Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

The equation ∂tu = u∂xx2u − (c − 1)(∂xu)2 is known in literature as a qualitative mathematical model of some biological phenomena. Here this equation is derived as a model of the groundwater flow in a water-absorbing fissurized porous rock; therefore, we refer to this equation as a filtration-absorption equation. A family of self-similar solutions to this equation is constructed. Numerical investigation of the evolution of non-self-similar solutions to the Cauchy problems having compactly supported initial conditions is performed. Numerical experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still far from the ultimate state: identical zero. An open problem caused by the nonuniqueness of the solution of the Cauchy problem is discussed.

Altered Zn Compartmentation in the Root Symplasm and Stimulated Zn Absorption into the Leaf as Mechanisms Involved in Zn Hyperaccumulation in Thlaspi caerulescens

We investigated Zn compartmentation in the root, Zn transport into the xylem, and Zn absorption into leaf cells in Thlaspi caerulescens, a Zn-hyperaccumulator species, and compared them with those of a related nonaccumulator species, Thlaspi arvense. 65Zn-compartmental analysis conducted with roots of the two species indicated that a significant fraction of symplasmic Zn was stored in the root vacuole of T. arvense, and presumably became unavailable for loading into the xylem and subsequent translocation to the shoot. In T. caerulescens, however, a smaller fraction of the absorbed Zn was stored in the root vacuole and was readily transported back into the cytoplasm. We conclude that in T. caerulescens, Zn absorbed by roots is readily available for loading into the xylem. This is supported by analysis of xylem exudate collected from detopped Thlaspi species seedlings. When seedlings of the two species were grown on either low (1 μm) or high (50 μm) Zn, xylem sap of T. caerulescens contained approximately 5-fold more Zn than that of T. arvense. This increase was not correlated with a stimulated production of any particular organic or amino acid. The capacity of Thlaspi species cells to absorb 65Zn was studied in leaf sections and leaf protoplasts. At low external Zn levels (10 and 100 μm), there was no difference in leaf Zn uptake between the two Thlaspi species. However, at 1 mm Zn2+, 2.2-fold more Zn accumulated in leaf sections of T. caerulescens. These findings indicate that altered tonoplast Zn transport in root cells and stimulated Zn uptake in leaf cells play a role in the dramatic Zn hyperaccumulation expressed in T. caerulescens.

X-ray absorption fine structure as a monitor of zinc coordination sites during oogenesis of Xenopus laevis.

The x-ray absorption fine structure (XAFS) zinc K-edge steps for intact stages I,II and V,VI Xenopus laevis oocytes demonstrate that the zinc concentration is about 3 and 1 mM, respectively. However, the chi(k) function for the early stage oocytes differs markedly from that for the late one. Analysis of the XAFS data for stage I,II oocytes indicates that zinc is bound to 2.0 +/- 0.5 sulfur atoms at an average coordination distance of 2.29 +/- 0.02 angstroms and 2.0 +/- 0.5 nitrogen or oxygen (N/O) atoms at 2.02 +/- 0.02 angstroms. In marked contrast, in stage V,VI oocytes, zinc is bound to 4.1 +/- 0.4 N/O atoms at an average distance of 1.98 +/- 0.01 angstroms. Our previous studies demonstrated that 90% of the zinc in stage VI oocytes is sequestered within yolk platelets, associated with a single molecule, lipovitellin, the proteolytically processed product of vitellogenin. XAFS analysis of yolk platelets, lipovitellin, and vitellogenin demonstrates that zinc is bound to 4.0 +/- 0.5 N/O ligands at an average distance of 1.98 +/- 0.01 angstroms in each case, identical to that of stage V,VI oocytes. The higher shell contributions in the Fourier transforms indicate that two of the N/O zinc ligands are His in both stage V,VI and I,II oocytes. The results show that in stage I,II oocytes, there is a high concentration of a zinc protein whose zinc coordination site likely is composed of (His)2(Cys)2, such as, e.g., TFIIIA. As the oocytes develop, the predominant zinc species becomes one that exhibits the (His)2(N/0)2 zinc site found in lipovitellin. Hence, the ligands to the zinc atoms in intact oocytes and the changes that take place as a function of oogenesis and after their fertilization, during embryogenesis, now can be examined and explored.

Apolipoprotein E competitively inhibits receptor-dependent low density lipoprotein uptake by the liver but has no effect on cholesterol absorption or synthesis in the mouse.

This study examines the question of whether apolipoprotein E (apoE) alters steady-state concentrations of plasma cholesterol carried in low density lipoproteins (LDL-C) by acting as a competitive inhibitor of hepatic LDL uptake or by altering the rate of net cholesterol delivery from the intestinal lumen to the liver. To differentiate between these two possibilities, rates of cholesterol absorption and synthesis and the kinetics of hepatic LDL-C transport were measured in vivo in mice with either normal (apoE+/+) or zero (apoE-/-) levels of circulating apoE. Rates of cholesterol absorption were essentially identical in both genotypes and equaled approximately 44% of the daily dietary load of cholesterol. This finding was consistent with the further observation that the rates of cholesterol synthesis in the liver (approximately 2,000 nmol/h) and extrahepatic tissues (approximately 3,000 nmol/h) were also essentially identical in the two groups of mice. However, the apparent Michaelis constant for receptor-dependent hepatic LDL-C uptake was markedly lower in the apoE-/- mice (44 +/- 4 mg/dl) than in the apoE+/+ animals (329 +/- 77 mg/dl) even though the maximal transport velocity for this uptake process was essentially the same (approximately 400 micrograms/h per g) in the two groups of mice. These studies, therefore, demonstrate that apoE-containing lipoproteins can act as potent competitive inhibitors of hepatic LDL-C transport and so can significantly increase steady-state plasma LDL-C levels. This apolipoprotein plays no role, however, in the regulation of cholesterol absorption, sterol biosynthesis, or hepatic LDL receptor number, at least in the mouse.

Basolateral membrane Na+/H+ exchange enhances HCO3- absorption in rat medullary thick ascending limb: evidence for functional coupling between basolateral and apical membrane Na+/H+ exchangers.

The role of basolateral membrane Na+/H+ exchange in transepithelial HCO3- absorption (JHCO3) was examined in the isolated, perfused medullary thick ascending limb (MTAL) of the rat. In Na(+)-free solutions, addition of Na+ to the bath resulted in a rapid, amiloride-sensitive increase in intracellular pH. In MTALs perfused and bathed with solutions containing 146 mM Na+ and 25 mM HCO3-, bath addition of amiloride (1 mM) or 5-(N-ethyl-N-isopropyl) amiloride (EIPA, 50 microM) reversibly inhibited JHCO3 by 50%. Evidence that the inhibition of JHCO3 by bath amiloride was the result of inhibition of Na+/H+ exchange included the following: (i) the IC50 for amiloride was 5-10 microM, (ii) EIPA was a 50-fold more potent inhibitor than amiloride, (iii) the inhibition by bath amiloride was Na+ dependent, and (iv) significant inhibition was observed with EIPA as low as 0.1 microM. Fifty micromolar amiloride or 1 microM EIPA inhibited JHCO3 by 35% when added to the bath but had no effect when added to the tubule lumen, indicating that addition of amiloride to the bath did not directly inhibit apical membrane Na+/H+ exchange. In experiments in which apical Na+/H+ exchange was assessed from the initial rate of cell acidification following luminal EIPA addition, bath EIPA secondarily inhibited apical Na+/H+ exchange activity by 46%. These results demonstrate basolateral membrane Na+/H+ exchange enhances transepithelial HCO3- absorption in the MTAL. This effect appears to be the result of cross-talk in which an increase in basolateral membrane Na+/H+ exchange activity secondarily increases apical membrane Na+/H+ exchange activity.

Determination of absorption curves, dissolution profiles and establishment of in vitro-in vivo correlation by in silico methods using GastroPlusTM and DDDPlusTM

The use of computer programs to predict drug absorption in humans and to simulate dissolution profiles has become a valuable tool in the pharmaceutical area. The objective of this study was to use in silico methods through software GastroPlusTM and DDDPlusTM to simulate drug absorption curves and dissolution profiles, and to establish in vitro-in vivo correlations (IVIVCs). The work presented herein is divided into five chapters and includes the drugs ketoprofen, pyrimethamine, metronidazole, fluconazole, carvedilol and doxazosin. In Chapter 1, simulated plasma curves for ketoprofen matrix tablets are presented and IVIVC was established. The use of simulated intrinsic dissolution tests for pyrimethamine and metronidazole as a tool for biopharmaceutics classification is detailed in Chapter 2. In Chapter 3, simulation of plasma curves for fluconazole capsules with different dissolution profiles is demonstrated as a tool for biowaiver. IVIVC studies were also conducted for carvedilol immediate-release tablets from dissolution profiles in Chapter 4. Chapter 5 covers the application of simulated dissolution tests for development of doxazosin extended-release formulations. Simulation of plasma curves and IVIVC using the software GastroPlusTM as well as intrinsic dissolution tests and dissolution profiles using the software DDDPlusTM proved to be a tool of wide application in predicting biopharmaceutical characteristics of drugs and formulations, allowing the reduction of time and costs of experimental laboratory work.

A gradient estimate to a degenerate parabolic equation with a singular absorption term: The global quenching phenomena

We prove global existence of nonnegative solutions to the one dimensional degenerate parabolic problems containing a singular term. We also show the global quenching phenomena for L1 initial datums. Moreover, the free boundary problem is considered in this paper.

Long-range effects on optical absorption in quasiperiodic lattices

We consider exciton optical absorption in quasiperiodic lattices, focusing our attention on the Fibonacci case as a typical example. The absorption spectrum is evaluated by solving numerically the equation of motion of the Frenkel-exciton problem on the lattice, in which on-site energies take on two values according to the Fibonacci sequence. We find that the quasiperiodic order causes the occurrence of well-defined characteristic features in the absorption spectra. We also develop an analytical method that relates satellite lines with the Fourier pattern of the lattice. Our predictions can be used to determine experimentally the long-range quasiperiodic order from optical measurements.

X-ray absorption study of the ferromagnetic Cu moment at the YBa_(2)Cu_(3)O_(7)/La_(2/3)Ca_(1/3)MnO_(3) interface and variation of its exchange interaction with the Mn moment

With x-ray absorption spectroscopy and polarized neutron reflectometry we studied how the magnetic proximity effect at the interface between the cuprate high-TC superconductor YBa_(2)Cu_(3)O_(7) (YBCO) and the ferromagnet La_(2/3)Ca_(1/3)MnO_(3) (LCMO) is related to the electronic and magnetic properties of the LCMO layers. In particular, we explored how the magnitude of the ferromagnetic Cu moment on the YBCO side depends on the strength of the antiferromagnetic (AF) exchange coupling with the Mn moment on the LCMO side. We found that the Cu moment remains sizable if the AF coupling with the Mn moments is strongly reduced or even entirely suppressed. The ferromagnetic order of the Cu moments thus seems to be intrinsic to the interfacial CuO_(2) planes and related to a weakly ferromagnetic intraplanar exchange interaction. The latter is discussed in terms of the partial occupation of the Cu 3d_(3z^(2)−r^(2)) orbitals, which occurs in the context of the so-called orbital reconstruction of the interfacial Cu ions.

Combined simulation-optimization methodology for the design of environmental conscious absorption systems

This work addresses the optimization of ammonia–water absorption cycles for cooling and refrigeration applications with economic and environmental concerns. Our approach combines the capabilities of process simulation, multi-objective optimization (MOO), cost analysis and life cycle assessment (LCA). The optimization task is posed in mathematical terms as a multi-objective mixed-integer nonlinear program (moMINLP) that seeks to minimize the total annualized cost and environmental impact of the cycle. This moMINLP is solved by an outer-approximation strategy that iterates between primal nonlinear programming (NLP) subproblems with fixed binaries and a tailored mixed-integer linear programming (MILP) model. The capabilities of our approach are illustrated through its application to an ammonia–water absorption cycle used in cooling and refrigeration applications.

Absorption cross-sections of hole polarons in glassy and β-phase polyfluorene

Absorption induced by electrochemically injected holes is studied in poly-9,9-dioctylfluorene (PFO) films. Injected charges form positive polarons which are delocalised over four fluorene units in the glassy phase and about seven fluorene units in its β-phase. Polaron absorption cross-sections at the 640 nm peak are similar to the published values of chemically reduced oligofluorenes in solution. The absorption cross-section of polaron in the β-phase at 470 nm is about eight times smaller than the stimulated emission cross-section derived from published data. This indicates that β-phase-rich PFO is an attractive candidate for a light-emitting layer in double-heterostructure organic laser diodes.

Discussing the physical meaning of the absorption feature at 2.1 keV in 4U 1538–52

High resolution X-ray spectroscopy is a powerful tool for studying the nature of the matter surrounding the neutron star in X-ray binaries and its interaction between the stellar wind and the compact object. In particular, absorption features in their spectra could reveal the presence of atmospheres of the neutron star or their magnetic field strength. Here we present an investigation of the absorption feature at 2.1 keV in the X-ray spectrum of the high mass X-ray binary 4U 1538–52 based on our previous analysis of the XMM-Newton data. We study various possible origins and discuss the different physical scenarios in order to explain this feature. A likely interpretation is that the feature is associated with atomic transitions in an O/Ne neutron star atmosphere or of hydrogen and helium like Fe or Si ions formed in the stellar wind of the donor.

Identifying student and teacher difficulties in interpreting atomic spectra using a quantum model of emission and absorption of radiation

Our study sets out to identify the difficulties that high school students, teachers, and university students encounter when trying to explain atomic spectra. To do so, we identify the key concepts that any quantum model for the emission and absorption of electromagnetic radiation must include to account for the gas spectra and we then design two questionnaires, one for teachers and the other for students. By analyzing the responses, we conclude that (i) teachers lack a quantum model for the emission and absorption of electromagnetic radiation capable of explaining the spectra, (ii) teachers and students share the same difficulties, and (iii) these difficulties concern the model of the atom, the model of radiation, and the model of the interaction between them.