scholarly journals Mathematical Modelling to Determine the Greatest Height of Trees

2021 ◽  
Author(s):  
Tohya Kanahama ◽  
Motohiro Sato
Keyword(s):  
Mathematical Modelling ◽  
Simple Form ◽  
Weight Distribution ◽  
Special Functions ◽  
Scaling Law ◽  
Critical Height ◽  
Wide Range ◽  
Weight Distributions ◽  
Simple Scaling ◽  
Shape Quantification

Abstract This study aimed to analyse the critical height of a column whose weight varies vertically in order to obtain a simple scaling law for a tree where the weight distribution considered. We modelled trees as cantilevers that were fixed to the ground and formulated a self-buckling problem for various weight distributions. A formula for calculating the critical height was derived in a simple form that did not include special functions. We obtained a theoretical clarification of the effect of the weight distribution of heavy columns on the buckling behaviour. A widely applicable scaling law for trees was obtained. We found that an actual tree manages to distribute the weight of its trunk and branches along its vertical extent in a manner that adequately secures its critical height. The method and findings of this study are applicable to a wide range of fields, such as the simplification of complicated buckling problems and the study of tree shape quantification.

scholarly journals Hierarchy and extremes in selections from pools of randomized proteins

2016 ◽  
Vol 113 (13) ◽  
pp. 3482-3487 ◽  
Author(s):  
Sébastien Boyer ◽  
Dipanwita Biswas ◽  
Ananda Kumar Soshee ◽  
Natale Scaramozzino ◽  
Clément Nizak ◽  
...  
Keyword(s):  
High Throughput Sequencing ◽  
Scaling Law ◽  
Natural Populations ◽  
Value Theory ◽  
Darwinian Evolution ◽  
Future Evolution ◽  
Synthetic Protein ◽  
Simple Scaling ◽  
Protein Libraries

Variation and selection are the core principles of Darwinian evolution, but quantitatively relating the diversity of a population to its capacity to respond to selection is challenging. Here, we examine this problem at a molecular level in the context of populations of partially randomized proteins selected for binding to well-defined targets. We built several minimal protein libraries, screened them in vitro by phage display, and analyzed their response to selection by high-throughput sequencing. A statistical analysis of the results reveals two main findings. First, libraries with the same sequence diversity but built around different “frameworks” typically have vastly different responses; second, the distribution of responses of the best binders in a library follows a simple scaling law. We show how an elementary probabilistic model based on extreme value theory rationalizes the latter finding. Our results have implications for designing synthetic protein libraries, estimating the density of functional biomolecules in sequence space, characterizing diversity in natural populations, and experimentally investigating evolvability (i.e., the potential for future evolution).

scholarly journals A scaled MP-PIC method for bubbling fluidization

2021 ◽  
Author(s):  
Xing Zhao ◽  
Yong Jiang ◽  
Fei Li ◽  
Wei Wang
Keyword(s):  
Fluidized Beds ◽  
Volume Fraction ◽  
Phase Particle ◽  
Scaling Law ◽  
Coarse Graining ◽  
Coarse Grained ◽  
Particle In Cell ◽  
Wide Range ◽  
Pic Method ◽  
Multi Phase

Coarse-grained methods have been widely used in simulations of gas-solid fluidization. However, as a key parameter, the coarse-graining ratio, and its relevant scaling law is still far from reaching a consensus. In this work, a scaling law is developed based on a similarity analysis, and then it is used to scale the multi-phase particle-in-cell (MP-PIC) method, and validated in the simulation of two bubbling fluidized beds. The simulation result shows this scaled MP-PIC can reduce the errors of solids volume fraction and velocity distributions over a wide range of coarse-graining ratios. In future, we expect that a scaling law with consideration of the heterogeneity inside a parcel or numerical particle will further improve the performance of coarse-grained modeling in simulation of fluidized beds.

scholarly journals MicroRNAs: Small Regulators of Tissue Regeneration

2017 ◽  
Vol 3 ◽  
pp. 6
Author(s):  
Madjid Momeni-Moghaddam ◽  
Elnaz Yossefi ◽  
Fatemeh Oladi
Keyword(s):  
Small Molecules ◽  
Tissue Regeneration ◽  
Protein Production ◽  
Special Functions ◽  
Cellular Events ◽  
Organ Regeneration ◽  
Wide Range ◽  
Range Of Functions ◽  
Transcriptional Gene Regulation ◽  
Common Cell

MicroRNAs (miRNAs) are small molecules that are involved in the regulation of cellular events. They can monitor protein production using a kind of gene expression inhibition called post transcriptional gene regulation. Nowadays a lot of them have been found in different kind of cellular process so they have a wide range of functions from common cell tasks to roles in the regulation of special functions including regeneration of damaged tissues. In recent years, there has been an increasing interest in the field of miRNAs. This paper will review the research conducted on the roles of miRNAs in stem cells and tissue/organ regeneration.

Characterization of Elution Chromatography Fractions from CIS-Polybutadiene by GPC

1970 ◽  
Vol 43 (6) ◽  
pp. 1439-1450 ◽  
Author(s):  
W. V. Smith ◽  
S. Thiruvengada
Keyword(s):  
Molecular Weight ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Low Molecular Weight ◽  
Molecular Weight Distributions ◽  
Weight Distributions ◽  
Log Normal ◽  
Analytical Fractionation ◽  
Molecular Weight Fractions ◽  
Elution Chromatography

Abstract A preparative fractionation of about 23 g of a commercial cis-polybutadiene rubber is described. The method employed was a solvent elution chromatographic method with very little temperature gradient. The molecular weight distributions of the fractions obtained were determined by an analytical fractionation of 20 mg of polymer. The method was similar to the preparative fractionation and involved solvent elution chromatography. The fractions obtained were assayed for quantity, molecular weight, and molecular weight distribution by GPC. The low molecular weight fractions of the preparative fractionation had molecular weight distributions which could be closely approximated by two log normal distributions, the low molecular weight component having the narrower width. The ratio of weight to number average molecular weight was found to be about 1.1 for these samples. The higher molecular weight fractions could also be approximated by two log normal distributions; however, in these fractions the low molecular weight component had a very broad distribution but constituted only a small portion of the sample. The widths of the GPC curves of the fractions correlate satisfactorily with the molecular weight distributions found by the analytical refractionations. The GPC width is a sensitive criterion of the width of the molecular weight distribution even when only two columns are used. It is felt that the analytical fractionation procedure presented gives more detailed information on the molecular weight distribution than is easily obtainable from an ordinary GPC curve.

scholarly journals Mechanics of spontaneously formed nanoblisters trapped by transferred 2D crystals

2018 ◽  
Vol 115 (31) ◽  
pp. 7884-7889 ◽  
Author(s):  
Daniel A. Sanchez ◽  
Zhaohe Dai ◽  
Peng Wang ◽  
Arturo Cantu-Chavez ◽  
Christopher J. Brennan ◽  
...  
Keyword(s):  
Scaling Law ◽  
New Physics ◽  
Adhesion Energy ◽  
Work Of Adhesion ◽  
Fourth Power ◽  
Layered Systems ◽  
Simple Scaling ◽  
Dynamics Simulations ◽  
2D Crystals ◽  
Good Agreement

Layered systems of 2D crystals and heterostructures are widely explored for new physics and devices. In many cases, monolayer or few-layer 2D crystals are transferred to a target substrate including other 2D crystals, and nanometer-scale blisters form spontaneously between the 2D crystal and its substrate. Such nanoblisters are often recognized as an indicator of good adhesion, but there is no consensus on the contents inside the blisters. While gas-filled blisters have been modeled and measured by bulge tests, applying such models to spontaneously formed nanoblisters yielded unrealistically low adhesion energy values between the 2D crystal and its substrate. Typically, gas-filled blisters are fully deflated within hours or days. In contrast, we found that the height of the spontaneously formed nanoblisters dropped only by 20–30% after 3 mo, indicating that probably liquid instead of gas is trapped in them. We therefore developed a simple scaling law and a rigorous theoretical model for liquid-filled nanoblisters, which predicts that the interfacial work of adhesion is related to the fourth power of the aspect ratio of the nanoblister and depends on the surface tension of the liquid. Our model was verified by molecular dynamics simulations, and the adhesion energy values obtained for the measured nanoblisters are in good agreement with those reported in the literature. This model can be applied to estimate the pressure inside the nanoblisters and the work of adhesion for a variety of 2D interfaces, which provides important implications for the fabrication and deformability of 2D heterostructures and devices.

Clocking the buildup dynamics of light-induced states through attosecond transient absorption spectrum

2021 ◽  
Author(s):  
Xiaoxia Wu ◽  
Shaofeng Zhang ◽  
Difa Ye
Keyword(s):  
Floquet Theory ◽  
Transient Absorption ◽  
Scaling Law ◽  
Time Lag ◽  
Time Dependent ◽  
Transient Absorption Spectroscopy ◽  
Transient Absorption Spectrum ◽  
Wide Range ◽  
Maximal Shift ◽  
Buildup Time

Abstract The buildup processes of the light-induced states (LISs) in attosecond transient absorption spectroscopy are studied by solving the time-dependent Schrödinger equation and compared with the quasistatic Floquet theory, revealing a time lag of the maximal shift and strongest absorbance of the LIS with respect to the zero delay that is referred to as the buildup time. We analytically derive a scaling law for the buildup time that confirms the numerical results over a wide range of detunings. Our theory verifies the commonly accepted scenario of nearly instantaneous response of matter to light if the pump field is blue-detuned, but some differences are found in the near-resonant and red-detuning cases. Implications of the buildup time in petahertz optoelectronics are discussed.

Phase Drift in Networks of Coupled Colpitts Oscillators

2021 ◽  
Vol 31 (04) ◽  
pp. 2130010
Author(s):  
Lourdes Coria ◽  
Horacio Lopez ◽  
Antonio Palacios ◽  
Visarath In ◽  
Patrick Longhini
Keyword(s):  
Collective Behavior ◽  
Traveling Wave ◽  
Scaling Law ◽  
Industrial Applications ◽  
Basins Of Attraction ◽  
Navigation Systems ◽  
Negative Effects ◽  
Phase Drift ◽  
Wide Range ◽  
Wave Patterns

In modern times, satellite-based global positioning and navigation systems, such as the GPS, include precise time-keeping devices, e.g. atomic clocks, which are crucial for navigation and for a wide range of economic and industrial applications. However, precise timing might not be available when the environment renders satellite equipment inoperable. In response to this critical need, we have been carrying out, over the past three years, theory and preliminary experiments [Buono et al., 2018a; Buono et al., 2018b; Palacios et al., 2020], towards developing a novel and inexpensive precision timing device that can function independently of GPS availability. The fundamental idea is to exploit collective behavior generated by networks of coupled nonlinear oscillators. Common sense may suggest that synchronized oscillations may lead to higher accuracy. Previous works show, however, that it is not synchronization but rather, traveling wave patterns, in which consecutive oscillators are out of phase by a constant amount, that can better reduce the negative effects of noise and material imperfections which cause phase drift. In this work we advance the state-of-art in the network-based concept by studying, mainly computationally, collective behavior in networks of Colpitts oscillators. These type of oscillators are chosen because they offer a wide range of advantages (such as the ability to tune up the oscillations over a broad frequency range). The results highlight the regions of parameter space, including coupling strength, where traveling wave patterns have the largest basins of attraction and the ability to reduce phase drift by a [Formula: see text] scaling law, where [Formula: see text] is the number of oscillators in the network. The results should also provide guidelines for follow-up design and fabrication tasks of a network-based technology for precision timing.

scholarly journals The Laplace equation in the exterior of the Hankel contour and novel identities for hypergeometric functions

2013 ◽  
Vol 469 (2157) ◽  
pp. 20130081 ◽  
Author(s):  
A. S. Fokas ◽  
M. L. Glasser
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Laplace Equation ◽  
Special Functions ◽  
Boundary Value ◽  
Zeta Functions ◽  
Neumann Boundary ◽  
Neumann Boundary Value Problem ◽  
Wide Range ◽  
Definition Of

By using conformal mappings, it is possible to express the solution of certain boundary-value problems for the Laplace equation in terms of a single integral involving the given boundary data. We show that such explicit formulae can be used to obtain novel identity for special functions. A convenient tool for deriving this type of identity is the so-called global relation , which has appeared recently in a wide range of boundary-value problems. As a concrete application, we analyse the Neumann boundary-value problem for the Laplace equation in the exterior of the Hankel contour, which appears in the definition of both the gamma and the Riemann zeta functions. By using the explicit solution of this problem, we derive a number of novel identities involving the hypergeometric function. Also, we point out an interesting connection between the solution of the above Neumann boundary-value problem for a particular set of Neumann data and the Riemann hypothesis.

scholarly journals Tuning the molecular weight distribution from atom transfer radical polymerization using deep reinforcement learning

2018 ◽  
Vol 3 (3) ◽  
pp. 496-508 ◽  
Author(s):  
Haichen Li ◽  
Christopher R. Collins ◽  
Thomas G. Ribelli ◽  
Krzysztof Matyjaszewski ◽  
Geoffrey J. Gordon ◽  
...  
Keyword(s):  
Molecular Weight ◽  
Reinforcement Learning ◽  
Atom Transfer Radical Polymerization ◽  
Radical Polymerization ◽  
Weight Distribution ◽  
In Silico ◽  
Atom Transfer ◽  
Polymer Molecular Weight ◽  
Molecular Weight Distributions ◽  
Weight Distributions

Combination of deep reinforcement learning and atom transfer radical polymerization gives precise in silico control on polymer molecular weight distributions.

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