A tripartite graph based methodology for steady-state solution of generalized multi-mode vapor compression systems

2021 ◽  
Vol 185 ◽  
pp. 116385
Author(s):  
Ransisi Huang ◽  
Vikrant Aute ◽  
Jiazhen Ling
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
State Solution ◽  
Vapor Compression ◽  
Tripartite Graph ◽  
Multi Mode ◽  
Vapor Compression Systems

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

Steady-state solution of traffic flow on a simple road network

2021 ◽  
Vol 33 (5) ◽  
pp. 950-957
Author(s):  
Yu-pei Lyu ◽  
Ming-min Guo ◽  
Peng Zhang ◽  
Rui Fang ◽  
Zhi-yang Lin ◽  
...  
Keyword(s):  
Steady State ◽  
Traffic Flow ◽  
Road Network ◽  
Steady State Solution ◽  
State Solution

Analytical Study of the Existence of a Hopf Bifurcation in the Tumor Cell Growth Model with Time Delay

2021 ◽  
Vol 3 (1) ◽  
pp. 20-28
Author(s):  
A. Yusnaeni ◽  
Kasbawati Kasbawati ◽  
Toaha Syamsuddin
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Immune System ◽  
Hopf Bifurcation ◽  
Delay Differential Equation ◽  
Immune Cells ◽  
Steady State Solution ◽  
State Solution ◽  
Activation Process ◽  
Delay Differential

AbstractIn this paper, we study a mathematical model of an immune response system consisting of a number of immune cells that work together to protect the human body from invading tumor cells. The delay differential equation is used to model the immune system caused by a natural delay in the activation process of immune cells. Analytical studies are focused on finding conditions in which the system undergoes changes in stability near a tumor-free steady-state solution. We found that the existence of a tumor-free steady-state solution was warranted when the number of activated effector cells was sufficiently high. By considering the lag of stimulation of helper cell production as the bifurcation parameter, a critical lag is obtained that determines the threshold of the stability change of the tumor-free steady state. It is also leading the system undergoes a Hopf bifurcation to periodic solutions at the tumor-free steady-state solution.Keywords: tumor–immune system; delay differential equation; transcendental function; Hopf bifurcation. AbstrakDalam makalah ini, dikaji model matematika dari sistem respon imun yang terdiri dari sejumlah sel imun yang bekerja sama untuk melindungi tubuh manusia dari invasi sel tumor. Persamaan diferensial tunda digunakan untuk memodelkan sistem kekebalan yang disebabkan oleh keterlambatan alami dalam proses aktivasi sel-sel imun. Studi analitik difokuskan untuk menemukan kondisi di mana sistem mengalami perubahan stabilitas di sekitar solusi kesetimbangan bebas tumor. Diperoleh bahwa solusi kesetimbangan bebas tumor dijamin ada ketika jumlah sel efektor yang diaktifkan cukup tinggi. Dengan mempertimbangkan tundaan stimulasi produksi sel helper sebagai parameter bifurkasi, didapatkan lag kritis yang menentukan ambang batas perubahan stabilitas dari solusi kesetimbangan bebas tumor. Parameter tersebut juga mengakibatkan sistem mengalami percabangan Hopf untuk solusi periodik pada solusi kesetimbangan bebas tumor.Kata kunci: sistem tumor–imun; persamaan differensial tundaan; fungsi transedental; bifurkasi Hopf.

The Effects of Energy Dissipation on the Transition to Planing of a Boat

1989 ◽  
Vol 33 (01) ◽  
pp. 35-46
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Steady State ◽  
Energy Dissipation ◽  
Detailed Analysis ◽  
Leading Edge ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Spray Formation ◽  
Propulsion Force

The problem of the transition to planing of a boat, in the presence of the effect of spray formation at the boat's leading edge, is investigated using a nonlinear steady-state solution of the equations of the theory of a directed fluid sheet for two-dimensional motion of an incompressible inviscid fluid. The motion of the fluid is coupled with the motion of the free-floating boat and detailed analysis is undertaken pertaining to such features as trim angle, sinkage, and propulsion force. The effects of the rate of energy dissipation arising from spray formation at the boat's leading edge, and changes in equilibrium depth, propulsion angle, and the boat's weight, are studied and shown to significantly influence the boat's planing characteristics.

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