23 problems

Let $n\geq 3$ and let $P$ be a slowness polynomial corresponding to a positive definite stiffness tensor. A polynomial contains a square if it has a nonconstant factor with exponen…

Experimental-observation conjecture. This effect could be observed experimentally in a modification of the Mullen–Lüthi–Stephen experiment.

High-frequency waves propagating through randomly varying media are modeled by a wavefield whose distribution is defined in the long-distance limit. Gaussian conjecture. High-frequ…

Let a wave field propagate over a long distance through a random medium, and let its scintillation index be the ratio of the variance of the intensity to the square of the average…

In the semilinear PDE system, let $\mathbf{\widetilde{u}}$ be the approximation … with $u_{-j}=\overline{u_j}$ and $\mathcal{J}=\{\pm1,\pm3,\ldots,\pm j_{\max}\}$ for odd…

The authors' approach concerns active exterior cloaking for the Helmholtz equation with complex wavenumbers, including media with losses or gain. 3D cloaking conjecture. Their appr…

A complex wave field is said to have circularly symmetric complex Gaussian statistics when its distribution is invariant under multiplication by a unit-modulus complex number and i…

Microlocal propagation conjecture. There exists $\beta<3/4$ such that, uniformly for $\varepsilon\in(0,1]$ and $t>0$,

Transit conjecture. General initial data semiclassically localized along $\mathcal{C}$ transit to the state $$ .

Let $k$ denote the wave number and let $\omega(k)$ denote the corresponding wave frequency in Cosserat elasticity. For the material discussed in the source, the wave speed $v(k)$ s…

Dispersive-focusing conjecture. Dispersive focusing in the early evolution of a wave packet may play an important role in promoting nonlinear wave interaction and the consequent tr…

Consider the overlapping FEM–BEM method for the stated wave-propagation problem, with overlapped region $\Omega_{12}$ bounded by the selected BEM boundary $\Gamma$. In the reported…

The near-field solution is computed for a heterogeneous wave-propagation problem with a smooth heterogeneous region and smooth refractive index, and the computed far-fields exhibit…

Ghost-source support conjecture. Cusp caustics always occur within the domain of support of ghost sources.

Ghost-source conjecture. Cusp caustics always coincide with ghost sources.

Let $f$ be a generic bistable function, let $C$ be the wave-speed parameter, and let $L_*(C)$ be the threshold appearing in the paper. A barrier is a blocking configuration in the…

Let $f$ be a generic bistable function, and let $lpha_*$ and $\beta_*$ denote the quantities associated with Lemma, viewed as functions of the relevant parameter $C$. Monotonicity…

Uniform stochastic regularity conjecture. The estimate holds, with constants $C_{\bold k}$ independent of the wavelength $\varepsilon$, for the stated Gaussian beam approximation a…

The methods concern evaluating far-field signals for time-domain wave propagation. In particular, consider linear hyperbolic systems which, apart from inhomogeneities, are time ind…

Let a distribution of relaxation processes cover all relaxation frequencies, with $Omeganu$ denoting the relaxation frequency of a process and with a given wave-frequency bandwidt…

Longitudinal-current dominance conjecture. For a narrow strip, the longitudinal current dominates over the transverse current, namely

The flux for the effective equation with a slowly varying oscillatory coefficient is conjectured to be … Here, $\tilde{f}_1$ and $\tilde{f}_2$ denote the corresponding components o…

Radial-profile conjecture. The radial cross section will keep its shape if multiplied by $r$.