One parameter family of Compacton Solutions in a class of Generalized Korteweg-DeVries Equations

We study the generalized Korteweg-DeVries equations derivable from the Lagrangian: $L(l,p) = \int \left( \frac{1}{2} \varphi_{x} \varphi_{t} - { {(\varphi_{x})^{l}} \over {l(l-1)}} + \alpha(\varphi_{x})^{p} (\varphi_{xx})^{2} \right) dx,$ where the usual fields $u(x,t)$ of the generalized KdV equation are defined by $u(x,t) = \varphi_{x}(x,t)$. For $p$ an arbitrary continuous parameter $0< p \leq 2 ,l=p+2$ we find compacton solutions to these equations which have the feature that their width is independent of the amplitude. This generalizes previous results which considered $p=1,2$. For the exact compactons we find a relation between the energy, mass and velocity of the solitons. We show that this relationship can also be obtained using a variational method based on the principle of least action.Comment: Latex 4 pages and one figure available on reques

A comparison of two magnetic ultra-cold neutron trapping concepts using a Halbach-octupole array

This paper describes a new magnetic trap for ultra-cold neutrons (UCNs) made from a 1.2 m long Halbach-octupole array of permanent magnets with an inner bore radius of 47 mm combined with an assembly of superconducting end coils and bias field solenoid. The use of the trap in a vertical, magneto-gravitational and a horizontal setup are compared in terms of the effective volume and ability to control key systematic effects that need to be addressed in high precision neutron lifetime measurements

Solitary Waves and Compactons in a class of Generalized Korteweg-DeVries Equations

We study the class of generalized Korteweg-DeVries equations derivable from the Lagrangian: L(l,p) = \int \left( \frac{1}{2} \vp_{x} \vp_{t} - { {(\vp_{x})^{l}} \over {l(l-1)}} + \alpha(\vp_{x})^{p} (\vp_{xx})^{2} \right) dx, where the usual fields $u(x,t)$ of the generalized KdV equation are defined by u(x,t) = \vp_{x}(x,t). This class contains compactons, which are solitary waves with compact support, and when $l=p+2$, these solutions have the feature that their width is independent of the amplitude. We consider the Hamiltonian structure and integrability properties of this class of KdV equations. We show that many of the properties of the solitary waves and compactons are easily obtained using a variational method based on the principle of least action. Using a class of trial variational functions of the form $u(x,t) = A(t) \exp \left[-\beta (t) \left|x-q(t) \right|^{2n} \right]$ we find soliton-like solutions for all $n$, moving with fixed shape and constant velocity, $c$. We show that the velocity, mass, and energy of the variational travelling wave solutions are related by $c = 2 r E M^{-1}$, where $r = (p+l+2)/(p+6-l)$, independent of $n$.\newline \newline PACS numbers: 03.40.Kf, 47.20.Ky, Nb, 52.35.SbComment: 16 pages. LaTeX. Figures available upon request (Postscript or hard copy

Machine Learning Can Predict the Timing and Size of Analog Earthquakes

Despite the growing spatiotemporal density of geophysical observations at subduction zones, predicting the timing and size of future earthquakes remains a challenge. Here we simulate multiple seismic cycles in a laboratory‐scale subduction zone. The model creates both partial and full margin ruptures, simulating magnitude M_w 6.2–8.3 earthquakes with a coefficient of variation in recurrence intervals of 0.5, similar to real subduction zones. We show that the common procedure of estimating the next earthquake size from slip‐deficit is unreliable. On the contrary, machine learning predicts well the timing and size of laboratory earthquakes by reconstructing and properly interpreting the spatiotemporally complex loading history of the system. These results promise substantial progress in real earthquake forecasting, as they suggest that the complex motion recorded by geodesists at subduction zones might be diagnostic of earthquake imminence

A Polyclonal Selex Aptamer Library Directly Allows Specific Labelling of the Human Gut Bacterium Blautia producta without Isolating Individual Aptamers

Recent studies have demonstrated that changes in the abundance of the intestinal bacterium Blautia producta, a potential probiotic, are closely associated with the development of various diseases such as obesity, diabetes, some neurodegenerative diseases, and certain cancers. However, there is still a lack of an effective method to detect the abundance of B. producta in the gut rapidly. Especially, DNA aptamers are now widely used as biometric components for medical testing due to their unique characteristics, including high chemical stability, low production cost, ease of chemical modification, low immunogenicity, and fast reproducibility. We successfully obtained a high-affinity nucleic acid aptamer library (B.p-R14) after 14 SELEX rounds, which efficiently discriminates B. producta in different analysis techniques including fluorometric suspension assays or fluorescence microscopy from other major gut bacteria in complex mixtures and even in human stool samples. These preliminary findings will be the basis towards aptamer-based biosensing applications for the fast and reliable monitoring of B. producta in the human gut microbiome

Polyclonal Aptamers for Specific Fluorescence Labeling and Quantification of the Health Relevant Human Gut Bacterium Parabacteroides distasonis

Single-stranded DNA aptamers as affinity molecules for the rapid, reliable detection of intestinal bacteria are of particular interest to equip health systems with novel robust and cheap diagnostic tools for monitoring the success of supplementation strategies with selected probiotic gut bacteria in the fight against major widespread threats, such as obesity and neurodegenerative diseases. The human gut bacterium Parabacteroides distasonis (P. distasonis) is positively associated with diseases such as obesity, non-alcoholic fatty liver disease and multiple sclerosis with reduced cell counts in these diseases and is thus a promising potential probiotic bacterium for future microbial supplementation. In this paper we report on the evolution of a specific polyclonal aptamer library by the fluorescence based FluCell-SELEX directed against whole cells of P. distasonis that specifically and efficiently binds and labels P. distasonis. The aptamer library showed high binding affinity and was suited to quantitatively discriminate P. distasonis from other prominent gut bacteria also in mixtures. We believe that this library against a promising probiotic bacterium as a prototype may open new routes towards the development of novel biosensors for the easy and efficient quantitative monitoring of microbial abundance in human microbiomes in general