arXiv subjects

Lillian St. Kleess

Publications and source records attributed to Lillian St. Kleess.

4 recordsLinked to original sources

arXiv2026

Experimental Collapse in Virophysics: Protocol-Resolved Observation, Inference, and Plaque-Assay Blindness

Virological measurements are often treated as reports of virion structure, mechanics, dielectric response, infectivity, or titer. In practice, an experiment observes a protocol-conditioned projection of a richer latent virion--environment ensemble. This paper defines this process as experimental collapse within protocol-resolved virophysics. Its central object is the null-inclusive observation operator $P_{\mathrm{obs},t}^{\varnothing}(\,\cdot\mid E\,) = \mathcal{M}_{E,t}^{\varnothing}P_{\mathrm{ref},t}$, which maps a reference latent ensemble to the observed ensemble generated by protocol $E$, including null outcomes. The formulation separates latent-state transformation, detection weighting, readout, and non-observation, making protocol effects explicit components rather than bias terms. The framework introduces protocol-conditioned latent ensembles, collapse functionals, protocol blindness, observation equivalence, Fisher-information observability, inverse inference, and multi-protocol consistency. It identifies collapse mechanisms including preparation, surface immobilization, mechanical loading, field steering, medium filtering, amplification, censoring, and detection thresholds. As a worked example, the plaque assay estimates an effective protocol-conditioned infectious concentration $Λ_{\mathrm{PFU}}=\int_Ψπ_{\mathrm{PFU}}(x;E_{\mathrm{PFU}})n_{\mathrm{ref}}(x),dx$, rather than total particle concentration. This recovers the Poisson plaque-count model and PFU titer formula in the dilute regime; extensions to overdispersion, zero inflation, plaque merging, endpoint dilution, neutralization, and morphology-augmented readouts recast deviations as protocol-conditioned information. Thus, virological data are outputs of explicit protocol kernels, clarifying what measurements report, miss, and how complementary assays can infer hidden latent virion structures.

physics.bio-ph↗

arXiv2026

Phase-Textured Complex Viscosity in Linear Viscous Flows: Non-Normality Without Advection, Corner Defects, and 3D Mode Coupling

We consider time-harmonic incompressible flow with a spatially resolved complex viscosity field $μ^*(\mathbf{x},ω)$ and, at fixed forcing frequency $ω>0$, its constitutive phase texture $φ(\mathbf{x})=\argμ^*(\mathbf{x},ω)$. In three-dimensional domains periodic in a spanwise direction $z$, $z$-dependence of $μ^*$ converts coefficient multiplication into convolution in spanwise Fourier index, yielding an operator-valued Toeplitz/Laurent coupling of modes. Consequently, even spanwise-uniform forcing generically produces $κ\neq 0$ sidebands in the harmonic response as a \emph{linear, constitutive} effect. We place $μ^*$ at the closure level $\hat{\boldsymbolτ}=2\,μ^*(\mathbf{x},ω)\mathbf{D}(\hat{\mathbf{v}})$, as the boundary value of the Laplace transform of a causal stress-memory kernel. Under the passivity condition $\Reμ^*(\mathbf{x},ω)\ge μ_{\min}>0$, the oscillatory Stokes/Oseen operators are realized as m-sectorial operators associated with coercive sectorial forms on bounded Lipschitz (including cornered) domains, yielding existence, uniqueness, and frequency-dependent stability bounds. Spatial variation of $φ$ renders the viscous operator intrinsically non-normal even in the absence of advection, so amplification is governed by resolvent geometry (and associated pseudospectra), not by eigenvalues alone. In the pure-phase class $μ^*(\mathbf{x},ω)=μ_0(ω)e^{iφ(\mathbf{x})}$, the texture strength is quantified by $μ_0(ω)\|\nablaφ\|_{L^\infty}$.

math.AP↗

arXiv2025

Open-System Virus Particle Physics: A Path-Integral Viral Lattice Theory Using Non-Self Adjoint Stochastic PDEs and Fock-Space Formalism

We develop a comprehensive theoretical biophysics model grounded in a path integral perspective and an m-sectorial open-system framework, to describe complex, damped viral phonon dynamics in resource limited and noise driven environments. By unifying wave mechanics (via PDEs with multiplicative noise), Markov jumps for occupant or arrangement transitions, and second quantized (Fock-space) expansions, our construction accommodates an unbounded number of viral lattices in a single global wavefunction. In doing so, we capture how an entire population potentially numbering in the millions may be represented by a single operator theoretic state, or orbit, whose evolution is governed by non-unitary semigroups with potential equilibrium or non equilibrium steady states. This approach admits action functionals over the space of system trajectories, enabling large deviation and flux analyses whenever detailed balance is broken by sustained resource inputs, as often happens in real infections. Such a global wavefunction thus synthesizes PDE wavefront modes, occupant transitions, and stochastically induced rearrangements into a single evolution equation, capturing how local capsid vibrations might catalyze large scale replication bursts, and vice versa. Our proofs show that, despite unbounded occupant expansions or morphological continuums, solutions remain finite norm over finite times. The well posedness extends to non-self-adjoint operators with complex damping, irreversibility, and operator-valued-noise, thus mirroring host constraints and immune factors that restrict virus proliferation. Our formalism invites direct experimental cross validation, from single virion tracking to population assays, and offers predictive insights for resource limited replication, capsid reorganizations, and potential intervention strategies in modern virology.

physics.bio-ph↗

arXiv2025

Viral Lattice Theory: A Biophysical Model for Virion Motion

We present a rigorously formulated, novel operator-based framework that merges ideas from condensed matter physics, continuum mechanics, and quantum-inspired theory to analyze collective virion behavior in complex environments. By modeling metabolically inert virions, whose main interactions are Coulombic and Lennard-Jones, as nodes in a viral lattice linked by effective springs, we obtain collective vibrational modes akin to phonons in solids. A coupled, complex-valued displacement field PDE underpins our approach, enabling wave mechanics and functional analysis to define key observables, ranging from stress fields and thermodynamic responses to effective Hamiltonians. We interpret the apparent stochasticity of virion motion as deterministic chaos arising from rapid transitions among 'viral phonon' modes that store and redistribute energy from the host. Short-lived lattice states (picoseconds) may thus help sustain infectivity in aerosolized droplets of respiratory virions. Extending our operator framework, we derive an uncertainty-like relation coupling a virion's self-stiffness operator with its phononic frequency operator, underscoring fundamental limits on specifying capsid rigidity and vibrational response. We also explore transient coherence effects, akin to entanglement witness operators, which may expose critical correlations affecting capsid resilience or genome release. Our approach invites experimental validation via advanced imaging, high-resolution spectroscopy, and mechanical perturbations. By integrating aspects of soft matter physics, crystallography, statistical mechanics, and wave-based modeling, this methodology suggests new antiviral strategies targeting specific vibrational modes and guides the rational design of virus-based vectors in therapeutic or diagnostic applications.

physics.bio-ph↗