Coupling conditions for isothermal gas flow and applications to valves

We consider an isothermal gas flowing through a straight pipe and study the effects of a two-way electronic valve on the flow. The valve is either open or closed according to the pressure gradient and is assumed to act without any time or reaction delay. We first give a notion of coupling solution for the corresponding Riemann problem; then, we highlight and investigate several important properties for the solver, such as coherence, consistence, continuity on initial data and invariant domains. In particular, the notion of coherence introduced here is new and related to commuting behaviors of valves. We provide explicit conditions on the initial data in order that each of these properties is satisfied. The modeling we propose can be easily extended to a very wide class of valves

Nierówności typu Schwarza dla funkcji harmonicznych w kole jednostkowym spełniających pewien warunek sektorowy

https://doi.org/10.26485/0459-6854/2018/68.2/10

On Coefficient Functionals for Functions with Coefficients Bounded by 1

In this paper, we discuss two well-known coefficient functionals a 2 a 4 − a 3 2 and a 4 − a 2 a 3 . The first one is called the Hankel determinant of order 2. The second one is a special case of Zalcman functional. We consider them for functions in the class Q R ( 1 2 ) of analytic functions with real coefficients which satisfy the condition Re f ( z ) z > 1 2 for z in the unit disk Δ . It is known that all coefficients of f ∈ Q R ( 1 2 ) are bounded by 1. We find the upper bound of a 2 a 4 − a 3 2 and the bound of | a 4 − a 2 a 3 | . We also consider a few subclasses of Q R ( 1 2 ) and we estimate the above mentioned functionals. In our research two different methods are applied. The first method connects the coefficients of a function in a given class with coefficients of a corresponding Schwarz function or a function with positive real part. The second method is based on the theorem of formulated by Szapiel. According to this theorem, we can point out the extremal functions in this problem, that is, functions for which equalities in the estimates hold. The obtained estimates significantly extend the results previously established for the discussed classes. They allow to compare the behavior of the coefficient functionals considered in the case of real coefficients and arbitrary coefficients

Coupling conditions for isothermal gas flow and applications to valves

We consider an isothermal gas flowing through a straight pipe and study the effects of a two-way electronic valve on the flow. The valve is either open or closed according to the pressure gradient and is assumed to act without any time or reaction delay. We first give a notion of coupling solution for the corresponding Riemann problem; then, we highlight and investigate several important properties for the solver, such as coherence, consistence, continuity on initial data and invariant domains. In particular, the notion of coherence introduced here is new and related to commuting behaviors of valves. We provide explicit conditions on the initial data in order that each of these properties is satisfied. The modeling we propose can be easily extended to a very wide class of valves

Coupling conditions for isothermal gas flow and applications to valves

We consider an isothermal gas flowing through a straight pipe and study the effects of a two-way electronic valve on the flow. The valve is either open or closed according to the pressure gradient and is assumed to act without any time or reaction delay. We first give a notion of coupling solution for the corresponding Riemann problem; then, we highlight and investigate several important properties for the solver, such as coherence, consistence, continuity on initial data and invariant domains. In particular, the notion of coherence introduced here is new and related to commuting behaviors of valves. We provide explicit conditions on the initial data in order that each of these properties is satisfied. The modeling we propose can be easily extended to a very wide class of valves