The attraction between a flexible filament and a point vortex

2012 ◽  
Vol 697 ◽  
pp. 481-503 ◽  
Author(s):  
Silas Alben
Keyword(s):  
Point Vortex ◽  
Critical Time ◽  
Power Laws ◽  
Vortex Sheet ◽  
Separation Distance ◽  
Temporal Distance ◽  
Pressure Loading ◽  
Governing Equations ◽  
Flexible Filament ◽  
Wide Range

AbstractWe determine the inviscid dynamics of a point vortex in the vicinity of a flexible filament. For a wide range of filament bending rigidities, the filament is attracted to the point vortex, which generally moves tangentially to it. We find evidence that the point vortex collides with the filament at a critical time, with the separation distance tending to zero like a square root of temporal distance from the critical time. Concurrent with the collision, we find divergences of pressure loading on the filament, filament vortex sheet strength, filament curvature and velocity. We derive the corresponding power laws using the governing equations.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

scholarly journals Scaffold Hopping of α-Rubromycin Enables Direct Access to FDA-Approved Cromoglicic Acid as a SARS-CoV-2 MPro Inhibitor

2021 ◽  
Vol 14 (6) ◽  
pp. 541
Author(s):  
Hani A. Alhadrami ◽  
Ahmed M. Sayed ◽  
Heba Al-Khatabi ◽  
Nabil A. Alhakamy ◽  
Mostafa E. Rateb
Keyword(s):  
Binding Free Energy ◽  
Human Fibroblasts ◽  
Critical Time ◽  
Dynamics Simulation ◽  
Direct Access ◽  
Energy Calculation ◽  
Wide Range ◽  
Normal Human ◽  
Novel Scaffold

The COVID-19 pandemic is still active around the globe despite the newly introduced vaccines. Hence, finding effective medications or repurposing available ones could offer great help during this serious situation. During our anti-COVID-19 investigation of microbial natural products (MNPs), we came across α-rubromycin, an antibiotic derived from Streptomyces collinus ATCC19743, which was able to suppress the catalytic activity (IC50 = 5.4 µM and Ki = 3.22 µM) of one of the viral key enzymes (i.e., MPro). However, it showed high cytotoxicity toward normal human fibroblasts (CC50 = 16.7 µM). To reduce the cytotoxicity of this microbial metabolite, we utilized a number of in silico tools (ensemble docking, molecular dynamics simulation, binding free energy calculation) to propose a novel scaffold having the main pharmacophoric features to inhibit MPro with better drug-like properties and reduced/minimal toxicity. Nevertheless, reaching this novel scaffold synthetically is a time-consuming process, particularly at this critical time. Instead, this scaffold was used as a template to explore similar molecules among the FDA-approved medications that share its main pharmacophoric features with the aid of pharmacophore-based virtual screening software. As a result, cromoglicic acid (aka cromolyn) was found to be the best hit, which, upon in vitro MPro testing, was 4.5 times more potent (IC50 = 1.1 µM and Ki = 0.68 µM) than α-rubromycin, with minimal cytotoxicity toward normal human fibroblasts (CC50 > 100 µM). This report highlights the potential of MNPs in providing unprecedented scaffolds with a wide range of therapeutic efficacy. It also revealed the importance of cheminformatics tools in speeding up the drug discovery process, which is extremely important in such a critical situation.

scholarly journals Discovering governing equations from data by sparse identification of nonlinear dynamical systems

2016 ◽  
Vol 113 (15) ◽  
pp. 3932-3937 ◽  
Author(s):  
Steven L. Brunton ◽  
Joshua L. Proctor ◽  
J. Nathan Kutz
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Measurement Data ◽  
Climate Science ◽  
Model Complexity ◽  
Governing Equations ◽  
Canonical Systems ◽  
Nonlinear Dynamical ◽  
Balance Accuracy ◽  
Wide Range

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

scholarly journals Collapse of n Point Vortices, Formation of the Vortex Sheets and Transport of Passive Markers

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 943
Author(s):  
Henryk Kudela
Keyword(s):  
Differential Equations ◽  
Point Vortex ◽  
Optimization Procedure ◽  
Vortex Sheet ◽  
Point Vortices ◽  
Vortex Sheets ◽  
Impermeable Barrier ◽  
Initial Location ◽  
Passive Tracers ◽  
Initial Iterate

In this paper, the motion of the n-vortex system as it collapses to a point in finite time is studied. The motion of vortices is described by the set of ordinary differential equations that we are able to solve analytically. The explicit formula for the solution demands the initial location of collapsing vortices. To find the collapsing locations of vortices, the algebraic, nonlinear system of equations was built. The solution of that algebraic system was obtained using Newton’s procedure. A good initial iterate needs to be provided to succeed in the application of Newton’s procedure. An unconstrained Leverber–Marquart optimization procedure was used to find such a good initial iterate. The numerical studies were conducted, and numerical evidence was presented that if in a collapsing system n=50 point vortices include a few vortices with much greater intensities than the others in the set, the vortices with weaker intensities organize themselves onto the vortex sheet. The collapsing locations depend on the value of the Hamiltonian. By changing the Hamiltonian values in a specific interval, the collapsing curves can be obtained. All points on the collapse curves with the same Hamiltonian value represent one collapsing system of vortices. To show the properties of vortex sheets created by vortices, the passive tracers were used. Advection of tracers by the velocity induced by vortices was calculated by solving the proper differential equations. The vortex sheets are an impermeable barrier to inward and outward fluxes of tracers. Arising vortex structures are able to transport the passive tracers. In this paper, several examples showing the diversity of collapsing structures with the vortex sheet are presented. The collapsing phenomenon of many vortices, their ability to self organize and the transportation of the passive tracers are novelties in the context of point vortex dynamics.

scholarly journals Size-Resolved Evaluation of Simulated Deep Tropical Convection

2018 ◽  
Vol 146 (7) ◽  
pp. 2161-2182 ◽  
Author(s):  
Fabian Senf ◽  
Daniel Klocke ◽  
Matthias Brueck
Keyword(s):  
Deep Convection ◽  
Winter Season ◽  
Power Laws ◽  
Moist Convection ◽  
Modeling Framework ◽  
Western Atlantic ◽  
Spatial Coupling ◽  
Wide Range ◽  
Realistic Representation ◽  
Deep Moist Convection

Abstract Deep moist convection is an inherently multiscale phenomenon with organization processes coupling convective elements to larger-scale structures. A realistic representation of the tropical dynamics demands a simulation framework that is capable of representing physical processes across a wide range of scales. Therefore, storm-resolving numerical simulations at 2.4 km have been performed covering the tropical Atlantic and neighboring parts for 2 months. The simulated cloud fields are combined with infrared geostationary satellite observations, and their realism is assessed with the help of object-based evaluation methods. It is shown that the simulations are able to develop a well-defined intertropical convergence zone. However, marine convective activity measured by the cold cloud coverage is considerably underestimated, especially for the winter season and the western Atlantic. The spatial coupling across the resolved scales leads to simulated cloud number size distributions that follow power laws similar to the observations, with slopes steeper in winter than summer and slopes steeper over ocean than over land. The simulated slopes are, however, too steep, indicating too many small and too few large tropical cloud cells. It is also discussed that the number of larger cells is less influenced by multiday variability of environmental conditions. Despite the identified deficits, the analyzed simulations highlight the great potential of this modeling framework for process-based studies of tropical deep convection.

On the Role of Enduring Contact in Powder Lubrication

2005 ◽  
Vol 128 (1) ◽  
pp. 168-175 ◽  
Author(s):  
J. Y. Jang ◽  
M. M. Khonsari
Keyword(s):  
Analytical Solution ◽  
Flow Velocity ◽  
Volume Fraction ◽  
Flow Characteristics ◽  
Kinetic Regime ◽  
Governing Equations ◽  
Wide Range ◽  
Fraction Distribution ◽  
Powder Lubrication

This paper is devoted to a study of the enduring contact between granules of powder lubricants in an effort to better understand the flow characteristics of powder lubricants. Appropriate formulation of the governing equations is reported that can be used for prediction of the flow velocity, pseudo temperature, and volume fraction distribution of powders for a wide range of operating speeds. A set of parametric simulations and a limiting analytical solution is presented for predicting the behavior of a powder lubricant under low operating speeds when the enduring contact tends to dominate the kinetic regime. The limiting solution shows that below a certain sliding speed the volume fraction remains unchanged due to the effect of the enduring contact. It is also shown that below this limiting speed the enduring contact plays a major role and should not be neglected.

Long Time Computation of Two-Dimensional Vortex Sheet by Point Vortex Method

2003 ◽  
Vol 72 (8) ◽  
pp. 1968-1976 ◽  
Author(s):  
Sun-Chul Kim ◽  
June-Yub Lee ◽  
Sung-Ik Sohn
Keyword(s):  
Point Vortex ◽  
Vortex Method ◽  
Vortex Sheet ◽  
Two Dimensional ◽  
Long Time

scholarly journals Emergence of power laws in the pharmacokinetics of paclitaxel due to competing saturable processes.

2008 ◽  
Vol 11 (3) ◽  
pp. 77 ◽  
Author(s):  
Jack A Tuszynski ◽  
Rebeccah E. Marsh ◽  
Michael B. Sawyer ◽  
Kenneth J.E. Vos
Keyword(s):  
Power Law ◽  
Fractional Power ◽  
Area Under The Curve ◽  
Power Laws ◽  
Dose Dependence ◽  
Power Exponent ◽  
Least Squares Regression ◽  
Time Data ◽  
Concentration Time ◽  
Wide Range

Purpose: This study presents the results of power law analysis applied to the pharmacokinetics of paclitaxel. Emphasis is placed on the role that the power exponent can play in the investigation and quantification of nonlinear pharmacokinetics and the elucidation of the underlying physiological processes. Methods: Forty-one sets of concentration-time data were inferred from 20 published clinical trial studies, and 8 sets of area under the curve (AUC) and maximum concentration (Cmax) values as a function of dose were collected. Both types of data were tested for a power law relationship using least squares regression analysis. Results: Thirty-nine of the concentration-time curves were found to exhibit power law tails, and two dominant fractal exponents emerged. Short infusion times led to tails with a single power exponent of -1.57 ± 0.14, while long infusion times resulted in steeper tails characterized by roughly twice the exponent. The curves following intermediate infusion times were characterized by two consecutive power laws; an initial short slope with the larger alpha value was followed by a crossover to a long-time tail characterized by the smaller exponent. The AUC and Cmax parameters exhibited a power law dependence on the dose, with fractional power exponents that agreed with each other and with the exponent characterizing the shallow decline. Computer simulations revealed that a two- or three-compartment model with both saturable distribution and saturable elimination can produce the observed behaviour. Furthermore, there is preliminary evidence that the nonlinear dose-dependence is correlated with the power law tails. Conclusion: Assessment of data from published clinical trials suggests that power laws accurately describe the concentration-time curves and non-linear dose-dependence of paclitaxel, and the power exponents provide insight into the underlying drug mechanisms. The interplay between two saturable processes can produce a wide range of behaviour, including concentration-time curves with exponential, power law, and dual power law tails.

scholarly journals On the Use of Asymptotic Solutions to Plane Ice—Water Problems

1969 ◽  
Vol 8 (53) ◽  
pp. 285-300 ◽  
Author(s):  
G. S. H. Lock
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Solutions ◽  
Variable Properties ◽  
Governing Equations ◽  
Freezing And Thawing ◽  
One Dimensional ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Water Problems ◽  
Ice Water

The paper considers one-dimensional freezing and thawing of ice–water systems for the conditions first examined by Stefan. An order-of-magnitude analysis applied to the governing equations and boundary conditions quantifies the error resulting from the neglect of various factors. Principal among these are density difference, initial superheat and variable properties.Asymptotic solutions for the temperature distribution and interface history are developed for a wide range of boundary conditions: prescribed temperature or heat flux, prescribed convection and prescribed radiation. Comparison with known results reveals the general adequacy of the asymptotic solutions and an estimate of the error incurred.

scholarly journals RESTRICTIONS ON THE HYPOTHETICAL LONG RANGE INTERACTIONS FROM THE CASIMIR-TYPE NULL EXPERIMENT WITH THREE TEST BODIES

1994 ◽  
Vol 09 (29) ◽  
pp. 2671-2680 ◽  
Author(s):  
M. BORDAG ◽  
V. M. MOSTEPANENKO ◽  
I. YU. SOKOLOV
Keyword(s):  
Long Range ◽  
Power Law ◽  
Casimir Force ◽  
Power Laws ◽  
Gravitational Attraction ◽  
Spherical Lens ◽  
Plane Plate ◽  
Wide Range ◽  
Long Range Interactions

A realistic null experiment is suggested in which the Casimir force between a plane plate and a spherical lens is compensated by the force of gravitational attraction. This configuration is shown to be very sensitive to the existence of additional hypothetical forces of Yukawa-type or power laws. From the suggested null experiment the restrictions on the Yukawa constant α can be strengthened by a factor up to 1000 in a wide range 10−8 m < λ < 10−4 m and by a factor of 10 for λ from several centimeters to several meters. For power law interactions the strengthening of restrictions by a factor of 20 is possible for the force decreasing as r−5.

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