Symmetric Assumption Research Articles

A Global Multidimensional Shock Wave for the Steady Supersonic Isothermal Flow

In the reference (Cui and Yin, Pacific J. Math. 233:257---289, 2007), under the assumptions that the supersonic incoming flow is isothermal and symmetrically perturbed with respect to a uniform supersonic constant state, the authors have shown the global existence and stability of a symmetric supersonic conic shock for such a supersonic flow past a circular cone. In this paper, we will remove all the symmetric assumptions in the previous paper and study the global existence problem on a really multidimensional shock wave. More concretely, we establish the global existence and stability of a three-dimensional supersonic conic shock wave for a perturbed steady supersonic isothermal flow past an infinitely long conic body.

A New Regression Model: Modal Linear Regression

ABSTRACTThe mode of a distribution provides an important summary of data and is often estimated on the basis of some non‐parametric kernel density estimator. This article develops a new data analysis tool called modal linear regression in order to explore high‐dimensional data. Modal linear regression models the conditional mode of a response Y given a set of predictors x as a linear function of x. Modal linear regression differs from standard linear regression in that standard linear regression models the conditional mean (as opposed to mode) of Y as a linear function of x. We propose an expectation–maximization algorithm in order to estimate the regression coefficients of modal linear regression. We also provide asymptotic properties for the proposed estimator without the symmetric assumption of the error density. Our empirical studies with simulated data and real data demonstrate that the proposed modal regression gives shorter predictive intervals than mean linear regression, median linear regression and MM‐estimators.

Influence of steel-concrete interaction in dissipative zones of frames: I - Experimental study

In the case of seismic-resistant composite dual moment resisting and eccentrically braced frames, the current design practice is to avoid the disposition of shear connectors in the expected plastic zones, and consequently to consider a symmetric moment or shear plastic hinges, which occur only in the steel beam or link. Even without connectors, the real behavior of the hinge may be different from the symmetric assumption since the reinforced concrete slab is connected to the steel element close to the hinge locations, and also due to contact friction between the concrete slab and the steel element. At a larger level, the structural response in the case of important seismic motions depends directly on the elasto-plastic behavior of elements and hinges. The numerical investigation presented in this study summarizes the results of elasto-plastic analyses of several steel frames, considering the interaction of the steel beam with the concrete slab. Several parameters, such as the inter-story drift, plastic rotation requirements and behavior factors q were monitored. In order to obtain accurate results, adequate models of plastic hinges are proposed for both the composite short link and composite reduced beam sections.

Influence of steel-concrete interaction in dissipative zones of frames: II - Numerical study

In the case of seismic-resistant composite dual moment resisting and eccentrically braced frames, the current design practice is to avoid the disposition of shear connectors in the expected plastic zones, and consequently to consider a symmetric moment or shear plastic hinges, which occur only in the steel beam or link. Even without connectors, the real behavior of the hinge may be different from the symmetric assumption since the reinforced concrete slab is connected to the steel element close to the hinge locations, and also due to contact friction between the concrete slab and the steel element. At a larger level, the structural response in the case of important seismic motions depends directly on the elasto-plastic behavior of elements and hinges. The numerical investigation presented in this study summarizes the results of elasto-plastic analyses of several steel frames, considering the interaction of the steel beam with the concrete slab. Several parameters, such as the inter-story drift, plastic rotation requirements and behavior factors q were monitored. In order to obtain accurate results, adequate models of plastic hinges are proposed for both the composite short link and composite reduced beam sections.

An Accelerated Method for Simulating Population Dynamics

AbstractWe present an accelerated method for stochastically simulating the dynamics of heterogeneous cell populations. The algorithm combines a Monte Carlo approach for simulating the biochemical kinetics in single cells with a constant-number Monte Carlo method for simulating the reproductive fitness and the statistical characteristics of growing cell populations. To benchmark accuracy and performance, we compare simulation results with those generated from a previously validated population dynamics algorithm. The comparison demonstrates that the accelerated method accurately simulates population dynamics with significant reductions in runtime under commonly invoked steady-state and symmetric cell division assumptions. Considering the increasing complexity of cell population models, the method is an important addition to the arsenal of existing algorithms for simulating cellular and population dynamics that enables efficient, coarse-grained exploration of parameter space.

Axisymmetric and three dimensional flow modeling within thermal vapor compressors

Thermal vapor compressor (TVC) is a device for compressing vapor in water–steam cycles and frequently used in desalination systems. Large amounts of useless vapor can be compressed by this device and the efficiency of a desalination unit is effectively enhanced through this process. Motive steam is injected into the TVC through a convergent–divergent nozzle and accelerated to supersonic velocities. The low pressure steam is entrained at the upstream zone and mixed with this highly compressible motive flow within the TVC. In the current study, the flow field of an experimental TVC is scrutinized in both axisymmetric and three-dimensional approaches and compared with experimental measurements. Since the steam collector at the suction surface of the TVC has a curved shape and may undermine the symmetry of the flow on either side of the central axis, the second objective of this study is to reveal the deviation of the symmetric assumption from the real non-symmetric condition of entering steam flow into the TVC. Results show that the presence of a bending at the inlet side has approximately negligible effects on the mixing phenomenon and the flow remains symmetric around the central axis. Hence, there is no need to consider the collector geometry in further simulations and the performance parameters of the TVC would be sufficiently obtained through an axisymmetric method with a substantial reduction in the computational cost and time.

A dissipative dynamical method based on discrete variational principle：stationary shapes of three-dimensional vesicle

In this article, the dissipative dynamical evolution method based on the discrete variational principle is applied to a three-dimensional (3D) vesicle system. The stationary shapes of vesicles are obtained through the minimization of membrane bending energy without any symmetric assumption, which is an outstanding merit of our method. Aiming at a 3D vesicle system with certain parameter settings, a series of axisymmetric shapes are achieved by our method. The simulation results are in good agreement with those obtained with axisymmetric assumption, which indicates that our method can describe the deformation of 3D vesicle with extremely high precision. In addition, a shape transition between two stable states with great difference is studied, which further implies the capability of our proposed method in simulating large deformations regarding the 3D membrane. We believe that we have provided a very powerful simulation method for the future studies of bio-membrane deformations.

Symmetric Assumptions in the Theory of Disruptive Innovation: Theoretical & Managerial Implications

The literature on disruptive innovation has successfully explained why firms often encounter problems under conditions of discontinuous change. It states that incumbent firms fail to invest in new ...

One-Dimensional Constrained Coulomb Structure Control with Charge Saturations

A Coulomb structure is a cluster of free-flying satellites which maintains its shape through inter-vehicle electrostatic forces. These Coulomb forces are generated using on-board charge emission devices. This paper investigates the 1-D restricted motion of a 3-craft cluster. Two charge feedback strategies are discussed where the charge saturation limitation is considered. First a continuous formation shape feedback control strategy is presented. Next a saturated control strategy is developed to arrest any relative velocities of the Coulomb structure. If the structure can be brought to rest, then the continuous charge control can be engaged to achieve the desired virtual structure. The saturated feedback control is developed using Lyapunov's direct method and can control the separation rates between the satellites by changing the signs of the three saturated charge products. Implementable real-charge solutions are ensured through scaling the Lyapunov function rate. The control is shown to be Lyapunov stable. Because of the limitations of the control charge magnitudes, certain initial conditions will not lead to the desired zero relative motion rates. Conditions under which the relative motion of the Coulomb structure can be stabilized are analyzed through investigating the total energy of the system in the symmetric motion assumption. The general convergence areas are illustrated numerically in various state planes. Simulations demonstrate the performance of the control.

Outage Analysis of Block-Fading Gaussian Interference Channels

This paper considers the asymptotic behavior of the outage probability of a two-source block-fading single-antenna Gaussian interference channel in the high-SNR regime by means of the diversity-multiplexing tradeoff. A general setting where the user rates and the average channel gains are not restricted to be symmetric is investigated. This asymmetric scenario allows to analyze networks with “mixed” interference, i.e., when different sources are at different distance from their intended destination, that are not possible under the commonly used symmetric assumption. Inner and outer bounds for the diversity are derived. The outer bound is based on the recent “to within one bit” capacity result of Etkin for the unfaded Gaussian channel and is a re-derivation of a known bound for which an error is pointed out. The inner bound is based on the Han and Kobayashi achievable region both without rate splitting and with a rate spitting inspired by the “to within one bit” capacity result. An analytical comparison of the diversity upper and lower bounds for a general channel seems difficult; by numerical evaluations, the two bounds are shown to coincide for a fairly large set of channel parameters.

Numerical Analysis of Nodal Sets for Eigenvalues of Aharonov–Bohm Hamiltonians on the Square with Application to Minimal Partitions

This paper is devoted to presenting numerical simulations and a theoretical interpretation of results for determining the minimal k-partitions of a domain Ω as considered in [Helffer et al. 09]. More precisely, using the double-covering approach introduced by B. Helffer, M. and T. Hoffmann-Ostenhof, and M. Owen and further developed for questions of isospectrality by the authors in collaboration with T. Hoffmann-Ostenhof and S. Terracini in [Helffer et al. 09, Bonnaillie-Noël et al. 09], we analyze the variation of the eigenvalues of the one-pole Aharonov–Bohm Hamiltonian on the square and the nodal picture of the associated eigenfunctions as a function of the pole. This leads us to discover new candidates for minimal k-partitions of the square with a specific topological type and without any symmetric assumption, in contrast to our previous works [Bonnaillie-Noël et al. 10, Bonnaillie-Noël et al. 09]. This illustrates also recent results of B. Noris and S. Terracini; see [Noris and Terracini 10]. This finally supports or disproves conjectures for the minimal 3- and 5-partitions on the square.

Symmetric and asymmetric committees

This paper studies the assignment of decision makers to two committees that make decisions by a simple majority rule. There is an even number of decision makers at each of the various skill levels and each committee has an odd number of members. Surprisingly, even with the symmetric assumptions in the spirit of Condorcet, a symmetric composition of committees is not always optimal. In other words, decision makers with different skill levels should not generally be evenly divided among the committees. However, in the special case of only two skill levels, it is optimal to compose the committees evenly.

Symmetric and Asymmetric Committees

This paper studies the assignment of decision makers to two committees that make decisions by a simple majority rule. There is an even number of decision makers at each of various skill levels and each committee has an odd number of members. Surprisingly, even with the symmetric assumptions in the spirit of Condorcet, a symmetric composition of committees is not always optimal. In other words, decision makers with different skill levels should not generally be evenly divided among the committees. However, in the special case of only two skill levels, it is optimal to compose the committees evenly.

Abel inversion for deriving refractivity profile from down-looking GPS radio occultation: simulation analysis

Down-looking (DL) Global Positioning System (GPS) radio occultation can produce an estimate of the atmospheric refractivity profile. The main observations are the bending angle as a function of the impact parameter. DL provides both negative as well as positive elevation angle measurements. Abel inversion can be operated on a profile of partial bending angle found by subtracting the positive elevation measurement from the negative one with the same impact parameter. Abel inversion requires the spherical symmetrical assumption. Basically, partial bending calculation removes the ionospheric bending and hence it is possible to use a single frequency GPS receiver. The current paper introduces a simulation data for the case of a receiver on mountain top. The simulation uses model refractivity from MSISE-90 model as well as radiosonde data. Random noises are added to the bending angle profile before inversion. The result shows that it is possible to produce accurate vertical refractivity profile below the receiver altitude. The calculation of the water vapor profile is also made using temperature profile information from the MSISE-90 model as well as radiosonde. The errors in the retrieved vapor profile are always less than 0.1 mbar.

Valuation, Downside Risk Measures and Asymmetrical Information: A Portfolio Optimization Approach

This paper presents an optimal portfolio algorithm under equilibrium conditions to evaluate future cash flows. The Algorithm employs expected return-risk approximation of utility function and bivariate distribution of cash flows of an investment and returns on market portfolios. The proposed procedure replaces the traditional discounting cash flow valuation approach that employs CAPM Risk Adjusted Cost of Capital (RACC). Only under symmetrical distribution assumption the proposed procedure and the conventional CAPM yields identical valuation. When downside risk measure is employed and asymmetrical distribution is assumed, then the proposed algorithm and the three moment extensions of CAPM may yield close but not necessarily identical valuation, while Estrada's downside risk extension of CAPM leads to erroneous valuation. The impact of skewness on valuation under symmetrical, as well as asymmetrical, information is examined in this paper by shifting a cash flow by Mean Variance Preserving Shifts (MVPS) that preserve both means and variance but generate skewer cash flow and Third-degree Stochastic Dominance (TSD). The proposed equilibrium valuation algorithm of this paper yields discount rates that consider downside risk measures as well as higher moments of the distribution.

Retrieval and validation of ionospheric measurements from COSMIC radio occultation

The relative total electron content （TEC） is obtained through the combination of COSMIC radio occultation ionospheric measurements L1 and L2 phase. The TEC data are then calibrated by non-occultation observation data on the auxiliary side to remove portion of TEC above the LEO orbit altitude. The electron density profile can be retrieved from TEC by Abel integral transformation，with a spherically symmetric assumption of electron density and an approximation of signal straight-line propagation. The computation standard deviation of F2-layer critical frequency f0F2 is about 059 MHz，and the standard deviation of F2-layer peak altitude hmF2 is about 3308 km，as through comparing 4903 COSMIC ionospheric occultation profiles with those from ionosonde stations，of which the longtitude deviations are less than 10°，the latitude deviations are less than 2°.

Advection scheme with 3rd high-order spatial interpolation at the middle temporal level and its application to saltwater intrusion in the Changjiang Estuary

A non-oscillatory advection scheme with 3rd high-order spatial interpolation at the middle temporal level coupled with a TVD limiter (the 3rd HSIMT-TVD scheme) was developed with the following features: (1) It uses a parabola to characterize a substance’s local distribution at nΔ t; (2) it determines the cell interface value at ( n + 0.5)Δ t by one-step backward tracing to its position at nΔ t; and (3) it uses Sweby’s TVD limiter to constrain the derived cell interface value to eliminate numerical oscillation. The 3rd HSIMT-TVD scheme was derived based on Sweby’s original TVD formula directly, thus the symmetric assumption of a TVD limiter is not necessary. 1D/2D tests suggest that the present scheme performs quite robustly compared to some other well-established schemes. The wavenumber two freshwater eddy instability has been successfully simulated using the present scheme. The derived model was then used to simulate the saltwater intrusion into the Changjiang Estuary, and the in situ data collected in February 2003 and February–March 2007 were used for validation. The model results were quite close to the measured data, and the main features of saltwater intrusion, such as saltwater spilling over from the North Branch, the salt wedge, and the stratification introduced by the wedge-like saltwater intrusion and the plume-like extension of diluted water, were simulated correctly. Furthermore, some other schemes were also used for comparison, and their differences are discussed.

Agglomeration under Forward-Looking Expectations: Potentials and Global Stability

This paper considers a class of migration dynamics with forward-looking agents in a multi-country solvable variant of the core-periphery model of Krugman (Journal of Political Economy 99 (1991)). We find that, under a symmetric externality assumption, our static model admits a potential function, which allows us to identify a stationary state that is uniquely absorbing and globally accessible under the perfect foresight dynamics whenever the degree of friction in relocation decisions is sufficiently small. In particular, when trade barriers are low enough, full agglomeration in the country with the highest barrier is the unique stable state for small frictions. New aspects in trade and tax policy that arise due to forward-looking behavior are discussed.

Agglomeration under forward-looking expectations: Potentials and global stability

This paper considers a class of migration dynamics with forward-looking agents in a multi-country solvable variant of the core–periphery model of Krugman [Krugman, P., 1991. Increasing returns and economic geography. Journal of Political Economy 99, 483–499]. We find that, under a symmetric externality assumption, our static model admits a potential function, which allows us to identify a stationary state that is uniquely absorbing and globally accessible under the perfect foresight dynamics whenever the degree of friction in relocation decisions is sufficiently small. In particular, when trade barriers are low enough, full agglomeration in the country with the highest barrier is the unique stable state for small frictions. New aspects in trade and tax policy that arise due to forward-looking behavior are discussed.

Irreversible Investment, Financing, and Bankruptcy Decisions in an Oligopoly

AbstractThis paper examines a firm's debt level, investment timing, and investment scale choices in a continuous-time model where the output price of a good that the firm produces depends on a stochastic demand-shift variable and the total industry supply of the good. Using the simple symmetric Cournot-Nash equilibrium assumption that all firms are identical and therefore follow the same financing and investment strategies, we show that competition decreases the output price and hence encourages a firm to wait for a higher demand level before it is profitable to invest. We also demonstrate how uncertainty, bankruptcy costs, and corporate taxation affect the firm's financing and investment decisions.