Inelastic Flows Research Articles

Power Plastics: A Hybrid Lagrangian/Eulerian Solver for Mesoscale Inelastic Flows

We present a novel hybrid Lagrangian/Eulerian method for simulating inelastic flows that generates high-quality particle distributions with adaptive volumes. At its core, our approach integrates an updated Lagrangian time discretization of continuum mechanics with the Power Particle-In-Cell geometric representation of deformable materials. As a result, we obtain material points described by optimized density kernels that precisely track the varying particle volumes both spatially and temporally. For efficient CFL-rate simulations, we also propose an implicit time integration for our system using a non-linear Gauss-Seidel solver inspired by X-PBD, viewing Eulerian nodal velocities as primal variables. We demonstrate the versatility of our method with simulations of mesoscale bubbles, sands, liquid, and foams.

Numerical investigation of non-Newtonian inelastic flows through conical nozzles

Numerical investigation of non-Newtonian inelastic flows through conical nozzles

Numerical Simulation of Non-Newtonian Inelastic Flows in Channel based on Artificial Compressibility Method

In this study, inelastic constitutive modelling is considered for the simulation of shear-thinning fluids through a circular channel. Numerical solutions are presented for power-law inelastic model, considering axisymmetric Poiseuille flow through a channel. The numerical simulation of such fluid is performed by using the Galerkin finite element approach based on artificial compression method (AC-method). Usually, the Naiver-Stoke partial differential equations are used to describe fluid activity. These models consist of two partial differential equations; a continuity equation (mass conservation) and time-dependent conservation of momentum, which are maintained in the cylindrical coordinate system (axisymmetric) flow in current study. The effects of many factors such as Reynolds number (Re) and artificial compressibility parameter (sac) are discussed in this study. In particular, this study confirms the effect of these parameters on the convergence level. To meet the method analysis, Poiseuille flow along a circular channel under an isothermal state is used as a simple test problem. This test is conducted by taking a circular section of the pipe. The Findings reveal that, there is a significant effect from the inelastic parameters upon the the velocity temporal convergence-rates of velocity, while for pressue, the change in convergence is modest. In addition, the rate of convergence is increased as the values of artificial compressibility parameter (sac) are decreased.

Providing Utility-Optimal Throughput Guarantees in Wireless LANs

With the pervasive use of IEEE 802.11 wireless local area networks (LANs), increasingly more application flows with different quality-of-service (QoS) requirements will be deployed therein, e.g., home multimedia. This paper is concerned with providing utility-optimal throughput guarantees when diverse application flows share the limited bandwidth. Our proposal provides the absolute throughput guarantees for inelastic flows (such as Internet Protocol television) and the proportional throughput guarantees for elastic flows (such as text message) while maximizing the entire system bandwidth utilization. To this end, we first establish a general theoretical framework on the utility-optimal problem. We then present the exact and approximate solutions and prove the existence and uniqueness of the approximate solution. Finally, extensive simulations are performed, which validate that the approximate solution can well achieve the desired objectives.

A novel contention-on-demand design for WiFi hotspots

In widely deployed wireless "hot-spot" networks, nodes frequently join or leave, and inelastic/elastic and saturated/nonsaturated flows coexist. In such dynamic and diverse environments, it is challenging to maximize the channel utilization while providing satisfactory user experiences. In this paper, we propose a novel contention-on-demand (CoD) MAC scheme to address this problem. The CoD scheme consists of a fixed-CW algorithm, a dynamic-CW algorithm, and an admission control rule. The fixed-CW algorithm allows elastic flows to access limited system bandwidth; the dynamic-CW algorithm enables inelastic flows to contend for channel on demand and quickly adapt to network change; and the admission control rule rejects overloaded traffic for providing good user experiences. We then perform an asymptotic analysis to develop a simple and practical admission control rule for homogeneous and heterogeneous traffic; our rule can not only adapt to the change in offered loads and node number, but also maximize the system utilization . Finally, extensive simulations verify that our scheme is very effective and our theoretical result is very accurate.

Integrable systems from inelastic curve flows in 2– and 3– dimensional Minkowski space

Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2– and 3– dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the modified Korteveg-de Vries (mKdV) equation and the nonlinear Schrödinger (NLS) equation in 2– and 3– dimensional Euclidean space, respectively. In 2–dimensional Minkowski space, timelike/spacelike inelastic curve flows are shown to yield the defocusing mKdV equation and its bi-Hamiltonian integrability structure, while inelastic null curve flows are shown to give rise to Burgers’ equation and its symmetry integrability structure. In 3–dimensional Minkowski space, the complex defocusing mKdV equation and the NLS equation along with their bi-Hamiltonian integrability structures are obtained from timelike inelastic curve flows, whereas spacelike inelastic curve flows yield an interesting variant of these two integrable equations in which complex numbers are replaced by hyperbolic (split-complex) numbers.

Motions of curves in the galilean space G3

In this article, we study the flows of curves in the Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and the intrinsic quantities of the inelastic flows of curves are independent of time. We show that the motion of curves in the Galilean 3-space and its equiform geometry are described by the inviscid and viscous Burgers' equations.

Subdivision Schemes Based Collocation Algorithms for Solution of Fourth Order Boundary Value Problems

We present two collocation algorithms based on interpolating and approximating subdivision schemes for the solution of fourth order boundary value problems arising in the mathematical modeling of viscoelastic, and inelastic flows, deformation of beams, arches, and load bearing members like street lights and robotic arms in multipurpose engineering systems. Numerical examples are given to illustrate the algorithms. We conclude that approximating schemes based collocation algorithms give better solution than interpolating schemes based collocation algorithms. Main purpose of this paper is to explore and seek the applications of interpolating and approximating subdivision schemes in the field of boundary value problems along with intrinsic comparison of the results obtained by algorithms based on these schemes. A comparison with other approaches of this type of boundary value problems in order to see the advantages of the proposed methods is also given.

Improved round robin queue management algorithm for elastic and inelastic traffic flows

In current scenario, network traffic flows need a start-time fair queuing algorithm which is computationally efficient and also which can achieve maximum fairness regardless of variation in a network capacity. To enhance the situation of congestion, an improved round robin IRR queue management algorithm for elastic and inelastic traffic flows is proposed. In this approach, the traffic flows are categorised into elastic traffic flows and in-elastic traffic flows. The scheduling process in the inelastic flows is handled by the BRR scheduler algorithm since they have large capacity requirements and delay constraints and elastic flows will be scheduled using DRR-SFF. The results are simulated with NS-2 and they show consistent improvement in the performance of the network.

Heterogeneous Resource Allocation Algorithm for Ad Hoc Networks with Utility Fairness

Resource allocation is expected to be a most important factor especially for heterogeneous applications in wireless ad hoc networks. In this paper, a novel heterogeneous resource allocation algorithm (HRA) is presented for ad hoc networks, supporting both elastic and inelastic traffic. First, by combining the first order Lagrangian method with pseudo utility, the original nonconvex problem is converted into a new convex one. Then, we successfully solve the heterogeneous problem with the dual-based decomposition approach. In addition, we integrate utility fairness into the resource allocation framework, which can adaptively manage the tradeoff between elastic and inelastic flows. Simulations show and prove that HRA converges fast and can achieve the global optimum starting from many different network conditions, such as elastic, inelastic, and hybrid scenario. With both considerations of flow rate and utility fairness, HRA improves the overall network utility and system throughput greatly.

Motions of Curves in the Pseudo-Galilean SpaceG31

We study the flows of curves in the pseudo-Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and intrinsic quantities of the inelastic flows of curves are independent of time. We show that the motions of curves in the pseudo-Galilean 3-space and its equiform geometry are described by the inviscid and viscous Burgers’ equations.

An effective queuing architecture for elastic and inelastic traffic with different dropping precedence in MANET

Mobile ad hoc network (MANET) is a group of self-organized mobile nodes that are associated with comparatively low bandwidth wireless links. This paper proposes an effective queuing architecture, which supports both elastic and inelastic traffic. The packets of inelastic flows are always stored ahead of those of the elastic flows. If a link is critically loaded by the inelastic traffic, it results in large delays and elastic traffic may have some delay constraints that are nonnegligible. The virtual queue algorithm reduces the experienced delay by comprising virtual queues that are served at a fraction of the actual service rate and by using the virtual queue-length values in utility function. Then, optimization framework is used in which scheduling algorithm allocates resource fairly in the network to meet the fairness objectives of both elastic and inelastic flows. Finally, priority dropping active queue management algorithm is designed based on proportional-integral design (PID) mechanism which provides the differentiated services for the different layers or frames according to their priority.

Inelastic flows of curves in 4D Galilean space

The flow of a curve is said to be inelastic, if in the former case, the arc-length is preserved, and in the latter case, if the intrinsic curvature is preserved. Physically, inelastic curve flow is characterized by the absence of any strain energy induced from the motion. In this paper, we investigate inextensible flows of curves in Galilean 4-space. Also, we give necessary and sufficient conditions for an inelastic curve flow are first expressed as a partial differential equation involving the curvature and torsion.

Marking algorithm of distinguishing three traffic load states with two encoding states for pre-congestion notification

Pre-congestion notification (PCN) gives an early warning of congestion by marking packets to protect the quality of service of inelastic flows. PCN defines two rates per link: admissible rate (AR) and supportable rate (SR), which divide the PCN traffic load into three states, “no pre-congestion,” “AR pre-congestion,” and “SR pre-congestion.” PCN admission control and flow termination control operate in accordance with these three states. However, only two PCN encoding states, unmarked and PCN marked, can be used due to the requirement of PCN encoding to survive tunneling through a currently used IPsec tunnel. We propose a marking algorithm, which uses the two encoding states, for distinguishing the three states of PCN traffic load. We also propose new admission and flow termination controls, which are based on the proposed marking algorithm, and evaluate their performance. Markings that require fewer PCN encoding states are preferable because the remaining encoding state can be used for a newly added PCN-based control in the future. Furthermore, distinguishing more states with fewer encoding states benefits not only PCN but also general marking techniques because header fields are limited; thus, valuable.

Steady and unsteady non-Newtonian inelastic flows in a planar T-junction

Steady and unsteady laminar flows in a planar 2D T-junction, having a dividing or bifurcating flow arrangement (one main channel with a side branch at 90°), are studied numerically for non-Newtonian inelastic fluids whose rheological characteristics are similar to those of blood. These computational fluid dynamics simulations explore a wide range of variation of inertia (through the Reynolds number, Re), flow rate ratio (proportion of extracted to inlet flow rates, β) and shear thinning (the power-law index of the model, n), and investigate their influence on the sizes and intensities of the recirculating eddies formed near the bifurcation, and on the resulting distribution of the shear stress fields. Such flow characteristics are relevant to hemodynamics, being related to the genesis and development of vascular diseases, like the formation of atherosclerotic plaques and thrombi near arterial bifurcations.To represent the decay of viscosity with shear rate we apply the Carreau-Yasuda equation, one of the most utilized Generalized Newtonian Fluid model in blood simulations. In many comparisons of the present parametric study it was require that the level of inertia was kept approximately the same when n was varied. This implied a consistent definition of Re with the viscosity calculated at a representative shear rate.

Dynamic Rate and Power Allocation in Wireless Ad Hoc Networks with Elastic and Inelastic Traffic

In this paper, we focus on the problem of dynamic rate and power allocation in wireless ad hoc networks with slow-fading channels, where a mixture of elastic and inelastic traffic is supported. A stochastic optimization problem incorporating the quality of service requirements of the two types of traffic is formulated, which aims to maximize the network performance by allocating the power for each link and controlling the service rates of all flows in the network. Since the utility functions of inelastic flows may be non-concave, which are difficult to be readily transformed to be concave, the proposed original problem is non-convex. However, despite the existing difficulty, a dynamic rate and power allocation algorithm (named DRPAA), is proposed to solve the original optimization problem. In DRPAA, both the stochastic duality theory and the particle swarm optimization approach are used, and this dynamic algorithm provides a good approximation to the optimal solution when the variation of the channel condition of each link gets larger. By using DRPAA, flow rates and link powers are dynamically allocated in each network state without the need for the distribution of the network states. Simulation results show that DRPAA has a good convergence speed and can efficiently utilize network resources to improve the network performance.

Precongestion notification: new QoS support for differentiated services IP networks

Admission control is a well-known technique to explicitly admit or block new flows in order to keep a network's traffic load at a moderate level and to guarantee QoS for admitted flows. Flow termination is a new flow control function that terminates some admitted flows when the network capacity does not suffice, such as in the case of unexpected failures. Admission control and flow termination are useful to protect QoS for inelastic flows that require a minimum bit rate. Examples are real-time applications like voice and video. Precongestion notification (PCN) provides feedback about load conditions on the path to boundary nodes. They use this information to implement lightweight admission control and flow termination without per-flow state on interior nodes of a domain. These mechanisms are significantly simpler than explicit reservation schemes. In the context of DiffServ, IP, MPLS, and Ethernet networks, we explain the concept of PCN-based admission control and flow termination, present recent standards of the IETF, and discuss benefits and limitations.

Protecting video service quality in multimedia access networks through PCN

The growing popularity of video-based services and their corresponding unpredictable bursty behavior makes the design of an admission control system an important research challenge. The pre-congestion notification (PCN) mechanism is a measurement-based approach, recently standardized by the IETF, optimized toward the admission of inelastic flows, where the number of flows is sufficiently large that individual bursts of flows can be compensated by silence periods of others. In this article, we discuss the implications of applying PCN to protect video services, which have less predictable behavior. Several algorithms for protecting video services in multimedia access networks are described. Through performance evaluation, we show the impact of these algorithms on the network utilization and video quality, and present guidelines on how to configure a PCN system.

On unified quality of service resource allocation scheme with fair and scalable traffic management for multiclass Internet services

This study concerns the problem of controlling multiclass (elastic, inelastic and unresponsive) Internet traffic without sacrificing quality of service (QoS) by adopting a unified `resource allocation and traffic management` approach. The aim is to minimise the need for relying on dedicated QoS traffic control mechanisms in order to avoid spiralling complicatedness that, in practice, leads to `robust yet fragile` Internet. In order to address this challenge, the authors first introduce an end-to-end non-convex network utility maximisation-based resource allocation algorithm to guarantee enhanced QoS to elastic and inelastic flows. Then, a pricing-based fair and scalable traffic management scheme, called Purge, is introduced to protect transmission control protocol-friendly traffic from unfairness attacks by unresponsive flows. Finally, the main contribution of this work, the unified algorithm, is developed by adapting Purge to complement link-control of the proposed resource allocation algorithm to enable it to enforce fairness while maintaining a scalable network core. The unified approach thus delivers QoS guarantees for multiclass traffic.

Optimal Scheduling for Fair Resource Allocation in Ad Hoc Networks With Elastic and Inelastic Traffic

This paper studies the problem of congestion control and scheduling in ad hoc wireless networks that have to support a mixture of best-effort and real-time traffic. Optimization and stochastic network theory have been successful in designing architectures for fair resource allocation to meet long-term throughput demands. However, to the best of our knowledge, strict packet delay deadlines were not considered in this framework previously. In this paper, we propose a model for incorporating the quality-of-service (QoS) requirements of packets with deadlines in the optimization framework. The solution to the problem results in a joint congestion control and scheduling algorithm that fairly allocates resources to meet the fairness objectives of both elastic and inelastic flows and per-packet delay requirements of inelastic flows.