983,881 research outputs found
A variational problem on Stiefel manifolds
In their paper on discrete analogues of some classical systems such as the
rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced
their analysis in the general context of flows on Stiefel manifolds. We
consider here a general class of continuous time, quadratic cost, optimal
control problems on Stiefel manifolds, which in the extreme dimensions again
yield these classical physical geodesic flows. We have already shown that this
optimal control setting gives a new symmetric representation of the rigid body
flow and in this paper we extend this representation to the geodesic flow on
the ellipsoid and the more general Stiefel manifold case. The metric we choose
on the Stiefel manifolds is the same as that used in the symmetric
representation of the rigid body flow and that used by Moser and Veselov. In
the extreme cases of the ellipsoid and the rigid body, the geodesic flows are
known to be integrable. We obtain the extremal flows using both variational and
optimal control approaches and elucidate the structure of the flows on general
Stiefel manifolds.Comment: 30 page
ScaRR: Scalable Runtime Remote Attestation for Complex Systems
The introduction of remote attestation (RA) schemes has allowed academia and
industry to enhance the security of their systems. The commercial products
currently available enable only the validation of static properties, such as
applications fingerprint, and do not handle runtime properties, such as
control-flow correctness. This limitation pushed researchers towards the
identification of new approaches, called runtime RA. However, those mainly work
on embedded devices, which share very few common features with complex systems,
such as virtual machines in a cloud. A naive deployment of runtime RA schemes
for embedded devices on complex systems faces scalability problems, such as the
representation of complex control-flows or slow verification phase.
In this work, we present ScaRR: the first Scalable Runtime Remote attestation
schema for complex systems. Thanks to its novel control-flow model, ScaRR
enables the deployment of runtime RA on any application regardless of its
complexity, by also achieving good performance. We implemented ScaRR and tested
it on the benchmark suite SPEC CPU 2017. We show that ScaRR can validate on
average 2M control-flow events per second, definitely outperforming existing
solutions.Comment: 14 page
Improving QC Relaxations of OPF Problems via Voltage Magnitude Difference Constraints and Envelopes for Trilinear Monomials
AC optimal power flow (AC~OPF) is a challenging non-convex optimization
problem that plays a crucial role in power system operation and control.
Recently developed convex relaxation techniques provide new insights regarding
the global optimality of AC~OPF solutions. The quadratic convex (QC) relaxation
is one promising approach that constructs convex envelopes around the
trigonometric and product terms in the polar representation of the power flow
equations. This paper proposes two methods for tightening the QC relaxation.
The first method introduces new variables that represent the voltage magnitude
differences between connected buses. Using "bound tightening" techniques, the
bounds on the voltage magnitude difference variables can be significantly
smaller than the bounds on the voltage magnitudes themselves, so constraints
based on voltage magnitude differences can tighten the relaxation. Second,
rather than a potentially weaker "nested McCormick" formulation, this paper
applies "Meyer and Floudas" envelopes that yield the convex hull of the
trilinear monomials formed by the product of the voltage magnitudes and
trignometric terms in the polar form of the power flow equations. Comparison to
a state-of-the-art QC implementation demonstrates the advantages of these
improvements via smaller optimality gaps.Comment: 8 pages, 1 figur
A Phase Field Model for Continuous Clustering on Vector Fields
A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.
Test Sequence Generation for Java7 Fork/Join Using Interference Dependence
Test sequence generation through code is mainly done by using some sort of a flow graph viz. Control Flow Graph (CFG), Concurrent Control Flow Graph (CCFG), Event Graph etc. Approaches that use UML also need flow graph as an intermediate representation for final test sequence generation. In the present approach, a Flow Graph for a new concept i.e. Java7 Fork/Join is constructed and hence, by traversing the graph, test sequences are generated on the basis of all path and all node coverage criteria considering interference dependence. Further, interference dependencies are also represented in the form of a directed graph to aid the analysis of Java7 fork/join programs
A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media
We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media
Numerical simulation of separated flows
A new numerical method, based on the Vortex Method, for the simulation of two-dimensional separated flows, was developed and tested on a wide range of gases. The fluid is incompressible and the Reynolds number is high. A rigorous analytical basis for the representation of the Navier-Stokes equation in terms of the vorticity is used. An equation for the control of circulation around each body is included. An inviscid outer flow (computed by the Vortex Method) was coupled with a viscous boundary layer flow (computed by an Eulerian method). This version of the Vortex Method treats bodies of arbitrary shape, and accurately computes the pressure and shear stress at the solid boundary. These two quantities reflect the structure of the boundary layer. Several versions of the method are presented and applied to various problems, most of which have massive separation. Comparison of its results with other results, generally experimental, demonstrates the reliability and the general accuracy of the new method, with little dependence on empirical parameters. Many of the complex features of the flow past a circular cylinder, over a wide range of Reynolds numbers, are correctly reproduced
A Discontinuous Control Volume Finite Element Method for Multi-Phase Flow in Heterogeneous Porous Media
We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media
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