Transient Temperature Distributions in a Cylinder Heated by Microwaves

1996 ◽  
Vol 430 ◽  
Author(s):  
H. W. Jackson ◽  
M. Barmatz ◽  
P. Wagner
Keyword(s):  
Numerical Solutions ◽  
Single Mode ◽  
Dielectric Constants ◽  
Microwave Cavity ◽  
Transient Temperature ◽  
Hybrid Heating ◽  
Fine Mesh ◽  
Temperature Distributions ◽  
Analytic Expressions ◽  
Lossy Dielectric

AbstractTransient temperature distributions were calculated for a lossy dielectric cylinder coaxially aligned in a cylindrical microwave cavity excited in a single mode. Results were obtained for sample sizes that range from fibers to large cylinders. Realistic values for temperature dependent complex dielectric constants and thermophysical properties of the samples were used. Losses in cavity walls were taken into account as were realistic thermal emissivities at all surfaces. For a fine mesh of points in time, normal mode properties and microwave power absorption profiles were evaluated using analytic expressions. Those expressions correspond to exact solutions of Maxwell's equations within the framework of a cylindrical shell model. Heating produced by the microwave absorption was included in self-consistent numerical solutions of thermal equations. In this model, both direct microwave heating and radiant heating of the sample (hybrid heating) were studied by including a lossy dielectric tube surrounding the sample. Calculated results are discussed within the context of two parametric studies. One is concerned with relative merits of microwave and hybrid heating of fibers, rods, and larger cylinders. The other is concerned with thermal runaway.

Comparison Of Finite-Difference And Analytic Microwave Calculation Methods

1996 ◽  
Vol 430 ◽  
Author(s):  
F. I. Friedlander ◽  
H. W. Jackson ◽  
M. Barmatz ◽  
P. Wagner
Keyword(s):  
Finite Difference ◽  
Numerical Evaluation ◽  
Normal Modes ◽  
Materials Processing ◽  
Calculation Methods ◽  
Power Absorption ◽  
Microwave Cavities ◽  
Analytic Expressions ◽  
Lossy Dielectric ◽  
Electromagnetic Solver

AbstractNormal modes and power absorption distributions in microwave cavities containing lossy dielectric samples were calculated for problems of interest in materials processing. The calculations were performed both using a commercially available finite-difference electromagnetic solver and by numerical evaluation of exact analytic expressions. Results obtained by the two methods applied to identical physical situations were compared. Our studies validate the accuracy of the finite-difference electromagnetic solver. Relative advantages of the analytic and finitedifference methods are discussed.

The Transient Temperature Distribution in a Slab Subject to Thermal Radiation

1965 ◽  
Vol 87 (1) ◽  
pp. 117-130 ◽  
Author(s):  
R. D. Zerkle ◽  
J. Edward Sunderland
Keyword(s):  
Temperature Distribution ◽  
Thermal Radiation ◽  
Radiant Heat ◽  
Analog Computer ◽  
Graphical Form ◽  
Transient Temperature ◽  
Transient Temperature Distribution ◽  
Temperature Distributions ◽  
Approximate Analytical Solutions ◽  
Wide Range

The transient, one-dimensional temperature distribution is determined for a slab, insulated on one face, and subjected to thermal radiation at the other face. The slab is initially at a uniform temperature and is assumed to be homogeneous, isotropic, and opaque; the physical properties are assumed to be independent of temperature. Transient temperature distributions for both heating and cooling situations are obtained by means of a thermal-electrical analog computer. A diode limiter circuit is used to simulate the nonlinear radiant heat flux. The transient temperature distributions are presented in a dimensionless, graphical form for a wide range of variables. Approximate analytical solutions are also given which complement and extend the solution charts over ranges of parameters not covered in the charts.

A Strategy for Fine Mesh Resolution in Contact Mechanics

2021 ◽  
Author(s):  
Gaurav Chauda ◽  
Daniel J. Segalman
Keyword(s):  
Degrees Of Freedom ◽  
Contact Problems ◽  
Boundary Integral ◽  
System Of Equations ◽  
Element Mesh ◽  
Contact Patch ◽  
Linear System Of Equations ◽  
Fine Mesh ◽  
Stiffness Matrices ◽  
Analytic Expressions

Abstract To obtain detail in elastic, frictional contact problems involving contact many — at least tens, and more suitably hundreds [1] — of nodes are necessary over the contact patch. Generally, this fine discretization results in intractable numbers of system equations that must be solved, but this problem is greatly mitigated when the elasticity of the contacting bodies is represented by elastic compliance matrices rather than stiffness matrices. An examination of the classical analytic expressions for the contact of disks — an example of smooth contact — shows that for most standard engineering metals, such as brass, steel, or titanium, the pressures that would cause more than one degree of arc of contact would push the materials past the elastic limit. The discretization necessary to capture the interface tractions would be on the order of at least tens of nodes. With the resulting boundary integral formulation would involve several hundreds of nodes over the disk, and the corresponding finite element mesh would have tens of thousands. The resulting linear system of equations must be solved at each load step and the numerical problem becomes extremely difficult or intractable. A compliance method of facilitating extremely fine contact patch resolution can be achieved by exploiting Fourier analysis and the Michell solution. The advantages of this compliance method are that only degrees of freedom on the surface are introduced and those not in the region of contact are eliminated from the system of equations to be solved.

scholarly journals Heisenberg-limited single-mode quantum metrology in a superconducting circuit

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
W. Wang ◽  
Y. Wu ◽  
Y. Ma ◽  
W. Cai ◽  
L. Hu ◽  
...  
Keyword(s):  
Single Mode ◽  
Coherence Time ◽  
Microwave Cavity ◽  
Phase Estimation ◽  
Quantum Metrology ◽  
Practical Applications ◽  
Infinite Dimensional ◽  
Noise Limit ◽  
Quantum Error ◽  
Shot Noise Limit

Abstract Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form $$\left( {\left| 0 \right\rangle + \left| N \right\rangle } \right)/\sqrt 2$$ 0 + N ∕ 2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼N−0.94. A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.

Interactions of cell volume, membrane potential, and membrane transport parameters

1980 ◽  
Vol 238 (5) ◽  
pp. C196-C206 ◽  
Author(s):  
E. Jakobsson
Keyword(s):  
Membrane Potential ◽  
Cell Volume ◽  
Membrane Transport ◽  
Numerical Solutions ◽  
Transport Equations ◽  
Time Varying ◽  
Transport Parameters ◽  
Animal Cells ◽  
Analytic Expressions ◽  
Solute Species

Equations have been written and solved that describe for animal cells the relationships among membrane transport, cell volume, membrane potential, and distribution of permeant solute. The essential system consists of n + 2 equations, where n is the number of permeant solute species. The n of the equations are the n transport equations for the permeant species, one for each species. The other two equations are statements of 1) the condition for bulk electroneutrality inside the cell and 2) the condition for isotonicity between the interior and exterior of the cell. Numerical solutions have been obtained in both the steady-state and time-varying cases for transport equations that are physically and phenomenologically reasonable. In addition to numerical solutions analytic expressions are presented that show the ranges of membrane parameters essential for volume regulation; for values of membrane parameters beyond explicitly defined bounds, the equations do not have real, positive solutions for cell volume.

scholarly journals Analysis of Propagation Characteristics along an Array of Silver Nanorods Using Dielectric Constants from Experimental Data and the Drude-Lorentz Model

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1280 ◽  
Author(s):  
Zong ◽  
Zhang
Keyword(s):  
Experimental Data ◽  
Propagation Constant ◽  
Single Mode ◽  
Expansion Method ◽  
Dielectric Constants ◽  
Fourier Series Expansion ◽  
Lorentz Model ◽  
Silver Nanorods ◽  
Complex Propagation ◽  
Multi Mode

In this study, the Fourier series expansion method (FSEM) was employed to calculate the complex propagation constants of plasma structures consisting of infinitely long, silver nanorod arrays in the range of 180–1900 nm, and the characteristics of the complex propagation constant were analyzed in depth. According to the results of FSEM using dielectric constants from Johnson experimental data, a multi-mode frequency band appears in the propagation stage, which can be adopted to achieve a multi-mode communication, multi-mode transceiver, integrated filter with single multi-mode combination. In the meantime, the comparison between the three sets of results with only single mode transmission of the generalized multipole technique (GMT) using dielectric constants from Johnson experimental data, FSEM using dielectric constants from Palik experimental data, and FSEM using dielectric function from Drude–Lorentz model suggested that the results of the four sets of complex propagation constants were well consistent with each other. Furthermore, a finite array of only 40 silver nanorods was studied, and the ability of guided waves when a finite array is excited by a plane wave at a specific wavelength was explored. According to different guiding abilities—propagation, attenuation, and cut off, it can be applied to waveguides, sensor, filters, etc.

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