Displacement current is two currents
The induced part grows as frequency squared and catches the Coulombic part at ωr ≈ c.
· “Frequency Dependence of the Displacement Current Density”
physics.class-ph
Classical Physics
Newtonian and relativistic dynamics; many particle systems; planetary motions; chaos in classical dynamics. Maxwell's equations and dynamics of charged systems and electromagnetic forces in materials. Vibrating systems such as membranes and cantilevers; optomechanics. Classical waves, including acoustics and elasticity; physics of music and musical instruments. Classical thermodynamics and heat flow problems.
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Stable levitation needs damping—but only within a bounded range
A six-degree-of-freedom model and experiments map the window of rotation speed and damping that keeps the magnet aloft.
When lattices don't match, one wave fans into many
A new matching rule lets a single Bloch mode excite multiple wave vectors and frequencies at a temporal interface.
· “Wave Scattering at temporal interfaces with spatial-translation-symmetry mismatch”
Connection's transverse-traceless part adds no degrees of freedom
Only constants survive in the symmetric transverse part; geodesics match autoparallels only in special cases.
Minimal correction makes faulty plasticity laws obey the Second Law
In a 1D elastoplastic bar, it finds the smallest additive fix keeping dissipation non-negative at every instant.
· “Solving the Dissipation Inequality not as a constitutive restriction”
Micromorphic theory follows from gauge invariance alone
Proving that arbitrary reference directors force the standard micromorphic energy—and classifying all first-order models that branch off it.
· “Geometric theory of generalised continua using moving frames”
Canonical map equates Bateman and Caldirola-Kanai scalar-field systems
Equivalence holds on any smooth expanding background—and only if the H-dot terms are kept.
Four constants stay fixed on optimal continuous-thrust orbital paths
Noether symmetries of a generalized Lagrangian give invariants that survive a 190-revolution LEO-to-GEO climb.
· “Conserved Quantities of Optimal Continuous-Thrust Trajectories in A Central Gravitational Field”
Reusing prior runs speeds up multiphysics parameter studies 20-fold
A reduced-order solver reuses the previous solution and basis, cutting a 343-run membrane study's cost to about 5% of naive.
Spring sphere crumples at 4-5 percent bond strain
Random kicks collapse closed spring networks at a sharp threshold, and speeds thermalize in one oscillation.
· “Geometry and dynamics of spring networks of spherical topology”
Abstract promises a superlensing theory
The abstract promises resolution bounds for pulse-illuminated superlenses, but the full text is a rotating-neutron-star paper.
· “Theory of superlensing with complex frequency illuminations”
Magnetic field tunes the speed limit of shear solitons in soft laminates
One effective dispersive wave equation with explicit coefficients governs nonlinear shear waves in layered magneto-active materials.
· “Nonlinear dispersive waves in soft elastic laminates under finite magneto-deformations”
Identical uniform B-fields can kick charges differently
The impulse from turning off the field is set by the vector potential, so the source matters.
A single parameter finds every orbit between two points
The angular-momentum parameter covers all conic paths; add flight time and one orbit remains.
· “Connect the dots ... finding all possible orbits between two points”
Doubling coordinates gives dissipative systems a Hamiltonian form
Any second-order equation of motion gets an explicit doubled Hamiltonian whose physical slice reproduces the original dissipative dynamics.
Bulk Bloch modes braid like strands
In a gapped three-band system, eigenmode exchange follows fixed braid words; acoustic cavities show it.
· “Topological Braiding of Bloch Eigenmodes Protected by Non-Abelian Quaternion Invariants”
Spring-loaded crane drive lifts loads near minimum energy
A passive track converts the carriage's harmonic motion into hoisting, cutting energy from 482 to 248 J per lift.
· “Energetically efficient, mediated mechanical system for precise control of hoisting operations”
Granular black-hole cluster could bend S2's orbit by 2026
Simulations predict declination residuals above the 30-microarcsec threshold in up to 60% of realizations at apocenter.
· “Impact of a granular mass distribution on the orbit of S2 in the Galactic center”
A symplectic integrator's accuracy depends on your coordinates
The distorted Hamiltonian a symplectic method samples changes with coordinates; a careful choice can raise the observed order.
· “On the coordinate system-dependence of the accuracy of symplectic numerical methods”
One envelope formula predicts decay under friction
Closed-form amplitudes and stopping times match numerics when total damping stays well below the natural frequency.
Photons lose energy to the gravity of the medium they cross
Friction from d'Alembert's principle gives a redshift that grows with density and distance squared.
Continuity alone forces Maxwell's field equations
If local conservation of charge holds in 3D space, the field equations must take Maxwellian form, and Newtonian physics fails.
· “On the "Universality" of the Form of Maxwell's Equations”
Two-tone ultrasound sorts microparticles by size on the fly
Resonance changes each beam's push, so particles of different sizes drift apart and can be collected separately.
· “Acoustic angular sorting of resonant subwavelength particles”
Elastodynamics takes symmetric first-order form in 11 variable sets
New writings unify compatibility, momentum, and differentiated material laws for anisotropic wave equations.
· “Alternative writings of classical elastodynamics equations as a first order symmetric system”
Every central-force orbit gains a third invariant via a Kepler twin
Mapping any bounded motion onto a Kepler ellipse yields a conserved vector and a dynamical symmetry group.
· “About the Keplerization of motion in any central force field”
The Second Law as a constraint
Admitting imperfect material laws, a dual-to-primal mapping yields entropy production as an equality with minimal excess fields.
· “The Second Law as a constraint and admitting the approximate nature of constitutive assumptions”
One model makes Einstein-de Sitter expansion the late-time attractor
In one dipole-conserving Hamiltonian, a homogeneous expanding ball and an arrow of time emerge from random data.
F=ma is a theorem, not an empirical law
A new derivation gets F=ma out of two physical principles, making it an identity between measured quantities.
A curl-force Hamiltonian becomes Liouville integrable at alpha = -beta
A second Hamiltonian, compatible Poisson brackets, and a Lax pair all appear on that locus; closed orbits alone mislead.
· “Integrable curl-force Hamiltonians: bi-Hamiltonian structure, separability, and periodic orbits”
Adding an oblique fiber family makes 2-D pantographic fabric complete
Two-family fabrics miss mixed second derivatives; a third oblique direction closes the gap.
· “On the synthesis of complete two-dimensional second-gradient continua: Tri-pantographic fabrics”
Dislocation emission shields cracks but does not toughen them
A single energy functional decides emission vs. cleavage; fracture resistance stays elastic in the dissipationless limit.
Exact resonances can't guarantee phonon energy diffusion
Matched frequencies and connected networks still trap energy in pairs; quasi-resonant processes do the real work.
· “Exact Resonances Are Not Sufficient for Phonon Energy Diffusion”
Boundary term alone yields Ostrogradsky's canonical pairs
In this paper, higher-derivative Hamiltonians come from the first variation's boundary term, not from ad hoc Ostrogradsky formulas.
· “The First Variational Formula and the Ostrogradsky Formalism”
Euclidean construction links orbits to inverse-square force
Two straightedge-and-compass proofs—orbit to force and force to orbit—recover the conic polar form without differential equations.
Sliding bar plus self-inductance equals a damped RLC oscillator
Retaining the induced field yields exact energy conservation and maps the bar's momentum onto capacitor charge.
· “The moving bar problem: an electromechanical damped oscillator”
Momentum transfer peaks at the ballistic limit in all impact tests
A single momentum bound unifies impacts from nanoscale films to concrete and shows why energy metrics inflate thin targets.
Flux, not volume, predicts three-body breakups
Counting phase-space flow toward breakup matches simulations at the one-percent level.
· “The simplest complexity: The story of the three-body problem”
Static friction is an emergent peak
Nanometer-scale sliding shows the static–kinetic gap is one universal overshoot from asperity reordering.
· “Collective Asperity Dynamics and the Origin of Static Friction”
Vector potential of any azimuthal current stays azimuthal
Short proof plus a closed Legendre-function form for the circular loop, simpler than textbook elliptic integrals.
· “The vector potential of a steady azimuthal current density. Once again”
Helical field spins a moving cylinder
No wires, no gears: a theory shows a copper cylinder can shed 80% of its speed and spin up to hundreds of revolutions per second.
· “Helical Field-Driven Translational-Rotational Conversion in Conductors”
CFD model predicts cooling-tower evaporation within 15%
Validated CFD reproduces cooling-tower temperatures and evaporation, a step toward plume prediction.
· “A CFD model for heat and mass transfer leading to plume formation within Wet Cooling Towers”
Permittivity alone fits measured PEDOT trilayer bending
Analytical and numerical solutions match measured deflection, blocking force, strain, and angle of the actuator.
· “Modeling of an electro-active pseudo-trilayer based on PEDOT, a semi-conductor polymer”
One derivative condition marks universal optical neural networks
The theorem makes universality a test: non-degenerate multivariate encoders suffice; free-space optics can build them.
· “Universality of physical neural networks with multivariate nonlinearity”
Phase-tracking swaps a resonator's modes around an exceptional point
Keeping resonance via phase lock, the device swaps its two modes in either encircling direction.
· “Dynamically encircling an exceptional point through phase-tracked closed-loop control”
Four independent proofs defend disputed vector potential
If the result stands, velocity- and Coulomb-gauge vector potentials follow from two scalar potentials, with gauge-invariant fields.
Three-particle collision count: one floor-plus-ceiling formula
Three particles on a line: collision count depends only on mass ratios and initial data via a rotation angle.
· “Analysis of Three-Particle Elastic Collisions Using Newtonian Mechanics and Vector Geometry”
Power-law cluster halos follow from symmetry and conservation
The inner-halo slope r^-2 to r^-2.5 follows from covariance plus conserved mass and energy, with no self-similarity assumption.
· “Origin of the power-law profile in a core-collapsing galactic globular-cluster model”
Laplacian of arsinh gains a delta term on the axis
The same identity produces the Coulomb-gauge function for a uniformly moving point charge.
· “Novel distributional Laplacians and a Coulomb-gauge problem”
The Lorenz gauge is guaranteed
Gauge freedom alone guarantees the Lorenz condition, no arbitrary imposition needed.
· “Is the Lorenz Gauge a Choice? Gauge Freedom and the Structure of Electrodynamics”
Stress–strain monotonicity mapped for 40+ elastic energies
At a glance, which models keep stress–strain one-to-one and monotone at large stretches.
Conformal symmetry proves action and reaction for resting particles
An inversion plus reflection swaps advanced and retarded impulses, making them equal and opposite for co-moving charges.
Harmonic balance maps stable pressure windows for buckled rings
New tables pinpoint, for modes 2 through 12, where pressurized ring shapes become self-intersecting.
· “Stability analysis of Euler's elastica ring using harmonic balance”
Dirac particle recoils along wave direction regardless of charge
The effect comes from the Lorentz force acting at the center of charge, not the center of mass.
· “Classical Dirac particle II. Interaction with an electromagnetic plane wave”
Wronskians yield new integrals of motion for extremals
Closed first-order systems built from the Jacobi equation yield conserved quantities for the calculus of variations.
· “Integrals of motion on extremals of the equation Euler-Lagrange”
Heat-bath coupling turns conservative systems into dissipative pairs
A new derivation shows forward and backward dynamics can emerge from state feedback, not assumed randomness.
Accelerated chasers retrace constant-speed pursuit curves
With straight-line targets, rest-start accelerated chases match classical uniform-motion pursuit curves.
Handedness of tight composite knots is visible in their geometry
Linear elastic rod theory links a knot's handedness to the shape it takes when pulled tight.
Three velocity channels triple acoustic data rates
Encoding separate streams on the x, y, and z components of particle velocity, one vector sensor recovers them in real time.
· “High-Capacity and Real-Time Acoustic Communication by Multiplexing Velocity”
Spring-coupled hoop and cylinder: friction moves the center of mass
The effect vanishes when both bodies have equal moments of inertia, and vertical spring placement restores a fixed center.
· “On the edge of complexity: The simplest not simple coupled mechanical system”
Unequal diffusion turns a locked chemical front into sun rays
Experiments and simulations show the ray count and rotation are set by flow rate and diffusivity ratio.
· “Radially Locked Sun-Ray Patterns in Autocatalytic Reaction-Diffusion-Advection Systems”
Entropy deficit scales as N^(-1/d) across 8 lattices
Configurational entropy's finite-size gap is a surface-to-volume effect linking geometry to plastic crystals and colloids
Fractal layout, not pin count, controls wave trapping
Koch-snowflake pins trap shear waves where circular arrays fail; response saturates by the third iteration.
· “Scattering of Antiplane Shear Waves by Fractals in Strain Gradient Elasticity”
Thermal and symmetry Mpemba effects reduce to one identity
A single relative-entropy split reveals that hot-cooling and symmetry-restoration anomalies are the same physics.
· “A resource theoretical unification of Mpemba effects: classical and quantum”
Elastic law turns a linear rock-failure rule into the Hoek-Brown curve
Rocks' curved strength envelope is the stress-space image of the linear Drucker-Prager criterion.
Ramanujan's 1729 tunes an oscillator to unit frequency
With rolling masses at (√1729−1)/36 of the other masses, the natural frequency is exactly √(k/m), not just close.
A single beam model contains Euler-Bernoulli and Timoshenko as limits
Raising two penalty coefficients turns a defect-rich continuum model first into Timoshenko, then Euler-Bernoulli.
· “A New Framework for Unidimensional Structures Based on Generalised Continua”
Fine bubbles suspend slurry solids
A 3D flume model validated to within ±15 percent shows which settings favour dewatering.
· “Numerical investigation on solids settling in a non-Newtonian slurry inside a horizontal flume”
Clock pulling pins wireless power at maximum efficiency
A phase-locked feedback loop locks the system onto the one state that maximizes efficiency, beating parity-time-symmetric designs.
· “Clock Pulling Enables Maximum-Efficiency Wireless Power Transfer”
Dry syringe seal leaks match contact-theory predictions
Using measured roughness and finite-element pressures, predicted leak rates fall inside the measured range.
· “Leakage at interfaces: a comprehensive study based on Persson contact mechanics theory”
Equilibrium distribution formula now extends into strong nonlinearity
The first-order four-wave correction keeps mode occupations accurate up to b = 200 in NSE, MMT, and FPUT-beta models.
· “The equilibrium distribution function for strongly nonlinear systems”
Singular fields stay finite-energy when spherical index ℓ > -1/2
Real-valued angular indices create a continuum of singular-but-finite field modes, testable in conical cavities.
· “Full Vectorial Maxwell Equations with Continuous Angular Indices”
Sudden-motion charge spoils claimed any-gauge formula
A direct Coulomb-gauge calculation gives a nonzero vector potential where the Yang-Nevels equation predicts zero.
Thread in Bell's spaceship paradox survives realistic engine jitter
At 80,000 m/s the thread's tension self-corrects and proper distance stays fixed forever.
3D impulse equations unmask a simulator's hidden collision model
A complete derivation of 3D car-crash impact shows Virtual CRASH behaves like PC-Crash, not as its manual claims.
· “Three-Dimensional Rigid-Body Impact Mechanics for Automobile Collisions”
One formula unifies every causal linear light boundary condition
Static, temporal, moving, and dispersive metasurface interfaces all reduce to special cases of a single spacetime formula.
· “Electromagnetic Boundary Conditions for Space--time Interfaces”
Noether’s theorem alone yields Einstein’s equations
Treating gauge potentials as 1-forms removes ad hoc symmetrization and fuses canonical and Hilbert tensors.
Exact resonances stall
6-wave resonances balance only opposing mode pairs, then freeze; nonlinear broadening finishes thermalization.
Quenched disorder yields the conformable derivative
Slow temperature sweeps then obey T^(1−µ) dψ/dT, with µ set by material disorder statistics.
· “Microscopic Origins of Conformable Dynamics: From Disorder to Deformation”
Gas shadowing can grow pebbles to 10 km in 100,000 years
A pressure imbalance between close pebbles offers a non-sticky route past the usual growth barriers.
One formula gives the vector potential in any gauge
A retarded part plus a gradient correction built from the scalar potential; fields still propagate at light speed
· “Direct, analytic solution for the electromagnetic vector potential in any gauge”