Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.

Studying thin film damping in a micro-beam resonator based on non-classical theories

In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamped micro-beam bound between two fixed layers. The microgap between the micro-beam and fixed layers is filled with air. As classical theories are not properly capable of predicting the size dependence behaviors of the micro-beam,and also behavior of micro-scale fluid media, hence in the presented model, equation of motion governing longitudinal displacement of the micro-beam has been extracted based on non-local elasticity theory. Furthermore, the fluid field has been modeled based on micro-polar theory. These coupled equations have been simplified using Newton-Laplace and continuity equations. After transforming to non-dimensional form and linearizing, the equations have been discretized and solved simultaneously using a Galerkin-based reduced order model. Considering slip boundary conditions and applying a complex frequency approach, the equivalent damping ratio and quality factor of the micro-beam resonator have been obtained. The obtained values for the quality factor have been compared to those based on classical theories. We have shown that applying non-classical theories underestimate the values of the quality factor obtained based on classical theo-ries. The effects of geometrical parameters of the micro-beam and micro-scale fluid field on the quality factor of the resonator have also been investigated.

The prescription rule analysis of the New Theory on Spleen Dampness Syndrome by Academician TONG Xiaolin

Objective To analyze the basic characteristics,drug features,prescription rules,and drug-symptom relationships of patients in the splenic deficiency and impairment stage,by data mining of medical records under the New Theory on Spleen Dampness Syndrome(Pi Dan Xin Lun,《脾瘅新论》).Methods Medical records listed in the“New Theory on Spleen Dampness Syndrome-Under-standing and Treatment of Metabolic Syndrome from the Perspective of Traditional Chinese Medicine”,and which were diagnosed with the spleen dampness syndrome at the splenic de-ficiency and impairment stage,during January 2004 and December 2016 were selected.These patients’data,including basic information,clinical symptoms,laboratory examination res-ults,traditional Chinese medicine(TCM)and western medicine diagnoses,treatment meth-ods,prescriptions,etc.,were collected.The collected data were subsequently compiled into a medical record database using the Epidata 3.1 data management software,followed by the use of Apriori algorithm provided in the SPSS Modeler 14.2 statistical software to investigate the association rules between drug-drug,drug-symptom,and drug-western medicine indices.Results(i)A total of 51 medical records were included,involving 17 types of syndromes.Among them,the top three with frequency≥3 included“Phlegm and blood stasis,and thoracic obstruction”“Deficiency-weakness of the spleen Qi,and static blood blocking collat-erals”,and“Deficiency-weakness of the spleen Qi,and static blood blocking collaterals”.Al-ternatively,of the 14 treatment methods,the top three treatments with frequency of≥3 in-cluded“Activating Yang and eliminating turbidity,and removing phlegm and dredging chan-nel blockage”“Strengthening the spleen and benefiting Qi,and eliminating phlegm to activ-ate the channels”,and“Warming Yang and benefiting Qi,and expelling cold to remove ob-structions”.Among the 15 prescriptions,the top three used with frequency≥3 included Huangqi Guizhi Wuwu Tang(黄芪桂枝五物汤),Gualou Xiebai Banxia Tang(瓜蒌薤白半夏汤),and Ganjiang Huangqin Huanglian Renshen Tang(干姜黄芩黄连人参汤).Lastly,of the 83 drugs used for a total of 476 times,those with frequency≥15 included Huanglian(Coptid-is Rhizoma),Huangqi(Astragali Radix),Jiudahuang(Wine-processed Rhei Radix et Rhizoma),Jixueteng(Spatholobi Caulis),Shengjiang(Zingiberis Rhizoma Recens),Huangqin(Scutellariae Radix),and Guizhi(Cinnamomi Ramulus).(ii)For the drug-drug associations,under the criteria of support≥15%and confidence=100%,seven second-order association rules,seven third-order rules,and six fourth-order roles were identified.The top-ranking rule of each was“Huangqin(Scutellariae Radix)→Huanglian(Coptidis Rhizoma)”“Ganjiang(Zingiberis Rhizoma)+Huangqin(Scutellariae Radix)→Huanglian(Coptidis Rhizoma)”,and“Baishao(Paeoniae Radix Alba)+Guizhi(Cinnamomi Ramulus)+Jixueteng(Spatho-lobi Caulis)→Huangqin(Scutellariae Radix)”,respectively.Alternatively,the drug-symptom associations were analyzed under the criteria of support≥5%and confidence=100%,which derived eight second-order association rules,31 third-order rules,and 30 fourth-order rules.The top-ranking association rule of each order was“Huangqi(Astragali Radix)→Limb ed-ema”“Guizhi(Cinnamomi Ramulus)+Jixueteng(Spatholobi Caulis)→Limb numbness and pain”,and“Guizhi(Cinnamomi Ramulus)+Jixueteng(Spatholobi Caulis)+Huangqi(As-tragali Radix)→Limb numbness and pain”,respectively.Similarly,the drug-western medi-cine index associations were investigated under the criteria of support≥5%and confidence=100%,and five second-order association rules,16 third-order rules,and 16 fourth-order rules were identified.In this category,the top-ranking association rule of each order was“Qinpi(Fraxini Cortex)→Uric acid”“Huanglian(Coptidis Rhizoma)+Ganjiang(Zingiberis Rhizoma)→Glycated hemoglobin”,and“Huanglian(Coptidis Rhizoma)+Ganjiang(Zing-iberis Rhizoma)+Huangqin(Scutellariae Radix)→Glycated hemoglobin”,respectively.Conclusion Through association rule mining,this study objectively and quantitatively demonstrated the drug-drug,drug-symptom,and drug-physicochemical index associations of patients with the spleen dampness syndrome at the splenic deficiency and impairment stage treated by Academician TONG Xiaolin.The results indicated that treatment for these patients adopted the“state-target”syndrome differentiation method.The drug combination was characterized by“small prescriptions”,targeting both the patient’s symptoms and signs(syndrome target)and western medicine indices(treatment target).This study could provide references for future research on the academic thoughts and medical experience of Academi-cian TONG Xiaolin.

Damping Solitary Wave in a Three-Dimensional Rectangular Geometry Plasma

The solitary waves of a viscous plasma confined in a cuboid under the three types of boundary condition are theoretically investigated in the present paper.By introducing a threedimensional rectangular geometry and employing the reductive perturbation theory,a quasi-Kd V equation is derived in the viscous plasma and a damping solitary wave is obtained.It is found that the damping rate increases as the viscosity coefficient increases,or increases as the length and width of the rectangle decrease,for all kinds of boundary condition.Nevertheless,the magnitude of the damping rate is dominated by the types of boundary condition.We thus observe the existence of a damping solitary wave from the fact that its amplitude disappears rapidly for a → 0and b → 0,or ν→ ＋∞.

A two-dimensional lithospheric magnetic anomaly field model of Egypt using the measurements from Swarm satellites

We use magnetic field data observed by the Swarm mission from 2014 to 2020 to construct,for the first time,a two-dimensional(2 D)lithospheric magnetic anomaly model of Egypt and its surrounding area.Nighttime data during quiet geomagnetic conditions has been expanded in terms of the Legendre polynomial in harmonic terms N=6-50.The damped least square method has been used to estimate the model coefficients based on the lithospheric magnetic data.Modeled data at two different altitudes(438-448 km and 503-511 km)were compared with the CHAOS model.Results exhibit that the 2 D model is superior to the CHAOS model in the capability of extracting more information about small-scale crustal anomaly field.At low altitudes(438-448 km),the strength of the anomaly field increases,but the noise of the external fields has greatly reduced at high altitudes(503-511 km).Besides,the magnetic anomaly field at low altitudes has illuminated short-scale anomalies that didn’t appear at high altitudes.Both the total and vertical magnetic anomaly vectors showed their ability to reveal tectonic structures compared with Moho depth map and the geological maps.