Phase Unwrapping and One-Dimensional Sign Problems

Sign problems in path integrals arise when different field configurations contribute with different signs or phases. Phase unwrapping describes a family of signal processing techniques in which phase differences between elements of a time series are integrated to construct non-compact unwrapped phase differences. By combining phase unwrapping with a cumulant expansion, path integrals with sign problems arising from phase fluctuations can be systematically approximated as linear combinations of path integrals without sign problems. This work explores phase unwrapping in zero-plus-one-dimensional complex scalar field theory. Results with improved signal-to-noise ratios for the spectrum of scalar field theory can be obtained from unwrapped phases, but the size of cumulant expansion truncation errors is found to be undesirably sensitive to the parameters of the phase unwrapping algorithm employed. It is argued that this numerical sensitivity arises from discretization artifacts that become large when phases fluctuate close to singularities of a complex logarithm in the definition of the unwrapped phase.Comment: 42 pages, 16 figures. Journal versio

Unwrapping phase fluctuations in one dimension

Correlation functions in one-dimensional complex scalar field theory provide a toy model for phase fluctuations, sign problems, and signal-to-noise problems in lattice field theory. Phase unwrapping techniques from signal processing are applied to lattice field theory in order to map compact random phases to noncompact random variables that can be numerically sampled without sign or signal-to-noise problems. A cumulant expansion can be used to reconstruct average correlation functions from moments of unwrapped phases, but points where the field magnitude fluctuates close to zero lead to ambiguities in the definition of the unwrapped phase and significant noise at higher orders in the cumulant expansion. Phase unwrapping algorithms that average fluctuations over physical length scales improve, but do not completely resolve, these issues in one dimension. Similar issues are seen in other applications of phase unwrapping, where they are found to be more tractable in higher dimensions.Comment: 14 pages, 7 figures. arXiv admin note: text overlap with arXiv:1806.0183

Simulating Atrazine Transport Using Root Zone Water Quality Model for Iowa Soil Profiles

The pesticide component of the Root Zone Water Quality Model (RZWQM) was calibrated and evaluated for two tillage systems: no-till (NT) and moldboard plow (MB). The RZWQM is a process-based model that simulates the water and chemical transport processes in the soil-crop-atmosphere system. Observed data on atrazine concentrations in the soil profile, for model calibration and testing, were obtained from a field study in Iowa. Two statistical parameters, maximum error (ME) and coefficient of determination (CD), were used to evaluate the ability of the RZWQM to predict atrazine concentrations in the soil profile. The ME, CD, and other statistical tests indicated that there was a significant difference between predicted and observed atrazine concentrations. Comparison of simulated vs. observed atrazine concentrations with 1:1 line showed that atrazine concentrations were overpredicted, especially in the later part of the growing season. However, the model correctly predicted depth of atrazine penetration in the soil profile. Also, the range of predicted atrazine concentrations was within the same order of magnitude as observed concentrations. Although observed atrazine concentrations were usually higher in surface layers under MB than in NT treatment, the model did not show any consistent tillage effects on atrazine distribution in the soil profile. The results from this simulation study indicated that the following factors may be critical and should be considered when simulating pesticide transport in the subsurface environment: (i) macropore flow, (ii) variation in Koc and pesticide half-life with depth, and (iii) interception of pesticide by surface residue during application

Movement of NO3-N and atrazine through soil columns as affected by lime application

Lime (CaCO3) applied to the soil, to minimize or neutralize the soil pH, can influence the fate and transport of other chemicals in soil. This study was conducted to investigate the effect of lime application on the movement of NO3-N and atrazine through soil columns under saturated and unsaturated conditions

Purification and characterization of a low molecular mass alkaliphilic lipase of Bacillus cereus MTCC 8372

A low molecular mass alkaliphilic extra-cellular lipase of Bacillus cereus MTCC 8372 was purified 35-fold by hydrophobic interaction (Octyl-Sepharose) chromatography. The purified enzyme was found to be electrophoretically pure by denaturing gel electrophoresis and possessed a molecular mass of approximately 8 kDa. It is a homopentamer of 40 kDa as revealed by native-PAGE. The lipase was optimally active at 55 &deg;C and retained approximately half of its original activity after 40 min incubation at 55 &deg;C. The enzyme was maximally active at pH 8.5. Mg 2+ , Cu 2+ , Ca 2+ , Hg 2+ , Al 3+ and Fe 3+ at 1 mM enhanced hydrolytic activity of the lipase. Interestingly, Hg 2+ ions synergized and Zn 2+ and Co 2+ ions antagonized the lipase activity. Among surfactants, Tween 80 promoted the lipase activity. Phenyl methyl sulfonyl fluoride (PMSF, 15 mM) decreased 98% of original activity of lipase. The lipase was highly specific towards p -nitrophenyl palmitate and showed a V max and K m of 0.70 mmol.mg &minus;1 .min &minus;1 and 32 mM for hydrolysis of p NPP.<br /

Cloning of mouse integrin alphaV cDNA and role of the alphaV-related matrix receptors in metanephric development.

Metanephrogenesis has been a long-standing model to study cell-matrix interactions. A number of adhesion molecules, including matrix receptors (i.e., integrins), are believed to be involved in such interactions. The integrins contain alpha and beta s ubunits and are present in various tissues in different heterodimeric forms. In this study, one of the members of the integrin superfamily, alphaV, was characterized, and its relevance in murine nephrogenesis was investigated. Mouse embryonic renal cDNA libraries were prepared and screened for alphaV, and multiple clones were isolated and sequenced. The deduced amino acid sequence of the alpha-v cDNA clones and hydropathic analysis revealed that it has a typical signal sequence and extracellular, transmembrane, and cytoplasmic domains, with multiple Ca2+ binding sites. No A(U)nA mRNA instability motifs were present. Conformational analysis revealed no rigid long-range-ordered structure in murine alphaV. The alphaV was expressed in the embryonic kidney at day 13 of the gestation, with a transcript size of approximately 7 kb. Its expression increased progressively during the later gestational stages and in the neonatal period. It was distributed in the epithelial elements of developing nephrons and was absent in the uninduced mesenchyme. In mature metanephroi, the expression was relatively high in the glomeruli and blood vessels, as compared to the tubules. Various heterodimeric associations of alphaV, i.e., with beta1, beta3, beta5, and beta6, were observed in metanephric tissues. Inclusion of alphaV-antisense-oligodeoxynucleotide or -antibody in metanephric culture induced dysmorphogenesis of the kidney with reduced population of the nephrons, disorganization of the ureteric bud branches, and reduction of mRNA and protein expressions of alphaV. The expressions of integrin beta3, beta5, and beta6 were unaltered. These findings suggest that the integrin alphaV is developmentally regulated, has a distinct spatio-temporal expression, and is relevant in the mammalian organogenesis

Occurrence of Atrazine and Degradates as Contaminants of Subsurface Drainage and Shallow Groundwater

Atrazine is a commonly used herbicide in corn (Zea mays L.) growing areas of the USA. Because of its heavy usage, moderate persistence, and mobility in soil, monitoring of atrazine movement under field conditions is essential to assess its potential to contaminate groundwater. Concentrations of atrazine, deisopropylatrazine (DIA), and deethylatrazine (DEA) were measured in subsurface drainage and shallow groundwater beneath continuous, no-till corn. Water samples were collected from the subsurface drain (tile) outlets and suction lysimeters in the growing seasons of 1990 and 1991, and analyzed for atrazine and two principle degradates using solid-phase extraction and HPLC. In 1990, atrazine concentration ranged from 1.3 to 5.1 µg L−1 in tile-drain water and from 0.5 to 20.5 µg L−1 in lysimeter water. In general, concentrations of parent and degradates in solution were atrazine \u3e DEA \u3e DIA. Lesser levels of atrazine were measured in 1991 from Plots 2 and 4; however, greater concentrations of atrazine (6.0–8.4 µg L−1) were measured from Plot 5. Throughout the two growing seasons, atrazine concentration in Plot 5 tile-drain water was greater than that of Plots 2 and 4, suggesting a preferential movement of atrazine. Concentrations of DIA and DEA ranged from 0.1 to 2.2 and 0.9 to 3.2 µg L−1, respectively, indicating that the degradation products by themselves or in combination with parent atrazine can exceed the maximum contaminant level (mcl) of 3 µg L−1 even though atrazine by itself may be \u3c3 µg L−1. The deethylatrazineto-atrazine ratio (DAR) is an indicator of residence time in soil during transport of atrazine to groundwater. In Plots 2 and 4, DAR values for tile-drain water ranged from 0.43 to 2.70 and 0.50 to 2.66, respectively. By comparison, a DAR of 0.38 to 0.60 was observed in Plot 5, suggesting less residence time in the soil

Synthesis of ethyl acetate employing celite-immobilized lipase of Bacillus cereus MTCC 8372

A wide range of fatty acid esters can be synthesized by esterification and transesterification reactions catalyzed by lipases in non-aqueous systems. In the present study, immobilization of a purified alkaline extra-cellular lipase of Bacillus cereus MTCC 8372 by adsorption on diatomaceous earth (celite) for synthesis of ethyl acetate via transesterification route was investigated. B. cereus lipase was deposited on celite (77% protein binding efficiency) by direct binding from aqueous solution. Immobilized lipase was used to synthesis of ethyl acetate from vinyl acetate and ethanol in n -nonane. Various reaction conditions, such as biocatalyst concentration, substrates concentration, choices of solvents ( n -alkanes), incubation time, temperature, molecular sieves (3&Aring; &times; 1.5 mm), and water activity(a w ), were optimized. The immobilized lipase (25 mg/ml) was used to perform transesterification in n -alkane(s) that resulted in approximately 73.7 mM of ethyl acetate at 55 &deg;C in n -nonane under shaking (160 rpm) after 15 h, when vinyl acetate and ethanol were used in a equimolar ratio (100 mM each). Addition of molecular sieves (3&Aring; &times; 1.5 mm) as well as effect of water activity of saturated salt solutions (KI, KCl and KNO 3 ) to the transesterification efficiency has inhibitory effect. Batch operational stability tests indicated that immobilized lipase had retained 50% of its original catalytic activity after four consecutive batches of 15 h each.<br /