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Interpreting RG flows as dynamical systems in the space of couplings we produce a variety of constraints, global (topological) as well as local. These constraints, in turn, rule out some of the proposed RG flows and also predict new phases…
The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield…
We critically discuss the concept of ``synchronized flow'' from a historical, empirical, and theoretical perspective. Problems related to the measurement of vehicle data are highlighted, and questionable interpretations are identified.…
We show that Property $(A)$ of subshifts and the semigroup, that is associated to subshifts with Property (A), are invariants of flow equivalence. We show for certain $\mathcal R$-graphs that their isomorphism is implied by the flow…
For a class of coalescing stochastic flows on the real line the existence of dual flows is proved. A stochastic flow and its dual are constructed as a forward and backward perfect cocycles over the same metric dynamical system. The metric…
We give a detailed proof for the estimates of products of norms for flows away from homoclinic tangency. The estimates we can prove is weaker than the expectation of experts.
In the spectral theory of non-self-adjoint operators there is a well-known operation of product of operator colligations. Many similar operations appear in the theory of infinite-dimensional groups as multiplications of double cosets. We…
We detect, by using symplectic topology, invariant measures with large rotation vectors for a class of Hamiltonian flows.
Lagrangian formulation of kinematic wave provides a more accurate representation than the most commonly used Eulerian formulation. Furthermore, Lagrangian representation offers a flexibility to study certain traffic phenomena (e.g. capacity…
The relation between flow and density is an essential quantitative characteristic to describe the efficiency of traffic systems. We have performed experiments with single-file motion of bicycles and compare the results with previous studies…
Consider a system of N components in which traffic arrives as separate but correlated nonhomogenous Poisson streams to each node rather than passing into the system at one entry point. A method is given to construct such systems…
A family of multi-value cellular automaton (CA) associated with traffic flow is presented in this paper. The family is obtained by extending the rule-184 CA, which is an ultradiscrete analogue to the Burgers equation. CA models in the…
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.
Vehicle-to-vehicle communications can change the driving behavior of drivers significantly by providing them rich information on downstream traffic flow conditions. This study seeks to model the varying car-following behaviors involving…
Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss…
Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated…
We present a theory for self-driven fluids, such as motorized cytoskeletal extracts or bacterial suspensions, that takes into account the underlying periodic duty cycle carried by the active particles of which the system is composed. We…
In this paper we construct examples of irrational behavior of multiplicities and mixed multiplicities of divisorial filtrations. The construction makes essential use of anti-positive intersection products.
A model with hyperchaos is studied by means of Lyapunov two-parameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the…
A paraconsistent type theory (an extension of a fragment of intuitionistic type theory by adding opposite types) is here extended by adding co-function types. It is shown that, in the extended paraconsistent type system, the opposite type…