Modeling Three-Dimensional Groundwater Flow and Solute Transport by the Finite Element Method With Parameter Estimation.

A general, systematic and improved numerical formulation for the three-dimensional (3-D) groundwater flow and solute transport problems was derived, using the finite element method. In the numerical formulation, a hidden mistake, which has appeared in many textbooks and journal papers dealing with the advective term of the general 3-D solute transport equation, was found and corrected. Some simpler and practical expressions for the leaky boundary condition, surface flux condition, and sources and sinks were proposed. To improve the conventional formulation for the time derivatives, a combination of the Galerkin method and the collocation method was developed. A more accurate scheme was derived to solve the resulting system of ordinary differential equations using the finite integration. Based on the numerical formulations, three computer models were developed for modeling (1) 3-D steady groundwater flow, (2) 3-D unsteady groundwater flow, and (3) 3-D solute transport. These models are rather general in terms of initial conditions, boundary conditions, and fluid and aquifer properties. The three models were tested using a variety of one-dimensional and two-dimensional analytical solutions and numerical models. Computed results showed that all these models are relatively simple, stable and accurate, and have little chance of experiencing any numerical problems. Component and parameter sensitivity analyses were also made. In general, these models are relatively insensitive to time step size, and the new solute transport model yields reasonable results even if the Peclet number reaches 50. In order to estimate model parameters, a fast, reliable, and derivative-free subroutine was developed by combining the quadratic interpolation search, the Golden section search, and the side-search algorithms, for finding the minimum of any user-defined 1-D function. With this 1-D subroutine, a general conjugate gradient search program was then developed to find the optimal set of parameters for any type of model. The program was tested using a variety of analytical functions and found to be accurate, fast and efficient. The program was applied to estimate parameters of the 3-D solute transport model, using two types of sampling methods and four types of data sets

Wave propagation in one-dimensional nonlinear acoustic metamaterials

The propagation of waves in the nonlinear acoustic metamaterials (NAMs) is fundamentally different from that in the conventional linear ones. In this article we consider two one-dimensional NAM systems featuring respectively a diatomic and a tetratomic meta unit-cell. We investigate the attenuation of the wave, the band structure and the bifurcations to demonstrate novel nonlinear effects, which can significantly expand the bandwidth for elastic wave suppression and cause nonlinear wave phenomena. Harmonic averaging approach, continuation algorithm, Lyapunov exponents are combined to study the frequency responses, the nonlinear modes, bifurcations of periodic solutions and chaos. The nonlinear resonances are studied and the influence of damping on hyper-chaotic attractors is evaluated. Moreover, a "quantum" behavior is found between the low-energy and high-energy orbits. This work provides an important theoretical base for the further understandings and applications of NAMs

Function annotation of hepatic retinoid x receptor α based on genome-wide DNA binding and transcriptome profiling.

BackgroundRetinoid x receptor α (RXRα) is abundantly expressed in the liver and is essential for the function of other nuclear receptors. Using chromatin immunoprecipitation sequencing and mRNA profiling data generated from wild type and RXRα-null mouse livers, the current study identifies the bona-fide hepatic RXRα targets and biological pathways. In addition, based on binding and motif analysis, the molecular mechanism by which RXRα regulates hepatic genes is elucidated in a high-throughput manner.Principal findingsClose to 80% of hepatic expressed genes were bound by RXRα, while 16% were expressed in an RXRα-dependent manner. Motif analysis predicted direct repeat with a spacer of one nucleotide as the most prevalent RXRα binding site. Many of the 500 strongest binding motifs overlapped with the binding motif of specific protein 1. Biological functional analysis of RXRα-dependent genes revealed that hepatic RXRα deficiency mainly resulted in up-regulation of steroid and cholesterol biosynthesis-related genes and down-regulation of translation- as well as anti-apoptosis-related genes. Furthermore, RXRα bound to many genes that encode nuclear receptors and their cofactors suggesting the central role of RXRα in regulating nuclear receptor-mediated pathways.ConclusionsThis study establishes the relationship between RXRα DNA binding and hepatic gene expression. RXRα binds extensively to the mouse genome. However, DNA binding does not necessarily affect the basal mRNA level. In addition to metabolism, RXRα dictates the expression of genes that regulate RNA processing, translation, and protein folding illustrating the novel roles of hepatic RXRα in post-transcriptional regulation

Case report: Heterozygous mutation in HTRA1 causing typical cerebral autosomal recessive arteriopathy with subcortical infarcts and leukoencephalopathy

Background: Cerebral autosomal recessive arteriopathy with subcortical infarcts and leukoencephalopathy (CARASIL) is an autosomal recessive disorder characterized by baldness, recurrent ischemic stroke, lumbago, headache, and dementia which is closely related to homozygous mutations of the high-temperature requirement serine peptidase A1 (HTRA1) gene. Heterozygous mutations of HTRA1 are usually considered to be non-pathogenic. Although it has been revealed that only a few patients with heterozygous mutations could present some manifestations, their clinical symptoms were atypical, milder, and always with a lower frequency of extra-neurological features. Here, a rare patient with heterozygous mutation of HTRA1 who had all typical features of CARASIL as well as severe clinical symptoms and rapid progression was initially reported in our study.Case presentation: A 43-year-old female patient presented with a gradual onset of headache and cognitive decline. As time progressed, her headache intensified and symptoms of dementia began to manifest gradually. During her early years, she had thinning hair and subsequently experienced two occurrences of ischemic strokes in her thirties. Furthermore, she also had a history of lumbago and urinary retention before visiting our hospital. The patient’s magnetic resonance imaging revealed the presence of widespread white matter lesions, infarctions, and microbleeds, in addition to lumbar disc herniation and degenerative lesions. The observed clinical characteristics had a strong correlation with CARASIL, and the patient was diagnosed with a heterozygous missense mutation of 905G>A (Arg302Gln) in the HTRA1 gene. The patient has been under continuous follow-up for a duration exceeding 3 years subsequent to her release from the hospital. She underwent cystostomy, and symptoms of bulbar paralysis developed in a progressive way. Currently, there has been a notable decrease in motor function and activities of daily living, resulting in the individual being confined to bed for a duration exceeding 1 year.Conclusion: This case suggests that patients carrying a heterozygous mutation in G905A may also have typical clinical features of CARASIL, which allows us to have a more comprehensive understanding of CARASIL

1-[(Z)-(5-Methyl-2-pyrid­yl)iminiometh­yl]-2-naphtholate

In the zwitterionic title compound, C17H14N2O, the dihedral angle between the naphthalene and pyridine ring systems is 3.56 (9)° and an intra­molecular N—H⋯O hydrogen bond generates an S(6) ring. In the crystal, mol­ecules are linked by C—H⋯O inter­actions