Two-cell Case Research Articles

Synchronous oscillations for a coupled cell-bulk ODE–PDE model with localized cells on $${\mathbb {R}}^2$$

In many micro- and macro-scale systems, collective dynamics occurs from the coupling of small spatially segregated, but dynamically active, units through a bulk diffusion field. This bulk diffusion field, which is both produced and sensed by the active units, can trigger and then synchronize oscillatory dynamics associated with the individual units. In this context, we analyze diffusion-induced synchrony for a class of cell-bulk ODE–PDE system in $${\mathbb {R}}^2$$ that has two spatially segregated dynamically active circular cells of small radius. By using strong localized perturbation theory in the limit of small cell radius, we calculate the steady-state solution and formulate the linear stability problem. For Sel’kov intracellular reaction kinetics, we analyze how the effect of bulk diffusion can trigger, via a Hopf bifurcation, either in-phase or anti-phase intracellular oscillations that would otherwise not occur for cells that are uncoupled from the bulk medium. Phase diagrams in parameter space where these oscillations occur are presented, and the theoretical results from the linear stability theory are validated from full numerical simulations of the ODE–PDE system. In addition, the two-cell case is extended to study the onset of synchronous oscillatory instabilities associated with an infinite hexagonal arrangement of small identical cells in $${\mathbb {R}}^2$$ with Sel’kov intracellular kinetics. This analysis for the hexagonal cell pattern relies on determining a new, computationally efficient, explicit formula for the regular part of a certain periodic reduced-wave Green’s function.

Relay Coordination Schemes for Two-Hop Networks: Two-Cell Case

The outage probability of a two-hop coordinated decode-and-forward relay network is investigated. The case of two interfering cells is considered. This is analogous to the case when network coordination is performed with the dominant cochannel interfering cell. Different levels of network coordination are studied and their performances are compared. Exact expressions are derived for of the system for each coordination method. The impact of user location randomness on the outage probability is investigated.

Shared Relay Networks with Linear Receivers at the Relay: Two-Cell Case

The downlink performance of a two-cell relay enhanced wireless network is investigated. A single relay is shared by the two base stations in the system. The relay is assumed to be placed in a geographic region covered by both base stations. The relay station is operating in the decode-and-forward mode. Closed-form approximations which estimate the exact results extremely closely are derived for the outage probability and the ergodic rate of the system. The impact of finite rate channel state information feedback on the user ergodic rate is examined.

Application of Graph Theory to the Multicell Beam Scheduling Problem

This paper applies combinatorial optimization techniques to improve the downlink transmission to multiple users in a network with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> cells, where intercell interference is a performance-limiting factor. A fair distribution of the signal-to-interference-plus-noise ratio (SINR) is desirable. A well-known technique to get a fair (balanced) SINR is max-min unicast beamforming (MBF). However, in a multicell network, there are conditions where MBF can result in a low balanced SINR. This happens if, e.g., two users are geographically close together and served by two base stations (BSs) from, e.g., two different interfering sectors. Then, the mutual interference among the two links will be large, and the balanced SINR among all jointly optimized links decreases. Therefore, the users must be scheduled such that these situations are avoided. In this paper, smart selection of active beams to avoid intercell interference is called beam scheduling and leads to a combinatorial optimization problem. This paper proposes a graph-theory-based problem that is closely related to the beam scheduling problem. The proposed algorithms maximize the sum rate or the minimum SINR among all users and slots. For the two-cell case, an optimal algorithm exists. In the N > 2-cell case, the beam scheduling problem is proven to be NP-hard. Based on the close relation between the beam scheduling problem and the multidimensional assignment problem (MAP), this paper presents suboptimal algorithms for N > 2 to maximize either the sum rate or the minimum SINR among all users and slots. The performance gain in terms of the mean sum rate or the minimum SINR is significant compared with random scheduling.

Constrained power allocation schemes for coordinated base station transmission using block diagonalization

Abstract In this study, we propose several power allocation schemes in a coordinated base station downlink transmission with per antenna and per base station power constraints. Block Diagonalization is employed to remove interference among users. For each set of power constraints, two schemes based on the waterfilling distribution are proposed and compared to the optimal solution, which can only be obtained numerically by using convex optimization. We show that the proposed schemes achieve a performance, in terms of weighted sum rate, very close to the optimal, without the heavy computational complexity required by the latter. The sum rates are compared first in a simplified two-user two-cell case where we also compare our approach to the previous solutions available in the literature. Then, we examine the performance in a multi-cell scenario where we also evaluate the degradation of the performance caused by imperfect channel state information.

Effects of curvature and cell–cell interaction on cell adhesion in microvessels

It has been found that both circulating blood cells and tumor cells are more easily adherent to curved microvessels than straight ones. This motivated us to investigate numerically the effect of the curvature of the curved vessel on cell adhesion. In this study, the fluid dynamics was carried out by the lattice Boltzmann method (LBM), and the cell dynamics was governed by the Newton's law of translation and rotation. The adhesive dynamics model involved the effect of receptor-ligand bonds between circulating cells and endothelial cells (ECs). It is found that the curved vessel would increase the simultaneous bond number, and the probability of cell adhesion is increased consequently. The interaction between traveling cells would also affect the cell adhesion significantly. For two-cell case, the simultaneous bond number of the rear cell is increased significantly, and the curvature of microvessel further enhances the probability of cell adhesion.

Non-cooperative resource competition game by virtual referee in multi-cell OFDMA networks

In this paper, a distributive non-cooperative game is proposed to perform sub-channel assignment, adaptive modulation, and power control for multi-cell multi-user orthogonal frequency division multiplexing access (OFDMA) networks. Each individual user's goal is to minimize his/her own transmitted power in a distributed manner under the constraints that the desirable rate is achieved and the transmitted power is bounded. The pure non-cooperative game may result in non-convergence or some undesirable Nash Equilibriums with low system and individual performances. To enhance the performances, a virtual referee is introduced to the networks and is in charge of monitoring and improving the outcome of non-cooperative competition for resources among the distributed users. If the game outcome is not desirable, either the required transmission rates should be reduced or some users should be prevented from using some radio resources such as sub-channels, so that the rest of users can share the limited resources more efficiently. Moreover, it can be shown that the introduction of the virtual referee does not increase the complexity of the networks. From the simulation results in a two-cell case, the proposed scheme reduces the transmitted power by 80% and 25% compared with the fixed channel assignment algorithm and the iterative water-filling algorithm in the literature, respectively. The achievable rate can be improved by 10%. In a multi-cell case, the proposed scheme can have up to 40% power reduction compared with the iterative water-filling algorithm when the co-channel interferences are severe.

Natural Balance of Multicell Converters: The Two-Cell Case

The multicell converter topology is said to possess a natural voltage balancing property. This paper is the first of a two-part series in which multicell converters are modelled for the general case of p-cells. This paper focuses on the development of the natural balancing theory for the two-cell case. An understanding of the two-cell case is fundamental to understanding the general balancing theory. The switching functions used in switching these converters are mathematically analyzed. Equivalent circuits are derived and presented. The switching and balancing properties of these converters are mathematically analyzed. The main conclusion of the analysis is that the natural balancing of these converters are influenced by three factors namely, the harmonic content of the reference waveform, the switching frequency and the load impedance. Mathematical tools are presented that can help designers to predict if balancing problems would occur for a particular set of operating conditions. As a result of the detailed understanding of the balancing mechanism that is gained through this theory it is shown that by adding a balance booster, the load impedance can be manipulated to improve the natural balancing of the converter. Simulation results are included to verify the presented balance theory and properties

Natural Balance of Multicell Converters: The General Case

This paper focuses on the development of the natural balancing theory for the p-cell case. It describes the relationship between the models for different numbers of cells in a generic model for a p-cell multicell converter. The model discussed is based on the same principles that were used to develop the two-cell model in , except that the mathematics is much more involved. The same conclusions that were found to be true for the two-cell case was also found to be true for the general case of p cells. These conclusions include that the natural balancing mechanism of multicell converters depends on the overlap of the groups of harmonics of the switching function as well as on the load impedance. It will also be shown that the self-balancing mechanism ensures safe operation under most operating conditions where a high enough switching frequency is chosen and the load is not purely reactive. Two new aspects of the balancing theory were identified in the p-cell case: 1) for fixed duty-cycle modulation there exists certain values of the duty-cycle that causes the natural balancing mechanism to fail and 2) for p-cell converters the balance booster concept can be extended to a number of balance boosters tuned to multiples of the switching frequency. A DesignTool based on the balancing theory was developed to aid practicing engineers in designing multicell converters

Exponential stability and global stability of cellular neural networks

In this paper, we present two types of matrix stability: complete stability and strong stability, and some properties of them. By using these properties, we discuss stability of cellular neural networks and obtain some conditions ensuring uniqueness, exponential stability and global asymptotic stability of the equilibrium point for cellular neural networks. In particular, in the two-cell case, the network is globally exponentially stable if and only if the feedback matrix minus the unit matrix is a complete stable matrix.

Calculation of the Three-Dimensional Field Vectors in Dielectrics

We have developed a culculation method of the applied electric field in a dielectric by measuring the difference in the output light intensity. At present, the direction of each applied field can be calculated when the dielectric is divided into four cells in which the applied fields are the same in intensity but differ in direction. Firstly, this paper shows how to determine the applied field intensity and direction when the electric field is applied to only one dielectric cell. Secondly, the method of numerical calculation of the applied field is described applying the method for one cell to a case where the dielectric is divided into two cells in which the intensity of the applied field is known but the direction is unknown. Finally, by extending the case of two cells, the flow of the numerical analysis and its result are described when the dielectric is divided into four cells under the same conditions as those for the two-cell case.

On the Accuracy of an Approximate Theory for the Ablation of Glassy Materials -- A Reply

and that Eqs. (2), (3), (4), and (5) all reduce, for large r, to the corresponding expressions for the one-cell case. The distribution of w with r for the two cases is shown in Fig. 2(a), and that of v in Fig. 2(b). A marked reduction in the maximum value of v for the two-cell as compared with the onecell case is evident, and there is a large region near the axis where v can be considered negligible in the two-cell case in comparison with the one-cell case. Burgers calculated the dissipation, using only the terms in v, and found the result to be of the third order in velocities and independent of viscosity. The same is found to be true in the two-cell case.