Related papers: Circuit Synthesis based on Prescribed Lagrangian
Quantum information protocols require various types of entanglement, such as Einstein-Podolsky-Rosen (EPR), Greenberger-Horne-Zeilinger (GHZ), and cluster states. In optics, on-demand preparation of these states has been realized by…
An exceptional point of degeneracy (EPD) occurs when both the eigenvalues and the corresponding eigenvectors of a square matrix coincide and the matrix has a nontrivial Jordan block structure. It is not easy to achieve an EPD exactly. In…
We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant electric field…
This paper presents a method for the synthesis of negative imaginary closed-loop systems with a prescribed degree of stability under the assumption of full state feedback. The approach extends existing work by using a perturbation method to…
We constructed an analog circuit generating fluctuations of which a probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by tuning the resistance. A theory…
Analyzing one example of LC circuit in [8], show its Lagrange problem only have other type critical points except for minimum type and maximum type under many circumstances. One novel variational principle is established instead of…
The general Lagrange-Euler formalism for the three memory circuit elements, namely, memristive, memcapacitive, and meminductive systems, is introduced. In addition, {\it mutual meminductance}, i.e. mutual inductance with a state depending…
A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…
Nonreciprocal devices effectively mimic the breaking of time-reversal symmetry for the subspace of dynamical variables that they couple, and can be used to create chiral information processing networks. We study the systematic inclusion of…
We construct the free Lagrangian of the magnetic sector of Carrollian electrodynamics. The construction relies on Helmholtz integrability condition for differential equations in a self consistent algorithm, working hand in hand with…
A new approach to designing FSS-based LP-CP converters is presented. It is based on the use of FSSs which exhibit dual diagonal symmetry, and a novel 4-port equivalent circuit able to describe the electrical behavior of the cells for the…
We present the design of an analog circuit which solves linear programming (LP) problems. In particular, the steady-state circuit voltages are the components of the LP optimal solution. The paper shows how to construct the circuit and…
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…
The structure of the Euler-Lagrange equations for a general Lagrangian theory is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to…
A phenomenological theory of rigid and saturated ferromagnetic conductors is constructed from a four-continuum model consisting of a rigid lattice continuum, a bound charge continuum for polarization, a circulating current continuum for…
The 3D incompressible Euler equation is an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or…
Rapid Single Flux Quantum (RSFQ) logic is a promising technology to supersede Complementary metal-oxide-semiconductor (CMOS) logic in some specialized areas due to providing ultra-fast and energy-efficient circuits. To realize a large-scale…
Reactive synthesis is a technology for the automatic construction of reactive systems from logical specifications. In these lecture notes, we study different algorithms for the reactive synthesis problem of linear-time temporal logic (LTL).…
In this paper, a new approach for constructing Lagrangians for driven and undriven linearly damped systems is proposed, by introducing a redefined time coordinate and an associated coordinate transformation to ensure that the resulting…
Electric circuits manipulate electric charge and magnetic flux via a small set of discrete components to implement useful functionality over continuous time-varying signals represented by currents and voltages. Much of the same…