The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms is demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems.
We take advantage of the fact that in λφ 4 problems, a large field cutoff φmax makes perturbative series converge toward values exponentially close to the exact values, to make optimal choices of φmax. For perturbative series terminated at even order, it is in principle possible to adjust φmax in order to obtain the exact result. For perturbative series terminated at odd order, the error can only be minimized. It is however possible to introduce a mass shift m 2 → m 2 (1+η) in order to obtain the exact result. We discuss weak and strong coupling methods to determine φmax and η. The numerical calculations in this article have been performed with a simple integral with one variable. We give arguments indicating that the qualitative features observed should extend to quantum mechanics and quantum field theory. We found that optimization at even order is more efficient that at odd order. We compare our methods with the linear δ-expansion (LDE) (combined with the principle of minimal sensitivity) which provides an upper envelope of for the accuracy curves of various Padé and Padé-Borel approximants. Our optimization method performs better than the LDE at strong and intermediate coupling, but not at weak coupling where it appears less robust and subject to further improvements. We also show that it is possible to fix the arbitrary parameter appearing in the LDE using the strong coupling expansion, in order to get accuracies comparable to ours.
We show that the use of wavelet bases for solving the momentum-space scattering integral equation leads to sparse matrices which can simplify the solution. Wavelet bases are applied to calculate the K-matrix for nucleon-nucleon scattering with the s-wave Malfliet-Tjon V potential. We introduce a new method, which uses special properties of the wavelets, for evaluating the singular part of the integral. Analysis of this test problem indicates that a significant reduction in computational size can be achieved for realistic few-body scattering problems.
The unicellular green alga Chlamydomonas reinhardtii has long served as model organism for studies on the circadian clock. This clock is present in all eukaryotes and some prokaryotes allowing them to anticipate and take advantage of the daily oscillations in the environment. Although much is known about the circadian clock in C. reinhardtii, the photoreceptors mediating entrainment of the clock to the daily changes of light remain obscure. Based on its circadian rhythm of phototaxis as a reporter of the clock’s phase, we show here that C. reinhardtii strain CC-124 is highly sensitive to blue light of 440 nm when resetting its circadian clock upon light pulses. Thus, CC-124 differs in this respect from what was previously reported for a cell wall-deficient strain. An action spectrum analysis revealed that CC-124 also responds with high sensitivity to green (540 nm), red (640–660 nm), and possibly UV-A (≤400 nm) light, and therefore shows similarities as well to what has been reported for the cell wall-deficient strain. We also investigated two RNA interference strains with reductions in the level of the blue light photoreceptor plant cryptochrome (CPH1). One of them, the strain with the greater reduction, surprisingly showed an increased sensitivity in clock resetting upon blue light pulses of 440 nm. This increase in sensitivity reverted to wild-type levels when the RNA interference strain reverted to wild-type protein levels. It suggests that plant cryptochrome in C. reinhardtii could function as negative rather than positive modulator of circadian clock resetting.
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