László Márk

Twisted Rings and Twisted Signals: The Sector Calculus of Rotational Twists

A twist can live in a signal or in a ring. A twisted signal returns after one period multiplied by a fixed phase. A twisted ring is a solid ring whose transported frame returns turned by an angle. This article shows that the two are one structure. On the flat model of the ring, t...

Solitons on Patterned Metasurfaces: Glide, Sector and Seam

A patterned metasurface is a lattice of resonators, and its symmetries decide where a Kerr soliton can exist, whether it radiates, and how its polarization survives a closure. This article follows these questions in the sector language of the Möbius–Klein Transform (MKT) canon. A...

Predictions from the Sector Framework for Space-Time Modulated Media

A medium whose properties are modulated in space and time can be built to pass a wave one way and block it the other, and the conditions that forbid this are known for a scalar permittivity, for a tensorial one, and for a response that depends on the wavevector. This article asks...

The Weight Ledger of Metasurface Susceptibilities: Symmetry, Counting and Design Rules

Every component of a metasurface susceptibility carries an azimuthal weight m about the surface normal. This article organizes the generalized sheet transition conditions by that single number and by three binary labels: the mirror parity, the transposition and, for sheets modula...

Predictions from the Sector Framework for Space-Time Modulated Media

A medium whose properties are modulated in space and time can be built to pass a wave one way and block it the other, and the conditions that forbid this are known for a scalar permittivity, for a tensorial one, and for a response that depends on the wavevector. This article asks...

Which Loops Can Carry a Burgers Vector? Selection Rules on Non-Orientable Geometry

The strength of a dislocation is its Burgers vector: the circulation of the distortion field along a loop encircling the defect line. This article pursues a single question: what happens to this circulation when the carrier geometry is non-orientable? The answer is a selection ru...

Which Loops Can Carry a Burgers Vector? Selection Rules on Non-Orientable Geometry

The strength of a dislocation is its Burgers vector: the circulation of the distortion field along a loop encircling the defect line. This article pursues a single question: what happens to this circulation when the carrier geometry is non-orientable? The answer is a selection ru...

Reciprocity and the adjoint medium – what the space-time symmetry preserves when the constitutive relation is not a scalar

A medium whose properties are modulated in space and time can be built to pass a wave one way and block it the other, and a body of work exists on how to do so. The opposite question is asked less often: what forbids it? For a medium described by a real scalar permittivity, one a...

Reciprocity by Design - The shape of the loss in space-time modulated media

A modulated medium whose permittivity depends on both position and time, and whose conductivity depends on position, may be invariant under an operation that reverses time and translates space at once. Two such space-time glide operations exist in one spatial dimension, and the l...

The adjoint medium beyond locality – how far the reciprocity criterion reaches

A medium modulated in space and time can be built to pass a wave one way and block it the other. The opposite question is asked less often: what forbids it? For a medium described by a real scalar permittivity one answer is known — if the modulation is unchanged by a shift of hal...

The Möbius and Klein Transforms: Spectral Analysis on Non-Orientable Manifolds

The classical Fourier transform is the harmonic analysis of the circle (and torus) – an orientable manifold. In analogy with the Fourier transform, we define two named, closed-form, unitary transform pairs on the two simplest non-orientable manifolds, the Möbius strip (the Möbius...

A Unified System of Tensor Invariants and Their Integral Reduction Theorems

This paper organizes the complete operator set and the integral theorems of classical vector analysis into a single unified system. The starting point is algebraic: the second-order tensor invariant of a third-order tensor, given by the general epsilon -dual formula (the dual is...

The Codimension-Three Rung. Twisted sections over a non-orientable link: the sector split of the Kondratiev indicial roots, a root-free window that triples, and the character ladder of lens rungs

The blow-up ladder of the framework's desingularization article was carried out for codimension-two centers, where the exceptional divisor is a circle; Section 9.10 explicitly left open the codimension-three rung and the full Kondratiev asymptotics. This article closes both. The...

Sum Rules and Sign Thresholds for Twisted Sector Sums. An exact sum rule over all 2d twist sectors, and a proved threshold: the regularized sum turns positive exactly when the twisted directions are at least as many as the untwisted ones

Assign to each direction of a d-dimensional lattice a twist label t_i\{0,1\} and consider the regularized alternating lattice sum Z_t(s)='_{n Z^d}(-1)^{n· t}|n|^{-s} — the family of 2^d sector sums that the framework's sector calculus produces on a d-torus with periodic or antipe...

The Codimension-Three Rung. Twisted sections over a non-orientable link: the sector split of the Kondratiev indicial roots, a root-free window that triples, and the character ladder of lens rungs

The blow-up ladder of the framework's desingularization article was carried out for codimension-two centers, where the exceptional divisor is a circle; Section 9.10 explicitly left open the codimension-three rung and the full Kondratiev asymptotics. This article closes both. The...

The Pairing Rulebook of the Brillouin Klein Bottle. Mirror circle, forbidden s-wave, and half-integer phase winding: the sector selections of Bogoliubov–de Gennes theory on non-orientable momentum space, with the Klein transform as the native mode machinery

A Brillouin zone can be a Klein bottle: under Z2 gauge fields the algebra of crystal symmetries becomes projective, a nonsymmorphic glide reflection appears in momentum space, and the fundamental domain is a Klein bottle instead of a torus — the experimentally realized Brillouin...

The Curl Spectrum on Non-Orientable Geometry: Sector Doublets, Vanishing Helicity, and Beltrami Pairs

The spectral theory of the curl operator on closed 3-manifolds is a developed and active field — but exclusively on oriented manifolds, because the definition of curl requires an orientation. This article opens the non-orientable column using the sector calculus. The key is a one...

Vortex and Fluxoid Selection Rules on Non-Orientable Superconductors. The loop dichotomy, the closure prohibition, and the pi-shifted Little–Parks ladder: which loops can carry a vortex — with an exact channel-discriminator identity and machine verification

Half-quantum fluxoid physics is measured reality: pi-shifted Little–Parks oscillations in beta-Bi2Pd rings, half-quantum features in Sr2RuO4 microrings, and a Ginzburg–Landau theory of the superconducting Möbius strip that found novel states near half-odd flux. What the literatur...

The Curl Spectrum on Non-Orientable Geometry: Sector Doublets, Vanishing Helicity, and Beltrami Pairs

The spectral theory of the curl operator on closed 3-manifolds is a developed and active field — but exclusively on oriented manifolds, because the definition of curl requires an orientation. This article opens the non-orientable column using the sector calculus. The key is a one...

The Weight Ledger of Metasurface Susceptibilities. Slice-adapted irreducible parametrization of dipole–quadrupole GSTCs: closed-form Neumann counting, incidence selection rules, exact rotation-equivariant fitting — and why C3 and C4 first part ways at the quadrupole

Metasurface modeling by generalized sheet transition conditions (GSTCs) suffers from a parameter explosion: the dipolar susceptibility tensors already carry 36 components, and the quadrupolar extension adds rank-3 objects of 27 components each. The established cure is Neumann's p...