each decision point, is to maximize expected net present value (NPV) of all earnings (arbitrage) minus the NPV of all expected system balancing penalties, along all financially/physically feasible future paths through state space. Given the capital costs for the various combinations of the physical parameters, the design and operating rules for a WPG plus ESD in a finite market may be jointly optimizable.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'. © 2017 The Author(s).

Preparation and characterization of the magnetic superconductor EuSr2RuCu2O8-δ (RuEu-1212) by partial melting

NASA Astrophysics Data System (ADS)

Yamaki, K.; Kitagawa, N.; Funahashi, S.; Bamba, Y.; Irie, A.

2018-07-01

In this study, fine single crystals of the magnetic superconductor EuSr2RuCu2O8-δ (RuEu-1212) were successfully prepared using the partial melting technique. The obtained single crystals had a cubic shape, which coincides with the results of previous studies of RuGd-1212 single crystals. The single crystals had a typical length of 20-30 μm and the diffraction pattern observed from a sample prepared by partial melting was consistent with patterns of previously reported polycrystalline RuEu-1212 samples. A sample subjected to prolonged sintering, which consisted of a large number of combined micro single crystals prepared by partial melting, exhibited a superconducting transition with Tc-onset of 30.9 K and Tc-zero of 10.5 K.

Method for construction of normalized cDNA libraries

DOEpatents

Soares, Marcelo B.; Efstratiadis, Argiris

1996-01-01

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3' noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to moderate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library.

Method for construction of normalized cDNA libraries

DOEpatents

Soares, M.B.; Efstratiadis, A.

1996-01-09

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form. The method comprises: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3` noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to moderate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library. 4 figs.

7 CFR 1000.76 - Payments by a handler operating a partially regulated distributing plant.

Code of Federal Regulations, 2010 CFR

2010-01-01

..., compute a Class I differential price by subtracting Class III price from the current month's Class I price... by which the Class I differential price exceeds the producer price differential, both prices to be... Class I differential price nor the adjusted producer price differential shall be less than zero; (3) For...

Graded levels of Pax2a and Pax8 regulate cell differentiation during sensory placode formation.

PubMed

McCarroll, Matthew N; Lewis, Zachary R; Culbertson, Maya Deza; Martin, Benjamin L; Kimelman, David; Nechiporuk, Alex V

2012-08-01

Pax gene haploinsufficiency causes a variety of congenital defects. Renal-coloboma syndrome, resulting from mutations in Pax2, is characterized by kidney hypoplasia, optic nerve malformation, and hearing loss. Although this underscores the importance of Pax gene dosage in normal development, how differential levels of these transcriptional regulators affect cell differentiation and tissue morphogenesis is still poorly understood. We show that differential levels of zebrafish Pax2a and Pax8 modulate commitment and behavior in cells that eventually contribute to the otic vesicle and epibranchial placodes. Initially, a subset of epibranchial placode precursors lie lateral to otic precursors within a single Pax2a/8-positive domain; these cells subsequently move to segregate into distinct placodes. Using lineage-tracing and ablation analyses, we show that cells in the Pax2a/8+ domain become biased towards certain fates at the beginning of somitogenesis. Experiments involving either Pax2a overexpression or partial, combinatorial Pax2a and Pax8 loss of function reveal that high levels of Pax favor otic differentiation whereas low levels increase cell numbers in epibranchial ganglia. In addition, the Fgf and Wnt signaling pathways control Pax2a expression: Fgf is necessary to induce Pax2a, whereas Wnt instructs the high levels of Pax2a that favor otic differentiation. Our studies reveal the importance of Pax levels during sensory placode formation and provide a mechanism by which these levels are controlled.

Graded levels of Pax2a and Pax8 regulate cell differentiation during sensory placode formation

PubMed Central

McCarroll, Matthew N.; Lewis, Zachary R.; Culbertson, Maya Deza; Martin, Benjamin L.; Kimelman, David; Nechiporuk, Alex V.

2012-01-01

Pax gene haploinsufficiency causes a variety of congenital defects. Renal-coloboma syndrome, resulting from mutations in Pax2, is characterized by kidney hypoplasia, optic nerve malformation, and hearing loss. Although this underscores the importance of Pax gene dosage in normal development, how differential levels of these transcriptional regulators affect cell differentiation and tissue morphogenesis is still poorly understood. We show that differential levels of zebrafish Pax2a and Pax8 modulate commitment and behavior in cells that eventually contribute to the otic vesicle and epibranchial placodes. Initially, a subset of epibranchial placode precursors lie lateral to otic precursors within a single Pax2a/8-positive domain; these cells subsequently move to segregate into distinct placodes. Using lineage-tracing and ablation analyses, we show that cells in the Pax2a/8+ domain become biased towards certain fates at the beginning of somitogenesis. Experiments involving either Pax2a overexpression or partial, combinatorial Pax2a and Pax8 loss of function reveal that high levels of Pax favor otic differentiation whereas low levels increase cell numbers in epibranchial ganglia. In addition, the Fgf and Wnt signaling pathways control Pax2a expression: Fgf is necessary to induce Pax2a, whereas Wnt instructs the high levels of Pax2a that favor otic differentiation. Our studies reveal the importance of Pax levels during sensory placode formation and provide a mechanism by which these levels are controlled. PMID:22745314

Isolation of genes negatively or positively co-expressed with human recombination activating gene 1 (RAG1) by differential display PCR (DD RT-PCR).

PubMed

Verkoczy, L K; Berinstein, N L

1998-10-01

Differential display PCR (DD RT-PCR) has been extensively used for analysis of differential gene expression, but continues to be hampered by technical limitations that impair its effectiveness. In order to isolate novel genes co-expressing with human RAG1, we have developed an effective, multi-tiered screening/purification approach which effectively complements the standard DD RT-PCR methodology. In 'primary' screens, standard DD RT-PCR was used, detecting 22 reproducible differentially expressed amplicons between clonally related cell variants with differential constitutive expression of RAG mRNAs. 'Secondary' screens used differential display (DD) amplicons as probes in low and high stringency northern blotting. Eight of 22 independent DD amplicons detected nine independent differentially expressed transcripts. 'Tertiary' screens used reconfirmed amplicons as probes in northern analysis of multiple RAG-and RAG+sources. Reconfirmed DD amplicons detected six independent RAG co-expressing transcripts. All DD amplicons reconfirmed by northern blot were a heterogeneous mixture of cDNAs, necessitating further purification to isolate single cDNAs prior to subcloning and sequencing. To effectively select the appropriate cDNAs from DD amplicons, we excised and eluted the cDNA(s) directly from regions of prior northern blots in which differentially expressed transcripts were detected. Sequences of six purified cDNA clones specifically detecting RAG co-expressing transcripts included matches to portions of the human RAG2 and BSAP regions and to four novel partial cDNAs (three with homologies to human ESTs). Overall, our results also suggest that even when using clonally related variants from the same cell line in addition to all appropriate internal controls previously reported, further screening and purification steps are still required in order to efficiently and specifically isolate differentially expressed genes by DD RT-PCR.

Thermal evolution of a partially differentiated H chondrite parent body

NASA Astrophysics Data System (ADS)

Abrahams, J. N. H.; Bryson, J. F. J.; Weiss, B. P.; Nimmo, F.

2016-12-01

It has traditionally been assumed that planetesimals either melted entirely or remained completely undifferentiated as they accreted. The unmelted textures and cooling histories of chondrites have been used to argue that these meteorites originated from bodies that never differentiated. However, paleomagnetic measurements indicate that some chondrites (e.g., the H chondrite Portales Valley and several CV chondrites) were magnetized by a core dynamo magnetic field, implying that their parent bodies were partially differentiated. It has been unclear, however, whether planetesimal histories consistent with dynamo production can also be consistent with the diversity of chondrite cooling rates and ages. To address this, we modeled the thermal evolution of the H chondrite parent body, considering a variety of accretion histories and parent body radii. We considered partial differentiation using two-stage accretion involving the initial formation and differentiation of a small body, followed by the later addition of low thermal conductivity chondritic material that remains mostly unmelted. We were able to reproduce the measured thermal evolution of multiple H chondrites for a range of parent body parameters, including initial radii from 70-150 km, chondritic layer thicknesses from 50 km to over 100 km, and second stage accretion times of 2.5-3 Myr after solar system formation. Our predicted rates of core cooling and crystallization are consistent with dynamo generation by compositional convection beginning 60-200 Myr after solar system formation and lasting for at least tens of millions of years. This is consistent with magnetic studies of Portales Valley [Bryson et al., this meeting]. In summary, we find that thermal models of partial differentiation are consistent the radiometric ages, magnetization, and cooling rates of a diversity H chondrites.

Some remarks on the numerical solution of parabolic partial differential equations

NASA Astrophysics Data System (ADS)

Campagna, R.; Cuomo, S.; Leveque, S.; Toraldo, G.; Giannino, F.; Severino, G.

2017-11-01

Numerous environmental/engineering applications relying upon the theory of diffusion phenomena into chaotic environments have recently stimulated the interest toward the numerical solution of parabolic partial differential equations (PDEs). In the present paper, we outline a formulation of the mathematical problem underlying a quite general diffusion mechanism in the natural environments, and we shortly emphasize some remarks concerning the applicability of the (straightforward) finite difference method. An illustration example is also presented.

The Refinement-Tree Partition for Parallel Solution of Partial Differential Equations

PubMed Central

Mitchell, William F.

1998-01-01

Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on distributed memory multiprocessors. An approach that periodically repartitions the grid is taken. The important properties of a partitioning algorithm are presented and discussed in this context. A partitioning algorithm based on the refinement tree of the adaptive grid is presented and analyzed in terms of these properties. Theoretical and numerical results are given. PMID:28009355

The Refinement-Tree Partition for Parallel Solution of Partial Differential Equations.

PubMed

Mitchell, William F

1998-01-01

Dynamic load balancing is considered in the context of adaptive multilevel methods for partial differential equations on distributed memory multiprocessors. An approach that periodically repartitions the grid is taken. The important properties of a partitioning algorithm are presented and discussed in this context. A partitioning algorithm based on the refinement tree of the adaptive grid is presented and analyzed in terms of these properties. Theoretical and numerical results are given.

Observability of discretized partial differential equations

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1988-01-01

It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

A convex penalty for switching control of partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clason, Christian; Rund, Armin; Kunisch, Karl

2016-01-19

A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. In conclusion, the efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

Numerical methods for large-scale, time-dependent partial differential equations

NASA Technical Reports Server (NTRS)

Turkel, E.

1979-01-01

A survey of numerical methods for time dependent partial differential equations is presented. The emphasis is on practical applications to large scale problems. A discussion of new developments in high order methods and moving grids is given. The importance of boundary conditions is stressed for both internal and external flows. A description of implicit methods is presented including generalizations to multidimensions. Shocks, aerodynamics, meteorology, plasma physics and combustion applications are also briefly described.

Spectral methods for time dependent partial differential equations

NASA Technical Reports Server (NTRS)

Gottlieb, D.; Turkel, E.

1983-01-01

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Stability analysis of multigrid acceleration methods for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Fay, John F.

1990-01-01

A calculation is made of the stability of various relaxation schemes for the numerical solution of partial differential equations. A multigrid acceleration method is introduced, and its effects on stability are explored. A detailed stability analysis of a simple case is carried out and verified by numerical experiment. It is shown that the use of multigrids can speed convergence by several orders of magnitude without adversely affecting stability.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

From crater functions to partial differential equations: a new approach to ion bombardment induced nonequilibrium pattern formation.

PubMed

Norris, Scott A; Brenner, Michael P; Aziz, Michael J

2009-06-03

We develop a methodology for deriving continuum partial differential equations for the evolution of large-scale surface morphology directly from molecular dynamics simulations of the craters formed from individual ion impacts. Our formalism relies on the separation between the length scale of ion impact and the characteristic scale of pattern formation, and expresses the surface evolution in terms of the moments of the crater function. We demonstrate that the formalism reproduces the classical Bradley-Harper results, as well as ballistic atomic drift, under the appropriate simplifying assumptions. Given an actual set of converged molecular dynamics moments and their derivatives with respect to the incidence angle, our approach can be applied directly to predict the presence and absence of surface morphological instabilities. This analysis represents the first work systematically connecting molecular dynamics simulations of ion bombardment to partial differential equations that govern topographic pattern-forming instabilities.

Partial differential equations constrained combinatorial optimization on an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Chandra, Rishabh

Partial differential equation-constrained combinatorial optimization (PDECCO) problems are a mixture of continuous and discrete optimization problems. PDECCO problems have discrete controls, but since the partial differential equations (PDE) are continuous, the optimization space is continuous as well. Such problems have several applications, such as gas/water network optimization, traffic optimization, micro-chip cooling optimization, etc. Currently, no efficient classical algorithm which guarantees a global minimum for PDECCO problems exists. A new mapping has been developed that transforms PDECCO problem, which only have linear PDEs as constraints, into quadratic unconstrained binary optimization (QUBO) problems that can be solved using an adiabatic quantum optimizer (AQO). The mapping is efficient, it scales polynomially with the size of the PDECCO problem, requires only one PDE solve to form the QUBO problem, and if the QUBO problem is solved correctly and efficiently on an AQO, guarantees a global optimal solution for the original PDECCO problem.

PetIGA: A framework for high-performance isogeometric analysis

DOE PAGES

Dalcin, Lisandro; Collier, Nathaniel; Vignal, Philippe; ...

2016-05-25

We present PetIGA, a code framework to approximate the solution of partial differential equations using isogeometric analysis. PetIGA can be used to assemble matrices and vectors which come from a Galerkin weak form, discretized with Non-Uniform Rational B-spline basis functions. We base our framework on PETSc, a high-performance library for the scalable solution of partial differential equations, which simplifies the development of large-scale scientific codes, provides a rich environment for prototyping, and separates parallelism from algorithm choice. We describe the implementation of PetIGA, and exemplify its use by solving a model nonlinear problem. To illustrate the robustness and flexibility ofmore » PetIGA, we solve some challenging nonlinear partial differential equations that include problems in both solid and fluid mechanics. Lastly, we show strong scaling results on up to 4096 cores, which confirm the suitability of PetIGA for large scale simulations.« less

On Partial Fraction Decompositions by Repeated Polynomial Divisions

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2017-01-01

We present a method for finding partial fraction decompositions of rational functions with linear or quadratic factors in the denominators by means of repeated polynomial divisions. This method does not involve differentiation or solving linear equations for obtaining the unknown partial fraction coefficients, which is very suitable for either…

A Model for the Oxidation of Carbon Silicon Carbide Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2004-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

Computer simulation of two-dimensional unsteady flows in estuaries and embayments by the method of characteristics : basic theory and the formulation of the numerical method

USGS Publications Warehouse

Lai, Chintu

1977-01-01

Two-dimensional unsteady flows of homogeneous density in estuaries and embayments can be described by hyperbolic, quasi-linear partial differential equations involving three dependent and three independent variables. A linear combination of these equations leads to a parametric equation of characteristic form, which consists of two parts: total differentiation along the bicharacteristics and partial differentiation in space. For its numerical solution, the specified-time-interval scheme has been used. The unknown, partial space-derivative terms can be eliminated first by suitable combinations of difference equations, converted from the corresponding differential forms and written along four selected bicharacteristics and a streamline. Other unknowns are thus made solvable from the known variables on the current time plane. The computation is carried to the second-order accuracy by using trapezoidal rule of integration. Means to handle complex boundary conditions are developed for practical application. Computer programs have been written and a mathematical model has been constructed for flow simulation. The favorable computer outputs suggest further exploration and development of model worthwhile. (Woodard-USGS)

Theory of Metastable State Relaxation for Non-Critical Binary Systems with Non-Conserved Order Parameter

NASA Technical Reports Server (NTRS)

Izmailov, Alexander; Myerson, Allan S.

1993-01-01

A new mathematical ansatz for a solution of the time-dependent Ginzburg-Landau non-linear partial differential equation is developed for non-critical systems such as non-critical binary solutions (solute + solvent) described by the non-conserved scalar order parameter. It is demonstrated that in such systems metastability initiates heterogeneous solute redistribution which results in formation of the non-equilibrium singly-periodic spatial solute structure. It is found how the time-dependent period of this structure evolves in time. In addition, the critical radius r(sub c) for solute embryo of the new solute rich phase together with the metastable state lifetime t(sub c) are determined analytically and analyzed.

Review of Nuclear Physics Experiments for Space Radiation

NASA Technical Reports Server (NTRS)

Norbury, John W.; Miller, Jack; Adamczyk, Anne M.; Heilbronn, Lawrence H.; Townsend, Lawrence W.; Blattnig, Steve R.; Norman, Ryan B.; Guetersloh, Stephen B.; Zeitlin, Cary J.

2011-01-01

Human space flight requires protecting astronauts from the harmful effects of space radiation. The availability of measured nuclear cross section data needed for these studies is reviewed in the present paper. The energy range of interest for radiation protection is approximately 100 MeV/n to 10 GeV/n. The majority of data are for projectile fragmentation partial and total cross sections, including both charge changing and isotopic cross sections. The cross section data are organized into categories which include charge changing, elemental, isotopic for total, single and double differential with respect to momentum, energy and angle. Gaps in the data relevant to space radiation protection are discussed and recommendations for future experiments are made.

Collective phase description of oscillatory convection

NASA Astrophysics Data System (ADS)

Kawamura, Yoji; Nakao, Hiroya

2013-12-01

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shaw cells exhibiting oscillatory convection on the basis of the derived phase equations.

Thermodynamic investigations on the growth of CuAlO2 delafossite crystals

NASA Astrophysics Data System (ADS)

Wolff, Nora; Klimm, Detlef; Siche, Dietmar

2018-02-01

Simultaneous differential thermal analysis (DTA) and thermogravimetric (TG) measurements with copper oxide/aluminum oxide mixtures were performed in atmospheres with varying oxygen partial pressures and with crucibles made of different materials. Only sapphire and platinum crucibles proved to be stable under conditions that are useful for the growth of CuAlO2 delafossite single crystals. Then the ternary phase diagram Al2O3-CuO-Cu and its isopleth section Cu2O-Al2O3 were redetermined. Millimeter sized crystals could be obtained from copper oxide melts with 1-2 mol% addition of aluminum oxide that are stable in platinum crucibles held in oxidizing atmosphere containing 15-21% oxygen.

Activation of single heteromeric GABAA receptor ion channels by full and partial agonists

PubMed Central

Mortensen, Martin; Kristiansen, Uffe; Ebert, Bjarke; Frølund, Bente; Krogsgaard-Larsen, Povl; Smart, Trevor G

2004-01-01

The linkage between agonist binding and the activation of a GABAA receptor ion channel is yet to be resolved. This aspect was examined on human recombinant α1β2γ2S GABAA receptors expressed in human embryonic kidney cells using the following series of receptor agonists: GABA, isoguvacine, 4,5,6,7-tetrahydroisoxazolo[5,4-c]pyridin-3-ol (THIP), isonipecotic acid, piperidine-4-sulphonic acid (P4S), imidazole-4-acetic acid (IAA), 5-(4-piperidyl)-3-isothiazolol (thio-4-PIOL) and 5-(4-piperidyl)-3-isoxazolol (4-PIOL). Whole-cell concentration–response curves enabled the agonists to be categorized into four classes based upon their maximum responses. Single channel analyses revealed that the channel conductance of 25–27 pS was unaffected by the agonists. However, two open states were resolved from the open period distributions with mean open times reduced 5-fold by the weakest partial agonists. Using saturating agonist concentrations, estimates of the channel shutting rate, α, ranged from 200 to 600 s−1. The shut period distributions were described by three or four components and for the weakest partial agonists, the interburst shut periods increased whilst the mean burst durations and longest burst lengths were reduced relative to the full agonists. From the burst analyses, the opening rates for channel activation, β, and the total dissociation rates, k−1, for the agonists leaving the receptor were estimated. The agonist efficacies were larger for the full agonists (E ∼7−9) compared to the weak partial agonists (∼0.4–0.6). Overall, changes in agonist efficacy largely determined the different agonist profiles with contributions from the agonist affinities and the degree of receptor desensitization. From this we conclude that GABAA receptor activation does not occur in a switch-like manner since the agonist recognition sites are flexible, accommodating diverse agonist structures which differentially influence the opening and shutting rates of the ion channel. PMID:14990676

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (4).

PubMed

Murase, Kenya

2016-01-01

Partial differential equations are often used in the field of medical physics. In this (final) issue, the methods for solving the partial differential equations were introduced, which include separation of variables, integral transform (Fourier and Fourier-sine transforms), Green's function, and series expansion methods. Some examples were also introduced, in which the integral transform and Green's function methods were applied to solving Pennes' bioheat transfer equation and the Fourier series expansion method was applied to Navier-Stokes equation for analyzing the wall shear stress in blood vessels.Finally, the author hopes that this series will be helpful for people who engage in medical physics.

Distinguishing autocrine and paracrine signals in hematopoietic stem cell culture using a biofunctional microcavity platform

NASA Astrophysics Data System (ADS)

Müller, Eike; Wang, Weijia; Qiao, Wenlian; Bornhäuser, Martin; Zandstra, Peter W.; Werner, Carsten; Pompe, Tilo

2016-08-01

Homeostasis of hematopoietic stem cells (HSC) in the mammalian bone marrow stem cell niche is regulated by signals of the local microenvironment. Besides juxtacrine, endocrine and metabolic cues, paracrine and autocrine signals are involved in controlling quiescence, proliferation and differentiation of HSC with strong implications on expansion and differentiation ex vivo as well as in vivo transplantation. Towards this aim, a cell culture analysis on a polymer microcavity carrier platform was combined with a partial least square analysis of a mechanistic model of cell proliferation. We could demonstrate the discrimination of specific autocrine and paracrine signals from soluble factors as stimulating and inhibitory effectors in hematopoietic stem and progenitor cell culture. From that we hypothesize autocrine signals to be predominantly involved in maintaining the quiescent state of HSC in single-cell niches and advocate our analysis platform as an unprecedented option for untangling convoluted signaling mechanisms in complex cell systems being it of juxtacrine, paracrine or autocrine origin.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

PubMed Central

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

The use of solution adaptive grids in solving partial differential equations

NASA Technical Reports Server (NTRS)

Anderson, D. A.; Rai, M. M.

1982-01-01

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

Multirate Integration Properties of Waveform Relaxation with Applications to Circuit Simulation and Parallel Computation

DTIC Science & Technology

1985-11-18

Greenberg and K. Sakallah at Digital Equipment Corporation, and C-F. Chen, L Nagel, and P. ,. Subrahmanyam at AT&T Bell Laboratories, both for providing...Circuit Theory McGraw-Hill, 1969. [37] R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics...McGraw-Hill, N.Y., 1965. Page 161 [44) R. Courant and D. Hilbert , Partial Differential Equations, Vol. 2 of Methods of Mathematical Physics

A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised

NASA Technical Reports Server (NTRS)

Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume

1998-01-01

We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Quantitative evaluation method for differentiation of C2C12 myoblasts by ultrasonic microscopy

NASA Astrophysics Data System (ADS)

Takanashi, Kyoichi; Washiya, Mamoru; Ota, Kazuki; Yoshida, Sachiko; Hozumi, Naohiro; Kobayashi, Kazuto

2017-07-01

Cell differentiation was evaluated by ultrasonic microscopy. However, there were some regions that showed a lower acoustic impedance than the culture liquid. It was considered that, in such regions, the cells were not perfectly in contact with the film substrate. Hence, a waveform analysis was performed, and compensated acoustic impedances in such regions were in a reasonable range of values. By the same analysis, the displacements of partially floated cells were also successfully calculated. The elapsed day transitions of the compensated acoustic impedances and displacements were successfully evaluated. In the process of differentiation, actin fibers comprising the cytoskeleton are supposed to loosen in order to induce cellular fusion. In addition, the progress in cell differentiation accompanied by a change into a three-dimensional structure can partially be assessed by the displacement between a cell and a cultured film. Hence, we believe that cell differentiation can be evaluated using an ultrasonic microscope.

Nonlinear dynamic simulation of single- and multi-spool core engines

NASA Technical Reports Server (NTRS)

Schobeiri, T.; Lippke, C.; Abouelkheir, M.

1993-01-01

In this paper a new computational method for accurate simulation of the nonlinear dynamic behavior of single- and multi-spool core engines, turbofan engines, and power generation gas turbine engines is presented. In order to perform the simulation, a modularly structured computer code has been developed which includes individual mathematical modules representing various engine components. The generic structure of the code enables the dynamic simulation of arbitrary engine configurations ranging from single-spool thrust generation to multi-spool thrust/power generation engines under adverse dynamic operating conditions. For precise simulation of turbine and compressor components, row-by-row calculation procedures were implemented that account for the specific turbine and compressor cascade and blade geometry and characteristics. The dynamic behavior of the subject engine is calculated by solving a number of systems of partial differential equations, which describe the unsteady behavior of the individual components. In order to ensure the capability, accuracy, robustness, and reliability of the code, comprehensive critical performance assessment and validation tests were performed. As representatives, three different transient cases with single- and multi-spool thrust and power generation engines were simulated. The transient cases range from operating with a prescribed fuel schedule, to extreme load changes, to generator and turbine shut down.

An Improved Heaviside Approach to Partial Fraction Expansion and Its Applications

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2009-01-01

In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in…

Application of the Sumudu Transform to Discrete Dynamic Systems

ERIC Educational Resources Information Center

Asiru, Muniru Aderemi

2003-01-01

The Sumudu transform is an integral transform introduced to solve differential equations and control engineering problems. The transform possesses many interesting properties that make visualization easier and application has been demonstrated in the solution of partial differential equations, integral equations, integro-differential equations and…

Effects of partial reinforcement and time between reinforced trials on terminal response rate in pigeon autoshaping.

PubMed

Gottlieb, Daniel A

2006-03-01

Partial reinforcement often leads to asymptotically higher rates of responding and number of trials with a response than does continuous reinforcement in pigeon autoshaping. However, comparisons typically involve a partial reinforcement schedule that differs from the continuous reinforcement schedule in both time between reinforced trials and probability of reinforcement. Two experiments examined the relative contributions of these two manipulations to asymptotic response rate. Results suggest that the greater responding previously seen with partial reinforcement is primarily due to differential probability of reinforcement and not differential time between reinforced trials. Further, once established, differences in responding are resistant to a change in stimulus and contingency. Secondary response theories of autoshaped responding (theories that posit additional response-augmenting or response-attenuating mechanisms specific to partial or continuous reinforcement) cannot fully accommodate the current body of data. It is suggested that researchers who study pigeon autoshaping train animals on a common task prior to training them under different conditions.

Hydrogel microstructure live-cell array for multiplexed analyses of cancer stem cells, tumor heterogeneity and differential drug response at single-element resolution.

PubMed

Afrimzon, E; Botchkina, G; Zurgil, N; Shafran, Y; Sobolev, M; Moshkov, S; Ravid-Hermesh, O; Ojima, I; Deutsch, M

2016-03-21

Specific phenotypic subpopulations of cancer stem cells (CSCs) are responsible for tumor development, production of heterogeneous differentiated tumor mass, metastasis, and resistance to therapies. The development of therapeutic approaches based on targeting rare CSCs has been limited partially due to the lack of appropriate experimental models and measurement approaches. The current study presents new tools and methodologies based on a hydrogel microstructure array (HMA) for identification and multiplex analyses of CSCs. Low-melt agarose integrated with type I collagen, a major component of the extracellular matrix (ECM), was used to form a solid hydrogel array with natural non-adhesive characteristics and high optical quality. The array contained thousands of individual pyramidal shaped, nanoliter-volume micro-chambers (MCs), allowing concomitant generation and measurement of large populations of free-floating CSC spheroids from single cells, each in an individual micro-chamber (MC). The optical live cell platform, based on an imaging plate patterned with HMA, was validated using CSC-enriched prostate and colon cancer cell lines. The HMA methodology and quantitative image analysis at single-element resolution clearly demonstrates several levels of tumor cell heterogeneity, including morphological and phenotypic variability, differences in proliferation capacity and in drug response. Moreover, the system facilitates real-time examination of single stem cell (SC) fate, as well as drug-induced alteration in expression of stemness markers. The technology may be applicable in personalized cancer treatment, including multiplex ex vivo analysis of heterogeneous patient-derived tumor specimens, precise detection and characterization of potentially dangerous cell phenotypes, and for representative evaluation of drug sensitivity of CSCs and other types of tumor cells.

Method for construction of normalized cDNA libraries

DOEpatents

Soares, Marcelo B.; Efstratiadis, Argiris

1998-01-01

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3' noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to appropriate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library. This invention also provides normalized cDNA libraries generated by the above-described method and uses of the generated libraries.

Method for construction of normalized cDNA libraries

DOEpatents

Soares, M.B.; Efstratiadis, A.

1998-11-03

This invention provides a method to normalize a directional cDNA library constructed in a vector that allows propagation in single-stranded circle form comprising: (a) propagating the directional cDNA library in single-stranded circles; (b) generating fragments complementary to the 3` noncoding sequence of the single-stranded circles in the library to produce partial duplexes; (c) purifying the partial duplexes; (d) melting and reassociating the purified partial duplexes to appropriate Cot; and (e) purifying the unassociated single-stranded circles, thereby generating a normalized cDNA library. This invention also provides normalized cDNA libraries generated by the above-described method and uses of the generated libraries. 19 figs.

Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

DTIC Science & Technology

1971-06-01

the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

Rapid differentiation of Francisella species and subspecies by fluorescent in situ hybridization targeting the 23S rRNA

PubMed Central

2010-01-01

Background Francisella (F.) tularensis is the causative agent of tularemia. Due to its low infectious dose, ease of dissemination and high case fatality rate, F. tularensis was the subject in diverse biological weapons programs and is among the top six agents with high potential if misused in bioterrorism. Microbiological diagnosis is cumbersome and time-consuming. Methods for the direct detection of the pathogen (immunofluorescence, PCR) have been developed but are restricted to reference laboratories. Results The complete 23S rRNA genes of representative strains of F. philomiragia and all subspecies of F. tularensis were sequenced. Single nucleotide polymorphisms on species and subspecies level were confirmed by partial amplification and sequencing of 24 additional strains. Fluorescent In Situ Hybridization (FISH) assays were established using species- and subspecies-specific probes. Different FISH protocols allowed the positive identification of all 4 F. philomiragia strains, and more than 40 F. tularensis strains tested. By combination of different probes, it was possible to differentiate the F. tularensis subspecies holarctica, tularensis, mediasiatica and novicida. No cross reactivity with strains of 71 clinically relevant bacterial species was observed. FISH was also successfully applied to detect different F. tularensis strains in infected cells or tissue samples. In blood culture systems spiked with F. tularensis, bacterial cells of different subspecies could be separated within single samples. Conclusion We could show that FISH targeting the 23S rRNA gene is a rapid and versatile method for the identification and differentiation of F. tularensis isolates from both laboratory cultures and clinical samples. PMID:20205957

A partial differential equation for pseudocontact shift.

PubMed

Charnock, G T P; Kuprov, Ilya

2014-10-07

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

Nonlinear grid error effects on numerical solution of partial differential equations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1980-01-01

Finite difference solutions of nonlinear partial differential equations require discretizations and consequently grid errors are generated. These errors strongly affect stability and convergence properties of difference models. Previously such errors were analyzed by linearizing the difference equations for solutions. Properties of mappings of decadence were used to analyze nonlinear instabilities. Such an analysis is directly affected by initial/boundary conditions. An algorithm was developed, applied to nonlinear Burgers equations, and verified computationally. A preliminary test shows that Navier-Stokes equations may be treated similarly.

Exact Solutions for the Integrable Sixth-Order Drinfeld-Sokolov-Satsuma-Hirota System by the Analytical Methods.

PubMed

Manafian Heris, Jalil; Lakestani, Mehrdad

2014-01-01

We establish exact solutions including periodic wave and solitary wave solutions for the integrable sixth-order Drinfeld-Sokolov-Satsuma-Hirota system. We employ this system by using a generalized (G'/G)-expansion and the generalized tanh-coth methods. These methods are developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that these methods, with the help of symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.

Parameter estimation problems for distributed systems using a multigrid method

NASA Technical Reports Server (NTRS)

Ta'asan, Shlomo; Dutt, Pravir

1990-01-01

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation.

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Dey, C.; Dey, S. K.

1983-01-01

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

DISCHARGE AND DEPTH BEHIND A PARTIALLY BREACHED DAM.

USGS Publications Warehouse

Chen, Cheng-lung

1987-01-01

The role that the velocity-distribution correction factor plays in the determination of the flood discharge and corresponding flow depth behind a partially breached dam is investigated. Assumption of a uniformly progressive flow for an established dam-break flood in a rectangular channel of infinite extent leads to the formulation of a theoretical relation between the depth and velocity of flow expressed in differential form. Integrating this ordinary differential equation, one can express the velocity in terms of the depth.

The role of single immediate loading implant in long Class IV Kennedy mandibular partial denture.

PubMed

Mohamed, Gehan F; El Sawy, Amal A

2012-10-01

The treatment of long-span Kennedy class IV considers a prosthodontic challenge. This study evaluated the integrity of principle abutments in long Kennedy class IV clinically and radiographically, when rehabilitated with conventional metallic partial denture as a control group and mandibular partial overdentures supported with single immediately loaded implant in symphyseal as a study group. Twelve male patients were divided randomly allotted into two equal groups. First group patients received removable metallic partial denture, whereas in the second group, patients received partial overdentures supported with single immediately loaded implant in symphyseal region. The partial dentures design in both groups was the same. Long-cone paralleling technique and transmission densitometer were used at the time of denture insertion, 3, 6, and 12 months. Gingival index, bone loss, and optical density were measured for principle abutments during the follow-up. A significant reduction in bone loss and density were detected in group II comparing with group I. Gingival index had no significant change (p-value < 0.05). A single symphyseal implant in long span class IV Kennedy can play a pivotal role to improve the integrity of the principle abutments and alveolar bone support. © 2010 Wiley Periodicals, Inc.

Introducing the Improved Heaviside Approach to Partial Fraction Decomposition to Undergraduate Students: Results and Implications from a Pilot Study

ERIC Educational Resources Information Center

Man, Yiu-Kwong

2012-01-01

Partial fraction decomposition is a useful technique often taught at senior secondary or undergraduate levels to handle integrations, inverse Laplace transforms or linear ordinary differential equations, etc. In recent years, an improved Heaviside's approach to partial fraction decomposition was introduced and developed by the author. An important…

Strongly nonlinear parabolic variational inequalities.

PubMed

Browder, F E; Brézis, H

1980-02-01

An existence and uniqueness result is established for a general class of variational inequalities for parabolic partial differential equations of the form partial differentialu/ partial differentialt + A(u) + g(u) = f with g nondecreasing but satisfying no growth condition. The proof is based upon a type of compactness result for solutions of variational inequalities that should find a variety of other applications.

Anomalous diffusion associated with nonlinear fractional derivative fokker-planck-like equation: exact time-dependent solutions

PubMed

Bologna; Tsallis; Grigolini

2000-08-01

We consider the d=1 nonlinear Fokker-Planck-like equation with fractional derivatives ( partial differential/ partial differentialt)P(x,t)=D( partial differential(gamma)/ partial differentialx(gamma))[P(x,t)](nu). Exact time-dependent solutions are found for nu=(2-gamma)/(1+gamma)(-infinity

Teacher structure as a predictor of students' perceived competence and autonomous motivation: The moderating role of differentiated instruction.

PubMed

Guay, Frédéric; Roy, Amélie; Valois, Pierre

2017-06-01

An important pedagogical practice is the provision of structure (Farkas & Grolnick, 2010, Motiv. Emot., 34, 266). According to self-determination theory (SDT; Deci & Ryan, 1985, Intrinsic motivation and self-determination in human behavior, Plenum, New York, NY), structure allows students to develop perceived competence in different school subjects, which in turn facilitates the development of autonomous motivation towards these subjects and limits the development of controlled motivation. In this study, we test a mediated moderation model that posits that teacher structure has a stronger positive effect on students' autonomous motivation (and a negative effect on controlled motivation) in French class when differentiated instruction is used, and that this moderation effect is mediated by perceived competence. To test this model, we used a sample of 27 elementary school teachers and 422 students from Quebec, a province of Canada. Data for teachers and students were collected with self-report measures. The method used was a correlational one with a single measurement time. Results revealed that (1) the effect of teacher structure on students' autonomous motivation was positive only when differentiated instruction strategies were frequently used, and this moderated effect was partially mediated by perceived competence, and (2) teacher structure was negatively associated with students' controlled motivation only when differentiated instruction was provided infrequently, and this moderated effect was not explained by perceived competence. These findings are discussed in the light of the literature on SDT and on differentiated instruction. © 2017 The British Psychological Society.

A Unified Introduction to Ordinary Differential Equations

ERIC Educational Resources Information Center

Lutzer, Carl V.

2006-01-01

This article describes how a presentation from the point of view of differential operators can be used to (partially) unify the myriad techniques in an introductory course in ordinary differential equations by providing students with a powerful, flexible paradigm that extends into (or from) linear algebra. (Contains 1 footnote.)

Role of Alternative Polyadenylation during Adipogenic Differentiation: An In Silico Approach

PubMed Central

Spangenberg, Lucía; Correa, Alejandro; Dallagiovanna, Bruno; Naya, Hugo

2013-01-01

Post-transcriptional regulation of stem cell differentiation is far from being completely understood. Changes in protein levels are not fully correlated with corresponding changes in mRNAs; the observed differences might be partially explained by post-transcriptional regulation mechanisms, such as alternative polyadenylation. This would involve changes in protein binding, transcript usage, miRNAs and other non-coding RNAs. In the present work we analyzed the distribution of alternative transcripts during adipogenic differentiation and the potential role of miRNAs in post-transcriptional regulation. Our in silico analysis suggests a modest, consistent, bias in 3′UTR lengths during differentiation enabling a fine-tuned transcript regulation via small non-coding RNAs. Including these effects in the analyses partially accounts for the observed discrepancies in relative abundance of protein and mRNA. PMID:24143171

(N+1)-dimensional fractional reduced differential transform method for fractional order partial differential equations

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Lu, Dianchen; Wang, Jun

2017-07-01

In this paper, we pursue the general form of the fractional reduced differential transform method (DTM) to (N+1)-dimensional case, so that fractional order partial differential equations (PDEs) can be resolved effectively. The most distinct aspect of this method is that no prescribed assumptions are required, and the huge computational exertion is reduced and round-off errors are also evaded. We utilize the proposed scheme on some initial value problems and approximate numerical solutions of linear and nonlinear time fractional PDEs are obtained, which shows that the method is highly accurate and simple to apply. The proposed technique is thus an influential technique for solving the fractional PDEs and fractional order problems occurring in the field of engineering, physics etc. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.

Homogeneous partial differential equations for superpositions of indeterminate functions of several variables

NASA Astrophysics Data System (ADS)

Asai, Kazuto

2009-02-01

We determine essentially all partial differential equations satisfied by superpositions of tree type and of a further special type. These equations represent necessary and sufficient conditions for an analytic function to be locally expressible as an analytic superposition of the type indicated. The representability of a real analytic function by a superposition of this type is independent of whether that superposition involves real-analytic functions or C^{\\rho}-functions, where the constant \\rho is determined by the structure of the superposition. We also prove that the function u defined by u^n=xu^a+yu^b+zu^c+1 is generally non-representable in any real (resp. complex) domain as f\\bigl(g(x,y),h(y,z)\\bigr) with twice differentiable f and differentiable g, h (resp. analytic f, g, h).

Accurate spectral solutions for the parabolic and elliptic partial differential equations by the ultraspherical tau method

NASA Astrophysics Data System (ADS)

Doha, E. H.; Abd-Elhameed, W. M.

2005-09-01

We present a double ultraspherical spectral methods that allow the efficient approximate solution for the parabolic partial differential equations in a square subject to the most general inhomogeneous mixed boundary conditions. The differential equations with their boundary and initial conditions are reduced to systems of ordinary differential equations for the time-dependent expansion coefficients. These systems are greatly simplified by using tensor matrix algebra, and are solved by using the step-by-step method. Numerical applications of how to use these methods are described. Numerical results obtained compare favorably with those of the analytical solutions. Accurate double ultraspherical spectral approximations for Poisson's and Helmholtz's equations are also noted. Numerical experiments show that spectral approximation based on Chebyshev polynomials of the first kind is not always better than others based on ultraspherical polynomials.

Isotropic differential phase contrast microscopy for quantitative phase bio-imaging.

PubMed

Chen, Hsi-Hsun; Lin, Yu-Zi; Luo, Yuan

2018-05-16

Quantitative phase imaging (QPI) has been investigated to retrieve optical phase information of an object and applied to biological microscopy and related medical studies. In recent examples, differential phase contrast (DPC) microscopy can recover phase image of thin sample under multi-axis intensity measurements in wide-field scheme. Unlike conventional DPC, based on theoretical approach under partially coherent condition, we propose a new method to achieve isotropic differential phase contrast (iDPC) with high accuracy and stability for phase recovery in simple and high-speed fashion. The iDPC is simply implemented with a partially coherent microscopy and a programmable thin-film transistor (TFT) shield to digitally modulate structured illumination patterns for QPI. In this article, simulation results show consistency of our theoretical approach for iDPC under partial coherence. In addition, we further demonstrate experiments of quantitative phase images of a standard micro-lens array, as well as label-free live human cell samples. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Evaluating Feynman integrals by the hypergeometry

NASA Astrophysics Data System (ADS)

Feng, Tai-Fu; Chang, Chao-Hsi; Chen, Jian-Bin; Gu, Zhi-Hua; Zhang, Hai-Bin

2018-02-01

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop B0 and massless C0 functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.

Auto-Bäcklund transformations for a matrix partial differential equation

NASA Astrophysics Data System (ADS)

Gordoa, P. R.; Pickering, A.

2018-07-01

We derive auto-Bäcklund transformations, analogous to those of the matrix second Painlevé equation, for a matrix partial differential equation. We also then use these auto-Bäcklund transformations to derive matrix equations involving shifts in a discrete variable, a process analogous to the use of the auto-Bäcklund transformations of the matrix second Painlevé equation to derive a discrete matrix first Painlevé equation. The equations thus derived then include amongst other examples a semidiscrete matrix equation which can be considered to be an extension of this discrete matrix first Painlevé equation. The application of this technique to the auto-Bäcklund transformations of the scalar case of our partial differential equation has not been considered before, and so the results obtained here in this scalar case are also new. Other equations obtained here using this technique include a scalar semidiscrete equation which arises in the case of the second Painlevé equation, and which does not seem to have been thus derived previously.

Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies

NASA Technical Reports Server (NTRS)

Thompson, J. F.; Thames, F. C.; Mastin, C. W.

1977-01-01

A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.

Solving Partial Differential Equations in a data-driven multiprocessor environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

NIR spectroscopic measurement of moisture content in Scots pine seeds.

PubMed

Lestander, Torbjörn A; Geladi, Paul

2003-04-01

When tree seeds are used for seedling production it is important that they are of high quality in order to be viable. One of the factors influencing viability is moisture content and an ideal quality control system should be able to measure this factor quickly for each seed. Seed moisture content within the range 3-34% was determined by near-infrared (NIR) spectroscopy on Scots pine (Pinus sylvestris L.) single seeds and on bulk seed samples consisting of 40-50 seeds. The models for predicting water content from the spectra were made by partial least squares (PLS) and ordinary least squares (OLS) regression. Different conditions were simulated involving both using less wavelengths and going from samples to single seeds. Reflectance and transmission measurements were used. Different spectral pretreatment methods were tested on the spectra. Including bias, the lowest prediction errors for PLS models based on reflectance within 780-2280 nm from bulk samples and single seeds were 0.8% and 1.9%, respectively. Reduction of the single seed reflectance spectrum to 850-1048 nm gave higher biases and prediction errors in the test set. In transmission (850-1048 nm) the prediction error was 2.7% for single seeds. OLS models based on simulated 4-sensor single seed system consisting of optical filters with Gaussian transmission indicated more than 3.4% error in prediction. A practical F-test based on test sets to differentiate models is introduced.

Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast

NASA Astrophysics Data System (ADS)

Mehta, Shalin B.; Sheppard, Colin J. R.

2010-05-01

Various methods that use large illumination aperture (i.e. partially coherent illumination) have been developed for making transparent (i.e. phase) specimens visible. These methods were developed to provide qualitative contrast rather than quantitative measurement-coherent illumination has been relied upon for quantitative phase analysis. Partially coherent illumination has some important advantages over coherent illumination and can be used for measurement of the specimen's phase distribution. However, quantitative analysis and image computation in partially coherent systems have not been explored fully due to the lack of a general, physically insightful and computationally efficient model of image formation. We have developed a phase-space model that satisfies these requirements. In this paper, we employ this model (called the phase-space imager) to elucidate five different partially coherent systems mentioned in the title. We compute images of an optical fiber under these systems and verify some of them with experimental images. These results and simulated images of a general phase profile are used to compare the contrast and the resolution of the imaging systems. We show that, for quantitative phase imaging of a thin specimen with matched illumination, differential phase contrast offers linear transfer of specimen information to the image. We also show that the edge enhancement properties of spiral phase contrast are compromised significantly as the coherence of illumination is reduced. The results demonstrate that the phase-space imager model provides a useful framework for analysis, calibration, and design of partially coherent imaging methods.

Amplitude reconstruction from complete photoproduction experiments and truncated partial-wave expansions

NASA Astrophysics Data System (ADS)

Workman, R. L.; Tiator, L.; Wunderlich, Y.; Döring, M.; Haberzettl, H.

2017-01-01

We compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the photoproduction of pseudoscalar mesons. The approach is pedagogical, showing in detail how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles).

Amplitude reconstruction from complete photoproduction experiments and truncated partial-wave expansions

DOE PAGES

Workman, R. L.; Tiator, L.; Wunderlich, Y.; ...

2017-01-19

Here, we compare the methods of amplitude reconstruction, for a complete experiment and a truncated partial-wave analysis, applied to the photoproduction of pseudoscalar mesons. The approach is pedagogical, showing in detail how the amplitude reconstruction (observables measured at a single energy and angle) is related to a truncated partial-wave analysis (observables measured at a single energy and a number of angles).

Factorial structure of the 'ToM Storybooks': A test evaluating multiple components of Theory of Mind.

PubMed

Bulgarelli, Daniela; Testa, Silvia; Molina, Paola

2015-06-01

This study examined the factorial structure of the Theory of Mind (ToM) Storybooks, a comprehensive 93-item instrument tapping the five components in Wellman's model of ToM (emotion recognition, understanding of desire and beliefs, ability to distinguish between physical and mental entities, and awareness of the link between perception and knowledge). A sample of 681 three- to eight-year-old Italian children was divided into three age groups to assess whether factorial structure varied across different age ranges. Partial credit model analysis was applied to the data, leading to the empirical identification of 23 composite variables aggregating the ToM Storybooks items. Confirmatory factor analysis was then conducted on the composite variables, providing support for the theoretical model. There were partial differences in the specific composite variables making up the dimensions for each of the three age groups. A single test evaluating distinct dimensions of ToM is a valuable resource for clinical practice which may be used to define differential profiles for specific populations. © 2014 The British Psychological Society.

A novel principle for partial agonism of liver X receptor ligands. Competitive recruitment of activators and repressors.

PubMed

Albers, Michael; Blume, Beatrix; Schlueter, Thomas; Wright, Matthew B; Kober, Ingo; Kremoser, Claus; Deuschle, Ulrich; Koegl, Manfred

2006-02-24

Partial, selective activation of nuclear receptors is a central issue in molecular endocrinology but only partly understood. Using LXRs as an example, we show here that purely agonistic ligands can be clearly and quantitatively differentiated from partial agonists by the cofactor interactions they induce. Although a pure agonist induces a conformation that is incompatible with the binding of repressors, partial agonists such as GW3965 induce a state where the interaction not only with coactivators, but also corepressors is clearly enhanced over the unliganded state. The activities of the natural ligand 22(R)-hydroxycholesterol and of a novel quinazolinone ligand, LN6500 can be further differentiated from GW3965 and T0901317 by their weaker induction of coactivator binding. Using biochemical and cell-based assays, we show that the natural ligand of LXR is a comparably weak partial agonist. As predicted, we find that a change in the coactivator to corepressor ratio in the cell will affect NCoR recruiting compounds more dramatically than NCoR-dissociating compounds. Our data show how competitive binding of coactivators and corepressors can explain the tissue-specific behavior of partial agonists and open up new routes to a rational design of partial agonists for LXRs.

Collective phase description of oscillatory convection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kawamura, Yoji, E-mail: ykawamura@jamstec.go.jp; Nakao, Hiroya

We formulate a theory for the collective phase description of oscillatory convection in Hele-Shaw cells. It enables us to describe the dynamics of the oscillatory convection by a single degree of freedom which we call the collective phase. The theory can be considered as a phase reduction method for limit-cycle solutions in infinite-dimensional dynamical systems, namely, stable time-periodic solutions to partial differential equations, representing the oscillatory convection. We derive the phase sensitivity function, which quantifies the phase response of the oscillatory convection to weak perturbations applied at each spatial point, and analyze the phase synchronization between two weakly coupled Hele-Shawmore » cells exhibiting oscillatory convection on the basis of the derived phase equations.« less

The Elasto-Plastic Stability of Plates

NASA Technical Reports Server (NTRS)

Ilyushin, A. A.

1947-01-01

This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.

Collisional excitation of interstellar PO(X2Π) by He: new ab initio potential energy surfaces and scattering calculations

NASA Astrophysics Data System (ADS)

Lique, François; Jiménez-Serra, Izaskun; Viti, Serena; Marinakis, Sarantos

2018-01-01

We present the first ab initio potential energy surfaces (PESs) for the PO(X2Π)-He van der Waals system. The PESs were obtained using the open-shell partially spin-restricted coupled cluster approach with single, double and perturbative triple excitations [UCCSD(T)]. The augmented correlation-consistent polarized valence triple-zeta (aug-cc-pVTZ) basis set was employed supplemented by mid-bond functions. Integral and differential cross sections for the rotational excitation in PO-He collisions were calculated using the new PES and compared with results in similar systems. Finally, our work presents the first hyperfine-resolved cross sections for this system that are needed for accurate modelling in astrophysical environments.

Distribution of rock, metals, and ices in Callisto.

PubMed

Anderson, J D; Schubert, G; Jacobson, R A; Lau, E L; Moore, W B; Sjogren, W L

1998-06-05

Radio Doppler data from a single encounter (C3) of the Galileo spacecraft with Callisto, the outermost Galilean moon of Jupiter, indicated that Callisto was probably undifferentiated. Now, similar data from a second encounter (C9) corroborate this conclusion, but more accurate data from a third encounter (C10) indicate that the rock and ice within Callisto have partially, but not completely, separated. Callisto may be differentiated into a rock-metal core less than 25 percent of Callisto's radius, an outer layer of clean ice less than 350 km thick, and a middle layer of mixed rock and ice. Models in which ice and rock are mixed all the way to the center of Callisto are also consistent with the data.

Activation of TRPV2 negatively regulates the differentiation of mouse brown adipocytes.

PubMed

Sun, Wuping; Uchida, Kunitoshi; Takahashi, Nobuyuki; Iwata, Yuko; Wakabayashi, Shigeo; Goto, Tsuyoshi; Kawada, Teruo; Tominaga, Makoto

2016-09-01

Transient receptor potential vanilloid 2 (TRPV2) acts as a Ca(2+)-permeable non-selective cation channel that has been reported to be sensitive to temperature, mechanical force, and some chemicals. We recently showed that TRPV2 is critical for maintenance of the thermogenic function of brown adipose tissue in mice. However, the involvement of TRPV2 in the differentiation of brown adipocytes remains unexplored. We found that the expression of TRPV2 was dramatically increased during the differentiation of brown adipocytes. Non-selective TRPV2 agonists (2-aminoethoxydiphenyl borate and lysophosphatidylcholine) inhibited the differentiation of brown adipocytes in a dose-dependent manner during the early stage of differentiation of brown adipocytes. The inhibition was rescued by a TRPV2-selective antagonist, SKF96365 (SKF). Mechanical force, which activates TRPV2, also inhibited the differentiation of brown adipocytes in a strength-dependent manner, and the effect was reversed by SKF. In addition, the inhibition of adipocyte differentiation by either TRPV2 ligand or mechanical stimulation was significantly smaller in the cells from TRPV2KO mice. Moreover, calcineurin inhibitors, cyclosporine A and FK506, partially reversed TRPV2 activation-induced inhibition of brown adipocyte differentiation. Thus, we conclude that TRPV2 might be involved in the modulation of brown adipocyte differentiation partially via a calcineurin pathway.

Experimental validation of a Lyapunov-based controller for the plasma safety factor and plasma pressure in the TCV tokamak

NASA Astrophysics Data System (ADS)

Mavkov, B.; Witrant, E.; Prieur, C.; Maljaars, E.; Felici, F.; Sauter, O.; the TCV-Team

2018-05-01

In this paper, model-based closed-loop algorithms are derived for distributed control of the inverse of the safety factor profile and the plasma pressure parameter β of the TCV tokamak. The simultaneous control of the two plasma quantities is performed by combining two different control methods. The control design of the plasma safety factor is based on an infinite-dimensional setting using Lyapunov analysis for partial differential equations, while the control of the plasma pressure parameter is designed using control techniques for single-input and single-output systems. The performance and robustness of the proposed controller is analyzed in simulations using the fast plasma transport simulator RAPTOR. The control is then implemented and tested in experiments in TCV L-mode discharges using the RAPTOR model predicted estimates for the q-profile. The distributed control in TCV is performed using one co-current and one counter-current electron cyclotron heating actuation.

Segmentation of Image Ensembles via Latent Atlases

PubMed Central

Van Leemput, Koen; Menze, Bjoern H.; Wells, William M.; Golland, Polina

2010-01-01

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. However, the availability of comprehensive, reliable and suitable manual segmentations for atlas construction is limited. We therefore propose a method for joint segmentation of corresponding regions of interest in a collection of aligned images that does not require labeled training data. Instead, a latent atlas, initialized by at most a single manual segmentation, is inferred from the evolving segmentations of the ensemble. The algorithm is based on probabilistic principles but is solved using partial differential equations (PDEs) and energy minimization criteria. We evaluate the method on two datasets, segmenting subcortical and cortical structures in a multi-subject study and extracting brain tumors in a single-subject multi-modal longitudinal experiment. We compare the segmentation results to manual segmentations, when those exist, and to the results of a state-of-the-art atlas-based segmentation method. The quality of the results supports the latent atlas as a promising alternative when existing atlases are not compatible with the images to be segmented. PMID:20580305

Formal Integrals and Noether Operators of Nonlinear Hyperbolic Partial Differential Systems Admitting a Rich Set of Symmetries

NASA Astrophysics Data System (ADS)

Startsev, Sergey Ya.

2017-05-01

The paper is devoted to hyperbolic (generally speaking, non-Lagrangian and nonlinear) partial differential systems possessing a full set of differential operators that map any function of one independent variable into a symmetry of the corresponding system. We demonstrate that a system has the above property if and only if this system admits a full set of formal integrals (i.e., differential operators which map symmetries into integrals of the system). As a consequence, such systems possess both direct and inverse Noether operators (in the terminology of a work by B. Fuchssteiner and A.S. Fokas who have used these terms for operators that map cosymmetries into symmetries and perform transformations in the opposite direction). Systems admitting Noether operators are not exhausted by Euler-Lagrange systems and the systems with formal integrals. In particular, a hyperbolic system admits an inverse Noether operator if a differential substitution maps this system into a system possessing an inverse Noether operator.

Ultrasound speckle reduction based on fractional order differentiation.

PubMed

Shao, Dangguo; Zhou, Ting; Liu, Fan; Yi, Sanli; Xiang, Yan; Ma, Lei; Xiong, Xin; He, Jianfeng

2017-07-01

Ultrasound images show a granular pattern of noise known as speckle that diminishes their quality and results in difficulties in diagnosis. To preserve edges and features, this paper proposes a fractional differentiation-based image operator to reduce speckle in ultrasound. An image de-noising model based on fractional partial differential equations with balance relation between k (gradient modulus threshold that controls the conduction) and v (the order of fractional differentiation) was constructed by the effective combination of fractional calculus theory and a partial differential equation, and the numerical algorithm of it was achieved using a fractional differential mask operator. The proposed algorithm has better speckle reduction and structure preservation than the three existing methods [P-M model, the speckle reducing anisotropic diffusion (SRAD) technique, and the detail preserving anisotropic diffusion (DPAD) technique]. And it is significantly faster than bilateral filtering (BF) in producing virtually the same experimental results. Ultrasound phantom testing and in vivo imaging show that the proposed method can improve the quality of an ultrasound image in terms of tissue SNR, CNR, and FOM values.

Dynamic correlation effects in fully differential cross sections for 75-keV proton-impact ionization of helium

NASA Astrophysics Data System (ADS)

Niu, Xiaojie; Sun, Shiyan; Wang, Fujun; Jia, Xiangfu

2017-08-01

The effect of final-state dynamic correlation is investigated for helium single ionization by 75-keV proton impact analyzing fully differential cross sections (FDCS). The final state is represented by a continuum correlated wave (CCW-PT) function which accounts for the interaction between the projectile and the residual target ion (PT interaction). This continuum correlated wave function partially includes the correlation of electron-projectile and electron-target relative motion as coupling terms of the wave equation. The transition matrix is evaluated using the CCW-PT function and the Born initial state. The analytical expression of the transition matrix has been obtained. We have shown that this series is strongly convergent and analyzed the contribution of their different terms to the FDCS within the perturbation method. Illustrative computations are performed in the scattering plane and in the perpendicular plane. Both the correlation effects and the PT interaction are checked by the preset calculations. Our results are compared with absolute experimental data as well as other theoretical models. We have shown that the dynamic correlation plays an important role in the single ionization of atoms by proton impact at intermediate projectile energies, especially at large transverse momentum transfer. While overall agreement between theory and the experimental data is encouraging, detailed agreement is lacking. The need for more theoretical and experimental work is emphasized.

Prolongation structures of nonlinear evolution equations

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.; Estabrook, F. B.

1975-01-01

A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.

Numerical method based on the lattice Boltzmann model for the Fisher equation.

PubMed

Yan, Guangwu; Zhang, Jianying; Dong, Yinfeng

2008-06-01

In this paper, a lattice Boltzmann model for the Fisher equation is proposed. First, the Chapman-Enskog expansion and the multiscale time expansion are used to describe higher-order moment of equilibrium distribution functions and a series of partial differential equations in different time scales. Second, the modified partial differential equation of the Fisher equation with the higher-order truncation error is obtained. Third, comparison between numerical results of the lattice Boltzmann models and exact solution is given. The numerical results agree well with the classical ones.

Computer transformation of partial differential equations into any coordinate system

NASA Technical Reports Server (NTRS)

Sullivan, R. D.

1977-01-01

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Partial differential equation models in macroeconomics.

PubMed

Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin

2014-11-13

The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1987-01-01

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

Improving the efficiency of single and multiple teleportation protocols based on the direct use of partially entangled states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fortes, Raphael; Rigolin, Gustavo, E-mail: rigolin@ifi.unicamp.br

We push the limits of the direct use of partially pure entangled states to perform quantum teleportation by presenting several protocols in many different scenarios that achieve the optimal efficiency possible. We review and put in a single formalism the three major strategies known to date that allow one to use partially entangled states for direct quantum teleportation (no distillation strategies permitted) and compare their efficiencies in real world implementations. We show how one can improve the efficiency of many direct teleportation protocols by combining these techniques. We then develop new teleportation protocols employing multipartite partially entangled states. The threemore » techniques are also used here in order to achieve the highest efficiency possible. Finally, we prove the upper bound for the optimal success rate for protocols based on partially entangled Bell states and show that some of the protocols here developed achieve such a bound. -- Highlights: •Optimal direct teleportation protocols using directly partially entangled states. •We put in a single formalism all strategies of direct teleportation. •We extend these techniques for multipartite partially entangle states. •We give upper bounds for the optimal efficiency of these protocols.« less

Preparation of fine single crystals of magnetic superconductor RuSr2GdCu2O8-δ by partial melting

NASA Astrophysics Data System (ADS)

Yamaki, Kazuhiro; Bamba, Yoshihiro; Irie, Akinobu

2018-03-01

In this study, fine uniform RuSr2GdCu2O8-δ (RuGd-1212) single crystals have been successfully prepared by partial melting. Synthesis temperature could be lowered to a value not exceeding the decomposition temperature of RuGd-1212 using the Sr-Gd-Cu-O flux. The crystals grown by alumina boats are cubic, which coincides with the result of a previous study of RuGd-1212 single crystals using platinum crucibles. The single crystals were up to 15 × 15 × 15 µm3 in size and their lattice constants were consistent with those of polycrystalline samples reported previously. Although the present size of single crystals is not sufficient for measurements, the partial melting technique will be beneficial for future progress of research using RuGd-1212 single crystals. Appropriate nominal composition, sintering atmosphere, and temperature are essential factors for growing RuGd-1212 single crystals.

Effect of partial heating at mid of vertical plate adjacent to porous medium

NASA Astrophysics Data System (ADS)

Mulla, Mohammed Fahimuddin; Pallan, Khalid. M.; Al-Rashed, A. A. A. A.

2018-05-01

Heat and mass transfer in porous medium due to heating of vertical plate at mid-section is analyzed for various physical parameters. The heat and mass transfer in porous medium is modeled with the help of momentum, energy and concentration equations in terms of non-dimensional partial differential equations. The partial differential equations are converted into simpler form of algebraic equations with the help of finite element method. A computer code is developed to assemble the matrix form of algebraic equations into global matrices and then to solve them in an iterative manner to obtain the temperature, concentration and streamline distribution inside the porous medium. It is found that the heat transfer behavior of porous medium heated at middle section is considerably different from other cases.

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras

PubMed Central

Gazizov, R. K.

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures. PMID:28265184

Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.

PubMed

Gainetdinova, A A; Gazizov, R K

2017-01-01

We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.

Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendices; Index.

Student Solution Manual for Foundation Mathematics for the Physical Sciences

NASA Astrophysics Data System (ADS)

Riley, K. F.; Hobson, M. P.

2011-03-01

1. Arithmetic and geometry; 2. Preliminary algebra; 3. Differential calculus; 4. Integral calculus; 5. Complex numbers and hyperbolic functions; 6. Series and limits; 7. Partial differentiation; 8. Multiple integrals; 9. Vector algebra; 10. Matrices and vector spaces; 11. Vector calculus; 12. Line, surface and volume integrals; 13. Laplace transforms; 14. Ordinary differential equations; 15. Elementary probability; Appendix.

Computational Algorithms or Identification of Distributed Parameter Systems

DTIC Science & Technology

1993-04-24

delay-differential equations, Volterra integral equations, and partial differential equations with memory terms . In particular we investigated a...tested for estimating parameters in a Volterra integral equation arising from a viscoelastic model of a flexible structure with Boltzmann damping. In...particular, one of the parameters identified was the order of the derivative in Volterra integro-differential equations containing fractional

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport.

PubMed

Zhang, Kejiang; Achari, Gopal; Li, Hua

2009-11-03

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability-possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.

Effects of partial slip boundary condition and radiation on the heat and mass transfer of MHD-nanofluid flow

NASA Astrophysics Data System (ADS)

Abd Elazem, Nader Y.; Ebaid, Abdelhalim

2017-12-01

In this paper, the effect of partial slip boundary condition on the heat and mass transfer of the Cu-water and Ag-water nanofluids over a stretching sheet in the presence of magnetic field and radiation. Such partial slip boundary condition has attracted much attention due to its wide applications in industry and chemical engineering. The flow is basically governing by a system of partial differential equations which are reduced to a system of ordinary differential equations. This system has been exactly solved, where exact analytical expression has been obtained for the fluid velocity in terms of exponential function, while the temperature distribution, and the nanoparticles concentration are expressed in terms of the generalized incomplete gamma function. In addition, explicit formulae are also derived from the rates of heat transfer and mass transfer. The effects of the permanent parameters on the skin friction, heat transfer coefficient, rate of mass transfer, velocity, the temperature profile, and concentration profile have been discussed through tables and graphs.

A Model for Siderophile Element Distribution in Planetary Differentiation

NASA Technical Reports Server (NTRS)

Humayun, M.; Rushmer, T.; Rankenburg, K.; Brandon, A. D.

2005-01-01

Planetary differentiation begins with partial melting of small planetesimals. At low degrees of partial melting, a sulfur-rich liquid segregates by physical mechanisms including deformation-assisted porous flow. Experimental studies of the physical mechanisms by which Fe-S melts segregate from the silicate matrix of a molten H chondrite are part of a companion paper. Geochemical studies of these experimental products revealed that metallic liquids were in equilibrium with residual metal in the H chondrite matrix. This contribution explores the geochemical signatures produced by early stages of core formation. Particularly, low-degree partial melt segregation of Fe-S liquids leaves residual metal in the silicate matrix. Some achondrites appear to be residues of partial melting, e.g., ureilites, which are known to contain metal. The metal in these achondrites may show a distinct elemental signature. To quantify the effect of sulfur on siderophile element contents of residual metal we have developed a model based on recent parametrizations of equilibrium solid metal-liquid metal partitioning experiments.

Differential effects of lipid depletion on membrane sodium-plus-potassium ion-dependent adenosine triphosphatase and potassium ion-dependent phosphatase.

PubMed Central

Wheeler, K P; Walker, J A

1975-01-01

The phospholipid-dependence of the (Na-++K-+)-dependent ATPase (adenosine triphosphatase) (EC 3.6.1.3) and associated K-+-dependent phosphatase activity (EC 3.6.1.7) have been compared. Unlike the (Na-++K-+)-dependent ATPase activities, the K-+-dependent phosphatase activities of a number of different preparations were not closely correlated with their total phospholipid contents. After partial lipid depletion with a single extraction in Lubrol W the residual ATPase and phosphatase activities were correlated, but their magnitudes were quite different: on average only about 5% of the former remained compared with 50% of the latter. A similar differential effect on these activities was found after extraction with deoxycholate. In contrast with the ATPase, consistent restoration of the phosphatase activity of Lubrol-extracted enzymes by added exogenous phospholipids was not observed. We conclude that, although the K-+-dependent phosphatase may be lipid-dependent, the lipid requirement must be different from that of the complete ATPase system, and this difference should help investigations of their relationship. PMID:167727

Is tapentadol different from classical opioids? A review of the evidence

PubMed Central

Langford, Richard M; Knaggs, Roger; Farquhar-Smith, Paul; Dickenson, Anthony H

2016-01-01

Tapentadol is a single molecule able to deliver analgesia by two distinct mechanisms, a feature which differentiates it from many other analgesics. Pre-clinical data demonstrate two mechanisms of action: mu-opioid receptor agonist activity and noradrenaline re-uptake inhibition. From these, one may predict that tapentadol would be applicable across a broad spectrum of pain from nociceptive to neuropathic. The evidence in animal models suggests that norepinephrine re-uptake inhibition (NRI) is a key mechanism and may even predominate over opioid actions in chronic (and especially neuropathic) pain states, reinforcing that tapentadol is different to classical opioids and may, therefore, be an a priori choice for the treatment of neuropathic and mixed pain. The clinical studies and subsequent practice experience and surveillance support the concept of opioid and non-opioid mechanisms of action. The reduced incidence of some of the typical opioid-induced side effects, compared to equianalgesic doses of classical opioids, supports the hypothesis that tapentadol analgesia is only partially mediated by opioid agonist mechanisms. Both the pre-clinical and clinical profiles appear to be differentiated from those of classical opioids. PMID:27867511

Is tapentadol different from classical opioids? A review of the evidence.

PubMed

Langford, Richard M; Knaggs, Roger; Farquhar-Smith, Paul; Dickenson, Anthony H

2016-11-01

Tapentadol is a single molecule able to deliver analgesia by two distinct mechanisms, a feature which differentiates it from many other analgesics. Pre-clinical data demonstrate two mechanisms of action: mu-opioid receptor agonist activity and noradrenaline re-uptake inhibition. From these, one may predict that tapentadol would be applicable across a broad spectrum of pain from nociceptive to neuropathic. The evidence in animal models suggests that norepinephrine re-uptake inhibition (NRI) is a key mechanism and may even predominate over opioid actions in chronic (and especially neuropathic) pain states, reinforcing that tapentadol is different to classical opioids and may, therefore, be an a priori choice for the treatment of neuropathic and mixed pain. The clinical studies and subsequent practice experience and surveillance support the concept of opioid and non-opioid mechanisms of action. The reduced incidence of some of the typical opioid-induced side effects, compared to equianalgesic doses of classical opioids, supports the hypothesis that tapentadol analgesia is only partially mediated by opioid agonist mechanisms. Both the pre-clinical and clinical profiles appear to be differentiated from those of classical opioids.

Composition and evolution of the eucrite parent body - Evidence from rare earth elements. [extraterrestrial basaltic melts

NASA Technical Reports Server (NTRS)

Consolmagno, G. J.; Drake, M. J.

1977-01-01

Quantitative modeling of the evolution of rare earth element (REE) abundances in the eucrites, which are plagioclase-pigeonite basalt achondrites, indicates that the main group of eucrites (e.g., Juvinas) might have been produced by approximately 10% equilibrium partial melting of a single type of source region with initial REE abundances which were chondritic relative and absolute. Since the age of the eucrites is about equal to that of the solar system, extensive chemical differentiation of the eucrite parent body prior to the formation of eucrites seems unlikely. If homogeneous accretion is assumed, the bulk composition of the eucrite parent body can be estimated; two estimates are provided, representing different hypotheses as to the ratio of metal to olivine in the parent body. Since a large number of differentiated olivine meteorites, which would represent material from the interior of the parent body, have not been detected, the eucrite parent body is thought to be intact. It is suggested that the asteroid 4 Vesta is the eucrite parent body.

Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

USGS Publications Warehouse

Huang, W.; Zheng, Lingyun; Zhan, X.

2002-01-01

Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

NASA Technical Reports Server (NTRS)

Yan, Jue; Shu, Chi-Wang; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Discussion summary: Fictitious domain methods

NASA Technical Reports Server (NTRS)

Glowinski, Rowland; Rodrigue, Garry

1991-01-01

Fictitious Domain methods are constructed in the following manner: Suppose a partial differential equation is to be solved on an open bounded set, Omega, in 2-D or 3-D. Let R be a rectangle domain containing the closure of Omega. The partial differential equation is first solved on R. Using the solution on R, the solution of the equation on Omega is then recovered by some procedure. The advantage of the fictitious domain method is that in many cases the solution of a partial differential equation on a rectangular region is easier to compute than on a nonrectangular region. Fictitious domain methods for solving elliptic PDEs on general regions are also very efficient when used on a parallel computer. The reason is that one can use the many domain decomposition methods that are available for solving the PDE on the fictitious rectangular region. The discussion on fictitious domain methods began with a talk by R. Glowinski in which he gave some examples of a variational approach to ficititious domain methods for solving the Helmholtz and Navier-Stokes equations.

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods. Appendix 2

NASA Technical Reports Server (NTRS)

Prudhomme, C.; Rovas, D. V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, A. T.; Turinici, G.; Zang, Thomas A., Jr. (Technical Monitor)

2002-01-01

We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Statistical theory for the Kardar-Parisi-Zhang equation in (1+1) dimensions.

PubMed

Masoudi, A A; Shahbazi, F; Davoudi, J; Tabar, M Reza Rahimi

2002-02-01

The Kardar-Parisi-Zhang (KPZ) equation in (1+1) dimensions dynamically develops sharply connected valley structures within which the height derivative is not continuous. We develop a statistical theory for the KPZ equation in (1+1) dimensions driven with a random forcing that is white in time and Gaussian-correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient P(h-h*, partial differential(x)h,t) when the forcing correlation length is much smaller than the system size and much larger than the typical sharp valley width. In the time scales before the creation of the sharp valleys, we find the exact generating function of h-h* and partial differential(x)h. The time scale of the sharp valley formation is expressed in terms of the force characteristics. In the stationary state, when the sharp valleys are fully developed, finite-size corrections to the scaling laws of the structure functions left angle bracket(h-h*)(n)(partial differential(x)h)(m)right angle bracket are also obtained.

A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations

NASA Astrophysics Data System (ADS)

Ke, Rihuan; Ng, Michael K.; Sun, Hai-Wei

2015-12-01

In this paper, we study the block lower triangular Toeplitz-like with tri-diagonal blocks system which arises from the time-fractional partial differential equation. Existing fast numerical solver (e.g., fast approximate inversion method) cannot handle such linear system as the main diagonal blocks are different. The main contribution of this paper is to propose a fast direct method for solving this linear system, and to illustrate that the proposed method is much faster than the classical block forward substitution method for solving this linear system. Our idea is based on the divide-and-conquer strategy and together with the fast Fourier transforms for calculating Toeplitz matrix-vector multiplication. The complexity needs O (MNlog2 ⁡ M) arithmetic operations, where M is the number of blocks (the number of time steps) in the system and N is the size (number of spatial grid points) of each block. Numerical examples from the finite difference discretization of time-fractional partial differential equations are also given to demonstrate the efficiency of the proposed method.

Algorithm refinement for stochastic partial differential equations: II. Correlated systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexander, Francis J.; Garcia, Alejandro L.; Tartakovsky, Daniel M.

2005-08-10

We analyze a hybrid particle/continuum algorithm for a hydrodynamic system with long ranged correlations. Specifically, we consider the so-called train model for viscous transport in gases, which is based on a generalization of the random walk process for the diffusion of momentum. This discrete model is coupled with its continuous counterpart, given by a pair of stochastic partial differential equations. At the interface between the particle and continuum computations the coupling is by flux matching, giving exact mass and momentum conservation. This methodology is an extension of our stochastic Algorithm Refinement (AR) hybrid for simple diffusion [F. Alexander, A. Garcia,more » D. Tartakovsky, Algorithm refinement for stochastic partial differential equations: I. Linear diffusion, J. Comput. Phys. 182 (2002) 47-66]. Results from a variety of numerical experiments are presented for steady-state scenarios. In all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm. For a non-stochastic version (i.e., using only deterministic continuum fluxes) the long-range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude.« less

Cooperation between both Wnt/β-catenin and PTEN/PI3K/Akt signaling promotes primitive hematopoietic stem cell self-renewal and expansion

PubMed Central

Perry, John M.; He, Xi C.; Sugimura, Ryohichi; Grindley, Justin C.; Haug, Jeffrey S.; Ding, Sheng; Li, Linheng

2011-01-01

Although self-renewal is the central property of stem cells, the underlying mechanism remains inadequately defined. Using a hematopoietic stem and progenitor cell (HSPC)-specific conditional induction line, we generated a compound genetic model bearing both Pten deletion and β-catenin activation. These double mutant mice exhibit a novel phenotype, including expansion of phenotypic long-term hematopoietic stem cells (LT-HSCs) without extensive differentiation. Unexpectedly, constitutive activation of β-catenin alone results in apoptosis of HSCs. However, together, the Wnt/β-catenin and PTEN/PI3k/Akt pathways interact to drive phenotypic LT-HSC expansion by inducing proliferation while simultaneously inhibiting apoptosis and blocking differentiation, demonstrating the necessity of complementary cooperation between the two pathways in promoting self-renewal. Mechanistically, β-catenin activation reduces multiple differentiation-inducing transcription factors, blocking differentiation partially through up-regulation of Inhibitor of differentiation 2 (Id2). In double mutants, loss of Pten enhances the HSC anti-apoptotic factor Mcl-1. All of these contribute in a complementary way to HSC self-renewal and expansion. While permanent, genetic alteration of both pathways in double mutant mice leads to expansion of phenotypic HSCs, these HSCs cannot function due to blocked differentiation. We developed a pharmacological approach to expand normal, functional HSCs in culture using factors that reversibly activate both Wnt/β-catenin and PI3K/Akt signaling simultaneously. We show for the first time that activation of either single pathway is insufficient to expand primitive HSCs, but in combination, both pathways drive self-renewal and expansion of HSCs with long-term functional capacity. PMID:21890648

Mathematics for Physics

NASA Astrophysics Data System (ADS)

Stone, Michael; Goldbart, Paul

2009-07-01

Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index.

Legendre-tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1986-01-01

The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

Legendre-Tau approximations for functional differential equations

NASA Technical Reports Server (NTRS)

Ito, K.; Teglas, R.

1983-01-01

The numerical approximation of solutions to linear functional differential equations are considered using the so called Legendre tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time differentiation. The approximate solution is then represented as a truncated Legendre series with time varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximations is made.

State-resolved differential and integral cross sections for the Ne + H{sub 2}{sup +} (v = 0–2, j = 0) → NeH{sup +} + H reaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Hui; Yao, Cui-Xia; He, Xiao-Hu

State-to-state quantum dynamic calculations for the proton transfer reaction Ne + H{sub 2}{sup +} (v = 0–2, j = 0) are performed on the most accurate LZHH potential energy surface, with the product Jacobi coordinate based time-dependent wave packet method including the Coriolis coupling. The J = 0 reaction probabilities for the title reaction agree well with previous results in a wide range of collision energy of 0.2-1.2 eV. Total integral cross sections are in reasonable agreement with the available experiment data. Vibrational excitation of the reactant is much more efficient in enhancing the reaction cross sections than translational andmore » rotational excitation. Total differential cross sections are found to be forward-backward peaked with strong oscillations, which is the indication of the complex-forming mechanism. As the collision energy increases, state-resolved differential cross section changes from forward-backward symmetric peaked to forward scattering biased. This forward bias can be attributed to the larger J partial waves, which makes the reaction like an abstraction process. Differential cross sections summed over two different sets of J partial waves for the v = 0 reaction at the collision energy of 1.2 eV are plotted to illustrate the importance of large J partial waves in the forward bias of the differential cross sections.« less

Computation techniques and computer programs to analyze Stirling cycle engines using characteristic dynamic energy equations

NASA Technical Reports Server (NTRS)

Larson, V. H.

1982-01-01

The basic equations that are used to describe the physical phenomena in a Stirling cycle engine are the general energy equations and equations for the conservation of mass and conversion of momentum. These equations, together with the equation of state, an analytical expression for the gas velocity, and an equation for mesh temperature are used in this computer study of Stirling cycle characteristics. The partial differential equations describing the physical phenomena that occurs in a Stirling cycle engine are of the hyperbolic type. The hyperbolic equations have real characteristic lines. By utilizing appropriate points along these curved lines the partial differential equations can be reduced to ordinary differential equations. These equations are solved numerically using a fourth-fifth order Runge-Kutta integration technique.

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

A shape-preserving oriented partial differential equation based on a new fidelity term for electronic speckle pattern interferometry fringe patterns denoising

NASA Astrophysics Data System (ADS)

Xu, Wenjun; Tang, Chen; Zheng, Tingyue; Qiu, Yue

2018-07-01

Oriented partial differential equations (OPDEs) have been demonstrated to be a powerful tool for preserving the integrity of fringes while filtering electronic speckle pattern interferometry (ESPI) fringe patterns. However, the main drawback of OPDEs-based methods is that many iterations are often needed, which causes the change in the shape of fringes. Change in the shape of fringes will affect the accuracy of subsequent fringe analysis. In this paper, we focus on preserving the shape of fringes while filtering, suggested here for the first time. We propose a shape-preserving OPDE for ESPI fringe patterns denoising by introducing a new fidelity term to the previous second-order single oriented PDE (SOOPDE). In our proposed fidelity term, the evolution image is subtracted from the shrinkage result of original noisy image by shearlet transform. Our proposed shape-preserving OPDE is capable of eliminating noise effectively, keeping the integrity of fringes, and more importantly, preserving the shape of fringes. We test the proposed shape-preserving OPDE on three computer-simulated and three experimentally obtained ESPI fringe patterns with poor quality. Furthermore, we compare our model with three representative filtering methods, including the widely used SOOPDE, shearlet transform and coherence-enhancing diffusion (CED). We also compare our proposed fidelity term with the traditional fidelity term. Experimental results show that the proposed shape-preserving OPDE not only yields filtered images with visual quality on par with those by CED which is the state-of-the-art method for ESPI fringe patterns denoising, but also keeps the shape of ESPI fringe patterns.

Conformational statistics of stiff macromolecules as solutions to partial differential equations on the rotation and motion groups

PubMed

Chirikjian; Wang

2000-07-01

Partial differential equations (PDE's) for the probability density function (PDF) of the position and orientation of the distal end of a stiff macromolecule relative to its proximal end are derived and solved. The Kratky-Porod wormlike chain, the Yamakawa helical wormlike chain, and the original and revised Marko-Siggia models are examples of stiffness models to which the present formulation is applied. The solution technique uses harmonic analysis on the rotation and motion groups to convert PDE's governing the PDF's of interest into linear algebraic equations which have mathematically elegant solutions.

On the removal of boundary errors caused by Runge-Kutta integration of non-linear partial differential equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.

1994-01-01

It has been previously shown that the temporal integration of hyperbolic partial differential equations (PDE's) may, because of boundary conditions, lead to deterioration of accuracy of the solution. A procedure for removal of this error in the linear case has been established previously. In the present paper we consider hyperbolic (PDE's) (linear and non-linear) whose boundary treatment is done via the SAT-procedure. A methodology is present for recovery of the full order of accuracy, and has been applied to the case of a 4th order explicit finite difference scheme.

Noniterative three-dimensional grid generation using parabolic partial differential equations

NASA Technical Reports Server (NTRS)

Edwards, T. A.

1985-01-01

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

Double diffusive conjugate heat transfer: Part III

NASA Astrophysics Data System (ADS)

Soudagar, Manzoor Elahi M.; Azeem

2018-05-01

The placement of a small solid wall towards cold surface of square porous cavity affects the heat transfer behavior of porous region due to restriction of fluid motion in the region occupied by solid wall. An investigation of heat transfer is carried out to understand the fluid flow and heat transfer behavior in porous cavity by solving the governing partial differential equations. Galerkin's approach is used to convert the partial differential equations into algebraic form of equations by applying finite element method. The heat transfer increases for solid towards right surface as compared to the case of solid at center of cavity.

Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gropp, W.D.; Keyes, D.E.

1988-03-01

The authors discuss the parallel implementation of preconditioned conjugate gradient (PCG)-based domain decomposition techniques for self-adjoint elliptic partial differential equations in two dimensions on several architectures. The complexity of these methods is described on a variety of message-passing parallel computers as a function of the size of the problem, number of processors and relative communication speeds of the processors. They show that communication startups are very important, and that even the small amount of global communication in these methods can significantly reduce the performance of many message-passing architectures.

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Chen, Lin-Jie; Ma, Chang-Feng

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form ut + αuux + βunux + γuxx + δuxxx + ζuxxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman-Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions.

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

NASA Astrophysics Data System (ADS)

Chen, Shanzhen; Jiang, Xiaoyun

2012-08-01

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1), the Helmholtz equation (α→0) and the wave equation (α=2) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.

An efficient numerical scheme for the study of equal width equation

NASA Astrophysics Data System (ADS)

Ghafoor, Abdul; Haq, Sirajul

2018-06-01

In this work a new numerical scheme is proposed in which Haar wavelet method is coupled with finite difference scheme for the solution of a nonlinear partial differential equation. The scheme transforms the partial differential equation to a system of algebraic equations which can be solved easily. The technique is applied to equal width equation in order to study the behaviour of one, two, three solitary waves, undular bore and soliton collision. For efficiency and accuracy of the scheme, L2 and L∞ norms and invariants are computed. The results obtained are compared with already existing results in literature.

Differentiation of magma oceans and the thickness of the depleted layer on Venus

NASA Technical Reports Server (NTRS)

Solomatov, V. S.; Stevenson, D. J.

1993-01-01

Various arguments suggest that Venus probably has no asthenosphere, and it is likely that beneath the crust there is a highly depleted and highly viscous mantle layer which was probably formed in the early history of the planet when it was partially or completely molten. Models of crystallization of magma oceans suggest that just after crystallization of a hypothetical magma ocean, the internal structure of Venus consists of a crust up to about 70 km thickness, a depleted layer up to about 500 km, and an enriched lower layer which probably consists of an undepleted 'lower mantle' and heavy enriched accumulates near the core-mantle boundary. Partial or even complete melting of Venus due to large impacts during the formation period eventually results in differentiation. However, the final result of such a differentiation can vary from a completely differentiated mantle to an almost completely preserved homogeneous mantle depending on competition between convection and differentiation: between low viscosity ('liquid') convection and crystal settling at small crystal fractions, or between high viscosity ('solid') convection and percolation at large crystal fractions.

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

NASA Astrophysics Data System (ADS)

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

2017-01-01

In this research article, we derive and analyze an efficient spectral method based on the operational matrices of three dimensional orthogonal Jacobi polynomials to solve numerically the mixed partial derivatives type multi-terms high dimensions generalized class of fractional order partial differential equations. We transform the considered fractional order problem to an easily solvable algebraic equations with the aid of the operational matrices. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some test problems are considered to confirm the accuracy and validity of the proposed numerical method. The convergence of the method is ensured by comparing our Matlab software simulations based obtained results with the exact solutions in the literature, yielding negligible errors. Moreover, comparative results discussed in the literature are extended and improved in this study.

Agonist-Directed Desensitization of the β2-Adrenergic Receptor

PubMed Central

Goral, Vasiliy; Jin, Yan; Sun, Haiyan; Ferrie, Ann M.; Wu, Qi; Fang, Ye

2011-01-01

The β2-adrenergic receptor (β2AR) agonists with reduced tachyphylaxis may offer new therapeutic agents with improved tolerance profile. However, receptor desensitization assays are often inferred at the single signaling molecule level, thus ligand-directed desensitization is poorly understood. Here we report a label-free biosensor whole cell assay with microfluidics to determine ligand-directed desensitization of the β2AR. Together with mechanistic deconvolution using small molecule inhibitors, the receptor desensitization and resensitization patterns under the short-term agonist exposure manifested the long-acting agonism of salmeterol, and differentiated the mechanisms of agonist-directed desensitization between a full agonist epinephrine and a partial agonist pindolol. This study reveals the cellular mechanisms of agonist-selective β2AR desensitization at the whole cell level. PMID:21541288

Solving the Cauchy-Riemann equations on parallel computers

NASA Technical Reports Server (NTRS)

Fatoohi, Raad A.; Grosch, Chester E.

1987-01-01

Discussed is the implementation of a single algorithm on three parallel-vector computers. The algorithm is a relaxation scheme for the solution of the Cauchy-Riemann equations; a set of coupled first order partial differential equations. The computers were chosen so as to encompass a variety of architectures. They are: the MPP, and SIMD machine with 16K bit serial processors; FLEX/32, an MIMD machine with 20 processors; and CRAY/2, an MIMD machine with four vector processors. The machine architectures are briefly described. The implementation of the algorithm is discussed in relation to these architectures and measures of the performance on each machine are given. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Conclusions are presented.

Differentiation-dependent rearrangements of actin filaments and microtubules hinder apical endocytosis in urothelial cells.

PubMed

Tratnjek, Larisa; Romih, Rok; Kreft, Mateja Erdani

2017-08-01

During differentiation, superficial urothelial cells (UCs) of the urinary bladder form the apical surface, which is almost entirely covered by urothelial plaques containing densely packed uroplakin particles. These urothelial plaques are the main structural components of the blood-urine permeability barrier in the urinary bladder. We have shown previously that endocytosis from the apical plasma membrane decreases during urothelial cell differentiation. Here, we investigated the role of actin filament and microtubule rearrangements in apical endocytosis of differentiating UCs cells using hyperplastic and normoplastic porcine urothelial models. Partially differentiated normal porcine UCs contained actin filaments in the subapical cytoplasm, while microtubules had a net-like appearance. In highly differentiated UCs, actin filaments mostly disappeared from the subapical cytoplasm and microtubules remained as a thin layer close to the apical plasma membrane. Inhibition of actin filament formation with cytochalasin-D in partially differentiated UCs caused a decrease in apical endocytosis. Depolymerisation of microtubules with nocodazole did not prevent endocytosis of the endocytotic marker WGA into the subapical cytoplasm; however, it abolished WGA transport to endolysosomal compartments in the central cytoplasm. Cytochalasin-D or nocodazole treatment did not significantly change apical endocytosis in highly differentiated UCs. In conclusion, we showed that the physiological differentiation-dependent or chemically induced redistribution and reorganization of actin filaments and microtubules impair apical endocytosis in UCs. Importantly, reduced apical endocytosis due to cytoskeletal rearrangements in highly differentiated UCs, together with the formation of rigid urothelial plaques, reinforces the barrier function of the urothelium.

Differential Effects of Full and Partial Notes on Learning Outcomes and Attendance

ERIC Educational Resources Information Center

Cornelius, Tara L.; Owen-DeSchryver, Jamie

2008-01-01

Although college instructors are increasingly providing students with online notes, research is equivocal on how such notes affect student outcomes. This study examined partial versus full notes in introductory psychology classes while controlling for initial levels of student knowledge and academic ability. Results suggested that students…

Single-port laparoscopic partial splenectomy: a case report.

PubMed

Hong, Tae Ho; Lee, Sang Kuon; You, Young Kyoung; Kim, Jun Gi

2010-10-01

With the better understanding of the importance of the spleen as a primary organ of the human immune system, there has been an increased interest in performing the partial splenectomy for a number of indications such as nonparasitic cysts, benign tumors, staging of lymphomas, etc. Moreover, laparoscopic partial splenectomy has been gaining more interest as the recommended approach for benign splenic disorders to preserve the splenic function with very low recurrence rates. Meanwhile, many surgeons have attempted to reduce the number and size of the ports in laparoscopic surgery with the aim of inducing less parietal trauma and fewer scars. One of these efforts is single-port laparoscopic surgery, which is a rapidly evolving field all over the world. Here, we describe a feasible method of single-port laparoscopic partial splenectomy for treating a benign splenic cyst that was located in the upper medial aspect of the spleen.

Viability and neural differentiation of mesenchymal stem cells derived from the umbilical cord following perinatal asphyxia.

PubMed

Aly, H; Mohsen, L; Badrawi, N; Gabr, H; Ali, Z; Akmal, D

2012-09-01

Hypoxia-ischemia is the leading cause of neurological handicaps in newborns worldwide. Mesenchymal stem cells (MSCs) collected from fresh cord blood of asphyxiated newborns have the potential to regenerate damaged neural tissues. The aim of this study was to examine the capacity for MSCs to differentiate into neural tissue that could subsequently be used for autologous transplantation. We collected cord blood samples from full-term newborns with perinatal hypoxemia (n=27), healthy newborns (n=14) and non-hypoxic premature neonates (n=14). Mononuclear cells were separated, counted, and then analyzed by flow cytometry to assess various stem cell populations. MSCs were isolated by plastic adherence and characterized by morphology. Cells underwent immunophenotyping and trilineage differentiation potential. They were then cultured in conditions favoring neural differentiation. Neural lineage commitment was detected using immunohistochemical staining for glial fibrillary acidic protein, tubulin III and oligodendrocyte marker O4 antibodies. Mononuclear cell count and viability did not differ among the three groups of infants. Neural differentiation was best demonstrated in the cells derived from hypoxia-ischemia term neonates, of which 69% had complete and 31% had partial neural differentiation. Cells derived from preterm neonates had the least amount of neural differentiation, whereas partial differentiation was observed in only 12%. These findings support the potential utilization of umbilical cord stem cells as a source for autologous transplant in asphyxiated neonates.

Local algebraic analysis of differential systems

NASA Astrophysics Data System (ADS)

Kaptsov, O. V.

2015-06-01

We propose a new approach for studying the compatibility of partial differential equations. This approach is a synthesis of the Riquier method, Gröbner basis theory, and elements of algebraic geometry. As applications, we consider systems including the wave equation and the sine-Gordon equation.

A theory of fine structure image models with an application to detection and classification of dementia.

PubMed

O'Neill, William; Penn, Richard; Werner, Michael; Thomas, Justin

2015-06-01

Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible.

Contamination levels of mercury in the muscle of female and male spiny dogfishes (Squalus acanthias) caught off the coast of Japan.

PubMed

Endo, Tetsuya; Hisamichi, Yohsuke; Kimura, Osamu; Kotaki, Yuichi; Kato, Yoshihisa; Ohta, Chiho; Koga, Nobuyuki; Haraguchi, Koichi

2009-11-01

We analyzed the total mercury (T-Hg) and stable isotopes of (13)C and (15)N in the muscle of spiny dogfish (Squalus acanthias) caught off the coast of Japan. The average body length of the female spiny dogfish sampled (94.9+/-20.2 cm, 50.5-131.0 cm, n=40) was significantly larger than that of the males sampled (77.8+/-10.8 cm, 55.5-94.0 cm, n=35), although the ages of the samples were unknown. The T-Hg concentration in the muscle samples rapidly increased after maturity in the females (larger than about 120 cm) and males (larger than about 90 cm), followed by a continued gradual increase. Contamination level of T-Hg in female muscle samples (0.387+/-0.378 microg(wet g)(-1), n=40) was slightly higher than that in male muscle samples (0.316+/-0.202 microg(wet g)(-1), n=35), probably due to the greater longevity of females. In contrast, the contamination level of T-Hg in females smaller than 94.0 cm in length (0.204+/-0.098 microg(wet g)(-1), n=20) was slightly lower than that in the males, probably due to the faster growth rate of females. Although the partial differential(13)C and partial differential(15)N values in the muscle samples increased with an increase in body length, there were no significant differences between the females (-17.2+/-0.4 per thousand and 12.4+/-0.9 per thousand, respectively) and males (-17.3+/-0.4 per thousand and 12.4+/-0.8 per thousand, respectively). A positive correlation was found between partial differential(13)C and partial differential(15)N values, suggesting trophic enrichment due to the growth.

A three operator split-step method covering a larger set of non-linear partial differential equations

NASA Astrophysics Data System (ADS)

Zia, Haider

2017-06-01

This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.

Financial aspects of partial cutting practices in central Appalachian hardwoods

Treesearch

Gary W. Miller; Gary W. Miller

1993-01-01

Uneven-aged silvicultural practices can be used to regenerate and manage many eastern hardwood stands. Single-tree selection methods are feasible in stands where a desirable shade-tolerant commercial species can be regenerated following periodic harvests. A variety of partial cutting practices, including single-tree selection and diameter-limit cutting have been used...

Accuracy of six elastic impression materials used for complete-arch fixed partial dentures.

PubMed

Stauffer, J P; Meyer, J M; Nally, J N

1976-04-01

1. The accuracy of four types of impression materials used to make a complete-arch fixed partial denture was evaluated by visual comparison and indirect measurement methods. 2. None of the tested materials allows safe finishing of a complete-arch fixed partial denture on a cast poured from one single master impression. 3. All of the tested materials can be used for impressions for a complete-arch fixed partial denture provided it is not finished on one single cast. Errors can be avoided by making a new impression with the fitted castings in place. Assembly and soldering should be done on the second cast. 4. In making the master fixed partial denture for this study, inaccurate soldering was a problem that was overcome with the use of epoxy glue. Hence, soldering seems to be a major source of inaccuracy for every fixed partial denture.

A Model for the Oxidation of C/SiC Composite Structures

NASA Technical Reports Server (NTRS)

Sullivan, Roy M.

2003-01-01

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of C/SiC composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. Within the mathematical formulation, two diffusion mechanisms are possible: (1) the relative diffusion of one species with respect to the mixture, which is concentration gradient driven and (2) the diffusion associated with the average velocity of the gas mixture, which is total gas pressure gradient driven. The result of the theoretical formulation is a set of two coupled nonlinear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations must be solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of space and time. The local rate of carbon oxidation is determined as a function of space and time using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The nonlinear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The end result is a numerical scheme capable of determining the variation of the local carbon oxidation rates as a function of space and time for any arbitrary C/SiC composite structures.

Dynamic characteristics of a variable-mass flexible missile

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Bankovskis, J.

1970-01-01

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

Discovery and Optimization of Low-Storage Runge-Kutta Methods

DTIC Science & Technology

2015-06-01

NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS DISCOVERY AND OPTIMIZATION OF LOW-STORAGE RUNGE-KUTTA METHODS by Matthew T. Fletcher June 2015... methods are an important family of iterative methods for approximating the solutions of ordinary differential equations (ODEs) and differential...algebraic equations (DAEs). It is common to use an RK method to discretize in time when solving time dependent partial differential equations (PDEs) with a

The decay widths, the decay constants, and the branching fractions of a resonant state

NASA Astrophysics Data System (ADS)

de la Madrid, Rafael

2015-08-01

We introduce the differential and the total decay widths of a resonant (Gamow) state decaying into a continuum of stable states. When the resonance has several decay modes, we introduce the corresponding partial decay widths and branching fractions. In the approximation that the resonance is sharp, the expressions for the differential, partial and total decay widths of a resonant state bear a close resemblance with the Golden Rule. In such approximation, the branching fractions of a resonant state are the same as the standard branching fractions obtained by way of the Golden Rule. We also introduce dimensionless decay constants along with their associated differential decay constants, and we express experimentally measurable quantities such as the branching fractions and the energy distributions of decay events in terms of those dimensionless decay constants.

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1974-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear ti surfaces. The spherical mean is the average of u over a constant ti surface. The conditions on the linear differential operator, L, and on the orthogonal coordinates (ti, eta, zeta) are established so that the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be determined directly as a problem with only space variable. Conditions are then established so that the spherical mean of the solution in one concial region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

Functional requirements of a mathematical model of the heart.

PubMed

Palladino, Joseph L; Noordergraaf, Abraham

2009-01-01

Functional descriptions of the heart, especially the left ventricle, are often based on the measured variables pressure and ventricular outflow, embodied as a time-varying elastance. The fundamental difficulty of describing the mechanical properties of the heart with a time-varying elastance function that is set a priori is described. As an alternative, a new functional model of the heart is presented, which characterizes the ventricle's contractile state with parameters, rather than variables. Each chamber is treated as a pressure generator that is time and volume dependent. The heart's complex dynamics develop from a single equation based on the formation and relaxation of crossbridge bonds. This equation permits the calculation of ventricular elastance via E(v) = partial differentialp(v)/ partial differentialV(v). This heart model is defined independently from load properties, and ventricular elastance is dynamic and reflects changing numbers of crossbridge bonds. In this paper, the functionality of this new heart model is presented via computed work loops that demonstrate the Frank-Starling mechanism and the effects of preload, the effects of afterload, inotropic changes, and varied heart rate, as well as the interdependence of these effects. Results suggest the origin of the equivalent of Hill's force-velocity relation in the ventricle.

Fast Maximum Entropy Moment Closure Approach to Solving the Boltzmann Equation

NASA Astrophysics Data System (ADS)

Summy, Dustin; Pullin, Dale

2015-11-01

We describe a method for a moment-based solution of the Boltzmann Equation (BE). This is applicable to an arbitrary set of velocity moments whose transport is governed by partial-differential equations (PDEs) derived from the BE. The equations are unclosed, containing both higher-order moments and molecular-collision terms. These are evaluated using a maximum-entropy reconstruction of the velocity distribution function f (c , x , t) , from the known moments, within a finite-box domain of single-particle velocity (c) space. Use of a finite-domain alleviates known problems (Junk and Unterreiter, Continuum Mech. Thermodyn., 2002) concerning existence and uniqueness of the reconstruction. Unclosed moments are evaluated with quadrature while collision terms are calculated using any desired method. This allows integration of the moment PDEs in time. The high computational cost of the general method is greatly reduced by careful choice of the velocity moments, allowing the necessary integrals to be reduced from three- to one-dimensional in the case of strictly 1D flows. A method to extend this enhancement to fully 3D flows is discussed. Comparison with relaxation and shock-wave problems using the DSMC method will be presented. Partially supported by NSF grant DMS-1418903.

A model for foam formation, stability, and breakdown in glass-melting furnaces.

PubMed

van der Schaaf, John; Beerkens, Ruud G C

2006-03-01

A dynamic model for describing the build-up and breakdown of a glass-melt foam is presented. The foam height is determined by the gas flux to the glass-melt surface and the drainage rate of the liquid lamellae between the gas bubbles. The drainage rate is determined by the average gas bubble radius and the physical properties of the glass melt: density, viscosity, surface tension, and interfacial mobility. Neither the assumption of a fully mobile nor the assumption of a fully immobile glass-melt interface describe the observed foam formation on glass melts adequately. The glass-melt interface appears partially mobile due to the presence of surface active species, e.g., sodium sulfate and silanol groups. The partial mobility can be represented by a single, glass-melt composition specific parameter psi. The value of psi can be estimated from gas bubble lifetime experiments under furnace conditions. With this parameter, laboratory experiments of foam build-up and breakdown in a glass melt are adequately described, qualitatively and quantitatively by a set of ordinary differential equations. An approximate explicit relationship for the prediction of the steady-state foam height is derived from the fundamental model.

Low-energy electron-impact single ionization of helium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Colgan, J.; Pindzola, M. S.; Childers, G.

2006-04-15

A study is made of low-energy electron-impact single ionization of ground-state helium. The time-dependent close-coupling method is used to calculate total integral, single differential, double differential, and triple differential ionization cross sections for impact electron energies ranging from 32 to 45 eV. For all quantities, the calculated cross sections are found to be in very good agreement with experiment, and for the triple differential cross sections, good agreement is also found with calculations made using the convergent close-coupling technique.

SCOUP: a probabilistic model based on the Ornstein-Uhlenbeck process to analyze single-cell expression data during differentiation.

PubMed

Matsumoto, Hirotaka; Kiryu, Hisanori

2016-06-08

Single-cell technologies make it possible to quantify the comprehensive states of individual cells, and have the power to shed light on cellular differentiation in particular. Although several methods have been developed to fully analyze the single-cell expression data, there is still room for improvement in the analysis of differentiation. In this paper, we propose a novel method SCOUP to elucidate differentiation process. Unlike previous dimension reduction-based approaches, SCOUP describes the dynamics of gene expression throughout differentiation directly, including the degree of differentiation of a cell (in pseudo-time) and cell fate. SCOUP is superior to previous methods with respect to pseudo-time estimation, especially for single-cell RNA-seq. SCOUP also successfully estimates cell lineage more accurately than previous method, especially for cells at an early stage of bifurcation. In addition, SCOUP can be applied to various downstream analyses. As an example, we propose a novel correlation calculation method for elucidating regulatory relationships among genes. We apply this method to a single-cell RNA-seq data and detect a candidate of key regulator for differentiation and clusters in a correlation network which are not detected with conventional correlation analysis. We develop a stochastic process-based method SCOUP to analyze single-cell expression data throughout differentiation. SCOUP can estimate pseudo-time and cell lineage more accurately than previous methods. We also propose a novel correlation calculation method based on SCOUP. SCOUP is a promising approach for further single-cell analysis and available at https://github.com/hmatsu1226/SCOUP.

Absence of NEFL in patient-specific neurons in early-onset Charcot-Marie-Tooth neuropathy.

PubMed

Sainio, Markus T; Ylikallio, Emil; Mäenpää, Laura; Lahtela, Jenni; Mattila, Pirkko; Auranen, Mari; Palmio, Johanna; Tyynismaa, Henna

2018-06-01

We used patient-specific neuronal cultures to characterize the molecular genetic mechanism of recessive nonsense mutations in neurofilament light ( NEFL ) underlying early-onset Charcot-Marie-Tooth (CMT) disease. Motor neurons were differentiated from induced pluripotent stem cells of a patient with early-onset CMT carrying a novel homozygous nonsense mutation in NEFL . Quantitative PCR, protein analytics, immunocytochemistry, electron microscopy, and single-cell transcriptomics were used to investigate patient and control neurons. We show that the recessive nonsense mutation causes a nearly total loss of NEFL messenger RNA (mRNA), leading to the complete absence of NEFL protein in patient's cultured neurons. Yet the cultured neurons were able to differentiate and form neuronal networks and neurofilaments. Single-neuron gene expression fingerprinting pinpointed NEFL as the most downregulated gene in the patient neurons and provided data of intermediate filament transcript abundancy and dynamics in cultured neurons. Blocking of nonsense-mediated decay partially rescued the loss of NEFL mRNA. The strict neuronal specificity of neurofilament has hindered the mechanistic studies of recessive NEFL nonsense mutations. Here, we show that such mutation leads to the absence of NEFL, causing childhood-onset neuropathy through a loss-of-function mechanism. We propose that the neurofilament accumulation, a common feature of many neurodegenerative diseases, mimics the absence of NEFL seen in recessive CMT if aggregation prevents the proper localization of wild-type NEFL in neurons. Our results suggest that the removal of NEFL as a proposed treatment option is harmful in humans.

Asymptotic analysis of the local potential approximation to the Wetterich equation

NASA Astrophysics Data System (ADS)

Bender, Carl M.; Sarkar, Sarben

2018-06-01

This paper reports a study of the nonlinear partial differential equation that arises in the local potential approximation to the Wetterich formulation of the functional renormalization group equation. A cut-off-dependent shift of the potential in this partial differential equation is performed. This shift allows a perturbative asymptotic treatment of the differential equation for large values of the infrared cut-off. To leading order in perturbation theory the differential equation becomes a heat equation, where the sign of the diffusion constant changes as the space-time dimension D passes through 2. When D  <  2, one obtains a forward heat equation whose initial-value problem is well-posed. However, for D  >  2 one obtains a backward heat equation whose initial-value problem is ill-posed. For the special case D  =  1 the asymptotic series for cubic and quartic models is extrapolated to the small infrared-cut-off limit by using Padé techniques. The effective potential thus obtained from the partial differential equation is then used in a Schrödinger-equation setting to study the stability of the ground state. For cubic potentials it is found that this Padé procedure distinguishes between a -symmetric theory and a conventional Hermitian theory (g real). For an theory the effective potential is nonsingular and has a stable ground state but for a conventional theory the effective potential is singular. For a conventional Hermitian theory and a -symmetric theory (g  >  0) the results are similar; the effective potentials in both cases are nonsingular and possess stable ground states.

Patterns of differentiation among endangered pondberry populations

Treesearch

Craig S Echt; Dennis Deemer; Danny Gustafson

2011-01-01

Pondberry, Lindera melissifolia, is an endangered and partially clonally reproducing shrub species found in isolated populations that inhabit seasonally wet depressions in forested areas of the lower Mississippi River alluvial valley and southeastern regions of the United States. With eleven microsatellite loci, we quantified population genetic differentiation and...

Single-Cell RNA-Sequencing: Assessment of Differential Expression Analysis Methods.

PubMed

Dal Molin, Alessandra; Baruzzo, Giacomo; Di Camillo, Barbara

2017-01-01

The sequencing of the transcriptomes of single-cells, or single-cell RNA-sequencing, has now become the dominant technology for the identification of novel cell types and for the study of stochastic gene expression. In recent years, various tools for analyzing single-cell RNA-sequencing data have been proposed, many of them with the purpose of performing differentially expression analysis. In this work, we compare four different tools for single-cell RNA-sequencing differential expression, together with two popular methods originally developed for the analysis of bulk RNA-sequencing data, but largely applied to single-cell data. We discuss results obtained on two real and one synthetic dataset, along with considerations about the perspectives of single-cell differential expression analysis. In particular, we explore the methods performance in four different scenarios, mimicking different unimodal or bimodal distributions of the data, as characteristic of single-cell transcriptomics. We observed marked differences between the selected methods in terms of precision and recall, the number of detected differentially expressed genes and the overall performance. Globally, the results obtained in our study suggest that is difficult to identify a best performing tool and that efforts are needed to improve the methodologies for single-cell RNA-sequencing data analysis and gain better accuracy of results.

Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle.

PubMed

Osche, G R

2000-08-20

Single- and multiple-pulse detection statistics are presented for aperture-averaged direct detection optical receivers operating against partially developed speckle fields. A partially developed speckle field arises when the probability density function of the received intensity does not follow negative exponential statistics. The case of interest here is the target surface that exhibits diffuse as well as specular components in the scattered radiation. An approximate expression is derived for the integrated intensity at the aperture, which leads to single- and multiple-pulse discrete probability density functions for the case of a Poisson signal in Poisson noise with an additive coherent component. In the absence of noise, the single-pulse discrete density function is shown to reduce to a generalized negative binomial distribution. The radar concept of integration loss is discussed in the context of direct detection optical systems where it is shown that, given an appropriate set of system parameters, multiple-pulse processing can be more efficient than single-pulse processing over a finite range of the integration parameter n.

Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Gerdt, Vladimir P.; Blinkov, Yuri A.; Mozzhilkin, Vladimir V.

2006-05-01

In this paper we present an algorithmic approach to the generation of fully conservative difference schemes for linear partial differential equations. The approach is based on enlargement of the equations in their integral conservation law form by extra integral relations between unknown functions and their derivatives, and on discretization of the obtained system. The structure of the discrete system depends on numerical approximation methods for the integrals occurring in the enlarged system. As a result of the discretization, a system of linear polynomial difference equations is derived for the unknown functions and their partial derivatives. A difference scheme is constructed by elimination of all the partial derivatives. The elimination can be achieved by selecting a proper elimination ranking and by computing a Gröbner basis of the linear difference ideal generated by the polynomials in the discrete system. For these purposes we use the difference form of Janet-like Gröbner bases and their implementation in Maple. As illustration of the described methods and algorithms, we construct a number of difference schemes for Burgers and Falkowich-Karman equations and discuss their numerical properties.

Use of partial least squares regression to impute SNP genotypes in Italian cattle breeds.

PubMed

Dimauro, Corrado; Cellesi, Massimo; Gaspa, Giustino; Ajmone-Marsan, Paolo; Steri, Roberto; Marras, Gabriele; Macciotta, Nicolò P P

2013-06-05

The objective of the present study was to test the ability of the partial least squares regression technique to impute genotypes from low density single nucleotide polymorphisms (SNP) panels i.e. 3K or 7K to a high density panel with 50K SNP. No pedigree information was used. Data consisted of 2093 Holstein, 749 Brown Swiss and 479 Simmental bulls genotyped with the Illumina 50K Beadchip. First, a single-breed approach was applied by using only data from Holstein animals. Then, to enlarge the training population, data from the three breeds were combined and a multi-breed analysis was performed. Accuracies of genotypes imputed using the partial least squares regression method were compared with those obtained by using the Beagle software. The impact of genotype imputation on breeding value prediction was evaluated for milk yield, fat content and protein content. In the single-breed approach, the accuracy of imputation using partial least squares regression was around 90 and 94% for the 3K and 7K platforms, respectively; corresponding accuracies obtained with Beagle were around 85% and 90%. Moreover, computing time required by the partial least squares regression method was on average around 10 times lower than computing time required by Beagle. Using the partial least squares regression method in the multi-breed resulted in lower imputation accuracies than using single-breed data. The impact of the SNP-genotype imputation on the accuracy of direct genomic breeding values was small. The correlation between estimates of genetic merit obtained by using imputed versus actual genotypes was around 0.96 for the 7K chip. Results of the present work suggested that the partial least squares regression imputation method could be useful to impute SNP genotypes when pedigree information is not available.

Comparison of the short-term efficacy of sequential treatment with intravesical single-port laparoscopic partial cystectomy with bladder preservation or open partial cystectomy in combination with cisplatin plus gemcitabine chemotherapy

PubMed Central

MAI, HAI-XING; LIU, JUN-LE; PEI, SHU-JUN; ZHAO, LI; QU, NAN; DONG, JIN-KAI; CHEN, BIAO; WANG, YA-LIN; HUANG, CHENG; CHEN, LI-JUN

2015-01-01

This study aimed to assess the short-term efficacy of sequential therapy for T2/T3a bladder cancer with intravesical single-port laparoscopic partial cystectomy or open partial cystectomy combined with cisplatin plus gemcitabine (GC) chemotherapy in a prospective randomized controlled study. Thirty patients with bladder cancer who underwent open partial cystectomy (group A) or single-port laparoscopic partial cystectomy (group B) and received standard GC chemotherapy were analyzed. Perioperative functional indicators and tumor recurrence during a 1-year postoperative follow-up were compared between the two groups. The baseline characteristics were comparable between the two groups. The mean operative time, amount of blood loss and duration of hospital stay were 90.3 min, 182.0 ml and 7.3 days, respectively, for group A, and 105.3 min, 49.3 ml and 5.8 days, respectively, for group B. No secondary postoperative bleeding, urine leakage, wound infection or other complications were observed in the two groups. Postoperative scarring was not evident in group B. The overall incidence of surgical complications, tumor recurrence rate and complications during chemotherapy in the postoperative follow-up period of 12 months were similar between the two groups. Single-port laparoscopic partial cystectomy surgery is an idea surgical method for the treatment of invasive bladder cancer, with good surgical effect, minimal invasiveness, rapid recovery and short hospital stay. The data from 1-year postoperative follow-up showed that laparoscopic surgery was superior with regard to perioperative bleeding, postoperative recovery and duration of indwelling urinary catheter use. However, regarding the tumor recurrence rate, long-term comparative details are required to determine the effect of laparoscopic surgery. PMID:26170915

Partial differential equation models in the socio-economic sciences.

PubMed

Burger, Martin; Caffarelli, Luis; Markowich, Peter A

2014-11-13

Mathematical models based on partial differential equations (PDEs) have become an integral part of quantitative analysis in most branches of science and engineering, recently expanding also towards biomedicine and socio-economic sciences. The application of PDEs in the latter is a promising field, but widely quite open and leading to a variety of novel mathematical challenges. In this introductory article of the Theme Issue, we will provide an overview of the field and its recent boosting topics. Moreover, we will put the contributions to the Theme Issue in an appropriate perspective. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Estimating varying coefficients for partial differential equation models.

PubMed

Zhang, Xinyu; Cao, Jiguo; Carroll, Raymond J

2017-09-01

Partial differential equations (PDEs) are used to model complex dynamical systems in multiple dimensions, and their parameters often have important scientific interpretations. In some applications, PDE parameters are not constant but can change depending on the values of covariates, a feature that we call varying coefficients. We propose a parameter cascading method to estimate varying coefficients in PDE models from noisy data. Our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed. The performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a PDE model arising from LIDAR data. © 2017, The International Biometric Society.

Survey of the status of finite element methods for partial differential equations

NASA Technical Reports Server (NTRS)

Temam, Roger

1986-01-01

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

An Elementary Introduction to Recently Developed Computational Methods for Solving Singularly Perturbed Partial Differential Equations Arising in Science and Engineering

NASA Astrophysics Data System (ADS)

Kumar, Manoj; Srivastava, Akanksha

2013-01-01

This paper presents a survey of innovative approaches of the most effective computational techniques for solving singular perturbed partial differential equations, which are useful because of their numerical and computer realizations. Many applied problems appearing in semiconductors theory, biochemistry, kinetics, theory of electrical chains, economics, solid mechanics, fluid dynamics, quantum mechanics, and many others can be modelled as singularly perturbed systems. Here, we summarize a wide range of research articles published by numerous researchers during the last ten years to get a better view of the present scenario in this area of research.

A semi-direct procedure using a local relaxation factor and its application to an internal flow problem

NASA Technical Reports Server (NTRS)

Chang, S. C.

1984-01-01

Generally, fast direct solvers are not directly applicable to a nonseparable elliptic partial differential equation. This limitation, however, is circumvented by a semi-direct procedure, i.e., an iterative procedure using fast direct solvers. An efficient semi-direct procedure which is easy to implement and applicable to a variety of boundary conditions is presented. The current procedure also possesses other highly desirable properties, i.e.: (1) the convergence rate does not decrease with an increase of grid cell aspect ratio, and (2) the convergence rate is estimated using the coefficients of the partial differential equation being solved.

Solution of partial differential equations on vector and parallel computers

NASA Technical Reports Server (NTRS)

Ortega, J. M.; Voigt, R. G.

1985-01-01

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Unsteady boundary layer flow over a sphere in a porous medium

NASA Astrophysics Data System (ADS)

Mohammad, Nurul Farahain; Waini, Iskandar; Kasim, Abdul Rahman Mohd; Majid, Nurazleen Abdul

2017-08-01

This study focuses on the problem of unsteady boundary layer flow over a sphere in a porous medium. The governing equations which consists of a system of dimensional partial differential equations is applied with dimensionless parameter in order to attain non-dimensional partial differential equations. Later, the similarity transformation is performed in order to attain nonsimilar governing equations. Afterwards, the nonsimilar governing equations are solved numerically by using the Keller-Box method in Octave programme. The effect of porosity parameter is examined on separation time, velocity profile and skin friction of the unsteady flow. The results attained are presented in the form of table and graph.

Analytical solutions for systems of partial differential-algebraic equations.

PubMed

Benhammouda, Brahim; Vazquez-Leal, Hector

2014-01-01

This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

Time-partitioning simulation models for calculation on parallel computers

NASA Technical Reports Server (NTRS)

Milner, Edward J.; Blech, Richard A.; Chima, Rodrick V.

1987-01-01

A technique allowing time-staggered solution of partial differential equations is presented in this report. Using this technique, called time-partitioning, simulation execution speedup is proportional to the number of processors used because all processors operate simultaneously, with each updating of the solution grid at a different time point. The technique is limited by neither the number of processors available nor by the dimension of the solution grid. Time-partitioning was used to obtain the flow pattern through a cascade of airfoils, modeled by the Euler partial differential equations. An execution speedup factor of 1.77 was achieved using a two processor Cray X-MP/24 computer.

Combination of oriented partial differential equation and shearlet transform for denoising in electronic speckle pattern interferometry fringe patterns.

PubMed

Xu, Wenjun; Tang, Chen; Gu, Fan; Cheng, Jiajia

2017-04-01

It is a key step to remove the massive speckle noise in electronic speckle pattern interferometry (ESPI) fringe patterns. In the spatial-domain filtering methods, oriented partial differential equations have been demonstrated to be a powerful tool. In the transform-domain filtering methods, the shearlet transform is a state-of-the-art method. In this paper, we propose a filtering method for ESPI fringe patterns denoising, which is a combination of second-order oriented partial differential equation (SOOPDE) and the shearlet transform, named SOOPDE-Shearlet. Here, the shearlet transform is introduced into the ESPI fringe patterns denoising for the first time. This combination takes advantage of the fact that the spatial-domain filtering method SOOPDE and the transform-domain filtering method shearlet transform benefit from each other. We test the proposed SOOPDE-Shearlet on five experimentally obtained ESPI fringe patterns with poor quality and compare our method with SOOPDE, shearlet transform, windowed Fourier filtering (WFF), and coherence-enhancing diffusion (CEDPDE). Among them, WFF and CEDPDE are the state-of-the-art methods for ESPI fringe patterns denoising in transform domain and spatial domain, respectively. The experimental results have demonstrated the good performance of the proposed SOOPDE-Shearlet.

Mapping human pluripotent stem cell differentiation pathways using high throughput single-cell RNA-sequencing.

PubMed

Han, Xiaoping; Chen, Haide; Huang, Daosheng; Chen, Huidong; Fei, Lijiang; Cheng, Chen; Huang, He; Yuan, Guo-Cheng; Guo, Guoji

2018-04-05

Human pluripotent stem cells (hPSCs) provide powerful models for studying cellular differentiations and unlimited sources of cells for regenerative medicine. However, a comprehensive single-cell level differentiation roadmap for hPSCs has not been achieved. We use high throughput single-cell RNA-sequencing (scRNA-seq), based on optimized microfluidic circuits, to profile early differentiation lineages in the human embryoid body system. We present a cellular-state landscape for hPSC early differentiation that covers multiple cellular lineages, including neural, muscle, endothelial, stromal, liver, and epithelial cells. Through pseudotime analysis, we construct the developmental trajectories of these progenitor cells and reveal the gene expression dynamics in the process of cell differentiation. We further reprogram primed H9 cells into naïve-like H9 cells to study the cellular-state transition process. We find that genes related to hemogenic endothelium development are enriched in naïve-like H9. Functionally, naïve-like H9 show higher potency for differentiation into hematopoietic lineages than primed cells. Our single-cell analysis reveals the cellular-state landscape of hPSC early differentiation, offering new insights that can be harnessed for optimization of differentiation protocols.

A time- and matrix-dependent TGFBR3–JUND–KRT5 regulatory circuit in single breast epithelial cells and basal-like premalignancies

PubMed Central

Wang, Chun-Chao; Bajikar, Sameer S.; Jamal, Leen; Atkins, Kristen A.; Janes, Kevin A.

2014-01-01

Basal-like breast carcinoma is characterized by poor prognosis and high intratumor heterogeneity. In an immortalized basal-like breast epithelial cell line, we identified two anti-correlated gene-expression programs that arise among single extracellular matrix (ECM)-attached cells during organotypic 3D culture. The first contains multiple TGFβ-related genes including TGFBR3, whereas the second contains JUND and the basal-like marker, KRT5. TGFBR3 and JUND interconnect through four negative-feedback loops to form a circuit that exhibits spontaneous damped oscillations in 3D culture. The TGFBR3–JUND circuit appears conserved in some premalignant lesions that heterogeneously express KRT5. The circuit depends on ECM engagement, as detachment causes a rewiring that is triggered by RPS6 dephosphorylation and maintained by juxtacrine tenascin C, which is critical for intraductal colonization of basal-like breast cancer cells in vivo. Intratumor heterogeneity need not stem from partial differentiation and could instead reflect dynamic toggling of cells between expression states that are not cell autonomous. PMID:24658685

Preface of the "Symposium on Mathematical Models and Methods to investigate Heterogeneity in Cell and Cell Population Biology"

NASA Astrophysics Data System (ADS)

Clairambault, Jean

2016-06-01

This session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria.

Multi-second magnetic coherence in a single domain spinor Bose–Einstein condensate

NASA Astrophysics Data System (ADS)

Palacios, Silvana; Coop, Simon; Gomez, Pau; Vanderbruggen, Thomas; Natali Martinez de Escobar, Y.; Jasperse, Martijn; Mitchell, Morgan W.

2018-05-01

We describe a compact, robust and versatile system for studying the macroscopic spin dynamics in a spinor Bose–Einstein condensate. Condensates of {}87{Rb} are produced by all-optical evaporation in a 1560 nm optical dipole trap, using a non-standard loading sequence that employs an ancillary 1529 nm beam for partial compensation of the strong differential light-shift induced by the dipole trap itself. We use near-resonant Faraday rotation probing to non-destructively track the condensate magnetization, and demonstrate few-Larmor-cycle tracking with no detectable degradation of the spin polarization. In the ferromagnetic F = 1 ground state, we observe the spin orientation between atoms in the condensate is preserved, such that they precess all together like one large spin in the presence of a magnetic field. We characterize this dynamics in terms of the single-shot magnetic coherence times {{ \\mathcal T }}1 and {{ \\mathcal T }}2* , and observe them to be of several seconds, limited only by the residence time of the atoms in the trap. At the densities used, this residence is restricted only by one-body losses set by the vacuum conditions.

Toward a computational model of hemostasis

NASA Astrophysics Data System (ADS)

Leiderman, Karin; Danes, Nicholas; Schoeman, Rogier; Neeves, Keith

2017-11-01

Hemostasis is the process by which a blood clot forms to prevent bleeding at a site of injury. The formation time, size and structure of a clot depends on the local hemodynamics and the nature of the injury. Our group has previously developed computational models to study intravascular clot formation, a process confined to the interior of a single vessel. Here we present the first stage of an experimentally-validated, computational model of extravascular clot formation (hemostasis) in which blood through a single vessel initially escapes through a hole in the vessel wall and out a separate injury channel. This stage of the model consists of a system of partial differential equations that describe platelet aggregation and hemodynamics, solved via the finite element method. We also present results from the analogous, in vitro, microfluidic model. In both models, formation of a blood clot occludes the injury channel and stops flow from escaping while blood in the main vessel retains its fluidity. We discuss the different biochemical and hemodynamic effects on clot formation using distinct geometries representing intra- and extravascular injuries.

Improved Sensitivity Relations in State Constrained Optimal Control

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bettiol, Piernicola, E-mail: piernicola.bettiol@univ-brest.fr; Frankowska, Hélène, E-mail: frankowska@math.jussieu.fr; Vinter, Richard B., E-mail: r.vinter@imperial.ac.uk

2015-04-15

Sensitivity relations in optimal control provide an interpretation of the costate trajectory and the Hamiltonian, evaluated along an optimal trajectory, in terms of gradients of the value function. While sensitivity relations are a straightforward consequence of standard transversality conditions for state constraint free optimal control problems formulated in terms of control-dependent differential equations with smooth data, their verification for problems with either pathwise state constraints, nonsmooth data, or for problems where the dynamic constraint takes the form of a differential inclusion, requires careful analysis. In this paper we establish validity of both ‘full’ and ‘partial’ sensitivity relations for an adjointmore » state of the maximum principle, for optimal control problems with pathwise state constraints, where the underlying control system is described by a differential inclusion. The partial sensitivity relation interprets the costate in terms of partial Clarke subgradients of the value function with respect to the state variable, while the full sensitivity relation interprets the couple, comprising the costate and Hamiltonian, as the Clarke subgradient of the value function with respect to both time and state variables. These relations are distinct because, for nonsmooth data, the partial Clarke subdifferential does not coincide with the projection of the (full) Clarke subdifferential on the relevant coordinate space. We show for the first time (even for problems without state constraints) that a costate trajectory can be chosen to satisfy the partial and full sensitivity relations simultaneously. The partial sensitivity relation in this paper is new for state constraint problems, while the full sensitivity relation improves on earlier results in the literature (for optimal control problems formulated in terms of Lipschitz continuous multifunctions), because a less restrictive inward pointing hypothesis is invoked in the proof, and because it is validated for a stronger set of necessary conditions.« less

An Introduction to Computational Physics

NASA Astrophysics Data System (ADS)

Pang, Tao

2010-07-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Parallel Algorithm Solves Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Documentation of spreadsheets for the analysis of aquifer-test and slug-test data

USGS Publications Warehouse

Halford, Keith J.; Kuniansky, Eve L.

2002-01-01

Several spreadsheets have been developed for the analysis of aquifer-test and slug-test data. Each spreadsheet incorporates analytical solution(s) of the partial differential equation for ground-water flow to a well for a specific type of condition or aquifer. The derivations of the analytical solutions were previously published. Thus, this report abbreviates the theoretical discussion, but includes practical information about each method and the important assumptions for the applications of each method. These spreadsheets were written in Microsoft Excel 9.0 (use of trade names does not constitute endorsement by the USGS). Storage properties should not be estimated with many of the spreadsheets because most are for analyzing single-well tests. Estimation of storage properties from single-well tests is generally discouraged because single-well tests are affected by wellbore storage and by well construction. These non-ideal effects frequently cause estimates of storage to be erroneous by orders of magnitude. Additionally, single-well tests are not sensitive to aquifer-storage properties. Single-well tests include all slug tests (Bouwer and Rice Method, Cooper, Bredehoeft, Papadopulos Method, and van der Kamp Method), the Cooper-Jacob straight-line Method, Theis recovery-data analysis, Jacob-Lohman method for flowing wells in a confined aquifer, and the step-drawdown test. Multi-well test spreadsheets included in this report are; Hantush-Jacob Leaky Aquifer Method and Distance-Drawdown Methods. The distance-drawdown method is an equilibrium or steady-state method, thus storage cannot be estimated.

Single-nucleus RNA-seq of differentiating human myoblasts reveals the extent of fate heterogeneity

PubMed Central

Zeng, Weihua; Jiang, Shan; Kong, Xiangduo; El-Ali, Nicole; Ball, Alexander R.; Ma, Christopher I-Hsing; Hashimoto, Naohiro; Yokomori, Kyoko; Mortazavi, Ali

2016-01-01

Myoblasts are precursor skeletal muscle cells that differentiate into fused, multinucleated myotubes. Current single-cell microfluidic methods are not optimized for capturing very large, multinucleated cells such as myotubes. To circumvent the problem, we performed single-nucleus transcriptome analysis. Using immortalized human myoblasts, we performed RNA-seq analysis of single cells (scRNA-seq) and single nuclei (snRNA-seq) and found them comparable, with a distinct enrichment for long non-coding RNAs (lncRNAs) in snRNA-seq. We then compared snRNA-seq of myoblasts before and after differentiation. We observed the presence of mononucleated cells (MNCs) that remained unfused and analyzed separately from multi-nucleated myotubes. We found that while the transcriptome profiles of myoblast and myotube nuclei are relatively homogeneous, MNC nuclei exhibited significant heterogeneity, with the majority of them adopting a distinct mesenchymal state. Primary transcripts for microRNAs (miRNAs) that participate in skeletal muscle differentiation were among the most differentially expressed lncRNAs, which we validated using NanoString. Our study demonstrates that snRNA-seq provides reliable transcriptome quantification for cells that are otherwise not amenable to current single-cell platforms. Our results further indicate that snRNA-seq has unique advantage in capturing nucleus-enriched lncRNAs and miRNA precursors that are useful in mapping and monitoring differential miRNA expression during cellular differentiation. PMID:27566152

Leukemic blast cell colony formation in semisolid culture with erythropoietin: a case report of acute poorly differentiated erythroid leukemia.

PubMed

Tomonaga, M; Jinnai, I; Tagawa, M; Amenomori, T; Nishino, K; Yao, E; Nonaka, H; Kuriyama, K; Yoshida, Y; Matsuo, T

1987-02-01

The bone marrow of a patient with acute undifferentiated leukemia developed unique colonies after a 14-day culture in erythropoietin (EPO)-containing methylcellulose. The colonies consisted of 20 to 200 nonhemoglobinized large blast cells. Cytogenetic analysis of single colonies revealed hypotetraploid karyotypes with several marker chromosomes that were identical to those found in directly sampled bone marrow. The concurrently formed erythroid bursts showed only normal karyotypes. No leukemic colony formation was observed in other culture systems with either colony-stimulating activity (CSA) or phytohemagglutinin-stimulated leukocyte-conditioned medium (PHA-LCM). The leukemic colonies exhibited a complete EPO-dose dependency similar to that of the patient's normal BFU-E. Although cytochemical and immunologic marker studies of the bone marrow cells failed to clarify the cell lineage of the leukemic cells with extraordinarily large cell size, ultrastructural study revealed erythroid differentiation such as siderosome formation in the cytoplasm and ferritin particles in the rhophecytosis invaginations. These findings indicate that the patient had poorly differentiated erythroid leukemia and that some of the clonogenic cells might respond to EPO in vitro. Corresponding to this biological feature, the leukemic cells were markedly decreased in number in response to repeated RBC transfusions, and partial remission was obtained. These observations suggest that erythroid leukemia distinct from erythroleukemia (M6) with a myeloblastic component, can develop as a minor entity of human acute leukemia.

Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry.

PubMed

Tang, Chen; Lu, Wenjing; Chen, Song; Zhang, Zhen; Li, Botao; Wang, Wenping; Han, Lin

2007-10-20

We extend and refine previous work [Appl. Opt. 46, 2907 (2007)]. Combining the coupled nonlinear partial differential equations (PDEs) denoising model with the ordinary differential equations enhancement method, we propose the new denoising and enhancing model for electronic speckle pattern interferometry (ESPI) fringe patterns. Meanwhile, we propose the backpropagation neural networks (BPNN) method to obtain unwrapped phase values based on a skeleton map instead of traditional interpolations. We test the introduced methods on the computer-simulated speckle ESPI fringe patterns and experimentally obtained fringe pattern, respectively. The experimental results show that the coupled nonlinear PDEs denoising model is capable of effectively removing noise, and the unwrapped phase values obtained by the BPNN method are much more accurate than those obtained by the well-known traditional interpolation. In addition, the accuracy of the BPNN method is adjustable by changing the parameters of networks such as the number of neurons.

Numerical study of unsteady Williamson fluid flow and heat transfer in the presence of MHD through a permeable stretching surface

NASA Astrophysics Data System (ADS)

Bibi, Madiha; Khalil-Ur-Rehman; Malik, M. Y.; Tahir, M.

2018-04-01

In the present article, unsteady flow field characteristics of the Williamson fluid model are explored. The nanosized particles are suspended in the flow regime having the interaction of a magnetic field. The fluid flow is induced due to a stretching permeable surface. The flow model is controlled through coupled partial differential equations to the used shooting method for a numerical solution. The obtained partial differential equations are converted into ordinary differential equations as an initial value problem. The shooting method is used to find a numerical solution. The mathematical modeling yields physical parameters, namely the Weissenberg number, the Prandtl number, the unsteadiness parameter, the magnetic parameter, the mass transfer parameter, the Lewis number, the thermophoresis parameter and Brownian parameters. It is found that the Williamson fluid velocity, temperature and nanoparticles concentration are a decreasing function of the unsteadiness parameter.

CANNABINOID AND OPIOID MODULATION OF SOCIAL PLAY BEHAVIOR IN ADOLESCENT RATS: DIFFERENTIAL BEHAVIORAL MECHANISMS

PubMed Central

Trezza, Viviana; Vanderschuren, Louk J.M.J.

2008-01-01

We have recently shown that the pharmacological mechanisms through which cannabinoid and opioid drugs influence social play behavior in adolescent rats can be partially dissociated. Here, we characterize the effects of the direct cannabinoid agonist WIN55,212-2, the indirect cannabinoid agonist URB597 and the opioid agonist morphine on social play at the behavioral level. By treating either one or both partners of the test dyad, we show that these drugs differentially affect play solicitation and play responsiveness. By testing these drugs in animals which were either familiar or unfamiliar to the test cage, we show that environmental factors differentially modulate the effects of cannabinoid and opioid drugs on social play. These results support and extend our previous findings suggesting that, although cannabinoid and opioid systems interact in the modulation of social play behavior in adolescent rats, they do so through partially dissociable behavioral and pharmacological mechanisms. PMID:18434104

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1975-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

On asymptotic behavior and energy distribution for some one-dimensional non-parabolic diffusion problems

NASA Astrophysics Data System (ADS)

Kim, Seonghak; Yan, Baisheng

2018-06-01

We study some non-parabolic diffusion problems in one space dimension, where the diffusion flux exhibits forward and backward nature of the Perona–Malik, Höllig or non-Fourier type. Classical weak solutions to such problems are constructed in a way to capture some expected and unexpected properties, including anomalous asymptotic behaviors and energy dissipation or allocation. Specific properties of solutions will depend on the type of the diffusion flux, but the primary method of our study relies on reformulating diffusion equations involved as an inhomogeneous partial differential inclusion and on constructing solutions from the differential inclusion by a combination of the convex integration and Baire’s category methods. In doing so, we introduce the appropriate notion of subsolutions of the partial differential inclusion and their transition gauge, which plays a pivotal role in dealing with some specific features of the constructed weak solutions.

Miura-type transformations for lattice equations and Lie group actions associated with Darboux-Lax representations

NASA Astrophysics Data System (ADS)

Berkeley, George; Igonin, Sergei

2016-07-01

Miura-type transformations (MTs) are an essential tool in the theory of integrable nonlinear partial differential and difference equations. We present a geometric method to construct MTs for differential-difference (lattice) equations from Darboux-Lax representations (DLRs) of such equations. The method is applicable to parameter-dependent DLRs satisfying certain conditions. We construct MTs and modified lattice equations from invariants of some Lie group actions on manifolds associated with such DLRs. Using this construction, from a given suitable DLR one can obtain many MTs of different orders. The main idea behind this method is closely related to the results of Drinfeld and Sokolov on MTs for the partial differential KdV equation. Considered examples include the Volterra, Narita-Itoh-Bogoyavlensky, Toda, and Adler-Postnikov lattices. Some of the constructed MTs and modified lattice equations seem to be new.

Apolipoprotein E promotes lipid accumulation and differentiation in human adipocytes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lasrich, Dorothee; Bartelt, Alexander; Grewal, Thomas, E-mail: thomas.grewal@sydney.edu.au

Several studies in mice indicate a role for apolipoprotein E (APOE) in lipid accumulation and adipogenic differentiation in adipose tissue. However, little is yet known if APOE functions in a similar manner in human adipocytes. This prompted us to compare lipid loading and expression of adipocyte differentiation markers in APOE-deficient and control adipocytes using the differentiated human mesenchymal stem cell line hMSC-Tert as well as primary human and mouse adipocytes as model systems. Differentiated hMSC-Tert were stably transduced with or without siRNA targeting APOE while murine adipocytes were isolated from wild type and Apoe knockout mice. Human APOE knockdown hMSC-Tertmore » adipocytes accumulated markedly less triglycerides compared to control cells. This correlated with strongly decreased gene expression levels of adipocyte markers such as adiponectin (ADIPOQ) and fatty acid binding protein 4 (FABP4) as well as the key transcription factor driving adipocyte differentiation, peroxisome proliferator activator receptor gamma (PPARG), in particular the PPARG2 isoform. Similarly, differentiation of murine Apoe-deficient adipocytes was characterized by reduced gene expression of Adipoq, Fabp4 and Pparg. Interestingly, incubation of APOE-deficient hMSC-Tert adipocytes with conditioned media from APOE3-overexpressing adipocytes or APOE-containing Very Low Density Lipoprotein (VLDL) partially restored triglyceride accumulation, but were unable to induce adipocyte differentiation, as judged by expression of adipocyte markers. Taken together, depletion of endogenous APOE in human adipocytes severely impairs lipid accumulation, which is associated with an inability to initiate differentiation. - Highlights: • Immortalized human mesenchymal stem cells were used to study adipocyte development. • Knockdown of endogenous APOE lead to impaired lipid accumulation and adipogenesis. • APOE supplementation partially restored lipid accumulation but not differentiation. • Findings suggest dual functions of APOE for lipid accumulation and differentiation.« less

Solving vertical and horizontal well hydraulics problems analytically in Cartesian coordinates with vertical and horizontal anisotropies

NASA Astrophysics Data System (ADS)

Batu, Vedat

2012-01-01

SummaryA new generalized three-dimensional analytical solution is developed for a partially-penetrating vertical rectangular parallelepiped well screen in a confined aquifer by solving the three-dimensional transient ground water flow differential equation in x- y- z Cartesian coordinates system for drawdown by taking into account the three principal hydraulic conductivities ( Kx, Ky, and Kz) along the x- y- z coordinate directions. The fully penetrating screen case becomes equivalent to the single vertical fracture case of Gringarten and Ramey (1973). It is shown that the new solution and Gringarten and Ramey solution (1973) match very well. Similarly, it is shown that this new solution for a horizontally tiny fully penetrating parallelepiped rectangular parallelepiped screen case match very well with Theis (1935) solution. Moreover, it is also shown that the horizontally tiny partially-penetrating parallelepiped rectangular well screen case of this new solution match very well with Hantush (1964) solution. This new analytical solution can also cover a partially-penetrating horizontal well by representing its screen interval with vertically tiny rectangular parallelepiped. Also the solution takes into account both the vertical anisotropy ( azx = Kz/ Kx) as well as the horizontal anisotropy ( ayx = Ky/ Kx) and has potential application areas to analyze pumping test drawdown data from partially-penetrating vertical and horizontal wells by representing them as tiny rectangular parallelepiped as well as line sources. The solution has also potential application areas for a partially-penetrating parallelepiped rectangular vertical fracture. With this new solution, the horizontal anisotropy ( ayx = Ky/ Kx) in addition to the vertical anisotropy ( azx = Kz/ Kx) can also be determined using observed drawdown data. Most importantly, with this solution, to the knowledge of the author, it has been shown the first time in the literature that some well-known well hydraulics problems can also be solved in Cartesian coordinates with some additional advantages other than the conventional cylindrical coordinates method.

Biomechanical comparison of double-row versus transtendon single-row suture anchor technique for repair of the grade III partial articular-sided rotator cuff tears.

PubMed

Zhang, Chun-Gang; Zhao, De-Wei; Wang, Wei-Ming; Ren, Ming-Fa; Li, Rui-Xin; Yang, Sheng; Liu, Yu-Peng

2010-11-01

For partial-thickness tears of the rotator cuff, double-row fixation and transtendon single-row fixation restore insertion site anatomy, with excellent results. We compared the biomechanical properties of double-row and transtendon single-row suture anchor techniques for repair of grade III partial articular-sided rotator cuff tears. In 10 matched pairs of fresh-frozen sheep shoulders, the infraspinatus tendon from 1 shoulder was repaired with a double-row suture anchor technique. This comprised placement of 2 medial anchors with horizontal mattress sutures at an angle of ≤ 45° into the medial margin of the infraspinatus footprint, just lateral to the articular surface, and 2 lateral anchors with horizontal mattress sutures. Standardized, 50% partial, articular-sided infraspinatus lesions were created in the contralateral shoulder. The infraspinatus tendon from the contralateral shoulder was repaired using two anchors with transtendon single-row mattress sutures. Each specimen underwent cyclic loading from 10 to 100 N for 50 cycles, followed by tensile testing to failure. Gap formation and strain over the footprint area were measured using a motion capture system; stiffness and failure load were determined from testing data. Gap formation for the transtendon single-row repair was significantly smaller (P < 0.05) when compared with the double-row repair for the first cycle ((1.74 ± 0.38) mm vs. (2.86 ± 0.46) mm, respectively) and the last cycle ((3.77 ± 0.45) mm vs. (5.89 ± 0.61) mm, respectively). The strain over the footprint area for the transtendon single-row repair was significantly smaller (P < 0.05) when compared with the double-row repair. Also, it had a higher mean ultimate tensile load and stiffness. For grade III partial articular-sided rotator cuff tears, transtendon single-row fixation exhibited superior biomechanical properties when compared with double-row fixation.

Structure parameters in rotating Couette-Poiseuille channel flow

NASA Technical Reports Server (NTRS)

Knightly, George H.; Sather, D.

1986-01-01

It is well-known that a number of steady state problems in fluid mechanics involving systems of nonlinear partial differential equations can be reduced to the problem of solving a single operator equation of the form: v + lambda Av + lambda B(v) = 0, v is the summation of H, lambda is the summation of one-dimensional Euclid space, where H is an appropriate (real or complex) Hilbert space. Here lambda is a typical load parameter, e.g., the Reynolds number, A is a linear operator, and B is a quadratic operator generated by a bilinear form. In this setting many bifurcation and stability results for problems were obtained. A rotating Couette-Poiseuille channel flow was studied, and it showed that, in general, the superposition of a Poiseuille flow on a rotating Couette channel flow is destabilizing.

Fluctuating hydrodynamics of multispecies nonreactive mixtures

DOE PAGES

Balakrishnan, Kaushik; Garcia, Alejandro L.; Donev, Aleksandar; ...

2014-01-22

In this study we discuss the formulation of the fluctuating Navier-Stokes equations for multispecies, nonreactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of nonequilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well asmore » reverse diffusion in a ternary mixture. Finally, good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multispecies fluids.« less

Scale Space for Camera Invariant Features.

PubMed

Puig, Luis; Guerrero, José J; Daniilidis, Kostas

2014-09-01

In this paper we propose a new approach to compute the scale space of any central projection system, such as catadioptric, fisheye or conventional cameras. Since these systems can be explained using a unified model, the single parameter that defines each type of system is used to automatically compute the corresponding Riemannian metric. This metric, is combined with the partial differential equations framework on manifolds, allows us to compute the Laplace-Beltrami (LB) operator, enabling the computation of the scale space of any central projection system. Scale space is essential for the intrinsic scale selection and neighborhood description in features like SIFT. We perform experiments with synthetic and real images to validate the generalization of our approach to any central projection system. We compare our approach with the best-existing methods showing competitive results in all type of cameras: catadioptric, fisheye, and perspective.

Dual-modality imaging

NASA Astrophysics Data System (ADS)

Hasegawa, Bruce; Tang, H. Roger; Da Silva, Angela J.; Wong, Kenneth H.; Iwata, Koji; Wu, Max C.

2001-09-01

In comparison to conventional medical imaging techniques, dual-modality imaging offers the advantage of correlating anatomical information from X-ray computed tomography (CT) with functional measurements from single-photon emission computed tomography (SPECT) or with positron emission tomography (PET). The combined X-ray/radionuclide images from dual-modality imaging can help the clinician to differentiate disease from normal uptake of radiopharmaceuticals, and to improve diagnosis and staging of disease. In addition, phantom and animal studies have demonstrated that a priori structural information from CT can be used to improve quantification of tissue uptake and organ function by correcting the radionuclide data for errors due to photon attenuation, partial volume effects, scatter radiation, and other physical effects. Dual-modality imaging therefore is emerging as a method of improving the visual quality and the quantitative accuracy of radionuclide imaging for diagnosis of patients with cancer and heart disease.

Modelling the balance between quiescence and cell death in normal and tumour cell populations.

PubMed

Spinelli, Lorenzo; Torricelli, Alessandro; Ubezio, Paolo; Basse, Britta

2006-08-01

When considering either human adult tissues (in vivo) or cell cultures (in vitro), cell number is regulated by the relationship between quiescent cells, proliferating cells, cell death and other controls of cell cycle duration. By formulating a mathematical description we see that even small alterations of this relationship may cause a non-growing population to start growing with doubling times characteristic of human tumours. Our model consists of two age structured partial differential equations for the proliferating and quiescent cell compartments. Model parameters are death rates from and transition rates between these compartments. The partial differential equations can be solved for the steady-age distributions, giving the distribution of the cells through the cell cycle, dependent on specific model parameter values. Appropriate formulas can then be derived for various population characteristic quantities such as labelling index, proliferation fraction, doubling time and potential doubling time of the cell population. Such characteristic quantities can be estimated experimentally, although with decreasing precision from in vitro, to in vivo experimental systems and to the clinic. The model can be used to investigate the effects of a single alteration of either quiescence or cell death control on the growth of the whole population and the non-trivial dependence of the doubling time and other observable quantities on particular underlying cell cycle scenarios of death and quiescence. The model indicates that tumour evolution in vivo is a sequence of steady-states, each characterised by particular death and quiescence rate functions. We suggest that a key passage of carcinogenesis is a loss of the communication between quiescence, death and cell cycle machineries, causing a defect in their precise, cell cycle dependent relationship.

Paleomagnetism of a primitive achondrite parent body: The acapulcoite-lodranites

NASA Astrophysics Data System (ADS)

Schnepf, N. R.; Weiss, B. P.; Andrade Lima, E.; Fu, R. R.; Uehara, M.; Gattacceca, J.; Wang, H.; Suavet, C. R.

2014-12-01

Primitive achondrites are a recently recognized meteorite grouping with textures and compositions intermediate between unmelted meteorites (chondrites) and igneous meteorites (achondrites). Their existence demonstrates prima facie that some planetesimals only experienced partial rather than complete melting. We present the first paleomagnetic measurements of acapulcoite-lodranite meteorites to determine the existence and intensity of ancient magnetic fields on their parent body. Our paleomagnetic study tests the hypothesis that their parent body had an advecting metallic core, with the goal of providing one of the first geophysical constraints on its large-scale structure and the extent of interior differentiation. In particular, by analyzing samples whose petrologic textures require an origin on a partially differentiated body, we will be able to critically test a recent proposal that some achondrites and chondrite groups could have originated on a single body (Weiss and Elkins-Tanton 2013). We analyzed samples of the meteorites Acapulco and Lodran. Like other acapulcoites and lodranites, these meteorites are granular rocks containing large (~0.1-0.3 mm) kamacite and taenite grains along with similarly sized silicate crystals. Many silicate grains contain numerous fine (1-10 μm) FeNi metal inclusions. Our compositional measurements and rock magnetic data suggest that tetrataenite is rare or absent. Bulk paleomagnetic measurements were done on four mutually oriented bulk samples of Acapulco and one bulk sample of Lodran. Alternating field (AF) demagnetization revealed that the magnetization of the bulk samples is highly unstable, likely due to the large (~0.1-0.3 mm) interstitial kamacite grains throughout the samples. To overcome this challenge, we are analyzing individual ~0.2 mm mutually oriented silicate grains extracted using a wire saw micromill. Preliminary SQUID microscopy measurements of a Lodran silicate grain suggest magnetization stable to AF levels of at least 25-40 mT.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

Negative differential conductance and super-Poissonian shot noise in single-molecule magnet junctions

PubMed Central

Xue, Hai-Bin; Liang, Jiu-Qing; Liu, Wu-Ming

2015-01-01

Molecular spintroinic device based on a single-molecule magnet is one of the ultimate goals of semiconductor nanofabrication technologies. It is thus necessary to understand the electron transport properties of a single-molecule magnet junction. Here we study the negative differential conductance and super-Poissonian shot noise properties of electron transport through a single-molecule magnet weakly coupled to two electrodes with either one or both of them being ferromagnetic. We predict that the negative differential conductance and super-Poissonian shot noise, which can be tuned by a gate voltage, depend sensitively on the spin polarization of the source and drain electrodes. In particular, the shot noise in the negative differential conductance region can be enhanced or decreased originating from the different formation mechanisms of negative differential conductance. The effective competition between fast and slow transport channels is responsible for the observed negative differential conductance and super-Poissonian shot noise. In addition, we further discuss the skewness and kurtosis properties of transport current in the super-Poissonian shot noise regions. Our findings suggest a tunable negative differential conductance molecular device, and the predicted properties of high-order current cumulants are very interesting for a better understanding of electron transport through single-molecule magnet junctions. PMID:25736094

Negative differential conductance and super-Poissonian shot noise in single-molecule magnet junctions.

PubMed

Xue, Hai-Bin; Liang, Jiu-Qing; Liu, Wu-Ming

2015-03-04

Molecular spintroinic device based on a single-molecule magnet is one of the ultimate goals of semiconductor nanofabrication technologies. It is thus necessary to understand the electron transport properties of a single-molecule magnet junction. Here we study the negative differential conductance and super-Poissonian shot noise properties of electron transport through a single-molecule magnet weakly coupled to two electrodes with either one or both of them being ferromagnetic. We predict that the negative differential conductance and super-Poissonian shot noise, which can be tuned by a gate voltage, depend sensitively on the spin polarization of the source and drain electrodes. In particular, the shot noise in the negative differential conductance region can be enhanced or decreased originating from the different formation mechanisms of negative differential conductance. The effective competition between fast and slow transport channels is responsible for the observed negative differential conductance and super-Poissonian shot noise. In addition, we further discuss the skewness and kurtosis properties of transport current in the super-Poissonian shot noise regions. Our findings suggest a tunable negative differential conductance molecular device, and the predicted properties of high-order current cumulants are very interesting for a better understanding of electron transport through single-molecule magnet junctions.

Description of three species of Isorchis (Digenea: Atractotrematidae) from Australia.

PubMed

Andres, Michael J; Pulis, Eric E; Overstreet, Robin M

2016-09-01

Three species of Isorchis Durio and Manter, 1969 are described from Australian waters. Isorchis megas sp. nov. is described from the spotbanded scat, Selenotoca multifasciata (Richardson), off Western Australia (WA) and Northern Territory (NT); Isorchis currani sp. nov. is described from S. multifasciata off NT; and Isorchis anomalus sp. nov. is described from the milkfish, Chanos chanos Forsskål, off WA. Isorchis megas sp. nov. can be differentiated from the other species of Isorchis by possessing a single, large egg that is greater than 20% of the body length; having a shorter body (the largest specimen is less than 500 μm); and utilizing a scatophagid rather than a chanid host. Isorchis currani sp. nov. can be differentiated from species of Isorchis other than I. megas sp. nov. by utilizing a scatophagid rather than a chanid host; it is differentiated from I. megas sp. nov. in having eggs that are 11-15% of the body length. Isorchis anomalus sp. nov. can be differentiated from all other species of Isorchis in possessing an irregular shaped genital pore rather than one that is circular to oblong. A Bayesian inference analysis of partial 28S rDNA sequences of the three new species of Isorchis and 30 other haploporoids revealed 1) the monophyly of the Atractotrematidae Yamaguti, 1939, 2) the two species of Isorchis infecting S. multifasciata were each other's closest relative, and 3) that Isorchis was most closely related to Pseudomegasolena Machida and Komiya, 1976 rather than Atractotrema Goto and Ozaki, 1929 although sequence data are not yet available for a member of Pseudisorchis Ahmad, 1985.

Real-time optical laboratory solution of parabolic differential equations

NASA Technical Reports Server (NTRS)

Casasent, David; Jackson, James

1988-01-01

An optical laboratory matrix-vector processor is used to solve parabolic differential equations (the transient diffusion equation with two space variables and time) by an explicit algorithm. This includes optical matrix-vector nonbase-2 encoded laboratory data, the combination of nonbase-2 and frequency-multiplexed data on such processors, a high-accuracy optical laboratory solution of a partial differential equation, new data partitioning techniques, and a discussion of a multiprocessor optical matrix-vector architecture.

Symmetry groups of integro-differential equations for linear thermoviscoelastic materials with memory

NASA Astrophysics Data System (ADS)

Zhou, L.-Q.; Meleshko, S. V.

2017-07-01

The group analysis method is applied to a system of integro-differential equations corresponding to a linear thermoviscoelastic model. A recently developed approach for calculating the symmetry groups of such equations is used. The general solution of the determining equations for the system is obtained. Using subalgebras of the admitted Lie algebra, two classes of partially invariant solutions of the considered system of integro-differential equations are studied.

FAST TRACK COMMUNICATION Quasi self-adjoint nonlinear wave equations

NASA Astrophysics Data System (ADS)

Ibragimov, N. H.; Torrisi, M.; Tracinà, R.

2010-11-01

In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation.

Spatial capture–recapture with partial identity: An application to camera traps

USGS Publications Warehouse

Augustine, Ben C.; Royle, J. Andrew; Kelly, Marcella J.; Satter, Christopher B.; Alonso, Robert S.; Boydston, Erin E.; Crooks, Kevin R.

2018-01-01

Camera trapping surveys frequently capture individuals whose identity is only known from a single flank. The most widely used methods for incorporating these partial identity individuals into density analyses discard some of the partial identity capture histories, reducing precision, and, while not previously recognized, introducing bias. Here, we present the spatial partial identity model (SPIM), which uses the spatial location where partial identity samples are captured to probabilistically resolve their complete identities, allowing all partial identity samples to be used in the analysis. We show that the SPIM outperforms other analytical alternatives. We then apply the SPIM to an ocelot data set collected on a trapping array with double-camera stations and a bobcat data set collected on a trapping array with single-camera stations. The SPIM improves inference in both cases and, in the ocelot example, individual sex is determined from photographs used to further resolve partial identities—one of which is resolved to near certainty. The SPIM opens the door for the investigation of trapping designs that deviate from the standard two camera design, the combination of other data types between which identities cannot be deterministically linked, and can be extended to the problem of partial genotypes.

Parallel Optimization of 3D Cardiac Electrophysiological Model Using GPU

PubMed Central

Xia, Yong; Zhang, Henggui

2015-01-01

Large-scale 3D virtual heart model simulations are highly demanding in computational resources. This imposes a big challenge to the traditional computation resources based on CPU environment, which already cannot meet the requirement of the whole computation demands or are not easily available due to expensive costs. GPU as a parallel computing environment therefore provides an alternative to solve the large-scale computational problems of whole heart modeling. In this study, using a 3D sheep atrial model as a test bed, we developed a GPU-based simulation algorithm to simulate the conduction of electrical excitation waves in the 3D atria. In the GPU algorithm, a multicellular tissue model was split into two components: one is the single cell model (ordinary differential equation) and the other is the diffusion term of the monodomain model (partial differential equation). Such a decoupling enabled realization of the GPU parallel algorithm. Furthermore, several optimization strategies were proposed based on the features of the virtual heart model, which enabled a 200-fold speedup as compared to a CPU implementation. In conclusion, an optimized GPU algorithm has been developed that provides an economic and powerful platform for 3D whole heart simulations. PMID:26581957

Parallel Optimization of 3D Cardiac Electrophysiological Model Using GPU.

PubMed

Xia, Yong; Wang, Kuanquan; Zhang, Henggui

2015-01-01

Large-scale 3D virtual heart model simulations are highly demanding in computational resources. This imposes a big challenge to the traditional computation resources based on CPU environment, which already cannot meet the requirement of the whole computation demands or are not easily available due to expensive costs. GPU as a parallel computing environment therefore provides an alternative to solve the large-scale computational problems of whole heart modeling. In this study, using a 3D sheep atrial model as a test bed, we developed a GPU-based simulation algorithm to simulate the conduction of electrical excitation waves in the 3D atria. In the GPU algorithm, a multicellular tissue model was split into two components: one is the single cell model (ordinary differential equation) and the other is the diffusion term of the monodomain model (partial differential equation). Such a decoupling enabled realization of the GPU parallel algorithm. Furthermore, several optimization strategies were proposed based on the features of the virtual heart model, which enabled a 200-fold speedup as compared to a CPU implementation. In conclusion, an optimized GPU algorithm has been developed that provides an economic and powerful platform for 3D whole heart simulations.

Stimulation of cAMP signalling allows isolation of clonal pancreatic precursor cells from adult mouse pancreas.

PubMed

Yamamoto, T; Yamato, E; Taniguchi, H; Shimoda, M; Tashiro, F; Hosoi, M; Sato, T; Fujii, S; Miyazaki, J-I

2006-10-01

Duct cells of the pancreas are thought to include latent progenitors of islet endocrine cells that can be induced to differentiate by appropriate morphogens. Here we developed a method for isolating pancreatic ductal epithelial cells from adult mice that overcomes the shortcomings of previous methods. Pancreatic ductal cells were grown in serum-free DMEM/F12 medium in the presence of cholera toxin or 8-bromo-cyclic adenosine monophosphate, which is known to be an intracellular cAMP generator. Single cell cloning was performed by limiting dilution in serum-free medium. The isolated clonal cells expressed high levels of cytokeratin and Ipf1 (formerly known as Pdx-1). Adenovirus-mediated expression of ngn3 (also known as Neurog3) and Ptf1a in these cells induced expression of insulin and somatostatin, and of carboxypeptidase A, respectively. Furthermore, albumin production was induced by dexamethasone or by long-term culture in serum-containing medium. Stimulation of the cAMP-dependent signalling allowed us to isolate clonal pancreatic ductal cells from adult mice. These cells are able to partially differentiate into endocrine cells, exocrine cells and hepatocyte-like cells and are therefore considered to have the characteristics of endodermal progenitor cells.

Longitudinal differentiation among pelagic populations in a planktic foraminifer

PubMed Central

Ujiié, Yurika; Asami, Takahiro; de Garidel-Thoron, Thibault; Liu, Hui; Ishitani, Yoshiyuki; de Vargas, Colomban

2012-01-01

Evolutionary processes in marine plankton have been assumed to be dependent on the oceanic circulation system, which transports plankton between populations in marine surface waters. Gene flow facilitated by oceanic currents along longitudinal gradients may efficiently impede genetic differentiation of pelagic populations in the absence of confounding marine environmental effects. However, how responsible oceanic currents are for the geographic distribution and dispersal of plankton is poorly understood. We examined the phylogeography of the planktic foraminifer Pulleniatina obliquiloculata in the Indo-Pacific Warm Pool (IPWP) by using partial small subunit ribosomal DNA (SSU rDNA) sequences. We found longitudinal clines in the frequencies of three distinct genetic types in the IPWP area. These frequencies were correlated with environmental factors that are characteristic of three water masses in the IPWP. Noteworthy, populations inhabiting longitudinally distant water masses at the Pacific and Indian sides of the IPWP were genetically different, despite transportation of individuals via oceanic currents. These results demonstrate that populations of pelagic plankton have diverged genetically among different water masses within a single climate zone. Changes of the oceanic circulation system could have impacted the geographic patterns of dispersal and divergence of pelagic plankton. PMID:22957176

Genome-wide Association Study Identifies Peanut Allergy-Specific Loci and Evidence of Epigenetic Mediation in U.S. Children

PubMed Central

Hong, Xiumei; Hao, Ke; Ladd-Acosta, Christine; Hansen, Kasper D; Tsai, Hui-Ju; Liu, Xin; Xu, Xin; Thornton, Timothy A.; Caruso, Deanna; Keet, Corinne A; Sun, Yifei; Wang, Guoying; Luo, Wei; Kumar, Rajesh; Fuleihan, Ramsay; Singh, Anne Marie; Kim, Jennifer S; Story, Rachel E; Gupta, Ruchi S; Gao, Peisong; Chen, Zhu; Walker, Sheila O.; Bartell, Tami R; Beaty, Terri H; Fallin, M Daniele; Schleimer, Robert; Holt, Patrick G; Nadeau, Kari Christine; Wood, Robert A; Pongracic, Jacqueline A; Weeks, Daniel E; Wang, Xiaobin

2015-01-01

Food allergy (FA) affects 2–10% of U.S. children and is a growing clinical and public health problem. Here we conduct the first genome-wide association study of well-defined FA, including specific subtypes (peanut, milk, and egg) in 2,759 U.S. participants (1,315 children; 1,444 parents) from the Chicago Food Allergy Study; and identify peanut allergy (PA)-specific loci in the HLA-DR and -DQ gene region at 6p21.32, tagged by rs7192 (p=5.5×10−8) and rs9275596 (p=6.8×10−10), in 2,197 participants of European ancestry. We replicate these associations in an independent sample of European ancestry. These associations are further supported by meta-analyses across the discovery and replication samples. Both single-nucleotide polymorphisms (SNPs) are associated with differential DNA methylation levels at multiple CpG sites (p<5×10−8); and differential DNA methylation of the HLA-DQB1 and HLA-DRB1 genes partially mediate the identified SNP-PA associations. This study suggests that the HLA-DR and -DQ gene region likely poses significant genetic risk for PA. PMID:25710614

Peridynamic Multiscale Finite Element Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costa, Timothy; Bond, Stephen D.; Littlewood, David John

The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic andmore » local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the art of local models with the flexibility and accuracy of the nonlocal peridynamic model. In the mixed locality method this coupling occurs across scales, so that the nonlocal model can be used to communicate material heterogeneity at scales inappropriate to local partial differential equation models. Additionally, the computational burden of the weak form of the peridynamic model is reduced dramatically by only requiring that the model be solved on local patches of the simulation domain which may be computed in parallel, taking advantage of the heterogeneous nature of next generation computing platforms. Addition- ally, we present a novel Galerkin framework, the 'Ambulant Galerkin Method', which represents a first step towards a unified mathematical analysis of local and nonlocal multiscale finite element methods, and whose future extension will allow the analysis of multiscale finite element methods that mix models across scales under certain assumptions of the consistency of those models.« less

An Introduction to Computational Physics - 2nd Edition

NASA Astrophysics Data System (ADS)

Pang, Tao

2006-01-01

Preface to first edition; Preface; Acknowledgements; 1. Introduction; 2. Approximation of a function; 3. Numerical calculus; 4. Ordinary differential equations; 5. Numerical methods for matrices; 6. Spectral analysis; 7. Partial differential equations; 8. Molecular dynamics simulations; 9. Modeling continuous systems; 10. Monte Carlo simulations; 11. Genetic algorithm and programming; 12. Numerical renormalization; References; Index.

Intuitive Understanding of Solutions of Partially Differential Equations

ERIC Educational Resources Information Center

Kobayashi, Y.

2008-01-01

This article uses diagrams that help the observer see how solutions of the wave equation and heat conduction equation are obtained. The analytical approach cannot necessarily show the mechanisms of the key to the solution without transforming the differential equation into a more convenient form by separation of variables. The visual clues based…

Partial wave analysis for folded differential cross sections

NASA Astrophysics Data System (ADS)

Machacek, J. R.; McEachran, R. P.

2018-03-01

The value of modified effective range theory (MERT) and the connection between differential cross sections and phase shifts in low-energy electron scattering has long been recognized. Recent experimental techniques involving magnetically confined beams have introduced the concept of folded differential cross sections (FDCS) where the forward (θ ≤ π/2) and backward scattered (θ ≥ π/2) projectiles are unresolved, that is the value measured at the angle θ is the sum of the signal for particles scattered into the angles θ and π - θ. We have developed an alternative approach to MERT in order to analyse low-energy folded differential cross sections for positrons and electrons. This results in a simplified expression for the FDCS when it is expressed in terms of partial waves and thereby enables one to extract the first few phase shifts from a fit to an experimental FDCS at low energies. Thus, this method predicts forward and backward angle scattering (0 to π) using only experimental FDCS data and can be used to determine the total elastic cross section solely from experimental results at low-energy, which are limited in angular range.

Tumor necrosis factor-alpha antagonists: differential clinical effects by different biotechnological molecules.

PubMed

Licastro, F; Chiappelli, M; Ianni, M; Porcellini, E

2009-01-01

Inhibitors of tumor necrosis factor-alpha have deeply changed the therapy of several inflammatory human diseases. For instance, clinical management of rheumatoid arthritis, psoriatic arthritis and ankylosing spondylitis have profoundly benefited after the introduction of new therapeutic tools, such as antagonist of TNF-alpha molecule. These drugs include etanercept, a soluble TNF-alpha receptor antagonist, three anti-TNF-alpha antibodies, adalimumab, infliximab, golimumab and certolizumab a humanized Fab fragment combined with polyethylene glycol. These compounds efficiently inhibit several TNF-alpha biological-mediated effects, however, they have also shown differential clinical efficacy in several trials from different autoimmune diseases. It is of clinical relevance that non-responders to one of these drugs often positively responded to another. Different mechanisms of action and diversity in pharmacokinetics of these three compounds may partially explain different clinical effects. However, partially diverse pathogenetic mechanisms in different diseases also contribute to differential therapeutic responses. Therefore, these apparently homogeneous agents can not be considered equivalent in their clinically efficacy. Differential therapeutic actions of these drugs may be advantageously used in clinical practice and further improve the great potential of individual TNF-alpha inhibitors.

Closed-form expressions for state-to-state charge-transfer differential cross sections in a modified Faddeev three-body approach

NASA Astrophysics Data System (ADS)

Adivi, E. Ghanbari; Brunger, M. J.; Bolorizadeh, M. A.; Campbell, L.

2007-02-01

The second-order Faddeev-Watson-Lovelace approximation in a modified form is applied to charge transfer from hydrogenlike target atoms by a fully stripped energetic projectile ion. The state-to-state, nlm→n'l'm' , partial transition amplitudes are calculated analytically. The method is specifically applied to the collision of protons with hydrogen atoms, where differential cross sections of different transitions are calculated for incident energies of 2.8 and 5.0MeV . It is shown that the Thomas peak is present in all transition cross sections. The partial cross sections are then summed and compared with the available forward-angle experimental data, showing good agreement.

Analytical Derivation of Power Laws in Firm Size Variables from Gibrat's Law and Quasi-inversion Symmetry: A Geomorphological Approach

NASA Astrophysics Data System (ADS)

Ishikawa, Atushi; Fujimoto, Shouji; Mizuno, Takayuki; Watanabe, Tsutomu

2014-03-01

We start from Gibrat's law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L. We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

PubMed

Shah, A A; Xing, W W; Triantafyllidis, V

2017-04-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

PubMed Central

Xing, W. W.; Triantafyllidis, V.

2017-01-01

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach. PMID:28484327

Separation of Variables and Superintegrability; The symmetry of solvable systems

NASA Astrophysics Data System (ADS)

Kalnins, Ernest G.; Kress, Jonathan M.; Miller, Willard, Jr.

2018-06-01

Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtaining explicit solutions of the partial differential equations of mathematical physics. The purpose of this book is to give an up-to-date presentation of the theory of separation of variables and its relation to superintegrability. Collating and presenting it in a unified, updated and a more accessible manner, the results scattered in the literature that the authors have prepared is an invaluable resource for mathematicians and mathematical physicists in particular, as well as science, engineering, geological and biological researchers interested in explicit solutions.

Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion

NASA Astrophysics Data System (ADS)

Zhang, Wei-Guo; Li, Zhe; Liu, Yong-Jun

2018-01-01

In this paper, we study the pricing problem of the continuously monitored fixed and floating strike geometric Asian power options in a mixed fractional Brownian motion environment. First, we derive both closed-form solutions and mixed fractional partial differential equations for fixed and floating strike geometric Asian power options based on delta-hedging strategy and partial differential equation method. Second, we present the lower and upper bounds of the prices of fixed and floating strike geometric Asian power options under the assumption that both risk-free interest rate and volatility are interval numbers. Finally, numerical studies are performed to illustrate the performance of our proposed pricing model.

Second-order oriented partial-differential equations for denoising in electronic-speckle-pattern interferometry fringes.

PubMed

Tang, Chen; Han, Lin; Ren, Hongwei; Zhou, Dongjian; Chang, Yiming; Wang, Xiaohang; Cui, Xiaolong

2008-10-01

We derive the second-order oriented partial-differential equations (PDEs) for denoising in electronic-speckle-pattern interferometry fringe patterns from two points of view. The first is based on variational methods, and the second is based on controlling diffusion direction. Our oriented PDE models make the diffusion along only the fringe orientation. The main advantage of our filtering method, based on oriented PDE models, is that it is very easy to implement compared with the published filtering methods along the fringe orientation. We demonstrate the performance of our oriented PDE models via application to two computer-simulated and experimentally obtained speckle fringes and compare with related PDE models.

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Spectral methods in time for a class of parabolic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ierley, G.; Spencer, B.; Worthing, R.

1992-09-01

In this paper, we introduce a fully spectral solution for the partial differential equation u[sub t] + uu[sub x] + vu[sub xx] + [mu]u[sub xxx] + [lambda]u[sub xxxx] = O. For periodic boundary conditions in space, the use of a Fourier expansion in x admits of a particularly efficient algorithm with respect to expansion of the time dependence in a Chebyshev series. Boundary conditions other than periodic may still be treated with reasonable, though lesser, efficiency. for all cases, very high accuracy is attainable at moderate computational cost relative to the expense of variable order finite difference methods in time.more » 14 refs., 9 figs.« less

Differential formulation of the gyrokinetic Landau operator

DOE PAGES

Hirvijoki, Eero; Brizard, Alain J.; Pfefferlé, David

2017-01-05

Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.

Complex partial status epilepticus: a recurrent problem.

PubMed Central

Cockerell, O C; Walker, M C; Sander, J W; Shorvon, S D

1994-01-01

Twenty patients with complex partial status epilepticus were identified retrospectively from a specialist neurology hospital. Seventeen patients experienced recurrent episodes of complex partial status epilepticus, often occurring at regular intervals, usually over many years, and while being treated with effective anti-epileptic drugs. No unifying cause for the recurrences, and no common epilepsy aetiologies, were identified. In spite of the frequency of recurrence and length of history, none of the patients showed any marked evidence of cognitive or neurological deterioration. Complex partial status epilepticus is more common than is generally recognised, should be differentiated from other forms of non-convulsive status, and is often difficult to treat. PMID:8021671

Growth and structural characterization of single crystals of the magnetic superconductor Ru1-xSr2-yGd1+yCu2+xO8-δ (RuGd-1212) obtained by the partial melting technique

NASA Astrophysics Data System (ADS)

Yamaki, K.; Bamba, Y.; Mochiku, T.; Funahashi, S.; Matsushita, Y.; Irie, A.

2018-05-01

In this study, cubic single crystals of the magnetic superconductor Ru1-xSr2-yGd1+yCu2+xO8-δ (RuGd-1212) with typical dimensions of 100-150 μm in length were grown by the partial melting technique. Multiple 00l reflections were first observed by XRD measurements of the bulk RuGd-1212 single crystals. The resistivity of the obtained crystals was roughly estimated to be ∼24-80 mΩ cm and no superconducting transition was observed down to 4.2 K. From the XRD measurements and refinement of the crystal structure, it was apparent that the Ru and Sr sites of the single-crystal RuGd-1212 were partially substituted by Cu and Gd, respectively. Oxygen defects were found to be minor (δ ≈ 0.1). The lattice parameters a and c of the single crystals were found to be larger and smaller, respectively, than those of a polycrystalline sample.

Selective accumulation of langerhans-type dendritic cells in small airways of patients with COPD

PubMed Central

2010-01-01

Background Dendritic cells (DC) linking innate and adaptive immune responses are present in human lungs, but the characterization of different subsets and their role in COPD pathogenesis remain to be elucidated. The aim of this study is to characterize and quantify pulmonary myeloid DC subsets in small airways of current and ex-smokers with or without COPD. Methods Myeloid DC were characterized using flowcytometry on single cell suspensions of digested human lung tissue. Immunohistochemical staining for langerin, BDCA-1, CD1a and DC-SIGN was performed on surgical resection specimens from 85 patients. Expression of factors inducing Langerhans-type DC (LDC) differentiation was evaluated by RT-PCR on total lung RNA. Results Two segregated subsets of tissue resident pulmonary myeloid DC were identified in single cell suspensions by flowcytometry: the langerin+ LDC and the DC-SIGN+ interstitial-type DC (intDC). LDC partially expressed the markers CD1a and BDCA-1, which are also present on their known blood precursors. In contrast, intDC did not express langerin, CD1a or BDCA-1, but were more closely related to monocytes. Quantification of DC in the small airways by immunohistochemistry revealed a higher number of LDC in current smokers without COPD and in COPD patients compared to never smokers and ex-smokers without COPD. Importantly, there was no difference in the number of LDC between current and ex-smoking COPD patients. In contrast, the number of intDC did not differ between study groups. Interestingly, the number of BDCA-1+ DC was significantly lower in COPD patients compared to never smokers and further decreased with the severity of the disease. In addition, the accumulation of LDC in the small airways significantly correlated with the expression of the LDC inducing differentiation factor activin-A. Conclusions Myeloid DC differentiation is altered in small airways of current smokers and COPD patients resulting in a selective accumulation of the LDC subset which correlates with the pulmonary expression of the LDC-inducing differentiation factor activin-A. This study identified the LDC subset as an interesting focus for future research in COPD pathogenesis. PMID:20307269

A population 'consensus', partial linkage map of Picea abies Karst. based on RAPD markers

Treesearch

G. Bucci; Thomas L. Kubisiak; W.L. Nance; P. Menozzi

1997-01-01

The authors built a "consensus" partial linkage map based on RAPD markers using 48 sibships of eight megagametophytes each from a natural population of Norway spruce. A RAPD linkage map for a single individual from the same population had previously been constructed. Using 30 random decamers that had yielded 83 RAPD markers in the single-tree map, eight...

[Application of single-retainer all-ceramic resin-bonded fixed partial denture in replacing single anterior tooth].

PubMed

Lili, Yang; Debiao, Du; Ruoyu, Ning; Deying, Chen; Junling, Wu

2017-08-01

Objective In this study, we aimed to evaluate the clinical effect of single-retainer all-ceramic resin-bonded fixed partial denture (RBFPD) on the single anterior tooth loss patients. Methods A total of 20 single-retainer all-ceramic RBFPD
were fabricated and evaluated in a two-year follow-up observation. The restorations were examined on the basis of the American Public Health Association (APHA) criteria. Results A total of 20 single-retainer all-ceramic RBFPD achieved class A evaluation after a six-month follow-up observation. One single-retainer all-ceramic RBFPD was classified as class B for secondary caries after a one-year follow-up observation. After a two-year follow-up observation, one single-retainer all-ceramic RBFPD was classified as class B because of secondary caries, and one single-retainer all-ceramic RBFPD was classified as class B because of fracture. Conclusion Single-retainer all-ceramic RBFPD is a promising and optional method in replacing single anterior tooth.

Single-cell entropy for accurate estimation of differentiation potency from a cell's transcriptome

NASA Astrophysics Data System (ADS)

Teschendorff, Andrew E.; Enver, Tariq

2017-06-01

The ability to quantify differentiation potential of single cells is a task of critical importance. Here we demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell's transcriptome in the context of an interaction network, without the need for feature selection. We show that signalling entropy provides a more accurate and robust potency estimate than other entropy-based measures, driven in part by a subtle positive correlation between the transcriptome and connectome. Signalling entropy identifies known cell subpopulations of varying potency and drug resistant cancer stem-cell phenotypes, including those derived from circulating tumour cells. It further reveals that expression heterogeneity within single-cell populations is regulated. In summary, signalling entropy allows in silico estimation of the differentiation potency and plasticity of single cells and bulk samples, providing a means to identify normal and cancer stem-cell phenotypes.

Single-cell entropy for accurate estimation of differentiation potency from a cell's transcriptome

PubMed Central

Teschendorff, Andrew E.; Enver, Tariq

2017-01-01

The ability to quantify differentiation potential of single cells is a task of critical importance. Here we demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell's transcriptome in the context of an interaction network, without the need for feature selection. We show that signalling entropy provides a more accurate and robust potency estimate than other entropy-based measures, driven in part by a subtle positive correlation between the transcriptome and connectome. Signalling entropy identifies known cell subpopulations of varying potency and drug resistant cancer stem-cell phenotypes, including those derived from circulating tumour cells. It further reveals that expression heterogeneity within single-cell populations is regulated. In summary, signalling entropy allows in silico estimation of the differentiation potency and plasticity of single cells and bulk samples, providing a means to identify normal and cancer stem-cell phenotypes. PMID:28569836

Survival of partially differentiated mouse embryonic stem cells in the scala media of the guinea pig cochlea.

PubMed

Hildebrand, Michael S; Dahl, Hans-Henrik M; Hardman, Jennifer; Coleman, Bryony; Shepherd, Robert K; de Silva, Michelle G

2005-12-01

The low regenerative capacity of the hair cells of the mammalian inner ear is a major obstacle for functional recovery following sensorineural hearing loss. A potential treatment is to replace damaged tissue by transplantation of stem cells. To test this approach, undifferentiated and partially differentiated mouse embryonic stem (ES) cells were delivered into the scala media of the deafened guinea pig cochlea. Transplanted cells survived in the scala media for a postoperative period of at least nine weeks, evidenced by histochemical and direct fluorescent detection of enhanced green fluorescent protein (EGFP). Transplanted cells were discovered near the spiral ligament and stria vascularis in the endolymph fluid of the scala media. In some cases, cells were observed close to the damaged organ of Corti structure. There was no evidence of significant immunological rejection of the implanted ES cells despite the absence of immunosuppression. Our surgical approach allowed efficient delivery of ES cells to the scala media while preserving the delicate structures of the cochlea. This is the first report of the survival of partially differentiated ES cells in the scala media of the mammalian cochlea, and it provides support for the potential of cell-based therapies for sensorineural hearing impairment.

Survival of Partially Differentiated Mouse Embryonic Stem Cells in the Scala Media of the Guinea Pig Cochlea

PubMed Central

Hildebrand, Michael S.; Dahl, Hans-Henrik M.; Hardman, Jennifer; Coleman, Bryony; Shepherd, Robert K.

2005-01-01

The low regenerative capacity of the hair cells of the mammalian inner ear is a major obstacle for functional recovery following sensorineural hearing loss. A potential treatment is to replace damaged tissue by transplantation of stem cells. To test this approach, undifferentiated and partially differentiated mouse embryonic stem (ES) cells were delivered into the scala media of the deafened guinea pig cochlea. Transplanted cells survived in the scala media for a postoperative period of at least nine weeks, evidenced by histochemical and direct fluorescent detection of enhanced green fluorescent protein (EGFP). Transplanted cells were discovered near the spiral ligament and stria vascularis in the endolymph fluid of the scala media. In some cases, cells were observed close to the damaged organ of Corti structure. There was no evidence of significant immunological rejection of the implanted ES cells despite the absence of immunosuppression. Our surgical approach allowed efficient delivery of ES cells to the scala media while preserving the delicate structures of the cochlea. This is the first report of the survival of partially differentiated ES cells in the scala media of the mammalian cochlea, and it provides support for the potential of cell-based therapies for sensorineural hearing impairment. PMID:16208453

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

A model and variance reduction method for computing statistical outputs of stochastic elliptic partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vidal-Codina, F., E-mail: fvidal@mit.edu; Nguyen, N.C., E-mail: cuongng@mit.edu; Giles, M.B., E-mail: mike.giles@maths.ox.ac.uk

We present a model and variance reduction method for the fast and reliable computation of statistical outputs of stochastic elliptic partial differential equations. Our method consists of three main ingredients: (1) the hybridizable discontinuous Galerkin (HDG) discretization of elliptic partial differential equations (PDEs), which allows us to obtain high-order accurate solutions of the governing PDE; (2) the reduced basis method for a new HDG discretization of the underlying PDE to enable real-time solution of the parameterized PDE in the presence of stochastic parameters; and (3) a multilevel variance reduction method that exploits the statistical correlation among the different reduced basismore » approximations and the high-fidelity HDG discretization to accelerate the convergence of the Monte Carlo simulations. The multilevel variance reduction method provides efficient computation of the statistical outputs by shifting most of the computational burden from the high-fidelity HDG approximation to the reduced basis approximations. Furthermore, we develop a posteriori error estimates for our approximations of the statistical outputs. Based on these error estimates, we propose an algorithm for optimally choosing both the dimensions of the reduced basis approximations and the sizes of Monte Carlo samples to achieve a given error tolerance. We provide numerical examples to demonstrate the performance of the proposed method.« less

NonMarkov Ito Processes with 1- state memory

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2010-08-01

A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.

Differential pathway coupling efficiency of the activated insulin receptor drives signaling selectivity by XMetA, an allosteric partial agonist antibody

USDA-ARS?s Scientific Manuscript database

XMetA, an anti-insulin receptor (IR) monoclonal antibody, is an allosteric partial agonist of the IR. We have previously reported that XMetA activates the “metabolic-biased” Akt kinase signaling pathway while having little or no effect on the “mitogenic” MAPK signaling pathwayof ERK 1/2. To inves...

Differential pathway coupling efficiency of the activated insulin receptor drives signaling selectivity by xmeta, an allosteric partial agonist antibody

USDA-ARS?s Scientific Manuscript database

XMetA, an anti-insulin receptor (IR) monoclonal antibody, is an allosteric partial agonist of the IR. We have previously reported that XMetA activates the “metabolic-biased” Akt kinase signaling pathway while having little or no effect on the “mitogenic” MAPK signaling pathwayof ERK 1/2. To inves...

Partial Fourier techniques in single-shot cross-term spatiotemporal encoded MRI.

PubMed

Zhang, Zhiyong; Frydman, Lucio

2018-03-01

Cross-term spatiotemporal encoding (xSPEN) is a single-shot approach with exceptional immunity to field heterogeneities, the images of which faithfully deliver 2D spatial distributions without requiring a priori information or using postacquisition corrections. xSPEN, however, suffers from signal-to-noise ratio penalties due to its non-Fourier nature and due to diffusion losses-especially when seeking high resolution. This study explores partial Fourier transform approaches that, acting along either the readout or the spatiotemporally encoded dimensions, reduce these penalties. xSPEN uses an orthogonal (e.g., z) gradient to read, in direct space, the low-bandwidth (e.g., y) dimension. This substantially changes the nature of partial Fourier acquisitions vis-à-vis conventional imaging counterparts. A suitable theoretical analysis is derived to implement these procedures, along either the spatiotemporally or readout axes. Partial Fourier single-shot xSPEN images were recorded on preclinical and human scanners. Owing to their reduction in the experiments' acquisition times, this approach provided substantial sensitivity gains vis-à-vis previous implementations for a given targeted in-plane resolution. The physical origins of these gains are explained. Partial Fourier approaches, particularly when implemented along the low-bandwidth spatiotemporal dimension, provide several-fold sensitivity advantages at minimal costs to the execution and processing of the single-shot experiments. Magn Reson Med 79:1506-1514, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Pipette-based Method to Study Embryoid Body Formation Derived from Mouse and Human Pluripotent Stem Cells Partially Recapitulating Early Embryonic Development Under Simulated Microgravity Conditions

NASA Astrophysics Data System (ADS)

Shinde, Vaibhav; Brungs, Sonja; Hescheler, Jürgen; Hemmersbach, Ruth; Sachinidis, Agapios

2016-06-01

The in vitro differentiation of pluripotent stem cells partially recapitulates early in vivo embryonic development. More recently, embryonic development under the influence of microgravity has become a primary focus of space life sciences. In order to integrate the technique of pluripotent stem cell differentiation with simulated microgravity approaches, the 2-D clinostat compatible pipette-based method was experimentally investigated and adapted for investigating stem cell differentiation processes under simulated microgravity conditions. In order to keep residual accelerations as low as possible during clinorotation, while also guaranteeing enough material for further analysis, stem cells were exposed in 1-mL pipettes with a diameter of 3.5 mm. The differentiation of mouse and human pluripotent stem cells inside the pipettes resulted in the formation of embryoid bodies at normal gravity (1 g) after 24 h and 3 days. Differentiation of the mouse pluripotent stem cells on a 2-D pipette-clinostat for 3 days also resulted in the formation of embryoid bodies. Interestingly, the expression of myosin heavy chain was downregulated when cultivation was continued for an additional 7 days at normal gravity. This paper describes the techniques for culturing and differentiation of pluripotent stem cells and exposure to simulated microgravity during culturing or differentiation on a 2-D pipette clinostat. The implementation of these methodologies along with -omics technologies will contribute to understand the mechanisms regulating how microgravity influences early embryonic development.

Impact of a Differential Learning Approach on Practical Exam Performance: A Controlled Study in a Preclinical Dental Course.

PubMed

Pabel, Sven-Olav; Pabel, Anne-Kathrin; Schmickler, Jan; Schulz, Xenia; Wiegand, Annette

2017-09-01

The aim of this study was to evaluate if differential learning in a preclinical dental course impacted the performance of dental students in a practical exam (preparation of a gold partial crown) immediately after the training session and 20 weeks later compared to conventional learning. This controlled study was performed in a preclinical course in operative dentistry at a dental school in Germany. Third-year students were trained in preparing gold partial crowns by using either the conventional learning (n=41) or the differential learning approach (n=32). The differential learning approach consisted of 20 movement exercises with a continuous change of movement execution during the learning session, while the conventional learning approach was mainly based on repetition, a methodological series of exercises, and correction of preparations during the training phase. Practical exams were performed immediately after the training session (T1) and 20 weeks later (T2, retention test). Preparations were rated by four independent and blinded examiners. At T1, no significant difference between the performance (exam passed) of the two groups was detected (conventional learning: 54.3%, differential learning: 68.0%). At T2, significantly more students passed the exam when trained by the differential learning approach (68.8%) than by the conventional learning approach (18.9%). Interrater reliability was moderate (Kappa: 0.57, T1) or substantial (Kappa: 0.67, T2), respectively. These results suggest that a differential learning approach can increase the manual skills of dental students.

Differential geometry based solvation model. III. Quantum formulation

PubMed Central

Chen, Zhan; Wei, Guo-Wei

2011-01-01

Solvation is of fundamental importance to biomolecular systems. Implicit solvent models, particularly those based on the Poisson-Boltzmann equation for electrostatic analysis, are established approaches for solvation analysis. However, ad hoc solvent-solute interfaces are commonly used in the implicit solvent theory. Recently, we have introduced differential geometry based solvation models which allow the solvent-solute interface to be determined by the variation of a total free energy functional. Atomic fixed partial charges (point charges) are used in our earlier models, which depends on existing molecular mechanical force field software packages for partial charge assignments. As most force field models are parameterized for a certain class of molecules or materials, the use of partial charges limits the accuracy and applicability of our earlier models. Moreover, fixed partial charges do not account for the charge rearrangement during the solvation process. The present work proposes a differential geometry based multiscale solvation model which makes use of the electron density computed directly from the quantum mechanical principle. To this end, we construct a new multiscale total energy functional which consists of not only polar and nonpolar solvation contributions, but also the electronic kinetic and potential energies. By using the Euler-Lagrange variation, we derive a system of three coupled governing equations, i.e., the generalized Poisson-Boltzmann equation for the electrostatic potential, the generalized Laplace-Beltrami equation for the solvent-solute boundary, and the Kohn-Sham equations for the electronic structure. We develop an iterative procedure to solve three coupled equations and to minimize the solvation free energy. The present multiscale model is numerically validated for its stability, consistency and accuracy, and is applied to a few sets of molecules, including a case which is difficult for existing solvation models. Comparison is made to many other classic and quantum models. By using experimental data, we show that the present quantum formulation of our differential geometry based multiscale solvation model improves the prediction of our earlier models, and outperforms some explicit solvation model. PMID:22112067

A theory of fine structure image models with an application to detection and classification of dementia

PubMed Central

Penn, Richard; Werner, Michael; Thomas, Justin

2015-01-01

Background Estimation of stochastic process models from data is a common application of time series analysis methods. Such system identification processes are often cast as hypothesis testing exercises whose intent is to estimate model parameters and test them for statistical significance. Ordinary least squares (OLS) regression and the Levenberg-Marquardt algorithm (LMA) have proven invaluable computational tools for models being described by non-homogeneous, linear, stationary, ordinary differential equations. Methods In this paper we extend stochastic model identification to linear, stationary, partial differential equations in two independent variables (2D) and show that OLS and LMA apply equally well to these systems. The method employs an original nonparametric statistic as a test for the significance of estimated parameters. Results We show gray scale and color images are special cases of 2D systems satisfying a particular autoregressive partial difference equation which estimates an analogous partial differential equation. Several applications to medical image modeling and classification illustrate the method by correctly classifying demented and normal OLS models of axial magnetic resonance brain scans according to subject Mini Mental State Exam (MMSE) scores. Comparison with 13 image classifiers from the literature indicates our classifier is at least 14 times faster than any of them and has a classification accuracy better than all but one. Conclusions Our modeling method applies to any linear, stationary, partial differential equation and the method is readily extended to 3D whole-organ systems. Further, in addition to being a robust image classifier, estimated image models offer insights into which parameters carry the most diagnostic image information and thereby suggest finer divisions could be made within a class. Image models can be estimated in milliseconds which translate to whole-organ models in seconds; such runtimes could make real-time medicine and surgery modeling possible. PMID:26029638

Differential gene expression in the siphonophore Nanomia bijuga (Cnidaria) assessed with multiple next-generation sequencing workflows.

PubMed

Siebert, Stefan; Robinson, Mark D; Tintori, Sophia C; Goetz, Freya; Helm, Rebecca R; Smith, Stephen A; Shaner, Nathan; Haddock, Steven H D; Dunn, Casey W

2011-01-01

We investigated differential gene expression between functionally specialized feeding polyps and swimming medusae in the siphonophore Nanomia bijuga (Cnidaria) with a hybrid long-read/short-read sequencing strategy. We assembled a set of partial gene reference sequences from long-read data (Roche 454), and generated short-read sequences from replicated tissue samples that were mapped to the references to quantify expression. We collected and compared expression data with three short-read expression workflows that differ in sample preparation, sequencing technology, and mapping tools. These workflows were Illumina mRNA-Seq, which generates sequence reads from random locations along each transcript, and two tag-based approaches, SOLiD SAGE and Helicos DGE, which generate reads from particular tag sites. Differences in expression results across workflows were mostly due to the differential impact of missing data in the partial reference sequences. When all 454-derived gene reference sequences were considered, Illumina mRNA-Seq detected more than twice as many differentially expressed (DE) reference sequences as the tag-based workflows. This discrepancy was largely due to missing tag sites in the partial reference that led to false negatives in the tag-based workflows. When only the subset of reference sequences that unambiguously have tag sites was considered, we found broad congruence across workflows, and they all identified a similar set of DE sequences. Our results are promising in several regards for gene expression studies in non-model organisms. First, we demonstrate that a hybrid long-read/short-read sequencing strategy is an effective way to collect gene expression data when an annotated genome sequence is not available. Second, our replicated sampling indicates that expression profiles are highly consistent across field-collected animals in this case. Third, the impacts of partial reference sequences on the ability to detect DE can be mitigated through workflow choice and deeper reference sequencing.

Differential Gene Expression in the Siphonophore Nanomia bijuga (Cnidaria) Assessed with Multiple Next-Generation Sequencing Workflows

PubMed Central

Siebert, Stefan; Robinson, Mark D.; Tintori, Sophia C.; Goetz, Freya; Helm, Rebecca R.; Smith, Stephen A.; Shaner, Nathan; Haddock, Steven H. D.; Dunn, Casey W.

2011-01-01

We investigated differential gene expression between functionally specialized feeding polyps and swimming medusae in the siphonophore Nanomia bijuga (Cnidaria) with a hybrid long-read/short-read sequencing strategy. We assembled a set of partial gene reference sequences from long-read data (Roche 454), and generated short-read sequences from replicated tissue samples that were mapped to the references to quantify expression. We collected and compared expression data with three short-read expression workflows that differ in sample preparation, sequencing technology, and mapping tools. These workflows were Illumina mRNA-Seq, which generates sequence reads from random locations along each transcript, and two tag-based approaches, SOLiD SAGE and Helicos DGE, which generate reads from particular tag sites. Differences in expression results across workflows were mostly due to the differential impact of missing data in the partial reference sequences. When all 454-derived gene reference sequences were considered, Illumina mRNA-Seq detected more than twice as many differentially expressed (DE) reference sequences as the tag-based workflows. This discrepancy was largely due to missing tag sites in the partial reference that led to false negatives in the tag-based workflows. When only the subset of reference sequences that unambiguously have tag sites was considered, we found broad congruence across workflows, and they all identified a similar set of DE sequences. Our results are promising in several regards for gene expression studies in non-model organisms. First, we demonstrate that a hybrid long-read/short-read sequencing strategy is an effective way to collect gene expression data when an annotated genome sequence is not available. Second, our replicated sampling indicates that expression profiles are highly consistent across field-collected animals in this case. Third, the impacts of partial reference sequences on the ability to detect DE can be mitigated through workflow choice and deeper reference sequencing. PMID:21829563

Electron-pair-production cross section in the tip region of the positron spectrum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sud, K.K.; Sharma, D.K.

1984-11-01

The radial integrals for electron-pair production in a point Coulomb potential have been expressed by Sud, Sharma, and Sud in terms of the matrix generalization of the GAMMA function. Two new partial differential equations in photon energy satisfied by the matrix GAMMA function are obtained. We have obtained, on integrating the partial differential equations, accurate radial integrals as a function of photon energy for the pair production by intermediate-energy photons. The cross section in the tip region of the spectrum are calculated for photons of energy 5.0 to 10.0 MeV for /sup 92/U. The new technique results in extensive savingmore » in computer time as the basic radial integrals in terms of the hypergeometric function F/sub 2/ are computed at one photon energy for each pair of partial waves. The results of our calculations are compared with plane-wave Born-approximation results and with the calculations of Dugne and of Deck, Moroi, and Alling.« less

GRHL3/GET1 and Trithorax Group Members Collaborate to Activate the Epidermal Progenitor Differentiation Program

PubMed Central

Hopkin, Amelia Soto; Gordon, William; Klein, Rachel Herndon; Espitia, Francisco; Daily, Kenneth; Zeller, Michael; Baldi, Pierre; Andersen, Bogi

2012-01-01

The antagonistic actions of Polycomb and Trithorax are responsible for proper cell fate determination in mammalian tissues. In the epidermis, a self-renewing epithelium, previous work has shown that release from Polycomb repression only partially explains differentiation gene activation. We now show that Trithorax is also a key regulator of epidermal differentiation, not only through activation of genes repressed by Polycomb in progenitor cells, but also through activation of genes independent of regulation by Polycomb. The differentiation associated transcription factor GRHL3/GET1 recruits the ubiquitously expressed Trithorax complex to a subset of differentiation genes. PMID:22829784

FPGA-based distributed computing microarchitecture for complex physical dynamics investigation.

PubMed

Borgese, Gianluca; Pace, Calogero; Pantano, Pietro; Bilotta, Eleonora

2013-09-01

In this paper, we present a distributed computing system, called DCMARK, aimed at solving partial differential equations at the basis of many investigation fields, such as solid state physics, nuclear physics, and plasma physics. This distributed architecture is based on the cellular neural network paradigm, which allows us to divide the differential equation system solving into many parallel integration operations to be executed by a custom multiprocessor system. We push the number of processors to the limit of one processor for each equation. In order to test the present idea, we choose to implement DCMARK on a single FPGA, designing the single processor in order to minimize its hardware requirements and to obtain a large number of easily interconnected processors. This approach is particularly suited to study the properties of 1-, 2- and 3-D locally interconnected dynamical systems. In order to test the computing platform, we implement a 200 cells, Korteweg-de Vries (KdV) equation solver and perform a comparison between simulations conducted on a high performance PC and on our system. Since our distributed architecture takes a constant computing time to solve the equation system, independently of the number of dynamical elements (cells) of the CNN array, it allows us to reduce the elaboration time more than other similar systems in the literature. To ensure a high level of reconfigurability, we design a compact system on programmable chip managed by a softcore processor, which controls the fast data/control communication between our system and a PC Host. An intuitively graphical user interface allows us to change the calculation parameters and plot the results.

Population response of the northern red-backed vole (Clethrionomys rutilus) to differentially cut white spruce forest.

Treesearch

Stephen D. West; R. Glenn Ford; John C. Zasada

1980-01-01

The population response of the northern red-backed vole (Clethrionomys rutilus) to a differentially cut white spruce (Picea glauca) forest 30 km southwest of Fairbanks, Alaska, was monitored by simultaneous livetrapping in a clearcut, in a partially cut or shelterwood area, and in an area of uncut forest. During the first...

Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions

ERIC Educational Resources Information Center

Aliev, Nihan; Jahanshahi, Mohammad

2002-01-01

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

Direct Shear Failure in Reinforced Concrete Beams under Impulsive Loading

DTIC Science & Technology

1983-09-01

115 References ............... ............................. 119 Tables . ............................. 124 Figures ............ 1..............30...8217. : = differentiable functions of time 1 = elastic modulus enhancement function 4) 41’ = constants for a given mode W’, = frequency w tfirst thickness-shear...are defined by linear partial differential equations. The analytic results are compared to data gathered on one-way slabs loaded with impulsive blast

A Probabilistic-Numerical Approximation for an Obstacle Problem Arising in Game Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gruen, Christine, E-mail: christine.gruen@univ-brest.fr

We investigate a two-player zero-sum stochastic differential game in which one of the players has more information on the game than his opponent. We show how to construct numerical schemes for the value function of this game, which is given by the solution of a quasilinear partial differential equation with obstacle.

Formation mechanism of fivefold deformation twins in a face-centered cubic alloy.

PubMed

Zhang, Zhenyu; Huang, Siling; Chen, Leilei; Zhu, Zhanwei; Guo, Dongming

2017-03-28

The formation mechanism considers fivefold deformation twins originating from the grain boundaries in a nanocrystalline material, resulting in that fivefold deformation twins derived from a single crystal have not been reported by molecular dynamics simulations. In this study, fivefold deformation twins are observed in a single crystal of face-centered cubic (fcc) alloy. A new formation mechanism is proposed for fivefold deformation twins in a single crystal. A partial dislocation is emitted from the incoherent twin boundaries (ITBs) with high energy, generating a stacking fault along {111} plane, and resulting in the nucleating and growing of a twin by the successive emission of partials. A node is fixed at the intersecting center of the four different slip {111} planes. With increasing stress under the indentation, ITBs come into being close to the node, leading to the emission of a partial from the node. This generates a stacking fault along a {111} plane, nucleating and growing a twin by the continuous emission of the partials. This process repeats until the formation of fivefold deformation twins.

Formation mechanism of fivefold deformation twins in a face-centered cubic alloy

NASA Astrophysics Data System (ADS)

Zhang, Zhenyu; Huang, Siling; Chen, Leilei; Zhu, Zhanwei; Guo, Dongming

2017-03-01

The formation mechanism considers fivefold deformation twins originating from the grain boundaries in a nanocrystalline material, resulting in that fivefold deformation twins derived from a single crystal have not been reported by molecular dynamics simulations. In this study, fivefold deformation twins are observed in a single crystal of face-centered cubic (fcc) alloy. A new formation mechanism is proposed for fivefold deformation twins in a single crystal. A partial dislocation is emitted from the incoherent twin boundaries (ITBs) with high energy, generating a stacking fault along {111} plane, and resulting in the nucleating and growing of a twin by the successive emission of partials. A node is fixed at the intersecting center of the four different slip {111} planes. With increasing stress under the indentation, ITBs come into being close to the node, leading to the emission of a partial from the node. This generates a stacking fault along a {111} plane, nucleating and growing a twin by the continuous emission of the partials. This process repeats until the formation of fivefold deformation twins.

Polymorphism of Paramecium pentaurelia (Ciliophora, Oligohymenophorea) strains revealed by rDNA and mtDNA sequences.

PubMed

Przyboś, Ewa; Tarcz, Sebastian; Greczek-Stachura, Magdalena; Surmacz, Marta

2011-05-01

Paramecium pentaurelia is one of 15 known sibling species of the Paramecium aurelia complex. It is recognized as a species showing no intra-specific differentiation on the basis of molecular fingerprint analyses, whereas the majority of other species are polymorphic. This study aimed at assessing genetic polymorphism within P. pentaurelia including new strains recently found in Poland (originating from two water bodies, different years, seasons, and clones of one strain) as well as strains collected from distant habitats (USA, Europe, Asia), and strains representing other species of the complex. We compared two DNA fragments: partial sequences (349 bp) of the LSU rDNA and partial sequences (618 bp) of cytochrome B gene. A correlation between the geographical origin of the strains and the genetic characteristics of their genotypes was not observed. Different genotypes were found in Kraków in two types of water bodies (Opatkowice-natural pond; Jordan's Park-artificial pond). Haplotype diversity within a single water body was not recorded. Likewise, seasonal haplotype differences between the strains within the artificial water body, as well as differences between clones originating from one strain, were not detected. The clustering of some strains belonging to different species was observed in the phylogenies. Copyright © 2010 Elsevier GmbH. All rights reserved.

Identification of a glycine-rich protein from the tick Rhipicephalus haemaphysaloides and evaluation of its vaccine potential against tick feeding.

PubMed

Zhou, Jinlin; Gong, Haiyan; Zhou, Yongzhi; Xuan, Xuenan; Fujisaki, Kozo

2006-12-01

A cDNA coding a glycine-rich protein was identified from the Rhipicephalus haemaphysaloides tick. The cDNA named here as RH50 was 1,823 bp, including a single open reading frame (ORF) of 1,518 nucleotides. The ORF encodes a polypeptide of 506 amino acid residues with a size of 50 kDa, as calculated by a computer. The predicted amino acid sequence of RH50 showed a low homology to sequences of some known extracellular matrix-like proteins. The native protein was identified in both the fed tick salivary gland lysates and extracts of cement material using the serum against the recombinant protein. Reverse transcription polymerase chain reaction results showed that RH50 mRNA was only transcribed in partially fed tick salivary glands, not in unfed tick salivary glands or partially fed tick midgut, fat body, or ovary. The differential expression of RH50 protein in fed tick salivary glands was confirmed by immunofluorescence. The low attachment rate both in the adult and nymphal tick, and the high mortality of immature ticks (nymph) feeding on recombinant RH50-immunized rabbits were found. These results show that the RH50 protein could be a useful candidate for anti-tick vaccine development.

Multigrid Methods

NASA Technical Reports Server (NTRS)

1981-01-01

Developments in numerical solution of certain types of partial differential equations by rapidly converging sequences of operations on supporting grids that range from very fine to very coarse are presented.

Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1982-01-01

Two efforts to numerically simulate the flow about the Augmentor-Wing airfoil in the cruise configuration using the GRAPE elliptic partial differential equation grid generator algorithm are discussed. The Augmentor-Wing consists of a main airfoil with a slotted trailing edge for blowing and two smaller airfoils shrouding the blowing jet. The airfoil and the algorithm are described, and the application of GRAPE to an unsteady viscous flow simulation and a transonic full-potential approach is considered. The procedure involves dividing a complicated flow region into an arbitrary number of zones and ensuring continuity of grid lines, their slopes, and their point distributions across the zonal boundaries. The method for distributing the body-surface grid points is discussed.

Towards developing robust algorithms for solving partial differential equations on MIMD machines

NASA Technical Reports Server (NTRS)

Saltz, Joel H.; Naik, Vijay K.

1988-01-01

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Learning partial differential equations via data discovery and sparse optimization

NASA Astrophysics Data System (ADS)

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Towards developing robust algorithms for solving partial differential equations on MIMD machines

NASA Technical Reports Server (NTRS)

Saltz, J. H.; Naik, V. K.

1985-01-01

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Automating Embedded Analysis Capabilities and Managing Software Complexity in Multiphysics Simulation, Part II: Application to Partial Differential Equations

DOE PAGES

Pawlowski, Roger P.; Phipps, Eric T.; Salinger, Andrew G.; ...

2012-01-01

A template-based generic programming approach was presented in Part I of this series of papers [Sci. Program. 20 (2012), 197–219] that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertaintymore » quantification results for a 3D PDE application.« less

An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

Learning partial differential equations via data discovery and sparse optimization.

PubMed

Schaeffer, Hayden

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.

Learning partial differential equations via data discovery and sparse optimization

PubMed Central

2017-01-01

We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection. PMID:28265183

Magnetohydrodynamic motion of a two-fluid plasma

DOE PAGES

Burby, Joshua W.

2017-07-21

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

Magnetohydrodynamic motion of a two-fluid plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burby, Joshua W.

Here, the two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell’s equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, asmore » well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure’s conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.« less

In vivo label-free lymphangiography of cutaneous lymphatic vessels in human burn scars using optical coherence tomography

PubMed Central

Gong, Peijun; Es’haghian, Shaghayegh; Harms, Karl-Anton; Murray, Alexandra; Rea, Suzanne; Wood, Fiona M.; Sampson, David D.; McLaughlin, Robert A.

2016-01-01

We present an automated, label-free method for lymphangiography of cutaneous lymphatic vessels in humans in vivo using optical coherence tomography (OCT). This method corrects for the variation in OCT signal due to the confocal function and sensitivity fall-off of a spectral-domain OCT system and utilizes a single-scattering model to compensate for A-scan signal attenuation to enable reliable thresholding of lymphatic vessels. A segment-joining algorithm is then incorporated into the method to mitigate partial-volume effects with small vessels. The lymphatic vessel images are augmented with images of the blood vessel network, acquired from the speckle decorrelation with additional weighting to differentiate blood vessels from the observed high decorrelation in lymphatic vessels. We demonstrate the method with longitudinal scans of human burn scar patients undergoing ablative fractional laser treatment, showing the visualization of the cutaneous lymphatic and blood vessel networks. PMID:28018713

Ionomer-Membrane Water Processing Methods

NASA Technical Reports Server (NTRS)

MacCallum, Taber K. (Inventor); Kelsey, Laura (Inventor)

2016-01-01

This disclosure provides water processing apparatuses, systems, and methods for recovering water from wastewater such as urine. The water processing apparatuses, systems, and methods can utilize membrane technology for extracting purified water in a single step. A containment unit can include an ionomer membrane, such as Nafion(TradeMark) over a hydrophobic microporous membrane, such as polytetrafluoroethylene (PTFE). The containment unit can be filled with wastewater, and the hydrophobic microporous membrane can be impermeable to liquids and solids of the wastewater but permeable to gases and vapors of the wastewater, and the ionomer membrane can be permeable to water vapor but impermeable to one or more contaminants of the gases and vapors. The containment unit can be exposed to a dry purge gas to maintain a water vapor partial pressure differential to drive permeation of the water vapor, and the water vapor can be collected and processed into potable water.

Ionomer-Membrane Water Processing Apparatus

NASA Technical Reports Server (NTRS)

MacCallum, Taber K. (Inventor); Kelsey, Laura (Inventor)

2016-01-01

This disclosure provides water processing apparatuses, systems, and methods for recovering water from wastewater such as urine. The water processing apparatuses, systems, and methods can utilize membrane technology for extracting purified water in a single step. A containment unit can include an ionomer membrane, such as Nafion(Registered Trademark), over a hydrophobic microporous membrane, such as polytetrafluoroethylene (PTFE). The containment unit can be filled with wastewater, and the hydrophobic microporous membrane can be impermeable to liquids and solids of the wastewater but permeable to gases and vapors of the wastewater, and the ionomer membrane can be permeable to water vapor but impermeable to one or more contaminants of the gases and vapors. The containment unit can be exposed to a dry purge gas to maintain a water vapor partial pressure differential to drive permeation of the water vapor, and the water vapor can be collected and processed into potable water.

Ionomer-Membrane Water Processing Apparatus

NASA Technical Reports Server (NTRS)

MacCallum, Taber K. (Inventor); Kelsey, Laura Katrina (Inventor)

2017-01-01

This disclosure provides water processing apparatuses, systems, and methods for recovering water from wastewater such as urine. The water processing apparatuses, systems, and methods can utilize membrane technology for extracting purified water in a single step. A containment unit can include an ionomer membrane, such as Nafion.RTM., over a hydrophobic microporous membrane, such as polytetrafluoroethylene (PTFE). The containment unit can be filled with wastewater, and the hydrophobic microporous membrane can be impermeable to liquids and solids of the wastewater but permeable to gases and vapors of the wastewater, and the ionomer membrane can be permeable to water vapor but impermeable to one or more contaminants of the gases and vapors. The containment unit can be exposed to a dry purge gas to maintain a water vapor partial pressure differential to drive permeation of the water vapor, and the water vapor can be collected and processed into potable water.

Diskoseismology: Probing accretion disks. II - G-modes, gravitational radiation reaction, and viscosity

NASA Technical Reports Server (NTRS)

Nowak, Michael A.; Wagoner, Robert V.

1992-01-01

A scalar potential is used to derive a single partial differential equation governing the oscillation of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the sun. Specifically, the eigenfunctions and eigenfrequencies of isothermal disks are computed, and the way in which these results can be generalized to other disk models is indicated. The (assumed) relatively small rates of growth or damping of the modes due to various mechanisms, in particular gravitational radiation reaction and parameterized models of viscosity are also computed. It is found that for certain parameters the p-modes are unstable to gravitational radiation reaction (CFS instability), while both the p-modes and g-modes are unstable to viscosity unless highly anisotropic viscosity models are considered.

Computer assisted diagnostic system in tumor radiography.

PubMed

Faisal, Ahmed; Parveen, Sharmin; Badsha, Shahriar; Sarwar, Hasan; Reza, Ahmed Wasif

2013-06-01

An improved and efficient method is presented in this paper to achieve a better trade-off between noise removal and edge preservation, thereby detecting the tumor region of MRI brain images automatically. Compass operator has been used in the fourth order Partial Differential Equation (PDE) based denoising technique to preserve the anatomically significant information at the edges. A new morphological technique is also introduced for stripping skull region from the brain images, which consequently leading to the process of detecting tumor accurately. Finally, automatic seeded region growing segmentation based on an improved single seed point selection algorithm is applied to detect the tumor. The method is tested on publicly available MRI brain images and it gives an average PSNR (Peak Signal to Noise Ratio) of 36.49. The obtained results also show detection accuracy of 99.46%, which is a significant improvement than that of the existing results.

Toward performance portability of the Albany finite element analysis code using the Kokkos library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Demeshko, Irina; Watkins, Jerry; Tezaur, Irina K.

Performance portability on heterogeneous high-performance computing (HPC) systems is a major challenge faced today by code developers: parallel code needs to be executed correctly as well as with high performance on machines with different architectures, operating systems, and software libraries. The finite element method (FEM) is a popular and flexible method for discretizing partial differential equations arising in a wide variety of scientific, engineering, and industrial applications that require HPC. This paper presents some preliminary results pertaining to our development of a performance portable implementation of the FEM-based Albany code. Performance portability is achieved using the Kokkos library. We presentmore » performance results for the Aeras global atmosphere dynamical core module in Albany. Finally, numerical experiments show that our single code implementation gives reasonable performance across three multicore/many-core architectures: NVIDIA General Processing Units (GPU’s), Intel Xeon Phis, and multicore CPUs.« less

Toward performance portability of the Albany finite element analysis code using the Kokkos library

DOE PAGES

Demeshko, Irina; Watkins, Jerry; Tezaur, Irina K.; ...

2018-02-05

Performance portability on heterogeneous high-performance computing (HPC) systems is a major challenge faced today by code developers: parallel code needs to be executed correctly as well as with high performance on machines with different architectures, operating systems, and software libraries. The finite element method (FEM) is a popular and flexible method for discretizing partial differential equations arising in a wide variety of scientific, engineering, and industrial applications that require HPC. This paper presents some preliminary results pertaining to our development of a performance portable implementation of the FEM-based Albany code. Performance portability is achieved using the Kokkos library. We presentmore » performance results for the Aeras global atmosphere dynamical core module in Albany. Finally, numerical experiments show that our single code implementation gives reasonable performance across three multicore/many-core architectures: NVIDIA General Processing Units (GPU’s), Intel Xeon Phis, and multicore CPUs.« less

Theory of Metastable State Relaxation in a Gravitational Field for Non-Critical Binary Systems with Non-Conserved Order Parameter

NASA Technical Reports Server (NTRS)

Izmailov, Alexander F.; Myerson, Allan S.

1993-01-01

A new mathematical ansatz is developed for solution of the time-dependent Ginzburg-Landau nonlinear partial differential equation describing metastable state relaxation in binary (solute+solvent) non-critical solutions with non-conserved scalar order parameter in presence of a gravitational field. It has been demonstrated analytically that in such systems metastability initiates heterogeneous solute redistribution which results in the formation of a non-equilibrium singly-periodic spatial solute structure in the new solute-rich phase. The critical radius of nucleation and the induction time in these systems are gravity-dependent. It has also been proved that metastable state relaxation in vertical columns of supersaturated non-critical binary solutions leads to formation of the solute concentration gradient. Analytical expression for this concentration gradient is found and analysed. It is concluded that gravity can initiate phase separation (nucleation or spinodal decomposition).

Mate Finding, Sexual Spore Production, and the Spread of Fungal Plant Parasites.

PubMed

Hamelin, Frédéric M; Castella, François; Doli, Valentin; Marçais, Benoît; Ravigné, Virginie; Lewis, Mark A

2016-04-01

Sexual reproduction and dispersal are often coupled in organisms mixing sexual and asexual reproduction, such as fungi. The aim of this study is to evaluate the impact of mate limitation on the spreading speed of fungal plant parasites. Starting from a simple model with two coupled partial differential equations, we take advantage of the fact that we are interested in the dynamics over large spatial and temporal scales to reduce the model to a single equation. We obtain a simple expression for speed of spread, accounting for both sexual and asexual reproduction. Taking Black Sigatoka disease of banana plants as a case study, the model prediction is in close agreement with the actual spreading speed (100 km per year), whereas a similar model without mate limitation predicts a wave speed one order of magnitude greater. We discuss the implications of these results to control parasites in which sexual reproduction and dispersal are intrinsically coupled.

Proceedings of the Dundee Conference (10th) Held in Dundee, Scotland on July 1988. Ordinary and Partial Differential Equations. Volume 2

DTIC Science & Technology

1988-07-01

a priori inequalities with applications to R J Knops boundary value problems 40 Singular systems of differential equations V G Sigiilito S L...Stochastic functional differential equations S E A Mohammed 100 Optimal control of variational inequalities 125 Ennio de Giorgi Colloquium V Barbu P Kr e...location of the period-doubled bifurcation point varies slightly with Zc [ 3 ]. In addition, no significant effect is found if a smoother functional

DOE Office of Scientific and Technical Information (OSTI.GOV)

Isa, Sharena Mohamad; Ali, Anati

In this paper, the hydromagnetic flow of dusty fluid over a vertical stretching sheet with thermal radiation is investigated. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformation. These nonlinear ordinary differential equations are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method (RKF45 Method). The behavior of velocity and temperature profiles of hydromagnetic fluid flow of dusty fluid is analyzed and discussed for different parameters of interest such as unsteady parameter, fluid-particle interaction parameter, the magnetic parameter, radiation parameter and Prandtl number on the flow.

Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating.

PubMed

Qasim, Muhammad; Khan, Ilyas; Shafie, Sharidan

2013-01-01

This article looks at the steady flow of Micropolar fluid over a stretching surface with heat transfer in the presence of Newtonian heating. The relevant partial differential equations have been reduced to ordinary differential equations. The reduced ordinary differential equation system has been numerically solved by Runge-Kutta-Fehlberg fourth-fifth order method. Influence of different involved parameters on dimensionless velocity, microrotation and temperature is examined. An excellent agreement is found between the present and previous limiting results.

[Differential diagnosis of chronic myeloic leucemia in infancy (author's transl)].

PubMed

Binder, C; Pichler, E; Radaskiewicz, T; Scheibenreiter, S

1976-01-01

A 3 months old girl presented with significant enlargement of liver, spleen and lymphnodes, with moderate anemia, thrombopenia and leucocytosis. In the differential count there was a shift to the left and an increase of monocyte-like cells (35%). Differential diagnosis included leucemoid reaction, infectious mononucleosis, myelo-proliferative disorder with a missing C chromosome and chronic myeloid leucemia. Clinical symptoms, cytochemistry and caryotype of bone marrow cells suggested infantile chronic myeloic leucemia and normal ALP index and possibly normal HbF. Treatment with 6-mercaptopurine was followed by partial remission. The therapeutic consequences of exact differential diagnosis are discussed.

Independent Evolution of Transcriptional Inactivation on Sex Chromosomes in Birds and Mammals

PubMed Central

Livernois, Alexandra M.; Waters, Shafagh A.; Deakin, Janine E.; Marshall Graves, Jennifer A.; Waters, Paul D.

2013-01-01

X chromosome inactivation in eutherian mammals has been thought to be tightly controlled, as expected from a mechanism that compensates for the different dosage of X-borne genes in XX females and XY males. However, many X genes escape inactivation in humans, inactivation of the X in marsupials is partial, and the unrelated sex chromosomes of monotreme mammals have incomplete and gene-specific inactivation of X-linked genes. The bird ZW sex chromosome system represents a third independently evolved amniote sex chromosome system with dosage compensation, albeit partial and gene-specific, via an unknown mechanism (i.e. upregulation of the single Z in females, down regulation of one or both Zs in males, or a combination). We used RNA-fluorescent in situ hybridization (RNA-FISH) to demonstrate, on individual fibroblast cells, inactivation of 11 genes on the chicken Z and 28 genes on the X chromosomes of platypus. Each gene displayed a reproducible frequency of 1Z/1X-active and 2Z/2X-active cells in the homogametic sex. Our results indicate that the probability of inactivation is controlled on a gene-by-gene basis (or small domains) on the chicken Z and platypus X chromosomes. This regulatory mechanism must have been exapted independently to the non-homologous sex chromosomes in birds and mammals in response to an over-expressed Z or X in the homogametic sex, highlighting the universal importance that (at least partial) silencing plays in the evolution on amniote dosage compensation and, therefore, the differentiation of sex chromosomes. PMID:23874231

The evolution of the moon and the terrestrial planets

NASA Technical Reports Server (NTRS)

Toksoez, M. N.; Johnston, D. H.

1974-01-01

The thermal evolutions of the Moon, Mars, Venus and Mercury are calculated theoretically starting from cosmochemical condensation models. An assortment of geological, geochemical and geophysical data are used to constrain both the present day temperatures and the thermal histories of the planets' interiors. Such data imply that the planets were heated during or shortly after formation and that all the terrestrial planets started their differentiations early in their history. The moon, smallest in size, is characterized as a differentiated body with a crust, a thick solid mantle and an interior region which may be partially molten. Mars, intermediate in size, is assumed to have differentiated an Fe-FeS core. Venus is characterized as a planet not unlike the earth in many respects. Core formation has occurred probably during the first billion years after the formation. Mercury, which probably has a large core, may have a 500 km thick solid lithosphere and a partially molten core if it is assumed that some heat sources exist in the core.

Period of vibration of axially vibrating truly nonlinear rod

NASA Astrophysics Data System (ADS)

Cveticanin, L.

2016-07-01

In this paper the axial vibration of a muscle whose fibers are parallel to the direction of muscle compression is investigated. The model is a clamped-free rod with a strongly nonlinear elastic property. Axial vibration is described by a nonlinear partial differential equation. A solution of the equation is constructed for special initial conditions by using the method of separation of variables. The partial differential equation is separated into two uncoupled strongly nonlinear second order differential equations. Both equations, with displacement function and with time function are exactly determined. Exact solutions are given in the form of inverse incomplete and inverse complete Beta function. Using boundary and initial conditions, the frequency of vibration is obtained. It has to be mentioned that the determined frequency represents the exact analytic description for the axially vibrating truly nonlinear clamped-free rod. The procedure suggested in this paper is applied for calculation of the frequency of the longissimus dorsi muscle of a cow. The influence of elasticity order and elasticity coefficient on the frequency property is tested.

Group invariant solution for a pre-existing fracture driven by a power-law fluid in impermeable rock

NASA Astrophysics Data System (ADS)

Fareo, A. G.; Mason, D. P.

2013-12-01

The effect of power-law rheology on hydraulic fracturing is investigated. The evolution of a two-dimensional fracture with non-zero initial length and driven by a power-law fluid is analyzed. Only fluid injection into the fracture is considered. The surrounding rock mass is impermeable. With the aid of lubrication theory and the PKN approximation a partial differential equation for the fracture half-width is derived. Using a linear combination of the Lie-point symmetry generators of the partial differential equation, the group invariant solution is obtained and the problem is reduced to a boundary value problem for an ordinary differential equation. Exact analytical solutions are derived for hydraulic fractures with constant volume and with constant propagation speed. The asymptotic solution near the fracture tip is found. The numerical solution for general working conditions is obtained by transforming the boundary value problem to a pair of initial value problems. Throughout the paper, hydraulic fracturing with shear thinning, Newtonian and shear thickening fluids are compared.

A Differential ECG Amplifier with Single-Ended Output

NASA Technical Reports Server (NTRS)

Katchis, L.

1972-01-01

Three-stage amplifier is used for ECG measurements which require conversion of differential input to single-ended output. Circuit may be useful in biological telemetry for amplification of signals from specimen-implanted sensors.

Linearized Model of an Actively Controlled Cable for a Carlina Diluted Telescope

NASA Astrophysics Data System (ADS)

Andersen, T.; Le Coroller, H.; Owner-Petersen, M.; Dejonghe, J.

2014-04-01

The Carlina thinned pupil telescope has a focal unit (``gondola'') suspended by cables over the primary mirror. To predict the structural behavior of the gondola system, a simulation building block of a single cable is needed. A preloaded cable is a strongly non-linear system and can be modeled either with partial differential equations or non-linear finite elements. Using the latter, we set up an iteration procedure for determination of the static cable form and we formulate the necessary second-order differential equations for such a model. We convert them to a set of first-order differential equations (an ``ABCD''-model). Symmetrical in-plane eigenmodes and ``axial'' eigenmodes are the only eigenmodes that play a role in practice for a taut cable. Using the model and a generic suspension, a parameter study is made to find the influence of various design parameters. We conclude that the cable should be as stiff and thick as practically possible with a fairly high preload. Steel or Aramid are suitable materials. Further, placing the cable winches on the gondola and not on the ground does not provide significant advantages. Finally, it seems that use of reaction-wheels and/or reaction-masses will make the way for more accurate control of the gondola position under wind load. An adaptive stage with tip/tilt/piston correction for subapertures together with a focus and guiding system for freezing the fringes must also be studied.

Phase-and-amplitude recovery from a single phase-contrast image using partially spatially coherent x-ray radiation

NASA Astrophysics Data System (ADS)

Beltran, Mario A.; Paganin, David M.; Pelliccia, Daniele

2018-05-01

A simple method of phase-and-amplitude extraction is derived that corrects for image blurring induced by partially spatially coherent incident illumination using only a single intensity image as input. The method is based on Fresnel diffraction theory for the case of high Fresnel number, merged with the space-frequency description formalism used to quantify partially coherent fields and assumes the object under study is composed of a single-material. A priori knowledge of the object’s complex refractive index and information obtained by characterizing the spatial coherence of the source is required. The algorithm was applied to propagation-based phase-contrast data measured with a laboratory-based micro-focus x-ray source. The blurring due to the finite spatial extent of the source is embedded within the algorithm as a simple correction term to the so-called Paganin algorithm and is also numerically stable in the presence of noise.

Four Methods for Analyzing Partial Interval Recording Data, with Application to Single-Case Research.

PubMed

Pustejovsky, James E; Swan, Daniel M

2015-01-01

Partial interval recording (PIR) is a procedure for collecting measurements during direct observation of behavior. It is used in several areas of educational and psychological research, particularly in connection with single-case research. Measurements collected using partial interval recording suffer from construct invalidity because they are not readily interpretable in terms of the underlying characteristics of the behavior. Using an alternating renewal process model for the behavior under observation, we demonstrate that ignoring the construct invalidity of PIR data can produce misleading inferences, such as inferring that an intervention reduces the prevalence of an undesirable behavior when in fact it has the opposite effect. We then propose four different methods for analyzing PIR summary measurements, each of which can be used to draw inferences about interpretable behavioral parameters. We demonstrate the methods by applying them to data from two single-case studies of problem behavior.

Polytomous Differential Item Functioning and Violations of Ordering of the Expected Latent Trait by the Raw Score

ERIC Educational Resources Information Center

DeMars, Christine E.

2008-01-01

The graded response (GR) and generalized partial credit (GPC) models do not imply that examinees ordered by raw observed score will necessarily be ordered on the expected value of the latent trait (OEL). Factors were manipulated to assess whether increased violations of OEL also produced increased Type I error rates in differential item…

Early differentiation of the Moon: Experimental and modeling studies

NASA Technical Reports Server (NTRS)

Longhi, J.

1986-01-01

Major accomplishments include the mapping out of liquidus boundaries of lunar and meteoritic basalts at low pressure; the refinement of computer models that simulate low pressure fractional crystallization; the development of a computer model to calculate high pressure partial melting of the lunar and Martian interiors; and the proposal of a hypothesis of early lunar differentiation based upon terrestrial analogs.

On the Well-Definedness of the Order of an Ordinary Differential Equation

ERIC Educational Resources Information Center

Dobbs, David E.

2006-01-01

It is proved that if the differential equations "y[(n)] = f(x,y,y[prime],...,y[(n-1)])" and "y[(m)] = g(x,y,y[prime],...,y[(m-1)])" have the same particular solutions in a suitable region where "f" and "g" are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical…

Portent of Heine's Reciprocal Square Root Identity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cohl, H W

Precise efforts in theoretical astrophysics are needed to fully understand the mechanisms that govern the structure, stability, dynamics, formation, and evolution of differentially rotating stars. Direct computation of the physical attributes of a star can be facilitated by the use of highly compact azimuthal and separation angle Fourier formulations of the Green's functions for the linear partial differential equations of mathematical physics.

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

NASA Technical Reports Server (NTRS)

Pflaum, Christoph

1996-01-01

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

Multilevel Mediation: Cumulative Contextual Risk, Maternal Differential Treatment, and Children's Behavior within Families

ERIC Educational Resources Information Center

Meunier, Jean Christophe; Boyle, Michael; O'Connor, Thomas G.; Jenkins, Jennifer M.

2013-01-01

This study tests the hypothesis that links between contextual risk and children's outcomes are partially explained by differential parenting. Using multi-informant measurement and including up to four children per family (M[subscript age] = 3.51, SD = 2.38) in a sample of 397 families, indirect effects (through maternal differential…

Bmi1 regulates murine intestinal stem cell proliferation and self-renewal downstream of Notch.

PubMed

López-Arribillaga, Erika; Rodilla, Verónica; Pellegrinet, Luca; Guiu, Jordi; Iglesias, Mar; Roman, Angel Carlos; Gutarra, Susana; González, Susana; Muñoz-Cánoves, Pura; Fernández-Salguero, Pedro; Radtke, Freddy; Bigas, Anna; Espinosa, Lluís

2015-01-01

Genetic data indicate that abrogation of Notch-Rbpj or Wnt-β-catenin pathways results in the loss of the intestinal stem cells (ISCs). However, whether the effect of Notch is direct or due to the aberrant differentiation of the transit-amplifying cells into post-mitotic goblet cells is unknown. To address this issue, we have generated composite tamoxifen-inducible intestine-specific genetic mouse models and analyzed the expression of intestinal differentiation markers. Importantly, we found that activation of β-catenin partially rescues the differentiation phenotype of Rbpj deletion mutants, but not the loss of the ISC compartment. Moreover, we identified Bmi1, which is expressed in the ISC and progenitor compartments, as a gene that is co-regulated by Notch and β-catenin. Loss of Bmi1 resulted in reduced proliferation in the ISC compartment accompanied by p16(INK4a) and p19(ARF) (splice variants of Cdkn2a) accumulation, and increased differentiation to the post-mitotic goblet cell lineage that partially mimics Notch loss-of-function defects. Finally, we provide evidence that Bmi1 contributes to ISC self-renewal. © 2015. Published by The Company of Biologists Ltd.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghafarian, M.; Ariaei, A., E-mail: ariaei@eng.ui.ac.ir

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique tomore » solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.« less

Genomic regions with a history of divergent selection affect fitness of hybrids between two butterfly species.

PubMed

Gompert, Zachariah; Lucas, Lauren K; Nice, Chris C; Fordyce, James A; Forister, Matthew L; Buerkle, C Alex

2012-07-01

Speciation is the process by which reproductively isolated lineages arise, and is one of the fundamental means by which the diversity of life increases. Whereas numerous studies have documented an association between ecological divergence and reproductive isolation, relatively little is known about the role of natural selection in genome divergence during the process of speciation. Here, we use genome-wide DNA sequences and Bayesian models to test the hypothesis that loci under divergent selection between two butterfly species (Lycaeides idas and L. melissa) also affect fitness in an admixed population. Locus-specific measures of genetic differentiation between L. idas and L. melissa and genomic introgression in hybrids varied across the genome. The most differentiated genetic regions were characterized by elevated L. idas ancestry in the admixed population, which occurs in L. idas-like habitat, consistent with the hypothesis that local adaptation contributes to speciation. Moreover, locus-specific measures of genetic differentiation (a metric of divergent selection) were positively associated with extreme genomic introgression (a metric of hybrid fitness). Interestingly, concordance of differentiation and introgression was only partial. We discuss multiple, complementary explanations for this partial concordance. © 2012 The Author(s).

Sweet taste in apple: the role of sorbitol, individual sugars, organic acids and volatile compounds.

PubMed

Aprea, Eugenio; Charles, Mathilde; Endrizzi, Isabella; Laura Corollaro, Maria; Betta, Emanuela; Biasioli, Franco; Gasperi, Flavia

2017-03-21

Sweetness is one of the main drivers of consumer preference, and thus is given high priority in apple breeding programmes. Due to the complexity of sweetness evaluation, soluble solid content (SSC) is commonly used as an estimation of this trait. Nevertheless, it has been demonstrated that SSC and sweet taste are poorly correlated. Though individual sugar content may vary greatly between and within apple cultivars, no previous study has tried to investigate the relationship between the amount of individual sugars, or ratios of these, and apple sweetness. In this work, we quantified the major sugars (sucrose, glucose, fructose, xylose) and sorbitol and explored their influence on perceived sweetness in apple; we also related this to malic acid content, SSC and volatile compounds. Our data confirmed that the correlation between sweetness and SSC is weak. We found that sorbitol content correlates (similarly to SSC) with perceived sweetness better than any other single sugar or total sugar content. The single sugars show no differentiable importance in determining apple sweetness. Our predictive model based on partial least squares regression shows that after sorbitol and SSC, the most important contribution to apple sweetness is provided by several volatile compounds, mainly esters and farnesene.

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pabst, M., E-mail: M.Pabst@fz-juelich.de

2014-06-14

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10{sup −4} so the Fourier-Bessel series can be approximatedmore » by elementary functions. The time development of the system is characterized by two time constants, τ{sub c} and τ{sub g}. The constant τ{sub c} describes the approach to the stationary state of the total charge and the potential. τ{sub c} is several orders of magnitude smaller than the geometry-dependent constant τ{sub g}, which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.« less

Games of age-dependent prevention of chronic infections by social distancing.

PubMed

Reluga, Timothy C; Li, Jing

2013-06-01

Epidemiological games combine epidemic modelling with game theory to assess strategic choices in response to risks from infectious diseases. In most epidemiological games studied thus-far, the strategies of an individual are represented with a single choice parameter. There are many natural situations where strategies can not be represented by a single dimension, including situations where individuals can change their behavior as they age. To better understand how age-dependent variations in behavior can help individuals deal with infection risks, we study an epidemiological game in an SI model with two life-history stages where social distancing behaviors that reduce exposure rates are age-dependent. When considering a special case of the general model, we show that there is a unique Nash equilibrium when the infection pressure is a monotone function of aggregate exposure rates, but non-monotone effects can appear even in our special case. The non-monotone effects sometimes result in three Nash equilibria, two of which have local invasion potential simultaneously. Returning to a general case, we also describe a game with continuous age-structure using partial-differential equations, numerically identify some Nash equilibria, and conjecture about uniqueness.

Differential relationship of recent self-reported stress and acute anxiety with divided attention performance.

PubMed

Petrac, D C; Bedwell, J S; Renk, K; Orem, D M; Sims, V

2009-07-01

There have been relatively few studies on the relationship between recent perceived environmental stress and cognitive performance, and the existing studies do not control for state anxiety during the cognitive testing. The current study addressed this need by examining recent self-reported environmental stress and divided attention performance, while controlling for state anxiety. Fifty-four university undergraduates who self-reported a wide range of perceived recent stress (10-item perceived stress scale) completed both single and dual (simultaneous auditory and visual stimuli) continuous performance tests. Partial correlation analysis showed a statistically significant positive correlation between perceived stress and the auditory omission errors from the dual condition, after controlling for state anxiety and auditory omission errors from the single condition (r = 0.41). This suggests that increased environmental stress relates to decreased divided attention performance in auditory vigilance. In contrast, an increase in state anxiety (controlling for perceived stress) was related to a decrease in auditory omission errors from the dual condition (r = - 0.37), which suggests that state anxiety may improve divided attention performance. Results suggest that further examination of the neurobiological consequences of environmental stress on divided attention and other executive functioning tasks is needed.

Genetics of resistance to the geminivirus, Bean dwarf mosaic virus, and the role of the hypersensitive response in common bean.

PubMed

Seo, Y-S; Gepts, P; Gilbertson, R L

2004-03-01

Bean dwarf mosaic virus (BDMV) is a single-stranded DNA virus (genus: Begomovirus, family: Geminiviridae) that infects common bean ( Phaseolus vulgaris L.) and causes stunted plant growth, and mosaic and mottle symptoms in leaves. BDMV shows differential pathogenicity in common bean, infecting germplasm of the Andean gene pool (e.g., the snap bean cultivar Topcrop), but not that of the Middle American gene pool (e.g., the pinto bean cultivar Othello). Resistance to BDMV in Othello is associated with development of a hypersensitive response (HR) in vascular (phloem) tissues. In this study, Middle American germplasm representing the four recognized races (i.e., Durango, Guatemala, Jalisco, and Mesoamerica) and the parents of Othello were inoculated with BDMV and a BDMV-green fluorescent protein (GFP) reporter. All genotypes showed partial or complete resistance to BDMV and BDMV-GFP, indicating the widespread distribution of resistance in the Middle American gene pool. A number of BDMV-resistant germplasm did not show the HR, indicating it is not correlated with resistance. In the F(1), F(2), and F(3) of reciprocal crosses between Othello and Topcrop, a single dominant allele, Bdm, conferred BDMV resistance.

Sweet taste in apple: the role of sorbitol, individual sugars, organic acids and volatile compounds

NASA Astrophysics Data System (ADS)

Aprea, Eugenio; Charles, Mathilde; Endrizzi, Isabella; Laura Corollaro, Maria; Betta, Emanuela; Biasioli, Franco; Gasperi, Flavia

2017-03-01

Sweetness is one of the main drivers of consumer preference, and thus is given high priority in apple breeding programmes. Due to the complexity of sweetness evaluation, soluble solid content (SSC) is commonly used as an estimation of this trait. Nevertheless, it has been demonstrated that SSC and sweet taste are poorly correlated. Though individual sugar content may vary greatly between and within apple cultivars, no previous study has tried to investigate the relationship between the amount of individual sugars, or ratios of these, and apple sweetness. In this work, we quantified the major sugars (sucrose, glucose, fructose, xylose) and sorbitol and explored their influence on perceived sweetness in apple; we also related this to malic acid content, SSC and volatile compounds. Our data confirmed that the correlation between sweetness and SSC is weak. We found that sorbitol content correlates (similarly to SSC) with perceived sweetness better than any other single sugar or total sugar content. The single sugars show no differentiable importance in determining apple sweetness. Our predictive model based on partial least squares regression shows that after sorbitol and SSC, the most important contribution to apple sweetness is provided by several volatile compounds, mainly esters and farnesene.

Partial melting of lower oceanic crust gabbro: Constraints from poikilitic clinopyroxene primocrysts

NASA Astrophysics Data System (ADS)

Leuthold, Julien; Lissenberg, C. Johan; O'Driscoll, Brian; Karakas, Ozge; Falloon, Trevor; Klimentyeva, Dina N.; Ulmer, Peter

2018-03-01

Successive magma batches underplate, ascend, stall and erupt along spreading ridges, building the oceanic crust. It is therefore important to understand the processes and conditions under which magma differentiates at mid ocean ridges. Although fractional crystallization is considered to be the dominant mechanism for magma differentiation, open-system igneous complexes also experience Melting-Assimilation-Storage-Hybridization (MASH, Hildreth and Moorbath, 1988) processes. Here, we examine crystal-scale records of partial melting in lower crustal gabbroic cumulates from the slow-spreading Atlantic oceanic ridge (Kane Megamullion; collected with Jason ROV) and the fast-spreading East Pacific Rise (Hess Deep; IODP expedition 345). Clinopyroxene oikocrysts in these gabbros preserve marked intra-crystal geochemical variations that point to crystallization-dissolution episodes of the gabbro eutectic assemblage. Kane Megamullion and Hess Deep clinopyroxene core1 primocrysts and their plagioclase inclusions indicate crystallization from high temperature basalt (>1160 and >1200°C, respectively), close to clinopyroxene saturation temperature (<50% and <25% crystallization). Step-like compatible Cr (and co-varying Al) and incompatible Ti, Zr, Y and rare earth elements (REE) decrease from anhedral core1 to overgrown core2, while Mg# and Sr/Sr* ratios increase. We show that partial resorption textures and geochemical zoning result from partial melting of REE-poor lower oceanic crust gabbroic cumulate (protolith) following intrusion by hot primitive mantle-derived melt, and subsequent overgrowth crystallization (refertilization) from a hybrid melt. In addition, towards the outer rims of crystals, Ti, Zr, Y and the REE strongly increase and Al, Cr, Mg#, Eu/Eu* and Sr/Sr* decrease, suggesting crystallization either from late-stage percolating relatively differentiated melt or from in situ trapped melt. Intrusion of primitive hot reactive melt and percolation of interstitial differentiated melt are two distinct MASH processes in the lower oceanic crust. They are potentially fundamental mechanisms for generating the wide compositional variation observed in mid-ocean ridge basalts. We furthermore propose that such processes operate at both slow- and fast-spreading ocean ridges. Thermal numerical modelling shows that the degree of lower crustal partial melting at slow-spreading ridges can locally increase up to 50%, but the overall crustal melt volume is low (less than ca. 5% of total mantle-derived and crustal melts; ca. 20% in fast-spreading ridges).

Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

PubMed

Murase, Kenya

2016-01-01

In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

A systematic literature review of Burgers' equation with recent advances

NASA Astrophysics Data System (ADS)

Bonkile, Mayur P.; Awasthi, Ashish; Lakshmi, C.; Mukundan, Vijitha; Aswin, V. S.

2018-06-01

Even if numerical simulation of the Burgers' equation is well documented in the literature, a detailed literature survey indicates that gaps still exist for comparative discussion regarding the physical and mathematical significance of the Burgers' equation. Recently, an increasing interest has been developed within the scientific community, for studying non-linear convective-diffusive partial differential equations partly due to the tremendous improvement in computational capacity. Burgers' equation whose exact solution is well known, is one of the famous non-linear partial differential equations which is suitable for the analysis of various important areas. A brief historical review of not only the mathematical, but also the physical significance of the solution of Burgers' equation is presented, emphasising current research strategies, and the challenges that remain regarding the accuracy, stability and convergence of various schemes are discussed. One of the objectives of this paper is to discuss the recent developments in mathematical modelling of Burgers' equation and thus open doors for improvement. No claim is made that the content of the paper is new. However, it is a sincere effort to outline the physical and mathematical importance of Burgers' equation in the most simplified ways. We throw some light on the plethora of challenges which need to be overcome in the research areas and give motivation for the next breakthrough to take place in a numerical simulation of ordinary / partial differential equations.

Single-mode, narrow-linewidth external cavity quantum cascade laser through optical feedback from a partial-reflector.

PubMed

Cendejas, Richard A; Phillips, Mark C; Myers, Tanya L; Taubman, Matthew S

2010-12-06

An external-cavity (EC) quantum cascade (QC) laser using optical feedback from a partial-reflector is reported. With this configuration, the otherwise multi-mode emission of a Fabry-Perot QC laser was made single-mode with optical output powers exceeding 40 mW. A mode-hop free tuning range of 2.46 cm(-1) was achieved by synchronously tuning the EC length and QC laser current. The linewidth of the partial-reflector EC-QC laser was measured for integration times from 100 μs to 4 seconds, and compared to a distributed feedback QC laser. Linewidths as small as 480 kHz were recorded for the EC-QC laser.

Incorporating Conservation Zone Effectiveness for Protecting Biodiversity in Marine Planning

PubMed Central

Makino, Azusa; Klein, Carissa J.; Beger, Maria; Jupiter, Stacy D.; Possingham, Hugh P.

2013-01-01

Establishing different types of conservation zones is becoming commonplace. However, spatial prioritization methods that can accommodate multiple zones are poorly understood in theory and application. It is typically assumed that management regulations across zones have differential levels of effectiveness (“zone effectiveness”) for biodiversity protection, but the influence of zone effectiveness on achieving conservation targets has not yet been explored. Here, we consider the zone effectiveness of three zones: permanent closure, partial protection, and open, for planning for the protection of five different marine habitats in the Vatu-i-Ra Seascape, Fiji. We explore the impact of differential zone effectiveness on the location and costs of conservation priorities. We assume that permanent closure zones are fully effective at protecting all habitats, open zones do not contribute towards the conservation targets and partial protection zones lie between these two extremes. We use four different estimates for zone effectiveness and three different estimates for zone cost of the partial protection zone. To enhance the practical utility of the approach, we also explore how much of each traditional fishing ground can remain open for fishing while still achieving conservation targets. Our results show that all of the high priority areas for permanent closure zones would not be a high priority when the zone effectiveness of the partial protection zone is equal to that of permanent closure zones. When differential zone effectiveness and costs are considered, the resulting marine protected area network consequently increases in size, with more area allocated to permanent closure zones to meet conservation targets. By distributing the loss of fishing opportunity equitably among local communities, we find that 84–88% of each traditional fishing ground can be left open while still meeting conservation targets. Finally, we summarize the steps for developing marine zoning that accounts for zone effectiveness. PMID:24223870

Computation of partially invariant solutions for the Einstein Walker manifolds' identifying equations

NASA Astrophysics Data System (ADS)

Nadjafikhah, Mehdi; Jafari, Mehdi

2013-12-01

In this paper, partially invariant solutions (PISs) method is applied in order to obtain new four-dimensional Einstein Walker manifolds. This method is based on subgroup classification for the symmetry group of partial differential equations (PDEs) and can be regarded as the generalization of the similarity reduction method. For this purpose, those cases of PISs which have the defect structure δ=1 and are resulted from two-dimensional subalgebras are considered in the present paper. Also it is shown that the obtained PISs are distinct from the invariant solutions that obtained by similarity reduction method.

Seismological Signature of Chemical Differentiation of Earth's Upper Mantle

NASA Astrophysics Data System (ADS)

Matsukage, K. N.; Nishihara, Y.; Karato, S.

2004-12-01

Chemical differentiation from a primitive rock (such as pyrolite) to harzburgite due to partial melting and melt extraction is one of the most important mechanisms that causes the chemical heterogeneity in Earth's upper mantle. In this study, we investigate the seismic signature of chemical differentiation that helps mapping chemical heterogeneity in the upper mantle. The relation between chemical differentiation and its seismological signature is not straightforward because a large number of unknown parameters are involved although the seismological observations provide only a few parameters (e.g., VP, VS, QP). Therefore it is critical to identify a small number of parameters by which the gross trend of chemical evolution can be described. The variation in major element composition in natural samples reflect complicated processes that include not only partial melting but also other complex processes (e.g., metasomatism, influx melting). We investigate the seismic velocities of hypothetical but well-defined simple chemical differentiation processes (e.g., partial melting of various pressure conditions, addition of Si-rich melt or fluid), which cover the chemical variation of the natural mantle peridotites with various tectonic settings (mid ocean ridge, island arc and continent). The seismic velocities of the peridotites were calculated to 13 GPa and 1730 K. We obtained two major conclusions. First is that the variations of seismic velocities of upper mantle peridotites can be interpreted in terms of a few distinct parameters. For one class of peridotites which is formed by simple partial melting (e.g. mid-ocean ridges peridotites), seismic velocities can be described in terms of one parameter, namely Mg# (=Mg/(Mg+Fe) atomic ratio). In contrast, some of the peridotites in the continental (cratonic) environment with high silica content and high Mg# need at least two parameters (such as Mg# and Opx# (the volume fraction of orthopyroxene)) are needed to characterize their seismic velocities. Second is the jump of seismic velocity at 300 km in harzburgite that is caused by orthorhombic (opx) to high-pressure monoclinic phase transition in MgSiO3 pyroxene. If opx-rich harzburgite (the maximum content of opx in continental harzburgite is ˜45 vol%) exists at around 300km, the maximum contrast of jump would be 2.5 % for VS and 0.9 % for VP. This phase transition will correspond to the seismological discontinuity around 300km (X-discontinuity).

Low temperature time resolved photoluminescence in ordered and disordered Cu2ZnSnS4 single crystals

NASA Astrophysics Data System (ADS)

Raadik, Taavi; Krustok, Jüri; Kauk-Kuusik, M.; Timmo, K.; Grossberg, M.; Ernits, K.; Bleuse, J.

2017-03-01

In this work we performed time-resolved micro-photoluminescence (TRPL) studies of Cu2ZnSnS4 (CZTS) single crystals grown in molten KI salt. The order/disorder degree of CZTS was varied by the thermal post treatment temperature. Photoluminescence spectra measured at T=8 K showed an asymmetric band with a peak position of 1.33 eV and 1.27 eV for partially ordered and disordered structures, respectively. Thermal activation energies were found to be ET (PO) =65±9 meV for partially ordered and ET (PD) =27±4 meV for partially disordered. These low activation energy values indicating to the defect cluster recombination model for both partially ordered and disordered structures. TRPL was measured for both crystals and their decay curves were fitted with a stretched exponential function, in order to describe the charge carriers' recombination dynamics at low temperature.

An experimental investigation on the ultimate strength of epoxy repaired braced partial infilled RC frames

NASA Astrophysics Data System (ADS)

Dubey, Shailendra Kumar Damodar; Kute, Sunil

2014-09-01

Due to earthquake, buildings are damaged partially or completely. Particularly structures with soft storey are mostly affected. In general, such damaged structures are repaired and reused. In this regard, an experimental investigation was planned and conducted on models of single-bay, single-storey of partial concrete infilled reinforced concrete (RC) frames up to collapse with corner, central and diagonal steel bracings. Such collapsed frames were repaired with epoxy resin and retested. The initiative was to identify the behaviour, extent of restored ultimate strength and deflection of epoxy-retrofitted frames in comparison to the braced RC frames. The performance of such frames has been considered only for lateral loads. In comparison to bare RC frames, epoxy repaired partial infilled frames have significant increase in the lateral load capacity. Central bracing is more effective than corner and diagonal bracing. For the same load, epoxy repaired frames have comparable deflection than similar braced frames.

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

NASA Technical Reports Server (NTRS)

Smith, R. C.; Bowers, K. L.; Lund, J.

1990-01-01

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE Office of Scientific and Technical Information (OSTI.GOV)

Engwer, C.; Falgout, R. D.; Yang, U. M.

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Inclusion of exact exchange in the noniterative partial-differential-equation method of electron-molecule scattering - Application to e-N2

NASA Technical Reports Server (NTRS)

Weatherford, C. A.; Onda, K.; Temkin, A.

1985-01-01

The noniterative partial-differential-equation (PDE) approach to electron-molecule scattering of Onda and Temkin (1983) is modified to account for the effects of exchange explicitly. The exchange equation is reduced to a set of inhomogeneous equations containing no integral terms and solved noniteratively in a difference form; a method for propagating the solution to large values of r is described; the changes in the polarization potential of the original PDE method required by the inclusion of exact static exchange are indicated; and the results of computations for e-N2 scattering in the fixed-nuclei approximation are presented in tables and graphs and compared with previous calculations and experimental data. Better agreement is obtained using the modified PDE method.

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

Mathematical Analysis and Optimization of Infiltration Processes

NASA Technical Reports Server (NTRS)

Chang, H.-C.; Gottlieb, D.; Marion, M.; Sheldon, B. W.

1997-01-01

A variety of infiltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial differential equation describing the evolution of the solid phase, coupled to one or more partial differential equations describing mass transport through a porous structure. This paper presents a detailed mathematical analysis of a relatively simple set of equations which is used to describe chemical vapor infiltration. The results demonstrate that the process is controlled by only two parameters, alpha and beta. The optimization problem associated with minimizing the infiltration time is also considered. Allowing alpha and beta to vary with time leads to significant reductions in the infiltration time, compared with the conventional case where alpha and beta are treated as constants.

Miscibility, Crystallization, and Rheological Behavior of Solution Casting Poly(3-hydroxybutyrate)/poly(ethylene succinate) Blends Probed by Differential Scanning Calorimetry, Rheology, and Optical Microscope Techniques

NASA Astrophysics Data System (ADS)

Sun, Wei-hua; Qiao, Xiao-ping; Cao, Qi-kun; Liu, Jie-ping

2010-02-01

The miscibility and crystallization of solution casting biodegradable poly(3-hydroxybutyrate)/poly(ethylene succinate) (PHB/PES) blends was investigated by differential scanning calorimetry, rheology, and optical microscopy. The blends showed two glass transition temperatures and a depression of melting temperature of PHB with compositions in phase diagram, which indicated that the blend was partially miscible. The morphology observation supported this result. It was found that the PHB and PES can crystallize simultaneously or upon stepwise depending on the crystallization temperatures and compositions. The spherulite growth rate of PHB increased with increasing of PES content. The influence of compositions on the spherulitic growth rate for the partially miscible polymer blends was discussed.

Stencil computations for PDE-based applications with examples from DUNE and hypre

DOE PAGES

Engwer, C.; Falgout, R. D.; Yang, U. M.

2017-02-24

Here, stencils are commonly used to implement efficient on–the–fly computations of linear operators arising from partial differential equations. At the same time the term “stencil” is not fully defined and can be interpreted differently depending on the application domain and the background of the software developers. Common features in stencil codes are the preservation of the structure given by the discretization of the partial differential equation and the benefit of minimal data storage. We discuss stencil concepts of different complexity, show how they are used in modern software packages like hypre and DUNE, and discuss recent efforts to extend themore » software to enable stencil computations of more complex problems and methods such as inf–sup–stable Stokes discretizations and mixed finite element discretizations.« less

Modeling tree crown dynamics with 3D partial differential equations.

PubMed

Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry

2014-01-01

We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.

Jeffrey fluid effect on free convective over a vertically inclined plate with magnetic field: A numerical approach

NASA Astrophysics Data System (ADS)

Rao, J. Anand; Raju, R. Srinivasa; Bucchaiah, C. D.

2018-05-01

In this work, the effect of magnetohydrodynamic natural or free convective of an incompressible, viscous and electrically conducting non-newtonian Jeffrey fluid over a semi-infinite vertically inclined permeable moving plate embedded in a porous medium in the presence of heat absorption, heat and mass transfer. By using non-dimensional quantities, the fundamental governing non-linear partial differential equations are transformed into linear partial differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational finite element method. The sway of important key parameters on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Finally the results are compared with the works published previously and found to be excellent agreement.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

Stable multi-domain spectral penalty methods for fractional partial differential equations

NASA Astrophysics Data System (ADS)

Xu, Qinwu; Hesthaven, Jan S.

2014-01-01

We propose stable multi-domain spectral penalty methods suitable for solving fractional partial differential equations with fractional derivatives of any order. First, a high order discretization is proposed to approximate fractional derivatives of any order on any given grids based on orthogonal polynomials. The approximation order is analyzed and verified through numerical examples. Based on the discrete fractional derivative, we introduce stable multi-domain spectral penalty methods for solving fractional advection and diffusion equations. The equations are discretized in each sub-domain separately and the global schemes are obtained by weakly imposed boundary and interface conditions through a penalty term. Stability of the schemes are analyzed and numerical examples based on both uniform and nonuniform grids are considered to highlight the flexibility and high accuracy of the proposed schemes.

Mean field games with congestion

NASA Astrophysics Data System (ADS)

Achdou, Yves; Porretta, Alessio

2018-03-01

We consider a class of systems of time dependent partial differential equations which arise in mean field type models with congestion. The systems couple a backward viscous Hamilton-Jacobi equation and a forward Kolmogorov equation both posed in $(0,T)\\times (\\mathbb{R}^N /\\mathbb{Z}^N)$. Because of congestion and by contrast with simpler cases, the latter system can never be seen as the optimality conditions of an optimal control problem driven by a partial differential equation. The Hamiltonian vanishes as the density tends to $+\\infty$ and may not even be defined in the regions where the density is zero. After giving a suitable definition of weak solutions, we prove the existence and uniqueness results of the latter under rather general assumptions. No restriction is made on the horizon $T$.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

NASA Astrophysics Data System (ADS)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Isostable reduction with applications to time-dependent partial differential equations.

PubMed

Wilson, Dan; Moehlis, Jeff

2016-07-01

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

Workload Characterization of CFD Applications Using Partial Differential Equation Solvers

NASA Technical Reports Server (NTRS)

Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)

1998-01-01

Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.

Online sequential Monte Carlo smoother for partially observed diffusion processes

NASA Astrophysics Data System (ADS)

Gloaguen, Pierre; Étienne, Marie-Pierre; Le Corff, Sylvain

2018-12-01

This paper introduces a new algorithm to approximate smoothed additive functionals of partially observed diffusion processes. This method relies on a new sequential Monte Carlo method which allows to compute such approximations online, i.e., as the observations are received, and with a computational complexity growing linearly with the number of Monte Carlo samples. The original algorithm cannot be used in the case of partially observed stochastic differential equations since the transition density of the latent data is usually unknown. We prove that it may be extended to partially observed continuous processes by replacing this unknown quantity by an unbiased estimator obtained for instance using general Poisson estimators. This estimator is proved to be consistent and its performance are illustrated using data from two models.

Multi-output differential technologies

NASA Astrophysics Data System (ADS)

Bidare, Srinivas R.

1997-01-01

A differential is a very old and proven mechanical device that allows a single input to be split into two outputs having equal torque irrespective of the output speeds. A standard differential is capable of providing only two outputs from a single input. A recently patented multi-output differential technology known as `Plural-Output Differential' allows a single input to be split into many outputs. This new technology is the outcome of a systematic study of complex gear trains (Bidare 1992). The unique feature of a differential (equal torque at different speeds) can be applied to simplify the construction and operation of many complex mechanical devices that require equal torque's or forces at multiple outputs. It is now possible to design a mechanical hand with three or more fingers with equal torque. Since these finger are powered via a differential they are `mechanically intelligent'. A prototype device is operational and has been used to demonstrate the utility and flexibility of the design. In this paper we shall review two devices that utilize the new technology resulting in increased performance, robustness with reduced complexity and cost.

CpG methylation patterns and decitabine treatment response in acute myeloid leukemia cells and normal hematopoietic precursors

PubMed Central

Negrotto, Soledad; Ng, Kwok Peng; Jankowska, Ania M.; Bodo, Juraj; Gopalan, Banu; Guinta, Kathryn; Mulloy, James C.; Hsi, Eric; Maciejewski, Jaroslaw; Saunthararajah, Yogen

2011-01-01

The DNA hypomethylating drug decitabine maintains normal hematopoietic stem cell (HSC) self-renewal but induces terminal differentiation in acute myeloid leukemia (AML) cells. The basis for these contrasting cell-fates, and for selective CpG hypomethylation by decitabine, is poorly understood. Promoter CpGs, with methylation measured by microarray, were classified by the direction of methylation change with normal myeloid maturation. In AML cells, the methylation pattern at maturation-responsive CpG suggested at least partial maturation. Consistent with partial maturation, in gene expression analyses, AML cells expressed high levels of the key lineage-specifying factor CEBPA, but relatively low levels of the key late-differentiation driver CEBPE. In methylation analysis by mass-spectrometry, CEBPE promoter CpG that are usually hypomethylated during granulocyte maturation were significantly hypermethylated in AML cells. Decitabine treatment induced cellular differentiation of AML cells, and the largest methylation decreases were at CpG that are hypomethylated with myeloid maturation, including CEBPE promoter CpG. In contrast, decitabine-treated normal HSC retained immature morphology, and methylation significantly decreased at CpG that are less methylated in immature cells. High expression of lineage-specifying factor and aberrant epigenetic repression of some key late-differentiation genes distinguishes AML cells from normal HSC and could explain the contrasting differentiation and methylation responses to decitabine. PMID:21836612

Phenolic Analysis and Theoretic Design for Chinese Commercial Wines' Authentication.

PubMed

Li, Si-Yu; Zhu, Bao-Qing; Reeves, Malcolm J; Duan, Chang-Qing

2018-01-01

To develop a robust tool for Chinese commercial wines' varietal, regional, and vintage authentication, phenolic compounds in 121 Chinese commercial dry red wines were detected and quantified by using high-performance liquid chromatography triple-quadrupole mass spectrometry (HPLC-QqQ-MS/MS), and differentiation abilities of principal component analysis (PCA), partial least squares discriminant analysis (PLS-DA), and orthogonal partial least squares discriminant analysis (OPLS-DA) were compared. Better than PCA and PLS-DA, OPLS-DA models used to differentiate wines according to their varieties (Cabernet Sauvignon or other varieties), regions (east or west Cabernet Sauvignon wines), and vintages (young or old Cabernet Sauvignon wines) were ideally established. The S-plot provided in OPLS-DA models showed the key phenolic compounds which were both statistically and biochemically significant in sample differentiation. Besides, the potential of the OPLS-DA models in deeper sample differentiating of more detailed regional and vintage information of wines was proved optimistic. On the basis of our results, a promising theoretic design for wine authentication was further proposed for the first time, which might be helpful in practical authentication of more commercial wines. The phenolic data of 121 Chinese commercial dry red wines was processed with different statistical tools for varietal, regional, and vintage differentiation. A promising theoretical design was summarized, which might be helpful for wine authentication in practical situation. © 2017 Institute of Food Technologists®.

Correlation effects in elastic e-N2 scattering

NASA Technical Reports Server (NTRS)

Huo, Winifred M.; Lima, Marco A. P.; Gibson, Thomas L.; Mckoy, Vincent

1987-01-01

The Schwinger multichannel formulation has been applied to study the role of electron correlation in low-energy e-N2 scattering. For the five nonresonant partial-wave channels studied here, angular correlation is found to be much more important than radial correlation. The calculated total and differential cross sections agree well with experiment except for the differential cross sections at 1.5 eV.

Multiscale functions, scale dynamics, and applications to partial differential equations

NASA Astrophysics Data System (ADS)

Cresson, Jacky; Pierret, Frédéric

2016-05-01

Modeling phenomena from experimental data always begins with a choice of hypothesis on the observed dynamics such as determinism, randomness, and differentiability. Depending on these choices, different behaviors can be observed. The natural question associated to the modeling problem is the following: "With a finite set of data concerning a phenomenon, can we recover its underlying nature? From this problem, we introduce in this paper the definition of multi-scale functions, scale calculus, and scale dynamics based on the time scale calculus [see Bohner, M. and Peterson, A., Dynamic Equations on Time Scales: An Introduction with Applications (Springer Science & Business Media, 2001)] which is used to introduce the notion of scale equations. These definitions will be illustrated on the multi-scale Okamoto's functions. Scale equations are analysed using scale regimes and the notion of asymptotic model for a scale equation under a particular scale regime. The introduced formalism explains why a single scale equation can produce distinct continuous models even if the equation is scale invariant. Typical examples of such equations are given by the scale Euler-Lagrange equation. We illustrate our results using the scale Newton's equation which gives rise to a non-linear diffusion equation or a non-linear Schrödinger equation as asymptotic continuous models depending on the particular fractional scale regime which is considered.

Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass

NASA Astrophysics Data System (ADS)

Malaeke, Hasan; Moeenfard, Hamid

2016-03-01

The objective of this paper is to study large amplitude flexural-extensional free vibration of non-uniform cantilever beams carrying a both transversely and axially eccentric tip mass. The effects of variable axial force is also taken into account. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. A numerical finite difference scheme is proposed to find the natural frequencies and mode shapes of the system which is validated specifically for a beam with linearly varying cross section. Using a single mode approximation in conjunction with the Lagrange method, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. These temporal coupled equations are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The qualitative and quantitative knowledge resulting from this research is expected to enable the study of the effects of eccentric tip mass and non-uniformity on the large amplitude flexural-extensional vibration of beams for improved dynamic performance.

Fluid flow and heat transfer of carbon nanotubes along a flat plate with Navier slip boundary

NASA Astrophysics Data System (ADS)

Khan, W. A.; Khan, Z. H.; Rahi, M.

2014-06-01

Homogeneous flow model is used to study the flow and heat transfer of carbon nanotubes (CNTs) along a flat plate subjected to Navier slip and uniform heat flux boundary conditions. This is the first paper on the flow and heat transfer of CNTs along a flat plate. Two types of CNTs, namely, single- and multi-wall CNTs are used with water, kerosene or engine oil as base fluids. The empirical correlations are used for the thermophysical properties of CNTs in terms of the solid volume fraction of CNTs. For the effective thermal conductivity of CNTs, Xue (Phys B Condens Matter 368:302-307, 2005) model has been used and the results are compared with the existing theoretical models. The governing partial differential equations and boundary conditions are converted into a set of nonlinear ordinary differential equations using suitable similarity transformations. These equations are solved numerically using a very efficient finite difference method with shooting scheme. The effects of the governing parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are investigated and presented in graphical and tabular forms. The numerical results of skin friction and Nusselt numbers are compared with the available data for special cases and are found in good agreement.

Chromosome speciation: Humans, Drosophila, and mosquitoes

PubMed Central

Ayala, Francisco J.; Coluzzi, Mario

2005-01-01

Chromosome rearrangements (such as inversions, fusions, and fissions) may play significant roles in the speciation between parapatric (contiguous) or partly sympatric (geographically overlapping) populations. According to the “hybrid-dysfunction” model, speciation occurs because hybrids with heterozygous chromosome rearrangements produce dysfunctional gametes and thus have low reproductive fitness. Natural selection will, therefore, promote mutations that reduce the probability of intercrossing between populations carrying different rearrangements and thus promote their reproductive isolation. This model encounters a disabling difficulty: namely, how to account for the spread in a population of a chromosome rearrangement after it first arises as a mutation in a single individual. The “suppressed-recombination” model of speciation points out that chromosome rearrangements act as a genetic filter between populations. Mutations associated with the rearranged chromosomes cannot flow from one to another population, whereas genetic exchange will freely occur between colinear chromosomes. Mutations adaptive to local conditions will, therefore, accumulate differentially in the protected chromosome regions so that parapatric or partially sympatric populations will genetically differentiate, eventually evolving into different species. The speciation model of suppressed recombination has recently been tested by gene and DNA sequence comparisons between humans and chimpanzees, between Drosophila species, and between species related to Anopheles gambiae, the vector of malignant malaria in Africa. PMID:15851677

Dynamics and Collapse in a Power System Model with Voltage Variation: The Damping Effect.

PubMed

Ma, Jinpeng; Sun, Yong; Yuan, Xiaoming; Kurths, Jürgen; Zhan, Meng

2016-01-01

Complex nonlinear phenomena are investigated in a basic power system model of the single-machine-infinite-bus (SMIB) with a synchronous generator modeled by a classical third-order differential equation including both angle dynamics and voltage dynamics, the so-called flux decay equation. In contrast, for the second-order differential equation considering the angle dynamics only, it is the classical swing equation. Similarities and differences of the dynamics generated between the third-order model and the second-order one are studied. We mainly find that, for positive damping, these two models show quite similar behavior, namely, stable fixed point, stable limit cycle, and their coexistence for different parameters. However, for negative damping, the second-order system can only collapse, whereas for the third-order model, more complicated behavior may happen, such as stable fixed point, limit cycle, quasi-periodicity, and chaos. Interesting partial collapse phenomena for angle instability only and not for voltage instability are also found here, including collapse from quasi-periodicity and from chaos etc. These findings not only provide a basic physical picture for power system dynamics in the third-order model incorporating voltage dynamics, but also enable us a deeper understanding of the complex dynamical behavior and even leading to a design of oscillation damping in electric power systems.

Identification and Partial Structural Characterization of Mass Isolated Valsartan and Its Metabolite with Messenger Tagging Vibrational Spectroscopy

NASA Astrophysics Data System (ADS)

Gorlova, Olga; Colvin, Sean M.; Brathwaite, Antonio; Menges, Fabian S.; Craig, Stephanie M.; Miller, Scott J.; Johnson, Mark A.

2017-08-01

Recent advances in the coupling of vibrational spectroscopy with mass spectrometry create new opportunities for the structural characterization of metabolites with great sensitivity. Previous studies have demonstrated this scheme on 300 K ions using very high power free electron lasers in the fingerprint region of the infrared. Here we extend the scope of this approach to a single investigator scale as well as extend the spectral range to include the OH stretching fundamentals. This is accomplished by detecting the IR absorptions in a linear action regime by photodissociation of weakly bound N2 molecules, which are attached to the target ions in a cryogenically cooled, rf ion trap. We consider the specific case of the widely used drug Valsartan and two isomeric forms of its metabolite. Advantages and challenges of the cold ion approach are discussed, including disentangling the role of conformers and the strategic choices involved in the selection of the charging mechanism that optimize spectral differentiation among candidate structural isomers. In this case, the Na+ complexes are observed to yield sharp resonances in the high frequency NH and OH stretching regions, which can be used to easily differentiate between two isomers of the metabolite. [Figure not available: see fulltext.

No-go for partially massless spin-2 Yang-Mills

DOE PAGES

Garcia-Saenz, Sebastian; Hinterbichler, Kurt; Joyce, Austin; ...

2016-02-05

There are various no-go results forbidding self-interactions for a single partially massless spin-2 field. Given the photon-like structure of the linear partially massless field, it is natural to ask whether a multiplet of such fields can interact under an internal Yang-Mills like extension of the partially massless symmetry. In this paper, we give two arguments that such a partially massless Yang-Mills theory does not exist. The first is that there is no Yang-Mills like non-abelian deformation of the partially massless symmetry, and the second is that cubic vertices with the appropriate structure constants do not exist.

Nonlinear differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis ismore » on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.« less

Rasch-Master's Partial Credit Model in the assessment of children's creativity in drawings.

PubMed

Nakano, Tatiana de Cássia; Primi, Ricardo

2014-01-01

The purpose of the present study was to use the Partial Credit Model to study the factors of the Test of Creativity in Children and identify which characteristics of the creative person would be more effective to differentiate subjects according to their ability level. A sample of 1426 students from first to eighth grades answered the instrument. The Partial Credits model was used to estimate the ability of the subjects and item difficulties on a common scale for each of the four factors, indicating which items required a higher level of creativity to be scored and will differentiate the more creative individuals. The results demonstrated that the greater part of the characteristics showed good fit indices, with values between 0.80 and 1.30 both infit and outfit, indicating a response pattern consistent with the model. The characteristics of Unusual Perspective, Expression of Emotion and Originality have been identified as better predictors of creative performance because requires greater ability level (usually above two standard deviation). These results may be used in the future development of an instrument's reduced form or simplification of the current correction model.

Negative differential resistance in partially fluorinated graphene films

NASA Astrophysics Data System (ADS)

Antonova, I. V.; Shojaei, S.; Sattari-Esfahlan, S. M.; Kurkina, Irina I.

2017-07-01

Partially fluorinated graphene films were created by chemical functionalization of graphene layers in an aqueous solution of hydrofluoric acid. The formation of graphene islands or graphene quantum dots (GQDs) and a fluorinated graphene network is demonstrated in such films. Negative differential resistance (NDR) resulting from the formation of the potential barrier system in the films was observed for different fluorination degrees of suspension. The origin of the NDR varies with an increase in the fluorination degree of the suspension. Numerical calculations were performed to elucidate the tunneling between adjacent energy levels and creation of NDR. It was found that in the case of films with smaller flake and smaller GQD sizes, multi-peak NDR appears in the I-V curve. We predict that the NDR peak position shifts towards lower voltage with a decrease in the GQD size. Surprisingly, we observed a negative step-like valley for positive biases in the I-V curve of samples. Our findings with detailed analysis shed light on understanding the mechanisms of the NDR phenomenon in a partially fluorinated graphene system.

Working memory component processes: isolating BOLD signal changes.

PubMed

Motes, Michael A; Rypma, Bart

2010-01-15

The chronology of the component processes subserving working memory (WM) and hemodynamic response lags has hindered the use of fMRI for exploring neural substrates of WM. In the present study, however, participants completed full trials that involved encoding two or six letters, maintaining the memory set over a delay, and then deciding whether a probe was in the memory set or not. Additionally, they completed encode-only, encode-and-maintain, and encode-and-decide partial trials intermixed with the full trials. The inclusion of partial trials allowed for the isolation of BOLD signal changes to the different trial periods. The results showed that only lateral and medial prefrontal cortex regions differentially responded to the 2- and 6-letter memory sets over the trial periods, showing greater activation to 6-letter sets during the encode and maintain trial periods. Thus, the data showed the differential involvement of PFC in the encoding and maintenance of supra- and sub-capacity memory sets and show the efficacy of using fMRI partial trial methods to study WM component processes.

Working Memory Component Processes: Isolating BOLD Signal-Changes

PubMed Central

Motes, Michael A.; Rypma, Bart

2009-01-01

The chronology of the component processes subserving working memory (WM) and hemodynamic response lags have hindered the use of fMRI for exploring neural substrates of WM. In the present study, however, participants completed full trials that involved encoding two or six letters, maintaining the memory-set over a delay, and then deciding whether a probe was in the memory-set or not. Additionally, they completed encode only, encode and maintain, and encode and decide partial-trials intermixed with the full-trials. The inclusion of partial-trials allowed for the isolation of BOLD signal-changes to the different trial-periods. The results showed that only lateral and medial prefrontal cortex regions differentially responded to the 2- and 6-letter memory-sets over the trial-periods, showing greater activation to 6-letter sets during the encode and maintain trial-periods. Thus, the data showed the differential involvement of PFC in the encoding and maintenance of supra- and sub-capacity memory-sets and show the efficacy of using fMRI partial-trial methods to study WM component processes. PMID:19732840

Diffusion maps for high-dimensional single-cell analysis of differentiation data.

PubMed

Haghverdi, Laleh; Buettner, Florian; Theis, Fabian J

2015-09-15

Single-cell technologies have recently gained popularity in cellular differentiation studies regarding their ability to resolve potential heterogeneities in cell populations. Analyzing such high-dimensional single-cell data has its own statistical and computational challenges. Popular multivariate approaches are based on data normalization, followed by dimension reduction and clustering to identify subgroups. However, in the case of cellular differentiation, we would not expect clear clusters to be present but instead expect the cells to follow continuous branching lineages. Here, we propose the use of diffusion maps to deal with the problem of defining differentiation trajectories. We adapt this method to single-cell data by adequate choice of kernel width and inclusion of uncertainties or missing measurement values, which enables the establishment of a pseudotemporal ordering of single cells in a high-dimensional gene expression space. We expect this output to reflect cell differentiation trajectories, where the data originates from intrinsic diffusion-like dynamics. Starting from a pluripotent stage, cells move smoothly within the transcriptional landscape towards more differentiated states with some stochasticity along their path. We demonstrate the robustness of our method with respect to extrinsic noise (e.g. measurement noise) and sampling density heterogeneities on simulated toy data as well as two single-cell quantitative polymerase chain reaction datasets (i.e. mouse haematopoietic stem cells and mouse embryonic stem cells) and an RNA-Seq data of human pre-implantation embryos. We show that diffusion maps perform considerably better than Principal Component Analysis and are advantageous over other techniques for non-linear dimension reduction such as t-distributed Stochastic Neighbour Embedding for preserving the global structures and pseudotemporal ordering of cells. The Matlab implementation of diffusion maps for single-cell data is available at https://www.helmholtz-muenchen.de/icb/single-cell-diffusion-map. fbuettner.phys@gmail.com, fabian.theis@helmholtz-muenchen.de Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Evaluation of full S1 gene sequencing of classical and variant infectious bronchitis viruses extracted from allantoic fluid and FTA cards.

PubMed

Manswr, Basim; Ball, Christopher; Forrester, Anne; Chantrey, Julian; Ganapathy, Kannan

2018-08-01

Sequence variability in the S1 gene determines the genotype of infectious bronchitis virus (IBV) strains. A single RT-PCR assay was developed to amplify and sequence the full S1 gene for six classical and variant IBVs (M41, D274, 793B, IS/885/00, IS/1494/06 and Q1) enriched in allantoic fluid (AF) or the same AF inoculated onto Flinders Technology Association (FTA) cards. Representative strains from each genotype were grown in specific-pathogen-free eggs and RNA was extracted from AF. Full S1 gene amplification was achieved using primer A and primer 22.51. Products were sequenced using primers A, 1050+, 1380+ and SX3+ to obtain short sequences covering the full gene. Following serial dilutions of AF, detection limits of the partial assay were higher than those of the full S1 gene. Partial S1 sequences exhibited higher-than-average nucleotide similarity percentages (79%; 352 bp) compared to full S1 sequences (77%; 1756 bp), suggesting that full S1 analysis allows greater strain differentiation. For IBV detection from AF-inoculated FTA cards, four serotypes were incubated for up to 21 days at three temperatures, 4°C, room temperature (approximately 24°C) and 40°C. RNA was extracted and tested with partial and full S1 protocols. Through partial sequencing, all IBVs were successfully detected at all sampling points and storage temperatures. In contrast, using full S1 sequencing it was not possible to amplify the gene beyond 14 days or when stored at 40°C. Data presented show that for full S1 sequencing, a substantial amount of RNA is needed. Field samples collected onto FTA cards are unlikely to yield such quantity or quality. AF: allantoic fluid; CD50: ciliostatic dose 50; FTA: Flinders Technology Association; IB: infectious bronchitis; IBV: infectious bronchitis virus.

Analytical results for post-buckling behaviour of plates in compression and in shear

NASA Technical Reports Server (NTRS)

Stein, M.

1985-01-01

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Comparison of transcript profiles in different life stages of the nematode Globodera pallida under different host potato genotypes.

PubMed

Palomares-Rius, Juan E; Hedley, Pete E; Cock, Peter J A; Morris, Jenny A; Jones, John T; Vovlas, Nikos; Blok, Vivian

2012-12-01

The potato cyst nematodes (PCNs) Globodera pallida and Globodera rostochiensis are important parasites of potato. PCNs undergo complex biotrophic interactions with their hosts that involve gene expression changes in both the nematode and the host plant. The aim of this study was to determine key genes that are differentially expressed in Globodera pallida life cycle stages and during the initiation of the feeding site in susceptible and partially resistant potato genotypes. For this purpose, two microarray experiments were designed: (i) a comparison of eggs, infective second-stage juveniles (J2s) and sedentary parasitic-stage J2s (SJ2); (ii) a comparison of SJ2s at 8 days after inoculation (DAI) in the susceptible cultivar (Desirée) and two partially resistant lines. The results showed differential expression of G. pallida genes during the stages studied, including previously characterized effectors. In addition, a large number of genes changed their expression between SJ2s in the susceptible cultivar and those infecting partially resistant lines; the number of genes with modified expression was lower when the two partially resistant lines were compared. Moreover, a histopathological study was performed at several time points (7, 14 and 30 DAI) and showed the similarities between both partially resistant lines with a delay and degeneration in the formation of the syncytia in comparison with the susceptible cultivar. Females at 30 DAI in partially resistant lines showed a delay in their development in comparison with those in the susceptible cultivar. © 2012 THE AUTHORS. MOLECULAR PLANT PATHOLOGY © 2012 BSPP AND BLACKWELL PUBLISHING LTD.